%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG140+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:37:05 EDT 2023 % Result : Unsatisfiable 18.34s 3.29s % Output : Proof 155.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG140+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 04:27:04 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.62/1.50 Prover 4: Preprocessing ... % 5.37/1.51 Prover 1: Preprocessing ... % 5.84/1.55 Prover 0: Preprocessing ... % 5.84/1.55 Prover 2: Preprocessing ... % 5.84/1.55 Prover 3: Preprocessing ... % 5.84/1.55 Prover 6: Preprocessing ... % 5.84/1.55 Prover 5: Preprocessing ... % 8.92/2.05 Prover 2: Constructing countermodel ... % 8.92/2.05 Prover 3: Constructing countermodel ... % 8.92/2.13 Prover 6: Constructing countermodel ... % 8.92/2.13 Prover 0: Constructing countermodel ... % 8.92/2.14 Prover 4: Constructing countermodel ... % 8.92/2.14 Prover 1: Constructing countermodel ... % 12.46/2.48 Prover 5: Constructing countermodel ... % 18.34/3.29 Prover 3: proved (2657ms) % 18.34/3.29 % 18.34/3.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.34/3.30 % 18.34/3.30 Prover 0: stopped % 18.81/3.31 Prover 5: stopped % 18.81/3.31 Prover 2: stopped % 18.81/3.33 Prover 6: stopped % 18.81/3.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.81/3.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.81/3.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.81/3.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.81/3.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.92/3.74 Prover 7: Preprocessing ... % 21.92/3.75 Prover 10: Preprocessing ... % 21.92/3.75 Prover 11: Preprocessing ... % 21.92/3.77 Prover 8: Preprocessing ... % 21.92/3.78 Prover 13: Preprocessing ... % 22.99/3.88 Prover 8: Constructing countermodel ... % 23.54/3.96 Prover 11: Constructing countermodel ... % 23.54/3.98 Prover 10: Constructing countermodel ... % 23.54/4.02 Prover 13: Constructing countermodel ... % 24.25/4.04 Prover 7: Constructing countermodel ... % 62.97/9.14 Prover 13: stopped % 62.97/9.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 63.37/9.24 Prover 16: Preprocessing ... % 65.29/9.43 Prover 16: Constructing countermodel ... % 108.16/15.10 Prover 16: stopped % 108.16/15.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 109.40/15.22 Prover 19: Preprocessing ... % 110.91/15.34 Prover 19: Constructing countermodel ... % 115.43/15.98 Prover 1: stopped % 136.13/18.91 Prover 19: stopped % 141.75/19.95 Prover 8: Found proof (size 382591) % 141.75/19.95 Prover 8: proved (16512ms) % 141.75/19.95 Prover 10: stopped % 141.75/19.95 Prover 4: stopped % 141.75/19.95 Prover 7: stopped % 141.75/19.95 Prover 11: stopped % 141.75/19.95 % 141.75/19.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 141.75/19.95 % 144.98/20.97 % SZS output start Proof for theBenchmark % 145.06/20.99 Assumptions after simplification: % 145.06/20.99 --------------------------------- % 145.06/20.99 % 145.06/20.99 (ax1) % 145.06/21.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.04 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.06/21.04 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.06/21.04 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 145.06/21.04 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 145.06/21.04 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 145.06/21.04 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.06/21.04 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 145.06/21.04 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.06/21.04 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 145.06/21.04 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 145.06/21.04 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 145.06/21.04 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 145.06/21.04 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 145.06/21.04 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 145.06/21.04 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 145.06/21.05 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 145.06/21.05 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 145.06/21.05 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 145.06/21.05 % 145.06/21.05 (ax10) % 145.06/21.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.05 (op(v0, v1) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.06/21.05 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.06/21.05 % 145.06/21.05 (ax11) % 145.06/21.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.05 (op(v0, v1) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.06/21.05 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.06/21.05 % 145.06/21.05 (ax12) % 145.06/21.05 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.05 (op(v0, v1) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.06/21.05 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.06/21.05 % 145.06/21.05 (ax13) % 145.06/21.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.06 (op(v0, v1) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.06/21.06 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.06/21.06 % 145.06/21.06 (ax14) % 145.06/21.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.06 (op(v0, v1) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.06/21.06 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.06/21.06 % 145.06/21.06 (ax15) % 145.06/21.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.06 (op(v0, v1) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.06/21.06 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.06/21.06 % 145.06/21.06 (ax16) % 145.06/21.06 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.06 (op(v0, v1) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.06/21.06 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.06/21.06 % 145.06/21.06 (ax17) % 145.06/21.07 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.07 (op(v0, v1) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.06/21.07 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.06/21.07 % 145.06/21.07 (ax18) % 145.06/21.07 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.07 (op(v0, v1) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.06/21.07 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.06/21.07 % 145.06/21.07 (ax19) % 145.06/21.07 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.06/21.07 (op(v0, v1) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.06/21.07 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.06/21.07 % 145.06/21.07 (ax2) % 145.51/21.09 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.51/21.09 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.51/21.09 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.51/21.09 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 145.51/21.09 op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & % 145.51/21.09 op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & % 145.51/21.09 op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.51/21.09 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 145.51/21.09 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.51/21.09 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 = % 145.51/21.09 e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 | % 145.51/21.09 v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 = % 145.51/21.09 e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 % 145.51/21.09 = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 % 145.51/21.09 | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = % 145.51/21.09 e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = % 145.51/21.09 e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 | % 145.51/21.09 v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 = % 145.51/21.09 e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5 % 145.51/21.09 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 | % 145.51/21.09 v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0 % 145.51/21.09 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3) % 145.51/21.09 & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | % 145.51/21.09 v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | % 145.51/21.09 v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | % 145.51/21.09 v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & % 145.51/21.09 (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 % 145.51/21.09 = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 | % 145.51/21.09 v1 = e0)))) % 145.51/21.09 % 145.51/21.09 (ax20) % 145.51/21.10 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.51/21.10 (op(v0, v1) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.51/21.10 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.51/21.10 % 145.51/21.10 (ax21) % 145.51/21.10 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.51/21.10 (op(v0, v1) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.51/21.10 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.51/21.10 % 145.51/21.10 (ax22) % 145.51/21.10 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.51/21.10 (op(v0, v1) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.51/21.10 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.51/21.10 % 145.51/21.10 (ax23) % 145.51/21.10 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.51/21.10 (op(v0, v1) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.51/21.10 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.51/21.10 % 145.51/21.10 (ax24) % 145.57/21.10 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.10 (op(v0, v1) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.57/21.10 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.57/21.10 % 145.57/21.10 (ax25) % 145.57/21.10 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.10 (op(v0, v1) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.57/21.10 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.57/21.10 % 145.57/21.10 (ax26) % 145.57/21.11 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.11 (op(v0, v1) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.57/21.11 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.57/21.11 % 145.57/21.11 (ax27) % 145.57/21.11 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.11 (op(v0, v1) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.57/21.11 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.57/21.11 % 145.57/21.11 (ax28) % 145.57/21.11 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.11 (op(v0, v1) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.57/21.11 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.57/21.11 % 145.57/21.11 (ax29) % 145.57/21.11 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.11 (op(v0, v1) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & % 145.57/21.11 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.57/21.11 % 145.57/21.11 (ax3) % 145.57/21.12 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.12 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.57/21.12 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.57/21.12 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 145.57/21.12 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 145.57/21.12 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 145.57/21.12 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 145.57/21.12 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 145.57/21.12 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 145.57/21.12 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 145.57/21.12 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 145.57/21.12 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 145.57/21.12 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 145.57/21.12 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 145.57/21.12 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 145.57/21.12 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 145.57/21.12 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 145.57/21.12 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 145.57/21.12 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.57/21.12 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 145.57/21.12 % 145.57/21.12 (ax4) % 145.57/21.12 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ % 145.57/21.12 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 145.57/21.12 % 145.57/21.12 (ax5) % 145.57/21.13 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.13 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 145.57/21.13 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 145.57/21.13 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: % 145.57/21.13 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: % 145.57/21.13 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 145.57/21.13 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (op(e3, v29) = v30 & % 145.57/21.13 op(e3, v27) = v28 & op(e3, v25) = v26 & op(e3, v3) = v31 & op(e3, e3) = v3 & % 145.57/21.13 op(e3, e2) = v29 & op(e3, e1) = v27 & op(e3, e0) = v25 & op(e2, v23) = v24 & % 145.57/21.13 op(e2, v20) = v21 & op(e2, v18) = v19 & op(e2, v2) = v22 & op(e2, e3) = v23 % 145.57/21.13 & op(e2, e2) = v2 & op(e2, e1) = v20 & op(e2, e0) = v18 & op(e1, v16) = v17 % 145.57/21.13 & op(e1, v14) = v15 & op(e1, v11) = v12 & op(e1, v1) = v13 & op(e1, e3) = % 145.57/21.13 v16 & op(e1, e2) = v14 & op(e1, e1) = v1 & op(e1, e0) = v11 & op(e0, v9) = % 145.57/21.13 v10 & op(e0, v7) = v8 & op(e0, v5) = v6 & op(e0, v0) = v4 & op(e0, e3) = v9 % 145.57/21.13 & op(e0, e2) = v7 & op(e0, e1) = v5 & op(e0, e0) = v0 & $i(v31) & $i(v30) & % 145.57/21.13 $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & % 145.57/21.13 $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 145.57/21.13 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 145.57/21.13 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 145.57/21.13 (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e3 | v2 = e2 | v1 = e1 | v0 % 145.57/21.13 = e0 | (v29 = e3 & v27 = e1 & v23 = e3 & v16 = e1) | (v29 = e3 & v25 = e0 % 145.57/21.13 & v23 = e3 & v9 = e0) | (v29 = e3 & v23 = e3 & v20 = e2 & v14 = e2) | % 145.57/21.13 (v29 = e3 & v23 = e3 & v18 = e2 & v7 = e2) | (v29 = e2 & v27 = e3 & v23 = % 145.57/21.13 e2 & v16 = e3) | (v29 = e2 & v25 = e3 & v23 = e2 & v9 = e3) | (v29 = e2 % 145.57/21.13 & v23 = e2 & v20 = e1 & v14 = e1) | (v29 = e2 & v23 = e2 & v18 = e0 & v7 % 145.57/21.13 = e0) | (v29 = e2 & v23 = e2 & e3 = e2) | (v27 = e3 & v25 = e0 & v16 = % 145.57/21.13 e3 & v9 = e0) | (v27 = e3 & v20 = e1 & v16 = e3 & v14 = e1) | (v27 = e3 % 145.57/21.13 & v16 = e3 & v11 = e1 & v5 = e1) | (v27 = e1 & v25 = e3 & v16 = e1 & v9 % 145.57/21.13 = e3) | (v27 = e1 & v20 = e2 & v16 = e1 & v14 = e2) | (v27 = e1 & v16 = % 145.57/21.13 e1 & v11 = e0 & v5 = e0) | (v27 = e1 & v16 = e1 & e3 = e1) | (v25 = e3 & % 145.57/21.13 v18 = e0 & v9 = e3 & v7 = e0) | (v25 = e3 & v11 = e0 & v9 = e3 & v5 = % 145.57/21.13 e0) | (v25 = e0 & v18 = e2 & v9 = e0 & v7 = e2) | (v25 = e0 & v11 = e1 & % 145.57/21.13 v9 = e0 & v5 = e1) | (v25 = e0 & v9 = e0 & e3 = e0) | (v20 = e2 & v18 = % 145.57/21.13 e0 & v14 = e2 & v7 = e0) | (v20 = e2 & v14 = e2 & v11 = e1 & v5 = e1) | % 145.57/21.13 (v20 = e1 & v18 = e2 & v14 = e1 & v7 = e2) | (v20 = e1 & v14 = e1 & v11 = % 145.57/21.13 e0 & v5 = e0) | (v20 = e1 & v14 = e1 & e2 = e1) | (v18 = e2 & v11 = e0 & % 145.57/21.13 v7 = e2 & v5 = e0) | (v18 = e0 & v11 = e1 & v7 = e0 & v5 = e1) | (v18 = % 145.57/21.13 e0 & v7 = e0 & e2 = e0) | (v11 = e0 & v5 = e0 & e1 = e0)) & (v3 = e2 | % 145.57/21.13 v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & % 145.57/21.13 (v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & (( ~ (v31 = e3) & ~ (v30 = e2) & % 145.57/21.13 ~ (v28 = e1) & ~ (v26 = e0)) | ( ~ (v24 = e3) & ~ (v22 = e2) & ~ (v21 % 145.57/21.13 = e1) & ~ (v19 = e0)) | ( ~ (v17 = e3) & ~ (v15 = e2) & ~ (v13 = % 145.57/21.13 e1) & ~ (v12 = e0)) | ( ~ (v10 = e3) & ~ (v8 = e2) & ~ (v6 = e1) & % 145.57/21.13 ~ (v4 = e0)))) % 145.57/21.13 % 145.57/21.13 (ax6) % 145.57/21.14 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.14 (op(v0, v1) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.57/21.14 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.57/21.14 % 145.57/21.14 (ax7) % 145.57/21.14 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.14 (op(v0, v1) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & % 145.57/21.14 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.57/21.14 % 145.57/21.14 (ax8) % 145.57/21.14 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.14 (op(v0, v1) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & % 145.57/21.14 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.57/21.14 % 145.57/21.14 (ax9) % 145.57/21.14 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 145.57/21.14 (op(v0, v1) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & % 145.57/21.14 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.57/21.14 % 145.57/21.14 (function-axioms) % 145.57/21.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 145.57/21.14 v2) = v1) | ~ (op(v3, v2) = v0)) % 145.57/21.14 % 145.57/21.14 Those formulas are unsatisfiable: % 145.57/21.14 --------------------------------- % 145.57/21.14 % 145.57/21.14 Begin of proof % 145.57/21.14 | % 145.57/21.14 | ALPHA: (ax1) implies: % 145.57/21.15 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.57/21.15 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 145.57/21.15 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 145.57/21.15 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 145.57/21.15 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 145.57/21.15 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 145.57/21.15 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.57/21.15 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 145.57/21.15 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 145.57/21.15 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 145.57/21.15 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 145.57/21.15 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 145.57/21.15 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 145.57/21.15 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 145.57/21.15 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 145.57/21.15 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 145.57/21.15 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 145.57/21.15 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 145.57/21.15 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 145.57/21.15 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 145.57/21.15 | = e0)) % 145.57/21.15 | % 145.57/21.15 | ALPHA: (ax2) implies: % 145.57/21.16 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.57/21.16 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 145.57/21.16 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 145.57/21.16 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11 % 145.57/21.16 | & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) % 145.57/21.16 | = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1, % 145.57/21.16 | e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 145.57/21.16 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 145.57/21.16 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 145.57/21.16 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 % 145.57/21.16 | = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = % 145.57/21.16 | e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13 % 145.57/21.16 | = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 = % 145.57/21.16 | e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 = % 145.57/21.16 | e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 = % 145.57/21.16 | e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 = % 145.57/21.16 | e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1) % 145.57/21.16 | & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 | % 145.57/21.16 | v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & % 145.57/21.16 | (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | % 145.57/21.16 | v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & % 145.57/21.16 | (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 % 145.57/21.16 | = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = % 145.57/21.16 | e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 | % 145.57/21.16 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8 % 145.57/21.16 | = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3) % 145.57/21.16 | & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 = % 145.57/21.16 | e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 % 145.57/21.16 | | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 % 145.57/21.16 | = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = % 145.57/21.16 | e0 | v1 = e0)))) % 145.57/21.16 | % 145.57/21.16 | ALPHA: (ax3) implies: % 145.57/21.17 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.57/21.17 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 145.57/21.17 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 145.57/21.17 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 145.57/21.17 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 145.57/21.17 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 145.57/21.17 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 145.57/21.17 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 145.57/21.17 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 145.57/21.17 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 145.57/21.17 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 145.57/21.17 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 145.57/21.17 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 145.57/21.17 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 145.57/21.17 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3, % 145.57/21.17 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 & % 145.57/21.17 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = % 145.57/21.17 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, % 145.57/21.17 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 145.57/21.17 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 145.57/21.17 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 145.57/21.17 | % 145.57/21.17 | ALPHA: (ax4) implies: % 145.57/21.17 | (4) ~ (e1 = e0) % 145.57/21.17 | (5) ~ (e2 = e0) % 145.57/21.17 | (6) ~ (e2 = e1) % 145.57/21.17 | (7) ~ (e3 = e0) % 145.57/21.17 | (8) ~ (e3 = e1) % 145.57/21.17 | (9) ~ (e3 = e2) % 145.57/21.17 | % 145.57/21.17 | ALPHA: (ax5) implies: % 145.57/21.19 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 145.57/21.19 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 145.57/21.19 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 145.57/21.19 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 145.57/21.19 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 145.57/21.19 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 145.57/21.19 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (op(e3, v29) = % 145.57/21.19 | v30 & op(e3, v27) = v28 & op(e3, v25) = v26 & op(e3, v3) = v31 & % 145.57/21.19 | op(e3, e3) = v3 & op(e3, e2) = v29 & op(e3, e1) = v27 & op(e3, e0) = % 145.57/21.19 | v25 & op(e2, v23) = v24 & op(e2, v20) = v21 & op(e2, v18) = v19 & % 145.57/21.19 | op(e2, v2) = v22 & op(e2, e3) = v23 & op(e2, e2) = v2 & op(e2, e1) = % 145.57/21.19 | v20 & op(e2, e0) = v18 & op(e1, v16) = v17 & op(e1, v14) = v15 & % 145.57/21.19 | op(e1, v11) = v12 & op(e1, v1) = v13 & op(e1, e3) = v16 & op(e1, e2) % 145.57/21.19 | = v14 & op(e1, e1) = v1 & op(e1, e0) = v11 & op(e0, v9) = v10 & % 145.57/21.19 | op(e0, v7) = v8 & op(e0, v5) = v6 & op(e0, v0) = v4 & op(e0, e3) = % 145.57/21.19 | v9 & op(e0, e2) = v7 & op(e0, e1) = v5 & op(e0, e0) = v0 & $i(v31) & % 145.57/21.19 | $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) % 145.57/21.19 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & % 145.57/21.19 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) % 145.57/21.19 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 145.57/21.19 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v3 = e3 | v2 = e3 | v1 = e3 | % 145.57/21.19 | v0 = e3) & (v3 = e3 | v2 = e2 | v1 = e1 | v0 = e0 | (v29 = e3 & % 145.57/21.19 | v27 = e1 & v23 = e3 & v16 = e1) | (v29 = e3 & v25 = e0 & v23 = % 145.57/21.19 | e3 & v9 = e0) | (v29 = e3 & v23 = e3 & v20 = e2 & v14 = e2) | % 145.57/21.19 | (v29 = e3 & v23 = e3 & v18 = e2 & v7 = e2) | (v29 = e2 & v27 = e3 % 145.57/21.19 | & v23 = e2 & v16 = e3) | (v29 = e2 & v25 = e3 & v23 = e2 & v9 = % 145.57/21.19 | e3) | (v29 = e2 & v23 = e2 & v20 = e1 & v14 = e1) | (v29 = e2 & % 145.57/21.19 | v23 = e2 & v18 = e0 & v7 = e0) | (v29 = e2 & v23 = e2 & e3 = e2) % 145.57/21.19 | | (v27 = e3 & v25 = e0 & v16 = e3 & v9 = e0) | (v27 = e3 & v20 = % 145.57/21.19 | e1 & v16 = e3 & v14 = e1) | (v27 = e3 & v16 = e3 & v11 = e1 & v5 % 145.57/21.19 | = e1) | (v27 = e1 & v25 = e3 & v16 = e1 & v9 = e3) | (v27 = e1 & % 145.57/21.19 | v20 = e2 & v16 = e1 & v14 = e2) | (v27 = e1 & v16 = e1 & v11 = % 145.57/21.19 | e0 & v5 = e0) | (v27 = e1 & v16 = e1 & e3 = e1) | (v25 = e3 & % 145.57/21.19 | v18 = e0 & v9 = e3 & v7 = e0) | (v25 = e3 & v11 = e0 & v9 = e3 & % 145.57/21.19 | v5 = e0) | (v25 = e0 & v18 = e2 & v9 = e0 & v7 = e2) | (v25 = e0 % 145.57/21.19 | & v11 = e1 & v9 = e0 & v5 = e1) | (v25 = e0 & v9 = e0 & e3 = e0) % 145.57/21.19 | | (v20 = e2 & v18 = e0 & v14 = e2 & v7 = e0) | (v20 = e2 & v14 = % 145.57/21.19 | e2 & v11 = e1 & v5 = e1) | (v20 = e1 & v18 = e2 & v14 = e1 & v7 % 145.57/21.19 | = e2) | (v20 = e1 & v14 = e1 & v11 = e0 & v5 = e0) | (v20 = e1 & % 145.57/21.19 | v14 = e1 & e2 = e1) | (v18 = e2 & v11 = e0 & v7 = e2 & v5 = e0) % 145.57/21.19 | | (v18 = e0 & v11 = e1 & v7 = e0 & v5 = e1) | (v18 = e0 & v7 = e0 % 145.57/21.19 | & e2 = e0) | (v11 = e0 & v5 = e0 & e1 = e0)) & (v3 = e2 | v2 = % 145.57/21.19 | e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) % 145.57/21.19 | & (v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & (( ~ (v31 = e3) & ~ % 145.57/21.19 | (v30 = e2) & ~ (v28 = e1) & ~ (v26 = e0)) | ( ~ (v24 = e3) & % 145.57/21.19 | ~ (v22 = e2) & ~ (v21 = e1) & ~ (v19 = e0)) | ( ~ (v17 = e3) & % 145.57/21.19 | ~ (v15 = e2) & ~ (v13 = e1) & ~ (v12 = e0)) | ( ~ (v10 = e3) % 145.57/21.19 | & ~ (v8 = e2) & ~ (v6 = e1) & ~ (v4 = e0)))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax6) implies: % 145.57/21.19 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e0) | ~ (v1 = e2) | ~ (v0 = e1))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax7) implies: % 145.57/21.19 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e0) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax8) implies: % 145.57/21.19 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e0) | ~ (v1 = e1) | ~ (v0 = e2))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax9) implies: % 145.57/21.19 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e0) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax10) implies: % 145.57/21.19 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e0) | ~ (v1 = e1) | ~ (v0 = e3))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax11) implies: % 145.57/21.19 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e0) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax12) implies: % 145.57/21.19 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.19 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.19 | e1) | ~ (v1 = e2) | ~ (v0 = e0))) % 145.57/21.19 | % 145.57/21.19 | ALPHA: (ax13) implies: % 145.57/21.20 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e1) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax14) implies: % 145.57/21.20 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e1) | ~ (v1 = e0) | ~ (v0 = e2))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax15) implies: % 145.57/21.20 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e1) | ~ (v1 = e3) | ~ (v0 = e2))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax16) implies: % 145.57/21.20 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e1) | ~ (v1 = e0) | ~ (v0 = e3))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax17) implies: % 145.57/21.20 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e1) | ~ (v1 = e2) | ~ (v0 = e3))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax18) implies: % 145.57/21.20 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e2) | ~ (v1 = e1) | ~ (v0 = e0))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax19) implies: % 145.57/21.20 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e2) | ~ (v1 = e3) | ~ (v0 = e0))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax20) implies: % 145.57/21.20 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e2) | ~ (v1 = e0) | ~ (v0 = e1))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax21) implies: % 145.57/21.20 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 145.57/21.20 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 145.57/21.20 | e2) | ~ (v1 = e3) | ~ (v0 = e1))) % 145.57/21.20 | % 145.57/21.20 | ALPHA: (ax22) implies: % 145.57/21.20 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.20 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.20 | e2) | ~ (v1 = e0) | ~ (v0 = e3))) % 146.03/21.20 | % 146.03/21.20 | ALPHA: (ax23) implies: % 146.03/21.20 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.20 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.20 | e2) | ~ (v1 = e1) | ~ (v0 = e3))) % 146.03/21.20 | % 146.03/21.20 | ALPHA: (ax24) implies: % 146.03/21.20 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.20 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.20 | e3) | ~ (v1 = e1) | ~ (v0 = e0))) % 146.03/21.20 | % 146.03/21.20 | ALPHA: (ax25) implies: % 146.03/21.20 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.21 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.21 | e3) | ~ (v1 = e2) | ~ (v0 = e0))) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (ax26) implies: % 146.03/21.21 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.21 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.21 | e3) | ~ (v1 = e0) | ~ (v0 = e1))) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (ax27) implies: % 146.03/21.21 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.21 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.21 | e3) | ~ (v1 = e2) | ~ (v0 = e1))) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (ax28) implies: % 146.03/21.21 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.21 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.21 | e3) | ~ (v1 = e0) | ~ (v0 = e2))) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (ax29) implies: % 146.03/21.21 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v1) = v2 & op(v0, % 146.03/21.21 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 = % 146.03/21.21 | e3) | ~ (v1 = e1) | ~ (v0 = e2))) % 146.03/21.21 | % 146.03/21.21 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 146.03/21.21 | (35) op(all_4_2, all_4_1) = all_4_0 & op(all_4_2, e0) = all_4_1 & op(e0, % 146.03/21.21 | e0) = all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~ % 146.03/21.21 | (all_4_0 = e1) | ~ (all_4_1 = e3) | ~ (all_4_2 = e2)) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (35) implies: % 146.03/21.21 | (36) op(e0, e0) = all_4_2 % 146.03/21.21 | (37) op(all_4_2, e0) = all_4_1 % 146.03/21.21 | (38) op(all_4_2, all_4_1) = all_4_0 % 146.03/21.21 | (39) ~ (all_4_0 = e1) | ~ (all_4_1 = e3) | ~ (all_4_2 = e2) % 146.03/21.21 | % 146.03/21.21 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 146.03/21.21 | (40) op(all_6_2, all_6_1) = all_6_0 & op(all_6_2, e1) = all_6_1 & op(e1, % 146.03/21.21 | e1) = all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~ % 146.03/21.21 | (all_6_0 = e2) | ~ (all_6_1 = e0) | ~ (all_6_2 = e3)) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (40) implies: % 146.03/21.21 | (41) op(e1, e1) = all_6_2 % 146.03/21.21 | (42) op(all_6_2, e1) = all_6_1 % 146.03/21.21 | (43) op(all_6_2, all_6_1) = all_6_0 % 146.03/21.21 | (44) ~ (all_6_0 = e2) | ~ (all_6_1 = e0) | ~ (all_6_2 = e3) % 146.03/21.21 | % 146.03/21.21 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives: % 146.03/21.21 | (45) op(all_8_2, all_8_1) = all_8_0 & op(all_8_2, e2) = all_8_1 & op(e2, % 146.03/21.21 | e2) = all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~ % 146.03/21.21 | (all_8_0 = e1) | ~ (all_8_1 = e0) | ~ (all_8_2 = e3)) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (45) implies: % 146.03/21.21 | (46) op(e2, e2) = all_8_2 % 146.03/21.21 | (47) op(all_8_2, e2) = all_8_1 % 146.03/21.21 | (48) op(all_8_2, all_8_1) = all_8_0 % 146.03/21.21 | (49) ~ (all_8_0 = e1) | ~ (all_8_1 = e0) | ~ (all_8_2 = e3) % 146.03/21.21 | % 146.03/21.21 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2 % 146.03/21.21 | gives: % 146.03/21.21 | (50) op(all_10_2, all_10_1) = all_10_0 & op(all_10_2, e3) = all_10_1 & % 146.03/21.21 | op(e3, e3) = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & ( % 146.03/21.21 | ~ (all_10_0 = e0) | ~ (all_10_1 = e2) | ~ (all_10_2 = e1)) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (50) implies: % 146.03/21.21 | (51) op(e3, e3) = all_10_2 % 146.03/21.21 | (52) op(all_10_2, e3) = all_10_1 % 146.03/21.21 | (53) op(all_10_2, all_10_1) = all_10_0 % 146.03/21.21 | (54) ~ (all_10_0 = e0) | ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 146.03/21.21 | % 146.03/21.21 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2 % 146.03/21.21 | gives: % 146.03/21.21 | (55) op(all_12_2, all_12_1) = all_12_0 & op(all_12_2, e0) = all_12_1 & % 146.03/21.21 | op(e0, e0) = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & ( % 146.03/21.21 | ~ (all_12_0 = e1) | ~ (all_12_1 = e2) | ~ (all_12_2 = e3)) % 146.03/21.21 | % 146.03/21.21 | ALPHA: (55) implies: % 146.03/21.21 | (56) op(e0, e0) = all_12_2 % 146.03/21.22 | (57) op(all_12_2, e0) = all_12_1 % 146.03/21.22 | (58) op(all_12_2, all_12_1) = all_12_0 % 146.03/21.22 | (59) ~ (all_12_0 = e1) | ~ (all_12_1 = e2) | ~ (all_12_2 = e3) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2 % 146.03/21.22 | gives: % 146.03/21.22 | (60) op(all_14_2, all_14_1) = all_14_0 & op(all_14_2, e2) = all_14_1 & % 146.03/21.22 | op(e2, e2) = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & ( % 146.03/21.22 | ~ (all_14_0 = e3) | ~ (all_14_1 = e1) | ~ (all_14_2 = e0)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (60) implies: % 146.03/21.22 | (61) op(e2, e2) = all_14_2 % 146.03/21.22 | (62) op(all_14_2, e2) = all_14_1 % 146.03/21.22 | (63) op(all_14_2, all_14_1) = all_14_0 % 146.03/21.22 | (64) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) | ~ (all_14_2 = e0) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2 % 146.03/21.22 | gives: % 146.03/21.22 | (65) op(all_16_2, all_16_1) = all_16_0 & op(all_16_2, e3) = all_16_1 & % 146.03/21.22 | op(e3, e3) = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & ( % 146.03/21.22 | ~ (all_16_0 = e2) | ~ (all_16_1 = e1) | ~ (all_16_2 = e0)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (65) implies: % 146.03/21.22 | (66) op(e3, e3) = all_16_2 % 146.03/21.22 | (67) op(all_16_2, e3) = all_16_1 % 146.03/21.22 | (68) op(all_16_2, all_16_1) = all_16_0 % 146.03/21.22 | (69) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) | ~ (all_16_2 = e0) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2 % 146.03/21.22 | gives: % 146.03/21.22 | (70) op(all_18_2, all_18_1) = all_18_0 & op(all_18_2, e1) = all_18_1 & % 146.03/21.22 | op(e1, e1) = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & ( % 146.03/21.22 | ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (70) implies: % 146.03/21.22 | (71) op(e1, e1) = all_18_2 % 146.03/21.22 | (72) op(all_18_2, e1) = all_18_1 % 146.03/21.22 | (73) op(all_18_2, all_18_1) = all_18_0 % 146.03/21.22 | (74) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2 % 146.03/21.22 | gives: % 146.03/21.22 | (75) op(all_20_2, all_20_1) = all_20_0 & op(all_20_2, e0) = all_20_1 & % 146.03/21.22 | op(e0, e0) = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & ( % 146.03/21.22 | ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (75) implies: % 146.03/21.22 | (76) op(e0, e0) = all_20_2 % 146.03/21.22 | (77) op(all_20_2, e0) = all_20_1 % 146.03/21.22 | (78) op(all_20_2, all_20_1) = all_20_0 % 146.03/21.22 | (79) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2 % 146.03/21.22 | gives: % 146.03/21.22 | (80) op(all_22_2, all_22_1) = all_22_0 & op(all_22_2, e2) = all_22_1 & % 146.03/21.22 | op(e2, e2) = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & ( % 146.03/21.22 | ~ (all_22_0 = e3) | ~ (all_22_1 = e0) | ~ (all_22_2 = e1)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (80) implies: % 146.03/21.22 | (81) op(e2, e2) = all_22_2 % 146.03/21.22 | (82) op(all_22_2, e2) = all_22_1 % 146.03/21.22 | (83) op(all_22_2, all_22_1) = all_22_0 % 146.03/21.22 | (84) ~ (all_22_0 = e3) | ~ (all_22_1 = e0) | ~ (all_22_2 = e1) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2 % 146.03/21.22 | gives: % 146.03/21.22 | (85) op(all_24_2, all_24_1) = all_24_0 & op(all_24_2, e3) = all_24_1 & % 146.03/21.22 | op(e3, e3) = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & ( % 146.03/21.22 | ~ (all_24_0 = e0) | ~ (all_24_1 = e1) | ~ (all_24_2 = e2)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (85) implies: % 146.03/21.22 | (86) op(e3, e3) = all_24_2 % 146.03/21.22 | (87) op(all_24_2, e3) = all_24_1 % 146.03/21.22 | (88) op(all_24_2, all_24_1) = all_24_0 % 146.03/21.22 | (89) ~ (all_24_0 = e0) | ~ (all_24_1 = e1) | ~ (all_24_2 = e2) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2 % 146.03/21.22 | gives: % 146.03/21.22 | (90) op(all_26_2, all_26_1) = all_26_0 & op(all_26_2, e0) = all_26_1 & % 146.03/21.22 | op(e0, e0) = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & ( % 146.03/21.22 | ~ (all_26_0 = e2) | ~ (all_26_1 = e1) | ~ (all_26_2 = e3)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (90) implies: % 146.03/21.22 | (91) op(e0, e0) = all_26_2 % 146.03/21.22 | (92) op(all_26_2, e0) = all_26_1 % 146.03/21.22 | (93) op(all_26_2, all_26_1) = all_26_0 % 146.03/21.22 | (94) ~ (all_26_0 = e2) | ~ (all_26_1 = e1) | ~ (all_26_2 = e3) % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2 % 146.03/21.22 | gives: % 146.03/21.22 | (95) op(all_28_2, all_28_1) = all_28_0 & op(all_28_2, e1) = all_28_1 & % 146.03/21.22 | op(e1, e1) = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & ( % 146.03/21.22 | ~ (all_28_0 = e3) | ~ (all_28_1 = e2) | ~ (all_28_2 = e0)) % 146.03/21.22 | % 146.03/21.22 | ALPHA: (95) implies: % 146.03/21.22 | (96) op(e1, e1) = all_28_2 % 146.03/21.22 | (97) op(all_28_2, e1) = all_28_1 % 146.03/21.22 | (98) op(all_28_2, all_28_1) = all_28_0 % 146.03/21.22 | % 146.03/21.22 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2 % 146.03/21.22 | gives: % 146.03/21.23 | (99) op(all_30_2, all_30_1) = all_30_0 & op(all_30_2, e2) = all_30_1 & % 146.03/21.23 | op(e2, e2) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & ( % 146.03/21.23 | ~ (all_30_0 = e0) | ~ (all_30_1 = e3) | ~ (all_30_2 = e1)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (99) implies: % 146.03/21.23 | (100) op(e2, e2) = all_30_2 % 146.03/21.23 | (101) op(all_30_2, e2) = all_30_1 % 146.03/21.23 | (102) op(all_30_2, all_30_1) = all_30_0 % 146.03/21.23 | (103) ~ (all_30_0 = e0) | ~ (all_30_1 = e3) | ~ (all_30_2 = e1) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2 % 146.03/21.23 | gives: % 146.03/21.23 | (104) op(all_32_2, all_32_1) = all_32_0 & op(all_32_2, e3) = all_32_1 & % 146.03/21.23 | op(e3, e3) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & % 146.03/21.23 | ( ~ (all_32_0 = e1) | ~ (all_32_1 = e0) | ~ (all_32_2 = e2)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (104) implies: % 146.03/21.23 | (105) op(e3, e3) = all_32_2 % 146.03/21.23 | (106) op(all_32_2, e3) = all_32_1 % 146.03/21.23 | (107) op(all_32_2, all_32_1) = all_32_0 % 146.03/21.23 | (108) ~ (all_32_0 = e1) | ~ (all_32_1 = e0) | ~ (all_32_2 = e2) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2 % 146.03/21.23 | gives: % 146.03/21.23 | (109) op(all_34_2, all_34_1) = all_34_0 & op(all_34_2, e0) = all_34_1 & % 146.03/21.23 | op(e0, e0) = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & % 146.03/21.23 | ( ~ (all_34_0 = e3) | ~ (all_34_1 = e2) | ~ (all_34_2 = e1)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (109) implies: % 146.03/21.23 | (110) op(e0, e0) = all_34_2 % 146.03/21.23 | (111) op(all_34_2, e0) = all_34_1 % 146.03/21.23 | (112) op(all_34_2, all_34_1) = all_34_0 % 146.03/21.23 | (113) ~ (all_34_0 = e3) | ~ (all_34_1 = e2) | ~ (all_34_2 = e1) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2 % 146.03/21.23 | gives: % 146.03/21.23 | (114) op(all_36_2, all_36_1) = all_36_0 & op(all_36_2, e1) = all_36_1 & % 146.03/21.23 | op(e1, e1) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) & % 146.03/21.23 | ( ~ (all_36_0 = e3) | ~ (all_36_1 = e0) | ~ (all_36_2 = e2)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (114) implies: % 146.03/21.23 | (115) op(e1, e1) = all_36_2 % 146.03/21.23 | (116) op(all_36_2, e1) = all_36_1 % 146.03/21.23 | (117) op(all_36_2, all_36_1) = all_36_0 % 146.03/21.23 | (118) ~ (all_36_0 = e3) | ~ (all_36_1 = e0) | ~ (all_36_2 = e2) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2 % 146.03/21.23 | gives: % 146.03/21.23 | (119) op(all_38_2, all_38_1) = all_38_0 & op(all_38_2, e3) = all_38_1 & % 146.03/21.23 | op(e3, e3) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) & % 146.03/21.23 | ( ~ (all_38_0 = e2) | ~ (all_38_1 = e0) | ~ (all_38_2 = e1)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (119) implies: % 146.03/21.23 | (120) op(e3, e3) = all_38_2 % 146.03/21.23 | (121) op(all_38_2, e3) = all_38_1 % 146.03/21.23 | (122) op(all_38_2, all_38_1) = all_38_0 % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2 % 146.03/21.23 | gives: % 146.03/21.23 | (123) op(all_40_2, all_40_1) = all_40_0 & op(all_40_2, e1) = all_40_1 & % 146.03/21.23 | op(e1, e1) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & % 146.03/21.23 | ( ~ (all_40_0 = e0) | ~ (all_40_1 = e3) | ~ (all_40_2 = e2)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (123) implies: % 146.03/21.23 | (124) op(e1, e1) = all_40_2 % 146.03/21.23 | (125) op(all_40_2, e1) = all_40_1 % 146.03/21.23 | (126) op(all_40_2, all_40_1) = all_40_0 % 146.03/21.23 | (127) ~ (all_40_0 = e0) | ~ (all_40_1 = e3) | ~ (all_40_2 = e2) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2 % 146.03/21.23 | gives: % 146.03/21.23 | (128) op(all_42_2, all_42_1) = all_42_0 & op(all_42_2, e2) = all_42_1 & % 146.03/21.23 | op(e2, e2) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) & % 146.03/21.23 | ( ~ (all_42_0 = e0) | ~ (all_42_1 = e1) | ~ (all_42_2 = e3)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (128) implies: % 146.03/21.23 | (129) op(e2, e2) = all_42_2 % 146.03/21.23 | (130) op(all_42_2, e2) = all_42_1 % 146.03/21.23 | (131) op(all_42_2, all_42_1) = all_42_0 % 146.03/21.23 | (132) ~ (all_42_0 = e0) | ~ (all_42_1 = e1) | ~ (all_42_2 = e3) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2 % 146.03/21.23 | gives: % 146.03/21.23 | (133) op(all_44_2, all_44_1) = all_44_0 & op(all_44_2, e0) = all_44_1 & % 146.03/21.23 | op(e0, e0) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & % 146.03/21.23 | ( ~ (all_44_0 = e3) | ~ (all_44_1 = e1) | ~ (all_44_2 = e2)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (133) implies: % 146.03/21.23 | (134) op(e0, e0) = all_44_2 % 146.03/21.23 | (135) op(all_44_2, e0) = all_44_1 % 146.03/21.23 | (136) op(all_44_2, all_44_1) = all_44_0 % 146.03/21.23 | (137) ~ (all_44_0 = e3) | ~ (all_44_1 = e1) | ~ (all_44_2 = e2) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2 % 146.03/21.23 | gives: % 146.03/21.23 | (138) op(all_46_2, all_46_1) = all_46_0 & op(all_46_2, e1) = all_46_1 & % 146.03/21.23 | op(e1, e1) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) & % 146.03/21.23 | ( ~ (all_46_0 = e0) | ~ (all_46_1 = e2) | ~ (all_46_2 = e3)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (138) implies: % 146.03/21.23 | (139) op(e1, e1) = all_46_2 % 146.03/21.23 | (140) op(all_46_2, e1) = all_46_1 % 146.03/21.23 | (141) op(all_46_2, all_46_1) = all_46_0 % 146.03/21.23 | (142) ~ (all_46_0 = e0) | ~ (all_46_1 = e2) | ~ (all_46_2 = e3) % 146.03/21.23 | % 146.03/21.23 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2 % 146.03/21.23 | gives: % 146.03/21.23 | (143) op(all_48_2, all_48_1) = all_48_0 & op(all_48_2, e2) = all_48_1 & % 146.03/21.23 | op(e2, e2) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & % 146.03/21.23 | ( ~ (all_48_0 = e1) | ~ (all_48_1 = e3) | ~ (all_48_2 = e0)) % 146.03/21.23 | % 146.03/21.23 | ALPHA: (143) implies: % 146.03/21.23 | (144) op(e2, e2) = all_48_2 % 146.03/21.23 | (145) op(all_48_2, e2) = all_48_1 % 146.03/21.24 | (146) op(all_48_2, all_48_1) = all_48_0 % 146.03/21.24 | (147) ~ (all_48_0 = e1) | ~ (all_48_1 = e3) | ~ (all_48_2 = e0) % 146.03/21.24 | % 146.03/21.24 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2 % 146.03/21.24 | gives: % 146.03/21.24 | (148) op(all_50_2, all_50_1) = all_50_0 & op(all_50_2, e3) = all_50_1 & % 146.03/21.24 | op(e3, e3) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) & % 146.03/21.24 | ( ~ (all_50_0 = e1) | ~ (all_50_1 = e2) | ~ (all_50_2 = e0)) % 146.03/21.24 | % 146.03/21.24 | ALPHA: (148) implies: % 146.03/21.24 | (149) op(e3, e3) = all_50_2 % 146.03/21.24 | (150) op(all_50_2, e3) = all_50_1 % 146.03/21.24 | (151) op(all_50_2, all_50_1) = all_50_0 % 146.03/21.24 | (152) ~ (all_50_0 = e1) | ~ (all_50_1 = e2) | ~ (all_50_2 = e0) % 146.03/21.24 | % 146.03/21.24 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2, % 146.03/21.24 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9, % 146.03/21.24 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives: % 146.03/21.24 | (153) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 = % 146.03/21.24 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) & % 146.03/21.24 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 = % 146.03/21.24 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) & % 146.03/21.24 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 = % 146.03/21.24 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) & % 146.03/21.24 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 = % 146.03/21.24 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) & % 146.03/21.24 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 = % 146.03/21.24 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) & % 146.03/21.24 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 = % 146.03/21.24 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) & % 146.03/21.24 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8 % 146.03/21.24 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11) % 146.03/21.24 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~ % 146.03/21.24 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 = % 146.03/21.24 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 = % 146.03/21.24 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 = % 146.03/21.24 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 = % 146.03/21.24 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 = % 146.03/21.24 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3, % 146.03/21.24 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 & % 146.03/21.24 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) = % 146.03/21.24 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1, % 146.03/21.24 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 & % 146.03/21.24 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) = % 146.03/21.24 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) % 146.03/21.24 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) & % 146.03/21.24 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) & % 146.03/21.24 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15) % 146.03/21.24 | % 146.03/21.24 | ALPHA: (153) implies: % 146.03/21.24 | (154) ~ (all_52_14 = all_52_15) % 146.03/21.24 | (155) ~ (all_52_13 = all_52_15) % 146.03/21.24 | (156) ~ (all_52_13 = all_52_14) % 146.03/21.24 | (157) ~ (all_52_12 = all_52_15) % 146.03/21.24 | (158) ~ (all_52_12 = all_52_14) % 146.03/21.24 | (159) ~ (all_52_12 = all_52_13) % 146.03/21.24 | (160) ~ (all_52_11 = all_52_15) % 146.03/21.24 | (161) ~ (all_52_10 = all_52_14) % 146.03/21.24 | (162) ~ (all_52_10 = all_52_11) % 146.03/21.24 | (163) ~ (all_52_9 = all_52_13) % 146.03/21.24 | (164) ~ (all_52_9 = all_52_11) % 146.03/21.24 | (165) ~ (all_52_9 = all_52_10) % 146.03/21.24 | (166) ~ (all_52_8 = all_52_12) % 146.03/21.24 | (167) ~ (all_52_8 = all_52_11) % 146.03/21.24 | (168) ~ (all_52_8 = all_52_10) % 146.03/21.24 | (169) ~ (all_52_8 = all_52_9) % 146.03/21.24 | (170) ~ (all_52_7 = all_52_15) % 146.03/21.24 | (171) ~ (all_52_7 = all_52_11) % 146.03/21.24 | (172) ~ (all_52_6 = all_52_14) % 146.03/21.24 | (173) ~ (all_52_6 = all_52_10) % 146.03/21.24 | (174) ~ (all_52_6 = all_52_7) % 146.03/21.24 | (175) ~ (all_52_5 = all_52_13) % 146.03/21.24 | (176) ~ (all_52_5 = all_52_9) % 146.03/21.24 | (177) ~ (all_52_5 = all_52_7) % 146.03/21.24 | (178) ~ (all_52_5 = all_52_6) % 146.03/21.24 | (179) ~ (all_52_4 = all_52_12) % 146.03/21.24 | (180) ~ (all_52_4 = all_52_8) % 146.03/21.24 | (181) ~ (all_52_4 = all_52_7) % 146.03/21.24 | (182) ~ (all_52_4 = all_52_6) % 146.03/21.24 | (183) ~ (all_52_4 = all_52_5) % 146.03/21.24 | (184) ~ (all_52_3 = all_52_15) % 146.03/21.24 | (185) ~ (all_52_3 = all_52_11) % 146.03/21.24 | (186) ~ (all_52_3 = all_52_7) % 146.03/21.24 | (187) ~ (all_52_2 = all_52_14) % 146.03/21.24 | (188) ~ (all_52_2 = all_52_10) % 146.03/21.24 | (189) ~ (all_52_2 = all_52_6) % 146.03/21.24 | (190) ~ (all_52_2 = all_52_3) % 146.03/21.24 | (191) ~ (all_52_1 = all_52_13) % 146.03/21.24 | (192) ~ (all_52_1 = all_52_9) % 146.03/21.24 | (193) ~ (all_52_1 = all_52_5) % 146.03/21.24 | (194) ~ (all_52_1 = all_52_3) % 146.03/21.24 | (195) ~ (all_52_1 = all_52_2) % 146.03/21.24 | (196) ~ (all_52_0 = all_52_12) % 146.03/21.24 | (197) ~ (all_52_0 = all_52_8) % 146.03/21.24 | (198) ~ (all_52_0 = all_52_4) % 146.03/21.24 | (199) ~ (all_52_0 = all_52_3) % 146.03/21.24 | (200) ~ (all_52_0 = all_52_2) % 146.03/21.24 | (201) ~ (all_52_0 = all_52_1) % 146.03/21.24 | (202) op(e0, e0) = all_52_15 % 146.03/21.24 | (203) op(e0, e1) = all_52_11 % 146.03/21.24 | (204) op(e0, e2) = all_52_7 % 146.03/21.24 | (205) op(e0, e3) = all_52_3 % 146.03/21.24 | (206) op(e1, e0) = all_52_14 % 146.03/21.24 | (207) op(e1, e1) = all_52_10 % 146.03/21.24 | (208) op(e1, e2) = all_52_6 % 146.03/21.24 | (209) op(e1, e3) = all_52_2 % 146.03/21.24 | (210) op(e2, e0) = all_52_13 % 146.03/21.24 | (211) op(e2, e1) = all_52_9 % 146.03/21.24 | (212) op(e2, e2) = all_52_5 % 146.03/21.24 | (213) op(e2, e3) = all_52_1 % 146.03/21.24 | (214) op(e3, e0) = all_52_12 % 146.03/21.24 | (215) op(e3, e1) = all_52_8 % 146.03/21.24 | (216) op(e3, e2) = all_52_4 % 146.03/21.24 | (217) op(e3, e3) = all_52_0 % 146.03/21.24 | % 146.03/21.24 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2, % 146.03/21.24 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9, % 146.03/21.24 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives: % 146.03/21.25 | (218) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2 % 146.03/21.25 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) = % 146.03/21.25 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3) % 146.03/21.25 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1, % 146.03/21.25 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 & % 146.03/21.25 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) & % 146.03/21.25 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) & % 146.03/21.25 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) & % 146.03/21.25 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) & % 146.03/21.25 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 | % 146.03/21.25 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 | % 146.03/21.25 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 | % 146.03/21.25 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 | % 146.03/21.25 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 | % 146.03/21.25 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 | % 146.03/21.25 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 | % 146.03/21.25 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 | % 146.03/21.25 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 | % 146.03/21.25 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 | % 146.03/21.25 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 | % 146.03/21.25 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3 % 146.03/21.25 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 = % 146.03/21.25 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13 % 146.03/21.25 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) & % 146.03/21.25 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) & % 146.03/21.25 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0) % 146.03/21.25 | % 146.03/21.25 | ALPHA: (218) implies: % 146.03/21.25 | (219) op(e0, e0) = all_54_15 % 146.03/21.25 | (220) op(e0, e1) = all_54_14 % 146.03/21.25 | (221) op(e0, e2) = all_54_13 % 146.03/21.25 | (222) op(e0, e3) = all_54_12 % 146.03/21.25 | (223) op(e1, e0) = all_54_11 % 146.03/21.25 | (224) op(e1, e1) = all_54_10 % 146.03/21.25 | (225) op(e1, e2) = all_54_9 % 146.03/21.25 | (226) op(e1, e3) = all_54_8 % 146.03/21.25 | (227) op(e2, e0) = all_54_7 % 146.03/21.25 | (228) op(e2, e1) = all_54_6 % 146.03/21.25 | (229) op(e2, e2) = all_54_5 % 146.03/21.25 | (230) op(e2, e3) = all_54_4 % 146.03/21.25 | (231) op(e3, e0) = all_54_3 % 146.03/21.25 | (232) op(e3, e1) = all_54_2 % 146.03/21.25 | (233) op(e3, e2) = all_54_1 % 146.03/21.25 | (234) op(e3, e3) = all_54_0 % 146.03/21.25 | (235) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 146.03/21.25 | (236) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 146.03/21.25 | (237) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 146.03/21.25 | (238) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 146.03/21.25 | (239) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 146.03/21.25 | (240) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 146.03/21.25 | (241) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 146.03/21.25 | (242) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 146.03/21.25 | (243) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 146.03/21.25 | (244) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 146.03/21.25 | (245) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 146.03/21.25 | (246) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 146.03/21.25 | (247) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 146.03/21.25 | (248) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 146.03/21.25 | (249) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 146.03/21.25 | (250) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 146.03/21.25 | % 146.03/21.25 | DELTA: instantiating (2) with fresh symbols all_56_0, all_56_1, all_56_2, % 146.03/21.25 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9, % 146.03/21.25 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives: % 146.03/21.26 | (251) op(e3, e3) = all_56_0 & op(e3, e2) = all_56_1 & op(e3, e1) = all_56_4 % 146.03/21.26 | & op(e3, e0) = all_56_9 & op(e2, e3) = all_56_2 & op(e2, e2) = % 146.03/21.26 | all_56_3 & op(e2, e1) = all_56_5 & op(e2, e0) = all_56_10 & op(e1, % 146.03/21.26 | e3) = all_56_6 & op(e1, e2) = all_56_7 & op(e1, e1) = all_56_8 & % 146.03/21.26 | op(e1, e0) = all_56_11 & op(e0, e3) = all_56_12 & op(e0, e2) = % 146.03/21.26 | all_56_13 & op(e0, e1) = all_56_14 & op(e0, e0) = all_56_15 & % 146.03/21.26 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & % 146.03/21.26 | $i(all_56_4) & $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & % 146.03/21.26 | $i(all_56_8) & $i(all_56_9) & $i(all_56_10) & $i(all_56_11) & % 146.03/21.26 | $i(all_56_12) & $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & % 146.03/21.26 | (all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3) & % 146.03/21.26 | (all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3) & % 146.03/21.26 | (all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2) & % 146.03/21.26 | (all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2) & % 146.03/21.26 | (all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1) & % 146.03/21.26 | (all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1) & % 146.03/21.26 | (all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0) & % 146.03/21.26 | (all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0) & % 146.03/21.26 | (all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3) & % 146.03/21.26 | (all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2) & % 146.03/21.26 | (all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1) & % 146.03/21.26 | (all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0) & % 146.03/21.26 | (all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3) & % 146.03/21.26 | (all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2) & % 146.03/21.26 | (all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1) & % 146.03/21.26 | (all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0) & % 146.03/21.26 | (all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3) & % 146.03/21.26 | (all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2) & % 146.03/21.26 | (all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1) & % 146.03/21.26 | (all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0) & % 146.03/21.26 | (all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3) & % 146.03/21.26 | (all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2) & % 146.03/21.26 | (all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1) & % 146.03/21.26 | (all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0) & % 146.03/21.26 | (all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3) & % 146.03/21.26 | (all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2) & % 146.03/21.26 | (all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1) & % 146.03/21.26 | (all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3) & % 146.03/21.26 | (all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2) & % 146.03/21.26 | (all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1) & % 146.03/21.26 | (all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) % 146.03/21.26 | & (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0))) % 146.03/21.26 | % 146.03/21.26 | ALPHA: (251) implies: % 146.03/21.26 | (252) op(e0, e0) = all_56_15 % 146.03/21.26 | (253) op(e0, e1) = all_56_14 % 146.03/21.26 | (254) op(e0, e2) = all_56_13 % 146.03/21.26 | (255) op(e0, e3) = all_56_12 % 146.03/21.26 | (256) op(e1, e0) = all_56_11 % 146.03/21.26 | (257) op(e1, e1) = all_56_8 % 146.03/21.26 | (258) op(e1, e2) = all_56_7 % 146.03/21.26 | (259) op(e1, e3) = all_56_6 % 146.03/21.26 | (260) op(e2, e0) = all_56_10 % 146.03/21.26 | (261) op(e2, e1) = all_56_5 % 146.03/21.26 | (262) op(e2, e2) = all_56_3 % 146.03/21.26 | (263) op(e2, e3) = all_56_2 % 146.03/21.26 | (264) op(e3, e0) = all_56_9 % 146.03/21.26 | (265) op(e3, e1) = all_56_4 % 146.03/21.26 | (266) op(e3, e2) = all_56_1 % 146.03/21.26 | (267) op(e3, e3) = all_56_0 % 146.03/21.26 | (268) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 146.03/21.26 | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 146.03/21.26 | (269) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 146.03/21.26 | (270) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 146.03/21.26 | (271) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 146.03/21.26 | (272) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 146.03/21.26 | (273) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 146.03/21.26 | (274) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 146.03/21.26 | (275) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 146.03/21.26 | (276) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 146.03/21.26 | (277) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 146.03/21.26 | (278) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 146.03/21.26 | (279) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 146.03/21.26 | (280) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 146.03/21.26 | (281) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 146.03/21.26 | (282) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 146.03/21.26 | (283) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 146.03/21.26 | (284) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 146.03/21.26 | (285) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 146.03/21.26 | (286) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 146.03/21.26 | (287) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 146.03/21.26 | (288) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 146.03/21.26 | (289) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 146.03/21.26 | (290) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 146.03/21.26 | (291) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 146.03/21.26 | (292) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 146.03/21.26 | (293) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 146.03/21.26 | (294) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 146.03/21.26 | (295) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 146.03/21.26 | (296) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 146.03/21.26 | (297) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 146.03/21.26 | (298) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 146.03/21.26 | % 146.03/21.26 | DELTA: instantiating (10) with fresh symbols all_58_0, all_58_1, all_58_2, % 146.03/21.26 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9, % 146.03/21.26 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15, % 146.03/21.26 | all_58_16, all_58_17, all_58_18, all_58_19, all_58_20, all_58_21, % 146.03/21.26 | all_58_22, all_58_23, all_58_24, all_58_25, all_58_26, all_58_27, % 146.03/21.26 | all_58_28, all_58_29, all_58_30, all_58_31 gives: % 146.03/21.27 | (299) op(e3, all_58_2) = all_58_1 & op(e3, all_58_4) = all_58_3 & op(e3, % 146.03/21.27 | all_58_6) = all_58_5 & op(e3, all_58_28) = all_58_0 & op(e3, e3) = % 146.03/21.27 | all_58_28 & op(e3, e2) = all_58_2 & op(e3, e1) = all_58_4 & op(e3, % 146.03/21.27 | e0) = all_58_6 & op(e2, all_58_8) = all_58_7 & op(e2, all_58_11) = % 146.03/21.27 | all_58_10 & op(e2, all_58_13) = all_58_12 & op(e2, all_58_29) = % 146.03/21.27 | all_58_9 & op(e2, e3) = all_58_8 & op(e2, e2) = all_58_29 & op(e2, % 146.03/21.27 | e1) = all_58_11 & op(e2, e0) = all_58_13 & op(e1, all_58_15) = % 146.03/21.27 | all_58_14 & op(e1, all_58_17) = all_58_16 & op(e1, all_58_20) = % 146.03/21.27 | all_58_19 & op(e1, all_58_30) = all_58_18 & op(e1, e3) = all_58_15 & % 146.03/21.27 | op(e1, e2) = all_58_17 & op(e1, e1) = all_58_30 & op(e1, e0) = % 146.03/21.27 | all_58_20 & op(e0, all_58_22) = all_58_21 & op(e0, all_58_24) = % 146.03/21.27 | all_58_23 & op(e0, all_58_26) = all_58_25 & op(e0, all_58_31) = % 146.03/21.27 | all_58_27 & op(e0, e3) = all_58_22 & op(e0, e2) = all_58_24 & op(e0, % 146.03/21.27 | e1) = all_58_26 & op(e0, e0) = all_58_31 & $i(all_58_0) & % 146.03/21.27 | $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & $i(all_58_4) & % 146.03/21.27 | $i(all_58_5) & $i(all_58_6) & $i(all_58_7) & $i(all_58_8) & % 146.03/21.27 | $i(all_58_9) & $i(all_58_10) & $i(all_58_11) & $i(all_58_12) & % 146.03/21.27 | $i(all_58_13) & $i(all_58_14) & $i(all_58_15) & $i(all_58_16) & % 146.03/21.27 | $i(all_58_17) & $i(all_58_18) & $i(all_58_19) & $i(all_58_20) & % 146.03/21.27 | $i(all_58_21) & $i(all_58_22) & $i(all_58_23) & $i(all_58_24) & % 146.03/21.27 | $i(all_58_25) & $i(all_58_26) & $i(all_58_27) & $i(all_58_28) & % 146.03/21.27 | $i(all_58_29) & $i(all_58_30) & $i(all_58_31) & (all_58_28 = e3 | % 146.03/21.27 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3) & (all_58_28 = e3 % 146.03/21.27 | | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | (all_58_2 = e3 % 146.03/21.27 | & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = % 146.03/21.27 | e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 % 146.03/21.27 | = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 146.03/21.27 | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 146.03/21.27 | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 146.03/21.27 | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 146.03/21.27 | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 146.03/21.27 | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 146.03/21.27 | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 146.03/21.27 | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 146.03/21.27 | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 146.03/21.27 | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 146.03/21.27 | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 146.03/21.27 | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) % 146.03/21.27 | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = % 146.03/21.27 | e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 146.03/21.27 | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 146.03/21.27 | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 146.03/21.27 | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) % 146.03/21.27 | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = % 146.03/21.27 | e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 146.03/21.27 | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 146.03/21.27 | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) % 146.03/21.27 | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = % 146.03/21.27 | e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 146.03/21.27 | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 146.03/21.27 | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) % 146.03/21.27 | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = % 146.03/21.27 | e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = % 146.03/21.27 | e0 & all_58_26 = e0 & e1 = e0)) & (all_58_28 = e2 | all_58_29 = % 146.03/21.27 | e2 | all_58_30 = e2 | all_58_31 = e2) & (all_58_28 = e1 | all_58_29 % 146.03/21.27 | = e1 | all_58_30 = e1 | all_58_31 = e1) & (all_58_28 = e0 | % 146.03/21.27 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0) & (( ~ (all_58_0 % 146.03/21.27 | = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ (all_58_5 % 146.03/21.27 | = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 146.03/21.27 | (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & % 146.03/21.27 | ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | % 146.03/21.27 | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & % 146.03/21.27 | ~ (all_58_27 = e0))) % 146.03/21.27 | % 146.03/21.27 | ALPHA: (299) implies: % 146.03/21.27 | (300) op(e0, e0) = all_58_31 % 146.03/21.27 | (301) op(e0, e1) = all_58_26 % 146.03/21.27 | (302) op(e0, e2) = all_58_24 % 146.03/21.27 | (303) op(e0, e3) = all_58_22 % 146.03/21.27 | (304) op(e0, all_58_31) = all_58_27 % 146.03/21.27 | (305) op(e0, all_58_26) = all_58_25 % 146.03/21.27 | (306) op(e0, all_58_24) = all_58_23 % 146.03/21.27 | (307) op(e0, all_58_22) = all_58_21 % 146.03/21.27 | (308) op(e1, e0) = all_58_20 % 146.03/21.27 | (309) op(e1, e1) = all_58_30 % 146.03/21.27 | (310) op(e1, e2) = all_58_17 % 146.03/21.27 | (311) op(e1, e3) = all_58_15 % 146.03/21.27 | (312) op(e1, all_58_30) = all_58_18 % 146.03/21.27 | (313) op(e1, all_58_20) = all_58_19 % 146.03/21.27 | (314) op(e1, all_58_17) = all_58_16 % 146.03/21.27 | (315) op(e1, all_58_15) = all_58_14 % 146.03/21.27 | (316) op(e2, e0) = all_58_13 % 146.03/21.27 | (317) op(e2, e1) = all_58_11 % 146.03/21.27 | (318) op(e2, e2) = all_58_29 % 146.03/21.27 | (319) op(e2, e3) = all_58_8 % 146.03/21.27 | (320) op(e2, all_58_29) = all_58_9 % 146.03/21.27 | (321) op(e2, all_58_13) = all_58_12 % 146.03/21.27 | (322) op(e2, all_58_11) = all_58_10 % 146.03/21.27 | (323) op(e2, all_58_8) = all_58_7 % 146.03/21.27 | (324) op(e3, e0) = all_58_6 % 146.03/21.27 | (325) op(e3, e1) = all_58_4 % 146.03/21.27 | (326) op(e3, e2) = all_58_2 % 146.03/21.27 | (327) op(e3, e3) = all_58_28 % 146.03/21.27 | (328) op(e3, all_58_28) = all_58_0 % 146.03/21.27 | (329) op(e3, all_58_6) = all_58_5 % 146.03/21.27 | (330) op(e3, all_58_4) = all_58_3 % 146.03/21.27 | (331) op(e3, all_58_2) = all_58_1 % 146.03/21.27 | (332) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 146.03/21.27 | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 146.03/21.27 | (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 146.03/21.27 | (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 146.03/21.27 | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 146.03/21.27 | (all_58_27 = e0)) % 146.03/21.27 | (333) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 146.03/21.27 | (334) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 146.03/21.27 | (335) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 146.03/21.28 | (336) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 146.03/21.28 | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 146.03/21.28 | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 146.03/21.28 | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 146.03/21.28 | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 146.03/21.28 | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 146.03/21.28 | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 146.03/21.28 | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 146.03/21.28 | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 146.03/21.28 | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 % 146.03/21.28 | = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 146.03/21.28 | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 % 146.03/21.28 | & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 146.03/21.28 | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 146.03/21.28 | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 % 146.03/21.28 | = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 146.03/21.28 | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 146.03/21.28 | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 % 146.03/21.28 | & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 146.03/21.28 | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 % 146.03/21.28 | = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 146.03/21.28 | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & % 146.03/21.28 | all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 % 146.03/21.28 | & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 146.03/21.28 | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 % 146.03/21.28 | = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 146.03/21.28 | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 146.03/21.28 | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 % 146.03/21.28 | & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 146.03/21.28 | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & % 146.03/21.28 | e1 = e0) % 146.03/21.28 | (337) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_20_2, e0, e0, % 146.03/21.28 | simplifying with (36), (76) gives: % 146.03/21.28 | (338) all_20_2 = all_4_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_34_2, e0, e0, % 146.03/21.28 | simplifying with (76), (110) gives: % 146.03/21.28 | (339) all_34_2 = all_20_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_44_2, e0, e0, % 146.03/21.28 | simplifying with (110), (134) gives: % 146.03/21.28 | (340) all_44_2 = all_34_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_52_15, e0, e0, % 146.03/21.28 | simplifying with (110), (202) gives: % 146.03/21.28 | (341) all_52_15 = all_34_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_52_15, e0, e0, % 146.03/21.28 | simplifying with (91), (202) gives: % 146.03/21.28 | (342) all_52_15 = all_26_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_54_15, e0, e0, % 146.03/21.28 | simplifying with (134), (219) gives: % 146.03/21.28 | (343) all_54_15 = all_44_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_15, e0, % 146.03/21.28 | e0, simplifying with (219), (252) gives: % 146.03/21.28 | (344) all_56_15 = all_54_15 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_15, all_58_31, e0, % 146.03/21.28 | e0, simplifying with (252), (300) gives: % 146.03/21.28 | (345) all_58_31 = all_56_15 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_58_31, e0, e0, % 146.03/21.28 | simplifying with (56), (300) gives: % 146.03/21.28 | (346) all_58_31 = all_12_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_56_14, e1, % 146.03/21.28 | e0, simplifying with (203), (253) gives: % 146.03/21.28 | (347) all_56_14 = all_52_11 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_14, all_58_26, e1, % 146.03/21.28 | e0, simplifying with (253), (301) gives: % 146.03/21.28 | (348) all_58_26 = all_56_14 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_58_26, e1, % 146.03/21.28 | e0, simplifying with (220), (301) gives: % 146.03/21.28 | (349) all_58_26 = all_54_14 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_56_13, e2, e0, % 146.03/21.28 | simplifying with (204), (254) gives: % 146.03/21.28 | (350) all_56_13 = all_52_7 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_13, all_58_24, e2, % 146.03/21.28 | e0, simplifying with (254), (302) gives: % 146.03/21.28 | (351) all_58_24 = all_56_13 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_58_24, e2, % 146.03/21.28 | e0, simplifying with (221), (302) gives: % 146.03/21.28 | (352) all_58_24 = all_54_13 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_12, all_58_22, e3, % 146.03/21.28 | e0, simplifying with (255), (303) gives: % 146.03/21.28 | (353) all_58_22 = all_56_12 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_12, all_58_22, e3, % 146.03/21.28 | e0, simplifying with (222), (303) gives: % 146.03/21.28 | (354) all_58_22 = all_54_12 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_58_22, e3, e0, % 146.03/21.28 | simplifying with (205), (303) gives: % 146.03/21.28 | (355) all_58_22 = all_52_3 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_11, all_56_11, e0, % 146.03/21.28 | e1, simplifying with (223), (256) gives: % 146.03/21.28 | (356) all_56_11 = all_54_11 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_11, all_58_20, e0, % 146.03/21.28 | e1, simplifying with (256), (308) gives: % 146.03/21.28 | (357) all_58_20 = all_56_11 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_58_20, e0, % 146.03/21.28 | e1, simplifying with (206), (308) gives: % 146.03/21.28 | (358) all_58_20 = all_52_14 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_46_2, e1, e1, % 146.03/21.28 | simplifying with (124), (139) gives: % 146.03/21.28 | (359) all_46_2 = all_40_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_46_2, e1, e1, % 146.03/21.28 | simplifying with (41), (139) gives: % 146.03/21.28 | (360) all_46_2 = all_6_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_10, e1, e1, % 146.03/21.28 | simplifying with (71), (224) gives: % 146.03/21.28 | (361) all_54_10 = all_18_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_8, e1, e1, % 146.03/21.28 | simplifying with (224), (257) gives: % 146.03/21.28 | (362) all_56_8 = all_54_10 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_56_8, e1, e1, % 146.03/21.28 | simplifying with (207), (257) gives: % 146.03/21.28 | (363) all_56_8 = all_52_10 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_56_8, e1, e1, % 146.03/21.28 | simplifying with (124), (257) gives: % 146.03/21.28 | (364) all_56_8 = all_40_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_56_8, e1, e1, % 146.03/21.28 | simplifying with (115), (257) gives: % 146.03/21.28 | (365) all_56_8 = all_36_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_8, all_58_30, e1, e1, % 146.03/21.28 | simplifying with (257), (309) gives: % 146.03/21.28 | (366) all_58_30 = all_56_8 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_58_30, e1, e1, % 146.03/21.28 | simplifying with (96), (309) gives: % 146.03/21.28 | (367) all_58_30 = all_28_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_7, e2, e1, % 146.03/21.28 | simplifying with (225), (258) gives: % 146.03/21.28 | (368) all_56_7 = all_54_9 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_17, e2, e1, % 146.03/21.28 | simplifying with (258), (310) gives: % 146.03/21.28 | (369) all_58_17 = all_56_7 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_58_17, e2, e1, % 146.03/21.28 | simplifying with (208), (310) gives: % 146.03/21.28 | (370) all_58_17 = all_52_6 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_56_6, e3, e1, % 146.03/21.28 | simplifying with (209), (259) gives: % 146.03/21.28 | (371) all_56_6 = all_52_2 % 146.03/21.28 | % 146.03/21.28 | GROUND_INST: instantiating (function-axioms) with all_56_6, all_58_15, e3, e1, % 146.03/21.28 | simplifying with (259), (311) gives: % 146.03/21.29 | (372) all_58_15 = all_56_6 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_58_15, e3, e1, % 146.03/21.29 | simplifying with (226), (311) gives: % 146.03/21.29 | (373) all_58_15 = all_54_8 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_7, all_56_10, e0, e2, % 146.03/21.29 | simplifying with (227), (260) gives: % 146.03/21.29 | (374) all_56_10 = all_54_7 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_56_10, all_58_13, e0, % 146.03/21.29 | e2, simplifying with (260), (316) gives: % 146.03/21.29 | (375) all_58_13 = all_56_10 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_58_13, e0, % 146.03/21.29 | e2, simplifying with (210), (316) gives: % 146.03/21.29 | (376) all_58_13 = all_52_13 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_6, all_56_5, e1, e2, % 146.03/21.29 | simplifying with (228), (261) gives: % 146.03/21.29 | (377) all_56_5 = all_54_6 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_56_5, all_58_11, e1, e2, % 146.03/21.29 | simplifying with (261), (317) gives: % 146.03/21.29 | (378) all_58_11 = all_56_5 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_58_11, e1, e2, % 146.03/21.29 | simplifying with (211), (317) gives: % 146.03/21.29 | (379) all_58_11 = all_52_9 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_52_5, e2, e2, % 146.03/21.29 | simplifying with (100), (212) gives: % 146.03/21.29 | (380) all_52_5 = all_30_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_54_5, e2, e2, % 146.03/21.29 | simplifying with (46), (229) gives: % 146.03/21.29 | (381) all_54_5 = all_8_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_5, all_56_3, e2, e2, % 146.03/21.29 | simplifying with (229), (262) gives: % 146.03/21.29 | (382) all_56_3 = all_54_5 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_3, e2, e2, % 146.03/21.29 | simplifying with (212), (262) gives: % 146.03/21.29 | (383) all_56_3 = all_52_5 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_3, e2, e2, % 146.03/21.29 | simplifying with (129), (262) gives: % 146.03/21.29 | (384) all_56_3 = all_42_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_56_3, e2, e2, % 146.03/21.29 | simplifying with (81), (262) gives: % 146.03/21.29 | (385) all_56_3 = all_22_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_58_29, e2, e2, % 146.03/21.29 | simplifying with (144), (318) gives: % 146.03/21.29 | (386) all_58_29 = all_48_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_58_29, e2, e2, % 146.03/21.29 | simplifying with (81), (318) gives: % 146.03/21.29 | (387) all_58_29 = all_22_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_58_29, e2, e2, % 146.03/21.29 | simplifying with (61), (318) gives: % 146.03/21.29 | (388) all_58_29 = all_14_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_56_2, e3, e2, % 146.03/21.29 | simplifying with (230), (263) gives: % 146.03/21.29 | (389) all_56_2 = all_54_4 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_56_2, all_58_8, e3, e2, % 146.03/21.29 | simplifying with (263), (319) gives: % 146.03/21.29 | (390) all_58_8 = all_56_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_8, e3, e2, % 146.03/21.29 | simplifying with (213), (319) gives: % 146.03/21.29 | (391) all_58_8 = all_52_1 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_56_9, e0, e3, % 146.03/21.29 | simplifying with (214), (264) gives: % 146.03/21.29 | (392) all_56_9 = all_52_12 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_6, e0, e3, % 146.03/21.29 | simplifying with (264), (324) gives: % 146.03/21.29 | (393) all_58_6 = all_56_9 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_58_6, e0, e3, % 146.03/21.29 | simplifying with (231), (324) gives: % 146.03/21.29 | (394) all_58_6 = all_54_3 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_56_4, e1, e3, % 146.03/21.29 | simplifying with (232), (265) gives: % 146.03/21.29 | (395) all_56_4 = all_54_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_56_4, all_58_4, e1, e3, % 146.03/21.29 | simplifying with (265), (325) gives: % 146.03/21.29 | (396) all_58_4 = all_56_4 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_58_4, e1, e3, % 146.03/21.29 | simplifying with (215), (325) gives: % 146.03/21.29 | (397) all_58_4 = all_52_8 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_56_1, e2, e3, % 146.03/21.29 | simplifying with (233), (266) gives: % 146.03/21.29 | (398) all_56_1 = all_54_1 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_56_1, all_58_2, e2, e3, % 146.03/21.29 | simplifying with (266), (326) gives: % 146.03/21.29 | (399) all_58_2 = all_56_1 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_58_2, e2, e3, % 146.03/21.29 | simplifying with (216), (326) gives: % 146.03/21.29 | (400) all_58_2 = all_52_4 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3, % 146.03/21.29 | simplifying with (120), (149) gives: % 146.03/21.29 | (401) all_50_2 = all_38_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_50_2, e3, e3, % 146.03/21.29 | simplifying with (105), (149) gives: % 146.03/21.29 | (402) all_50_2 = all_32_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_0, e3, e3, % 146.03/21.29 | simplifying with (120), (217) gives: % 146.03/21.29 | (403) all_52_0 = all_38_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_52_0, e3, e3, % 146.03/21.29 | simplifying with (51), (217) gives: % 146.03/21.29 | (404) all_52_0 = all_10_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_0, e3, e3, % 146.03/21.29 | simplifying with (149), (234) gives: % 146.03/21.29 | (405) all_54_0 = all_50_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_0, e3, e3, % 146.03/21.29 | simplifying with (234), (267) gives: % 146.03/21.29 | (406) all_56_0 = all_54_0 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_56_0, e3, e3, % 146.03/21.29 | simplifying with (66), (267) gives: % 146.03/21.29 | (407) all_56_0 = all_16_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_58_28, e3, e3, % 146.03/21.29 | simplifying with (149), (327) gives: % 146.03/21.29 | (408) all_58_28 = all_50_2 % 146.03/21.29 | % 146.03/21.29 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_58_28, e3, e3, % 146.03/21.29 | simplifying with (86), (327) gives: % 146.03/21.29 | (409) all_58_28 = all_24_2 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (399), (400) imply: % 146.03/21.29 | (410) all_56_1 = all_52_4 % 146.03/21.29 | % 146.03/21.29 | SIMP: (410) implies: % 146.03/21.29 | (411) all_56_1 = all_52_4 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (396), (397) imply: % 146.03/21.29 | (412) all_56_4 = all_52_8 % 146.03/21.29 | % 146.03/21.29 | SIMP: (412) implies: % 146.03/21.29 | (413) all_56_4 = all_52_8 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (393), (394) imply: % 146.03/21.29 | (414) all_56_9 = all_54_3 % 146.03/21.29 | % 146.03/21.29 | SIMP: (414) implies: % 146.03/21.29 | (415) all_56_9 = all_54_3 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (390), (391) imply: % 146.03/21.29 | (416) all_56_2 = all_52_1 % 146.03/21.29 | % 146.03/21.29 | SIMP: (416) implies: % 146.03/21.29 | (417) all_56_2 = all_52_1 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (378), (379) imply: % 146.03/21.29 | (418) all_56_5 = all_52_9 % 146.03/21.29 | % 146.03/21.29 | SIMP: (418) implies: % 146.03/21.29 | (419) all_56_5 = all_52_9 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (375), (376) imply: % 146.03/21.29 | (420) all_56_10 = all_52_13 % 146.03/21.29 | % 146.03/21.29 | SIMP: (420) implies: % 146.03/21.29 | (421) all_56_10 = all_52_13 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (372), (373) imply: % 146.03/21.29 | (422) all_56_6 = all_54_8 % 146.03/21.29 | % 146.03/21.29 | SIMP: (422) implies: % 146.03/21.29 | (423) all_56_6 = all_54_8 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (369), (370) imply: % 146.03/21.29 | (424) all_56_7 = all_52_6 % 146.03/21.29 | % 146.03/21.29 | SIMP: (424) implies: % 146.03/21.29 | (425) all_56_7 = all_52_6 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (357), (358) imply: % 146.03/21.29 | (426) all_56_11 = all_52_14 % 146.03/21.29 | % 146.03/21.29 | SIMP: (426) implies: % 146.03/21.29 | (427) all_56_11 = all_52_14 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (353), (354) imply: % 146.03/21.29 | (428) all_56_12 = all_54_12 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (353), (355) imply: % 146.03/21.29 | (429) all_56_12 = all_52_3 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (351), (352) imply: % 146.03/21.29 | (430) all_56_13 = all_54_13 % 146.03/21.29 | % 146.03/21.29 | SIMP: (430) implies: % 146.03/21.29 | (431) all_56_13 = all_54_13 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (348), (349) imply: % 146.03/21.29 | (432) all_56_14 = all_54_14 % 146.03/21.29 | % 146.03/21.29 | SIMP: (432) implies: % 146.03/21.29 | (433) all_56_14 = all_54_14 % 146.03/21.29 | % 146.03/21.29 | COMBINE_EQS: (408), (409) imply: % 146.03/21.29 | (434) all_50_2 = all_24_2 % 146.03/21.29 | % 146.03/21.29 | SIMP: (434) implies: % 146.03/21.29 | (435) all_50_2 = all_24_2 % 146.03/21.29 | % 146.03/21.30 | COMBINE_EQS: (386), (388) imply: % 146.03/21.30 | (436) all_48_2 = all_14_2 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (386), (387) imply: % 146.03/21.30 | (437) all_48_2 = all_22_2 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (366), (367) imply: % 146.03/21.30 | (438) all_56_8 = all_28_2 % 146.03/21.30 | % 146.03/21.30 | SIMP: (438) implies: % 146.03/21.30 | (439) all_56_8 = all_28_2 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (345), (346) imply: % 146.03/21.30 | (440) all_56_15 = all_12_2 % 146.03/21.30 | % 146.03/21.30 | SIMP: (440) implies: % 146.03/21.30 | (441) all_56_15 = all_12_2 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (406), (407) imply: % 146.03/21.30 | (442) all_54_0 = all_16_2 % 146.03/21.30 | % 146.03/21.30 | SIMP: (442) implies: % 146.03/21.30 | (443) all_54_0 = all_16_2 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (398), (411) imply: % 146.03/21.30 | (444) all_54_1 = all_52_4 % 146.03/21.30 | % 146.03/21.30 | SIMP: (444) implies: % 146.03/21.30 | (445) all_54_1 = all_52_4 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (389), (417) imply: % 146.03/21.30 | (446) all_54_4 = all_52_1 % 146.03/21.30 | % 146.03/21.30 | SIMP: (446) implies: % 146.03/21.30 | (447) all_54_4 = all_52_1 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (383), (384) imply: % 146.03/21.30 | (448) all_52_5 = all_42_2 % 146.03/21.30 | % 146.03/21.30 | SIMP: (448) implies: % 146.03/21.30 | (449) all_52_5 = all_42_2 % 146.03/21.30 | % 146.03/21.30 | COMBINE_EQS: (382), (384) imply: % 146.03/21.30 | (450) all_54_5 = all_42_2 % 146.03/21.30 | % 146.50/21.30 | SIMP: (450) implies: % 146.50/21.30 | (451) all_54_5 = all_42_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (384), (385) imply: % 146.50/21.30 | (452) all_42_2 = all_22_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (395), (413) imply: % 146.50/21.30 | (453) all_54_2 = all_52_8 % 146.50/21.30 | % 146.50/21.30 | SIMP: (453) implies: % 146.50/21.30 | (454) all_54_2 = all_52_8 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (377), (419) imply: % 146.50/21.30 | (455) all_54_6 = all_52_9 % 146.50/21.30 | % 146.50/21.30 | SIMP: (455) implies: % 146.50/21.30 | (456) all_54_6 = all_52_9 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (371), (423) imply: % 146.50/21.30 | (457) all_54_8 = all_52_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (457) implies: % 146.50/21.30 | (458) all_54_8 = all_52_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (368), (425) imply: % 146.50/21.30 | (459) all_54_9 = all_52_6 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (363), (365) imply: % 146.50/21.30 | (460) all_52_10 = all_36_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (363), (364) imply: % 146.50/21.30 | (461) all_52_10 = all_40_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (363), (439) imply: % 146.50/21.30 | (462) all_52_10 = all_28_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (362), (363) imply: % 146.50/21.30 | (463) all_54_10 = all_52_10 % 146.50/21.30 | % 146.50/21.30 | SIMP: (463) implies: % 146.50/21.30 | (464) all_54_10 = all_52_10 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (392), (415) imply: % 146.50/21.30 | (465) all_54_3 = all_52_12 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (374), (421) imply: % 146.50/21.30 | (466) all_54_7 = all_52_13 % 146.50/21.30 | % 146.50/21.30 | SIMP: (466) implies: % 146.50/21.30 | (467) all_54_7 = all_52_13 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (356), (427) imply: % 146.50/21.30 | (468) all_54_11 = all_52_14 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (428), (429) imply: % 146.50/21.30 | (469) all_54_12 = all_52_3 % 146.50/21.30 | % 146.50/21.30 | SIMP: (469) implies: % 146.50/21.30 | (470) all_54_12 = all_52_3 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (350), (431) imply: % 146.50/21.30 | (471) all_54_13 = all_52_7 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (347), (433) imply: % 146.50/21.30 | (472) all_54_14 = all_52_11 % 146.50/21.30 | % 146.50/21.30 | SIMP: (472) implies: % 146.50/21.30 | (473) all_54_14 = all_52_11 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (344), (441) imply: % 146.50/21.30 | (474) all_54_15 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (474) implies: % 146.50/21.30 | (475) all_54_15 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (405), (443) imply: % 146.50/21.30 | (476) all_50_2 = all_16_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (476) implies: % 146.50/21.30 | (477) all_50_2 = all_16_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (381), (451) imply: % 146.50/21.30 | (478) all_42_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (478) implies: % 146.50/21.30 | (479) all_42_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (361), (464) imply: % 146.50/21.30 | (480) all_52_10 = all_18_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (480) implies: % 146.50/21.30 | (481) all_52_10 = all_18_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (343), (475) imply: % 146.50/21.30 | (482) all_44_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (482) implies: % 146.50/21.30 | (483) all_44_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (403), (404) imply: % 146.50/21.30 | (484) all_38_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (484) implies: % 146.50/21.30 | (485) all_38_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (380), (449) imply: % 146.50/21.30 | (486) all_42_2 = all_30_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (486) implies: % 146.50/21.30 | (487) all_42_2 = all_30_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (460), (481) imply: % 146.50/21.30 | (488) all_36_2 = all_18_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (460), (461) imply: % 146.50/21.30 | (489) all_40_2 = all_36_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (489) implies: % 146.50/21.30 | (490) all_40_2 = all_36_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (460), (462) imply: % 146.50/21.30 | (491) all_36_2 = all_28_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (341), (342) imply: % 146.50/21.30 | (492) all_34_2 = all_26_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (492) implies: % 146.50/21.30 | (493) all_34_2 = all_26_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (401), (402) imply: % 146.50/21.30 | (494) all_38_2 = all_32_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (494) implies: % 146.50/21.30 | (495) all_38_2 = all_32_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (402), (435) imply: % 146.50/21.30 | (496) all_32_2 = all_24_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (402), (477) imply: % 146.50/21.30 | (497) all_32_2 = all_16_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (436), (437) imply: % 146.50/21.30 | (498) all_22_2 = all_14_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (498) implies: % 146.50/21.30 | (499) all_22_2 = all_14_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (359), (360) imply: % 146.50/21.30 | (500) all_40_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (500) implies: % 146.50/21.30 | (501) all_40_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (340), (483) imply: % 146.50/21.30 | (502) all_34_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (502) implies: % 146.50/21.30 | (503) all_34_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (479), (487) imply: % 146.50/21.30 | (504) all_30_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (452), (487) imply: % 146.50/21.30 | (505) all_30_2 = all_22_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (490), (501) imply: % 146.50/21.30 | (506) all_36_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (506) implies: % 146.50/21.30 | (507) all_36_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (485), (495) imply: % 146.50/21.30 | (508) all_32_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (508) implies: % 146.50/21.30 | (509) all_32_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (491), (507) imply: % 146.50/21.30 | (510) all_28_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (488), (491) imply: % 146.50/21.30 | (511) all_28_2 = all_18_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (339), (493) imply: % 146.50/21.30 | (512) all_26_2 = all_20_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (493), (503) imply: % 146.50/21.30 | (513) all_26_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (496), (497) imply: % 146.50/21.30 | (514) all_24_2 = all_16_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (496), (509) imply: % 146.50/21.30 | (515) all_24_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (504), (505) imply: % 146.50/21.30 | (516) all_22_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (516) implies: % 146.50/21.30 | (517) all_22_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (510), (511) imply: % 146.50/21.30 | (518) all_18_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (518) implies: % 146.50/21.30 | (519) all_18_2 = all_6_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (512), (513) imply: % 146.50/21.30 | (520) all_20_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (520) implies: % 146.50/21.30 | (521) all_20_2 = all_12_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (514), (515) imply: % 146.50/21.30 | (522) all_16_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (522) implies: % 146.50/21.30 | (523) all_16_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (499), (517) imply: % 146.50/21.30 | (524) all_14_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | SIMP: (524) implies: % 146.50/21.30 | (525) all_14_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (338), (521) imply: % 146.50/21.30 | (526) all_12_2 = all_4_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (513), (526) imply: % 146.50/21.30 | (527) all_26_2 = all_4_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (493), (527) imply: % 146.50/21.30 | (528) all_34_2 = all_4_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (483), (526) imply: % 146.50/21.30 | (529) all_44_2 = all_4_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (436), (525) imply: % 146.50/21.30 | (530) all_48_2 = all_8_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (402), (509) imply: % 146.50/21.30 | (531) all_50_2 = all_10_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (342), (527) imply: % 146.50/21.30 | (532) all_52_15 = all_4_2 % 146.50/21.30 | % 146.50/21.30 | COMBINE_EQS: (460), (507) imply: % 146.50/21.31 | (533) all_52_10 = all_6_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (380), (504) imply: % 146.50/21.31 | (534) all_52_5 = all_8_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (475), (526) imply: % 146.50/21.31 | (535) all_54_15 = all_4_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (361), (519) imply: % 146.50/21.31 | (536) all_54_10 = all_6_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (443), (523) imply: % 146.50/21.31 | (537) all_54_0 = all_10_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (441), (526) imply: % 146.50/21.31 | (538) all_56_15 = all_4_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (363), (533) imply: % 146.50/21.31 | (539) all_56_8 = all_6_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (384), (479) imply: % 146.50/21.31 | (540) all_56_3 = all_8_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (407), (523) imply: % 146.50/21.31 | (541) all_56_0 = all_10_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (346), (526) imply: % 146.50/21.31 | (542) all_58_31 = all_4_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (367), (510) imply: % 146.50/21.31 | (543) all_58_30 = all_6_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (386), (530) imply: % 146.50/21.31 | (544) all_58_29 = all_8_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (409), (515) imply: % 146.50/21.31 | (545) all_58_28 = all_10_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (349), (473) imply: % 146.50/21.31 | (546) all_58_26 = all_52_11 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (352), (471) imply: % 146.50/21.31 | (547) all_58_24 = all_52_7 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (373), (458) imply: % 146.50/21.31 | (548) all_58_15 = all_52_2 % 146.50/21.31 | % 146.50/21.31 | COMBINE_EQS: (394), (465) imply: % 146.50/21.31 | (549) all_58_6 = all_52_12 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (201), (404) imply: % 146.50/21.31 | (550) ~ (all_52_1 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (550) implies: % 146.50/21.31 | (551) ~ (all_52_1 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (200), (404) imply: % 146.50/21.31 | (552) ~ (all_52_2 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (552) implies: % 146.50/21.31 | (553) ~ (all_52_2 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (199), (404) imply: % 146.50/21.31 | (554) ~ (all_52_3 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (554) implies: % 146.50/21.31 | (555) ~ (all_52_3 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (198), (404) imply: % 146.50/21.31 | (556) ~ (all_52_4 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (556) implies: % 146.50/21.31 | (557) ~ (all_52_4 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (197), (404) imply: % 146.50/21.31 | (558) ~ (all_52_8 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (558) implies: % 146.50/21.31 | (559) ~ (all_52_8 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (196), (404) imply: % 146.50/21.31 | (560) ~ (all_52_12 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (560) implies: % 146.50/21.31 | (561) ~ (all_52_12 = all_10_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (193), (534) imply: % 146.50/21.31 | (562) ~ (all_52_1 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (188), (533) imply: % 146.50/21.31 | (563) ~ (all_52_2 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (184), (532) imply: % 146.50/21.31 | (564) ~ (all_52_3 = all_4_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (183), (534) imply: % 146.50/21.31 | (565) ~ (all_52_4 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (178), (534) imply: % 146.50/21.31 | (566) ~ (all_52_6 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (566) implies: % 146.50/21.31 | (567) ~ (all_52_6 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (177), (534) imply: % 146.50/21.31 | (568) ~ (all_52_7 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (568) implies: % 146.50/21.31 | (569) ~ (all_52_7 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (176), (534) imply: % 146.50/21.31 | (570) ~ (all_52_9 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (570) implies: % 146.50/21.31 | (571) ~ (all_52_9 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (175), (534) imply: % 146.50/21.31 | (572) ~ (all_52_13 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (572) implies: % 146.50/21.31 | (573) ~ (all_52_13 = all_8_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (173), (533) imply: % 146.50/21.31 | (574) ~ (all_52_6 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (170), (532) imply: % 146.50/21.31 | (575) ~ (all_52_7 = all_4_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (168), (533) imply: % 146.50/21.31 | (576) ~ (all_52_8 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (165), (533) imply: % 146.50/21.31 | (577) ~ (all_52_9 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (162), (533) imply: % 146.50/21.31 | (578) ~ (all_52_11 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (578) implies: % 146.50/21.31 | (579) ~ (all_52_11 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (161), (533) imply: % 146.50/21.31 | (580) ~ (all_52_14 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | SIMP: (580) implies: % 146.50/21.31 | (581) ~ (all_52_14 = all_6_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (160), (532) imply: % 146.50/21.31 | (582) ~ (all_52_11 = all_4_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (157), (532) imply: % 146.50/21.31 | (583) ~ (all_52_12 = all_4_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (155), (532) imply: % 146.50/21.31 | (584) ~ (all_52_13 = all_4_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (154), (532) imply: % 146.50/21.31 | (585) ~ (all_52_14 = all_4_2) % 146.50/21.31 | % 146.50/21.31 | REDUCE: (151), (531) imply: % 146.50/21.31 | (586) op(all_10_2, all_50_1) = all_50_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (150), (531) imply: % 146.50/21.31 | (587) op(all_10_2, e3) = all_50_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (146), (530) imply: % 146.50/21.31 | (588) op(all_8_2, all_48_1) = all_48_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (145), (530) imply: % 146.50/21.31 | (589) op(all_8_2, e2) = all_48_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (141), (360) imply: % 146.50/21.31 | (590) op(all_6_2, all_46_1) = all_46_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (140), (360) imply: % 146.50/21.31 | (591) op(all_6_2, e1) = all_46_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (136), (529) imply: % 146.50/21.31 | (592) op(all_4_2, all_44_1) = all_44_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (135), (529) imply: % 146.50/21.31 | (593) op(all_4_2, e0) = all_44_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (131), (479) imply: % 146.50/21.31 | (594) op(all_8_2, all_42_1) = all_42_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (130), (479) imply: % 146.50/21.31 | (595) op(all_8_2, e2) = all_42_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (126), (501) imply: % 146.50/21.31 | (596) op(all_6_2, all_40_1) = all_40_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (125), (501) imply: % 146.50/21.31 | (597) op(all_6_2, e1) = all_40_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (122), (485) imply: % 146.50/21.31 | (598) op(all_10_2, all_38_1) = all_38_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (121), (485) imply: % 146.50/21.31 | (599) op(all_10_2, e3) = all_38_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (117), (507) imply: % 146.50/21.31 | (600) op(all_6_2, all_36_1) = all_36_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (116), (507) imply: % 146.50/21.31 | (601) op(all_6_2, e1) = all_36_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (112), (528) imply: % 146.50/21.31 | (602) op(all_4_2, all_34_1) = all_34_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (111), (528) imply: % 146.50/21.31 | (603) op(all_4_2, e0) = all_34_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (107), (509) imply: % 146.50/21.31 | (604) op(all_10_2, all_32_1) = all_32_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (106), (509) imply: % 146.50/21.31 | (605) op(all_10_2, e3) = all_32_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (102), (504) imply: % 146.50/21.31 | (606) op(all_8_2, all_30_1) = all_30_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (101), (504) imply: % 146.50/21.31 | (607) op(all_8_2, e2) = all_30_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (98), (510) imply: % 146.50/21.31 | (608) op(all_6_2, all_28_1) = all_28_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (97), (510) imply: % 146.50/21.31 | (609) op(all_6_2, e1) = all_28_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (93), (527) imply: % 146.50/21.31 | (610) op(all_4_2, all_26_1) = all_26_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (92), (527) imply: % 146.50/21.31 | (611) op(all_4_2, e0) = all_26_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (88), (515) imply: % 146.50/21.31 | (612) op(all_10_2, all_24_1) = all_24_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (87), (515) imply: % 146.50/21.31 | (613) op(all_10_2, e3) = all_24_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (83), (517) imply: % 146.50/21.31 | (614) op(all_8_2, all_22_1) = all_22_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (82), (517) imply: % 146.50/21.31 | (615) op(all_8_2, e2) = all_22_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (78), (338) imply: % 146.50/21.31 | (616) op(all_4_2, all_20_1) = all_20_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (77), (338) imply: % 146.50/21.31 | (617) op(all_4_2, e0) = all_20_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (73), (519) imply: % 146.50/21.31 | (618) op(all_6_2, all_18_1) = all_18_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (72), (519) imply: % 146.50/21.31 | (619) op(all_6_2, e1) = all_18_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (68), (523) imply: % 146.50/21.31 | (620) op(all_10_2, all_16_1) = all_16_0 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (67), (523) imply: % 146.50/21.31 | (621) op(all_10_2, e3) = all_16_1 % 146.50/21.31 | % 146.50/21.31 | REDUCE: (63), (525) imply: % 146.50/21.32 | (622) op(all_8_2, all_14_1) = all_14_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (62), (525) imply: % 146.50/21.32 | (623) op(all_8_2, e2) = all_14_1 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (58), (526) imply: % 146.50/21.32 | (624) op(all_4_2, all_12_1) = all_12_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (57), (526) imply: % 146.50/21.32 | (625) op(all_4_2, e0) = all_12_1 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (331), (400) imply: % 146.50/21.32 | (626) op(e3, all_52_4) = all_58_1 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (330), (397) imply: % 146.50/21.32 | (627) op(e3, all_52_8) = all_58_3 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (329), (549) imply: % 146.50/21.32 | (628) op(e3, all_52_12) = all_58_5 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (328), (545) imply: % 146.50/21.32 | (629) op(e3, all_10_2) = all_58_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (323), (391) imply: % 146.50/21.32 | (630) op(e2, all_52_1) = all_58_7 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (322), (379) imply: % 146.50/21.32 | (631) op(e2, all_52_9) = all_58_10 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (321), (376) imply: % 146.50/21.32 | (632) op(e2, all_52_13) = all_58_12 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (320), (544) imply: % 146.50/21.32 | (633) op(e2, all_8_2) = all_58_9 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (315), (548) imply: % 146.50/21.32 | (634) op(e1, all_52_2) = all_58_14 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (314), (370) imply: % 146.50/21.32 | (635) op(e1, all_52_6) = all_58_16 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (313), (358) imply: % 146.50/21.32 | (636) op(e1, all_52_14) = all_58_19 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (312), (543) imply: % 146.50/21.32 | (637) op(e1, all_6_2) = all_58_18 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (307), (355) imply: % 146.50/21.32 | (638) op(e0, all_52_3) = all_58_21 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (306), (547) imply: % 146.50/21.32 | (639) op(e0, all_52_7) = all_58_23 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (305), (546) imply: % 146.50/21.32 | (640) op(e0, all_52_11) = all_58_25 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (304), (542) imply: % 146.50/21.32 | (641) op(e0, all_4_2) = all_58_27 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_34_1, e0, % 146.50/21.32 | all_4_2, simplifying with (603), (611) gives: % 146.50/21.32 | (642) all_34_1 = all_26_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_20_1, all_34_1, e0, % 146.50/21.32 | all_4_2, simplifying with (603), (617) gives: % 146.50/21.32 | (643) all_34_1 = all_20_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_34_1, e0, % 146.50/21.32 | all_4_2, simplifying with (603), (625) gives: % 146.50/21.32 | (644) all_34_1 = all_12_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_44_1, e0, % 146.50/21.32 | all_4_2, simplifying with (37), (593) gives: % 146.50/21.32 | (645) all_44_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_44_1, e0, % 146.50/21.32 | all_4_2, simplifying with (593), (611) gives: % 146.50/21.32 | (646) all_44_1 = all_26_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_18_1, all_40_1, e1, % 146.50/21.32 | all_6_2, simplifying with (597), (619) gives: % 146.50/21.32 | (647) all_40_1 = all_18_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_46_1, e1, % 146.50/21.32 | all_6_2, simplifying with (42), (591) gives: % 146.50/21.32 | (648) all_46_1 = all_6_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_40_1, all_46_1, e1, % 146.50/21.32 | all_6_2, simplifying with (591), (597) gives: % 146.50/21.32 | (649) all_46_1 = all_40_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_36_1, all_46_1, e1, % 146.50/21.32 | all_6_2, simplifying with (591), (601) gives: % 146.50/21.32 | (650) all_46_1 = all_36_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_46_1, e1, % 146.50/21.32 | all_6_2, simplifying with (591), (609) gives: % 146.50/21.32 | (651) all_46_1 = all_28_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_22_1, e2, % 146.50/21.32 | all_8_2, simplifying with (615), (623) gives: % 146.50/21.32 | (652) all_22_1 = all_14_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_42_1, e2, % 146.50/21.32 | all_8_2, simplifying with (47), (595) gives: % 146.50/21.32 | (653) all_42_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_42_1, e2, % 146.50/21.32 | all_8_2, simplifying with (595), (615) gives: % 146.50/21.32 | (654) all_42_1 = all_22_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_42_1, all_48_1, e2, % 146.50/21.32 | all_8_2, simplifying with (589), (595) gives: % 146.50/21.32 | (655) all_48_1 = all_42_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_48_1, e2, % 146.50/21.32 | all_8_2, simplifying with (589), (607) gives: % 146.50/21.32 | (656) all_48_1 = all_30_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_24_1, e3, % 146.50/21.32 | all_10_2, simplifying with (52), (613) gives: % 146.50/21.32 | (657) all_24_1 = all_10_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_24_1, all_32_1, e3, % 146.50/21.32 | all_10_2, simplifying with (605), (613) gives: % 146.50/21.32 | (658) all_32_1 = all_24_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_38_1, e3, % 146.50/21.32 | all_10_2, simplifying with (599), (605) gives: % 146.50/21.32 | (659) all_38_1 = all_32_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_38_1, all_50_1, e3, % 146.50/21.32 | all_10_2, simplifying with (587), (599) gives: % 146.50/21.32 | (660) all_50_1 = all_38_1 % 146.50/21.32 | % 146.50/21.32 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_50_1, e3, % 146.50/21.32 | all_10_2, simplifying with (587), (621) gives: % 146.50/21.32 | (661) all_50_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (660), (661) imply: % 146.50/21.32 | (662) all_38_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (662) implies: % 146.50/21.32 | (663) all_38_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (655), (656) imply: % 146.50/21.32 | (664) all_42_1 = all_30_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (664) implies: % 146.50/21.32 | (665) all_42_1 = all_30_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (648), (650) imply: % 146.50/21.32 | (666) all_36_1 = all_6_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (649), (650) imply: % 146.50/21.32 | (667) all_40_1 = all_36_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (667) implies: % 146.50/21.32 | (668) all_40_1 = all_36_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (650), (651) imply: % 146.50/21.32 | (669) all_36_1 = all_28_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (645), (646) imply: % 146.50/21.32 | (670) all_26_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (670) implies: % 146.50/21.32 | (671) all_26_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (653), (665) imply: % 146.50/21.32 | (672) all_30_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (654), (665) imply: % 146.50/21.32 | (673) all_30_1 = all_22_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (647), (668) imply: % 146.50/21.32 | (674) all_36_1 = all_18_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (674) implies: % 146.50/21.32 | (675) all_36_1 = all_18_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (659), (663) imply: % 146.50/21.32 | (676) all_32_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (676) implies: % 146.50/21.32 | (677) all_32_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (669), (675) imply: % 146.50/21.32 | (678) all_28_1 = all_18_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (666), (669) imply: % 146.50/21.32 | (679) all_28_1 = all_6_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (642), (643) imply: % 146.50/21.32 | (680) all_26_1 = all_20_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (680) implies: % 146.50/21.32 | (681) all_26_1 = all_20_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (643), (644) imply: % 146.50/21.32 | (682) all_20_1 = all_12_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (658), (677) imply: % 146.50/21.32 | (683) all_24_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (683) implies: % 146.50/21.32 | (684) all_24_1 = all_16_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (672), (673) imply: % 146.50/21.32 | (685) all_22_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (685) implies: % 146.50/21.32 | (686) all_22_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (678), (679) imply: % 146.50/21.32 | (687) all_18_1 = all_6_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (687) implies: % 146.50/21.32 | (688) all_18_1 = all_6_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (671), (681) imply: % 146.50/21.32 | (689) all_20_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (689) implies: % 146.50/21.32 | (690) all_20_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (657), (684) imply: % 146.50/21.32 | (691) all_16_1 = all_10_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (652), (686) imply: % 146.50/21.32 | (692) all_14_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (692) implies: % 146.50/21.32 | (693) all_14_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (682), (690) imply: % 146.50/21.32 | (694) all_12_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | SIMP: (694) implies: % 146.50/21.32 | (695) all_12_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (677), (691) imply: % 146.50/21.32 | (696) all_32_1 = all_10_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (643), (690) imply: % 146.50/21.32 | (697) all_34_1 = all_4_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (663), (691) imply: % 146.50/21.32 | (698) all_38_1 = all_10_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (647), (688) imply: % 146.50/21.32 | (699) all_40_1 = all_6_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (656), (672) imply: % 146.50/21.32 | (700) all_48_1 = all_8_1 % 146.50/21.32 | % 146.50/21.32 | COMBINE_EQS: (661), (691) imply: % 146.50/21.32 | (701) all_50_1 = all_10_1 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (586), (701) imply: % 146.50/21.32 | (702) op(all_10_2, all_10_1) = all_50_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (598), (698) imply: % 146.50/21.32 | (703) op(all_10_2, all_10_1) = all_38_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (604), (696) imply: % 146.50/21.32 | (704) op(all_10_2, all_10_1) = all_32_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (612), (657) imply: % 146.50/21.32 | (705) op(all_10_2, all_10_1) = all_24_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (620), (691) imply: % 146.50/21.32 | (706) op(all_10_2, all_10_1) = all_16_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (588), (700) imply: % 146.50/21.32 | (707) op(all_8_2, all_8_1) = all_48_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (594), (653) imply: % 146.50/21.32 | (708) op(all_8_2, all_8_1) = all_42_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (606), (672) imply: % 146.50/21.32 | (709) op(all_8_2, all_8_1) = all_30_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (614), (686) imply: % 146.50/21.32 | (710) op(all_8_2, all_8_1) = all_22_0 % 146.50/21.32 | % 146.50/21.32 | REDUCE: (622), (693) imply: % 146.50/21.33 | (711) op(all_8_2, all_8_1) = all_14_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (590), (648) imply: % 146.50/21.33 | (712) op(all_6_2, all_6_1) = all_46_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (596), (699) imply: % 146.50/21.33 | (713) op(all_6_2, all_6_1) = all_40_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (600), (666) imply: % 146.50/21.33 | (714) op(all_6_2, all_6_1) = all_36_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (608), (679) imply: % 146.50/21.33 | (715) op(all_6_2, all_6_1) = all_28_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (618), (688) imply: % 146.50/21.33 | (716) op(all_6_2, all_6_1) = all_18_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (592), (645) imply: % 146.50/21.33 | (717) op(all_4_2, all_4_1) = all_44_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (602), (697) imply: % 146.50/21.33 | (718) op(all_4_2, all_4_1) = all_34_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (610), (671) imply: % 146.50/21.33 | (719) op(all_4_2, all_4_1) = all_26_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (616), (690) imply: % 146.50/21.33 | (720) op(all_4_2, all_4_1) = all_20_0 % 146.50/21.33 | % 146.50/21.33 | REDUCE: (624), (695) imply: % 146.50/21.33 | (721) op(all_4_2, all_4_1) = all_12_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_12_0, all_26_0, all_4_1, % 146.50/21.33 | all_4_2, simplifying with (719), (721) gives: % 146.50/21.33 | (722) all_26_0 = all_12_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_44_0, all_4_1, % 146.50/21.33 | all_4_2, simplifying with (38), (717) gives: % 146.50/21.33 | (723) all_44_0 = all_4_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_34_0, all_44_0, all_4_1, % 146.50/21.33 | all_4_2, simplifying with (717), (718) gives: % 146.50/21.33 | (724) all_44_0 = all_34_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_26_0, all_44_0, all_4_1, % 146.50/21.33 | all_4_2, simplifying with (717), (719) gives: % 146.50/21.33 | (725) all_44_0 = all_26_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_20_0, all_44_0, all_4_1, % 146.50/21.33 | all_4_2, simplifying with (717), (720) gives: % 146.50/21.33 | (726) all_44_0 = all_20_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_40_0, all_6_1, % 146.50/21.33 | all_6_2, simplifying with (43), (713) gives: % 146.50/21.33 | (727) all_40_0 = all_6_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_40_0, all_6_1, % 146.50/21.33 | all_6_2, simplifying with (713), (715) gives: % 146.50/21.33 | (728) all_40_0 = all_28_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_36_0, all_46_0, all_6_1, % 146.50/21.33 | all_6_2, simplifying with (712), (714) gives: % 146.50/21.33 | (729) all_46_0 = all_36_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_46_0, all_6_1, % 146.50/21.33 | all_6_2, simplifying with (712), (715) gives: % 146.50/21.33 | (730) all_46_0 = all_28_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_18_0, all_46_0, all_6_1, % 146.50/21.33 | all_6_2, simplifying with (712), (716) gives: % 146.50/21.33 | (731) all_46_0 = all_18_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_30_0, all_8_1, % 146.50/21.33 | all_8_2, simplifying with (48), (709) gives: % 146.50/21.33 | (732) all_30_0 = all_8_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_14_0, all_30_0, all_8_1, % 146.50/21.33 | all_8_2, simplifying with (709), (711) gives: % 146.50/21.33 | (733) all_30_0 = all_14_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_42_0, all_48_0, all_8_1, % 146.50/21.33 | all_8_2, simplifying with (707), (708) gives: % 146.50/21.33 | (734) all_48_0 = all_42_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_30_0, all_48_0, all_8_1, % 146.50/21.33 | all_8_2, simplifying with (707), (709) gives: % 146.50/21.33 | (735) all_48_0 = all_30_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_22_0, all_48_0, all_8_1, % 146.50/21.33 | all_8_2, simplifying with (707), (710) gives: % 146.50/21.33 | (736) all_48_0 = all_22_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_10_0, all_38_0, % 146.50/21.33 | all_10_1, all_10_2, simplifying with (53), (703) gives: % 146.50/21.33 | (737) all_38_0 = all_10_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_38_0, % 146.50/21.33 | all_10_1, all_10_2, simplifying with (703), (704) gives: % 146.50/21.33 | (738) all_38_0 = all_32_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_24_0, all_38_0, % 146.50/21.33 | all_10_1, all_10_2, simplifying with (703), (705) gives: % 146.50/21.33 | (739) all_38_0 = all_24_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_50_0, % 146.50/21.33 | all_10_1, all_10_2, simplifying with (702), (704) gives: % 146.50/21.33 | (740) all_50_0 = all_32_0 % 146.50/21.33 | % 146.50/21.33 | GROUND_INST: instantiating (function-axioms) with all_16_0, all_50_0, % 146.50/21.33 | all_10_1, all_10_2, simplifying with (702), (706) gives: % 146.50/21.33 | (741) all_50_0 = all_16_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (740), (741) imply: % 146.50/21.33 | (742) all_32_0 = all_16_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (742) implies: % 146.50/21.33 | (743) all_32_0 = all_16_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (734), (736) imply: % 146.50/21.33 | (744) all_42_0 = all_22_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (734), (735) imply: % 146.50/21.33 | (745) all_42_0 = all_30_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (729), (731) imply: % 146.50/21.33 | (746) all_36_0 = all_18_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (729), (730) imply: % 146.50/21.33 | (747) all_36_0 = all_28_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (723), (724) imply: % 146.50/21.33 | (748) all_34_0 = all_4_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (724), (725) imply: % 146.50/21.33 | (749) all_34_0 = all_26_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (724), (726) imply: % 146.50/21.33 | (750) all_34_0 = all_20_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (744), (745) imply: % 146.50/21.33 | (751) all_30_0 = all_22_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (751) implies: % 146.50/21.33 | (752) all_30_0 = all_22_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (727), (728) imply: % 146.50/21.33 | (753) all_28_0 = all_6_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (753) implies: % 146.50/21.33 | (754) all_28_0 = all_6_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (737), (739) imply: % 146.50/21.33 | (755) all_24_0 = all_10_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (738), (739) imply: % 146.50/21.33 | (756) all_32_0 = all_24_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (756) implies: % 146.50/21.33 | (757) all_32_0 = all_24_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (746), (747) imply: % 146.50/21.33 | (758) all_28_0 = all_18_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (758) implies: % 146.50/21.33 | (759) all_28_0 = all_18_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (748), (750) imply: % 146.50/21.33 | (760) all_20_0 = all_4_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (749), (750) imply: % 146.50/21.33 | (761) all_26_0 = all_20_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (761) implies: % 146.50/21.33 | (762) all_26_0 = all_20_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (743), (757) imply: % 146.50/21.33 | (763) all_24_0 = all_16_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (763) implies: % 146.50/21.33 | (764) all_24_0 = all_16_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (733), (752) imply: % 146.50/21.33 | (765) all_22_0 = all_14_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (732), (752) imply: % 146.50/21.33 | (766) all_22_0 = all_8_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (754), (759) imply: % 146.50/21.33 | (767) all_18_0 = all_6_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (722), (762) imply: % 146.50/21.33 | (768) all_20_0 = all_12_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (768) implies: % 146.50/21.33 | (769) all_20_0 = all_12_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (755), (764) imply: % 146.50/21.33 | (770) all_16_0 = all_10_0 % 146.50/21.33 | % 146.50/21.33 | SIMP: (770) implies: % 146.50/21.33 | (771) all_16_0 = all_10_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (765), (766) imply: % 146.50/21.33 | (772) all_14_0 = all_8_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (760), (769) imply: % 146.50/21.33 | (773) all_12_0 = all_4_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (722), (773) imply: % 146.50/21.33 | (774) all_26_0 = all_4_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (743), (771) imply: % 146.50/21.33 | (775) all_32_0 = all_10_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (746), (767) imply: % 146.50/21.33 | (776) all_36_0 = all_6_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (744), (766) imply: % 146.50/21.33 | (777) all_42_0 = all_8_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (729), (776) imply: % 146.50/21.33 | (778) all_46_0 = all_6_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (734), (777) imply: % 146.50/21.33 | (779) all_48_0 = all_8_0 % 146.50/21.33 | % 146.50/21.33 | COMBINE_EQS: (741), (771) imply: % 146.50/21.33 | (780) all_50_0 = all_10_0 % 146.50/21.33 | % 146.50/21.33 | BETA: splitting (39) gives: % 146.50/21.33 | % 146.50/21.33 | Case 1: % 146.50/21.33 | | % 146.50/21.33 | | (781) ~ (all_4_0 = e1) % 146.50/21.33 | | % 146.50/21.33 | | BETA: splitting (44) gives: % 146.50/21.33 | | % 146.50/21.33 | | Case 1: % 146.50/21.33 | | | % 146.50/21.33 | | | (782) ~ (all_6_1 = e0) % 146.50/21.33 | | | % 146.50/21.33 | | | BETA: splitting (49) gives: % 146.50/21.33 | | | % 146.50/21.33 | | | Case 1: % 146.50/21.33 | | | | % 146.50/21.33 | | | | (783) ~ (all_8_1 = e0) % 146.50/21.33 | | | | % 146.50/21.33 | | | | BETA: splitting (54) gives: % 146.50/21.33 | | | | % 146.50/21.33 | | | | Case 1: % 146.50/21.33 | | | | | % 146.50/21.33 | | | | | (784) ~ (all_10_0 = e0) % 146.50/21.33 | | | | | % 146.50/21.33 | | | | | BETA: splitting (64) gives: % 146.50/21.33 | | | | | % 146.50/21.33 | | | | | Case 1: % 146.50/21.33 | | | | | | % 146.50/21.33 | | | | | | (785) ~ (all_14_2 = e0) % 146.50/21.33 | | | | | | % 146.50/21.33 | | | | | | REDUCE: (525), (785) imply: % 146.50/21.33 | | | | | | (786) ~ (all_8_2 = e0) % 146.50/21.33 | | | | | | % 146.50/21.33 | | | | | | BETA: splitting (69) gives: % 146.50/21.33 | | | | | | % 146.50/21.33 | | | | | | Case 1: % 146.50/21.33 | | | | | | | % 146.50/21.33 | | | | | | | (787) ~ (all_16_2 = e0) % 146.50/21.33 | | | | | | | % 146.50/21.33 | | | | | | | REDUCE: (523), (787) imply: % 146.50/21.33 | | | | | | | (788) ~ (all_10_2 = e0) % 146.50/21.33 | | | | | | | % 146.50/21.33 | | | | | | | BETA: splitting (74) gives: % 146.50/21.33 | | | | | | | % 146.50/21.33 | | | | | | | Case 1: % 146.50/21.33 | | | | | | | | % 146.50/21.33 | | | | | | | | (789) ~ (all_18_2 = e0) % 146.50/21.33 | | | | | | | | % 146.50/21.33 | | | | | | | | REDUCE: (519), (789) imply: % 146.50/21.33 | | | | | | | | (790) ~ (all_6_2 = e0) % 146.50/21.33 | | | | | | | | % 146.50/21.33 | | | | | | | | BETA: splitting (333) gives: % 146.50/21.33 | | | | | | | | % 146.50/21.33 | | | | | | | | Case 1: % 146.50/21.33 | | | | | | | | | % 146.50/21.33 | | | | | | | | | (791) all_58_28 = e0 % 146.50/21.34 | | | | | | | | | % 146.50/21.34 | | | | | | | | | REF_CLOSE: (545), (788), (791) are inconsistent by sub-proof % 146.50/21.34 | | | | | | | | | #865. % 146.50/21.34 | | | | | | | | | % 146.50/21.34 | | | | | | | | Case 2: % 146.50/21.34 | | | | | | | | | % 146.50/21.34 | | | | | | | | | (792) ~ (all_58_28 = e0) % 146.50/21.34 | | | | | | | | | (793) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 146.50/21.34 | | | | | | | | | % 146.50/21.34 | | | | | | | | | BETA: splitting (793) gives: % 146.50/21.34 | | | | | | | | | % 146.50/21.34 | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | (794) all_58_29 = e0 % 146.50/21.34 | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | REF_CLOSE: (544), (786), (794) are inconsistent by sub-proof % 146.50/21.34 | | | | | | | | | | #864. % 146.50/21.34 | | | | | | | | | | % 146.50/21.34 | | | | | | | | | Case 2: % 146.50/21.34 | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | (795) all_58_30 = e0 | all_58_31 = e0 % 146.50/21.34 | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | BETA: splitting (795) gives: % 146.50/21.34 | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | (796) all_58_30 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REF_CLOSE: (543), (790), (796) are inconsistent by sub-proof % 146.50/21.34 | | | | | | | | | | | #863. % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | Case 2: % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | (797) all_58_31 = e0 % 146.50/21.34 | | | | | | | | | | | (798) ~ (all_58_30 = e0) % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | COMBINE_EQS: (542), (797) imply: % 146.50/21.34 | | | | | | | | | | | (799) all_4_2 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | COMBINE_EQS: (538), (799) imply: % 146.50/21.34 | | | | | | | | | | | (800) all_56_15 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (564), (799) imply: % 146.50/21.34 | | | | | | | | | | | (801) ~ (all_52_3 = e0) % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (575), (799) imply: % 146.50/21.34 | | | | | | | | | | | (802) ~ (all_52_7 = e0) % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (582), (799) imply: % 146.50/21.34 | | | | | | | | | | | (803) ~ (all_52_11 = e0) % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (585), (799) imply: % 146.50/21.34 | | | | | | | | | | | (804) ~ (all_52_14 = e0) % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (38), (799) imply: % 146.50/21.34 | | | | | | | | | | | (805) op(e0, all_4_1) = all_4_0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (37), (799) imply: % 146.50/21.34 | | | | | | | | | | | (806) op(e0, e0) = all_4_1 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (641), (799) imply: % 146.50/21.34 | | | | | | | | | | | (807) op(e0, e0) = all_58_27 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (36), (799) imply: % 146.50/21.34 | | | | | | | | | | | (808) op(e0, e0) = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 146.50/21.34 | | | | | | | | | | | all_58_27, e0, e0, simplifying with (806), (807) % 146.50/21.34 | | | | | | | | | | | gives: % 146.50/21.34 | | | | | | | | | | | (809) all_58_27 = all_4_1 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 146.50/21.34 | | | | | | | | | | | all_58_27, e0, e0, simplifying with (807), (808) % 146.50/21.34 | | | | | | | | | | | gives: % 146.50/21.34 | | | | | | | | | | | (810) all_58_27 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | COMBINE_EQS: (809), (810) imply: % 146.50/21.34 | | | | | | | | | | | (811) all_4_1 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | SIMP: (811) implies: % 146.50/21.34 | | | | | | | | | | | (812) all_4_1 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (805), (812) imply: % 146.50/21.34 | | | | | | | | | | | (813) op(e0, e0) = all_4_0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 146.50/21.34 | | | | | | | | | | | e0, e0, simplifying with (808), (813) gives: % 146.50/21.34 | | | | | | | | | | | (814) all_4_0 = e0 % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | REDUCE: (781), (814) imply: % 146.50/21.34 | | | | | | | | | | | (815) ~ (e1 = e0) % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | BETA: splitting (103) gives: % 146.50/21.34 | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | (816) ~ (all_30_0 = e0) % 146.50/21.34 | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | REDUCE: (732), (816) imply: % 146.50/21.34 | | | | | | | | | | | | (817) ~ (all_8_0 = e0) % 146.50/21.34 | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | BETA: splitting (108) gives: % 146.50/21.34 | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | (818) ~ (all_32_1 = e0) % 146.50/21.34 | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | REDUCE: (696), (818) imply: % 146.50/21.34 | | | | | | | | | | | | | (819) ~ (all_10_1 = e0) % 146.50/21.34 | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | BETA: splitting (275) gives: % 146.50/21.34 | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | (820) all_56_6 = e0 % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | COMBINE_EQS: (371), (820) imply: % 146.50/21.34 | | | | | | | | | | | | | | (821) all_52_2 = e0 % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | SIMP: (821) implies: % 146.50/21.34 | | | | | | | | | | | | | | (822) all_52_2 = e0 % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | REDUCE: (190), (822) imply: % 146.50/21.34 | | | | | | | | | | | | | | (823) ~ (all_52_3 = e0) % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | REDUCE: (189), (822) imply: % 146.50/21.34 | | | | | | | | | | | | | | (824) ~ (all_52_6 = e0) % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | SIMP: (824) implies: % 146.50/21.34 | | | | | | | | | | | | | | (825) ~ (all_52_6 = e0) % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | REDUCE: (563), (822) imply: % 146.50/21.34 | | | | | | | | | | | | | | (826) ~ (all_6_2 = e0) % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | REDUCE: (209), (822) imply: % 146.50/21.34 | | | | | | | | | | | | | | (827) op(e1, e3) = e0 % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (42), (46), % 146.50/21.34 | | | | | | | | | | | | | | (47), (48), (51), (52), (169), (172), (180), % 146.50/21.34 | | | | | | | | | | | | | | (182), (185), (192), (208), (211), (213), (215), % 146.50/21.34 | | | | | | | | | | | | | | (216), (241), (246), (248), (250), (269), (276), % 146.50/21.34 | | | | | | | | | | | | | | (279), (280), (282), (286), (287), (293), (295), % 146.50/21.34 | | | | | | | | | | | | | | (297), (298), (332), (334), (335), (337), (347), % 146.50/21.34 | | | | | | | | | | | | | | (350), (411), (413), (417), (419), (425), (427), % 146.50/21.34 | | | | | | | | | | | | | | (429), (447), (454), (459), (537), (539), (540), % 146.50/21.34 | | | | | | | | | | | | | | (541), (543), (544), (545), (551), (555), (557), % 146.50/21.34 | | | | | | | | | | | | | | (559), (562), (567), (571), (574), (576), (577), % 146.50/21.34 | | | | | | | | | | | | | | (627), (629), (630), (633), (635), (637), (782), % 146.50/21.34 | | | | | | | | | | | | | | (783), (790), (795), (797), (801), (802), (803), % 146.50/21.34 | | | | | | | | | | | | | | (810), (819), (820), (825), (827), % 146.50/21.34 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.50/21.34 | | | | | | | | | | | | | | #800. % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | Case 2: % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | (828) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | BETA: splitting (828) gives: % 146.50/21.34 | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | (829) all_56_7 = e0 % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | COMBINE_EQS: (425), (829) imply: % 146.50/21.34 | | | | | | | | | | | | | | | (830) all_52_6 = e0 % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | SIMP: (830) implies: % 146.50/21.34 | | | | | | | | | | | | | | | (831) all_52_6 = e0 % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | REDUCE: (189), (831) imply: % 146.50/21.34 | | | | | | | | | | | | | | | (832) ~ (all_52_2 = e0) % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | REDUCE: (172), (831) imply: % 146.50/21.34 | | | | | | | | | | | | | | | (833) ~ (all_52_14 = e0) % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | REDUCE: (574), (831) imply: % 146.50/21.34 | | | | | | | | | | | | | | | (834) ~ (all_6_2 = e0) % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | REDUCE: (208), (831) imply: % 146.50/21.34 | | | | | | | | | | | | | | | (835) op(e1, e2) = e0 % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 146.50/21.34 | | | | | | | | | | | | | | | % 146.50/21.34 | | | | | | | | | | | | | | | Case 1: % 146.50/21.34 | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | (836) all_56_0 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | REF_CLOSE: (541), (788), (836) are inconsistent by sub-proof % 146.50/21.35 | | | | | | | | | | | | | | | | #799. % 146.50/21.35 | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | (837) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | BETA: splitting (837) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | (838) all_56_2 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (838) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | (839) all_52_1 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | REDUCE: (195), (839) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | (840) ~ (all_52_2 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | REDUCE: (194), (839) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | (841) ~ (all_52_3 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | REDUCE: (192), (839) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | (842) ~ (all_52_9 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | SIMP: (842) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | (843) ~ (all_52_9 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | REDUCE: (562), (839) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | (844) ~ (all_8_2 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | (845) all_56_4 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (845) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | (846) all_52_8 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | SIMP: (846) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | | (847) all_52_8 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | REDUCE: (180), (847) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | (848) ~ (all_52_4 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | REDUCE: (559), (847) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | (849) ~ (all_10_2 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | REDUCE: (215), (847) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | (850) op(e3, e1) = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | (851) all_54_1 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (848), (851) are inconsistent by sub-proof % 146.50/21.35 | | | | | | | | | | | | | | | | | | | #798. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | (852) ~ (all_54_1 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | (853) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | (854) all_54_0 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (788), (854) are inconsistent by sub-proof % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | #861. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | (855) ~ (all_54_0 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | (856) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | (857) all_54_11 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (468), (857) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | (858) all_52_14 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | REDUCE: (804), (858) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | (859) $false % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | CLOSE: (859) is inconsistent. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | (860) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | (861) all_54_8 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (861) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | (862) all_52_2 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (832), (862) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | (863) $false % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (863) is inconsistent. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | (864) ~ (all_54_8 = e0) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | (865) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | (866) all_54_6 = e0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (843), (866) are inconsistent by sub-proof % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | #797. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | (867) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | (868) all_56_12 = e3 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (868) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | (869) all_52_3 = e3 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (869) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | (870) all_52_3 = e3 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (870) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | (871) ~ (all_52_2 = e3) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (870) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | (872) ~ (all_10_2 = e3) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (872) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | (873) ~ (all_10_2 = e3) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_56_0 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (874) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_10_2 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (875) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_10_2 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (876) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_58_28 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (876) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (878) ~ (all_52_2 = e2) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (47), (293), (334), (371), (543), % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (544), (563), (783), (797), (832), (835), (838), % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (868), (874), (877), (878), (function-axioms) are % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #791. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (879) ~ (all_56_0 = e2) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (879) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | (880) ~ (all_10_2 = e2) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (856) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_54_0 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (881) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_10_2 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (882) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_10_2 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (883) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_58_28 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (883) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (885) ~ (all_52_2 = e1) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (873), (883) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (886) ~ (e3 = e1) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (883) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (887) op(e3, e1) = all_58_0 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (865) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_54_8 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (888) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_52_2 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (885), (889) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) $false % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (890) is inconsistent. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) ~ (all_54_8 = e1) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_54_8 = e3 | all_54_8 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (892) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_54_8 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (893) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_52_2 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (894) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) ~ (all_6_2 = e2) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (895) implies: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) ~ (all_6_2 = e2) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (871), (894) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) ~ (e3 = e2) % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) all_58_28 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (884), (898) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) e2 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (899) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) $false % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (900) is inconsistent. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (901) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_58_29 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_58_28 = e3 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (884), (903) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) e3 = e1 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (904) imply: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) $false % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (905) is inconsistent. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (42), (543), (782), (797), (850), (887), % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902), (906), (function-axioms) are inconsistent % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #789. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_58_30 = e2 | all_58_31 = e2 % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (543), (797), (896), (907) are inconsistent % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #817. % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_54_8 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (908) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) all_52_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (871), (909) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) $false % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (910) is inconsistent. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_54_0 = e3 | all_54_0 = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (873), (880), (911) are inconsistent by % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #814. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | (912) ~ (all_56_12 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (429), (912) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | (913) ~ (all_52_3 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (914) all_56_0 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (914) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_10_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (915) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_58_28 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (915) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (917) ~ (all_52_2 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (915) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (918) op(e3, all_10_1) = all_10_0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (915) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (919) op(e3, e3) = all_10_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (915) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (920) op(e3, e3) = all_58_0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (915) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (921) op(e3, e3) = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_0, e3, e3, simplifying with (919), (920) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_58_0 = all_10_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_58_0, % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (920), (921) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_58_0 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (922), (923) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (924) all_10_1 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (924) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_10_1 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (918), (925) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (926) op(e3, e3) = all_10_0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_10_0, % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (921), (926) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (927) all_10_0 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (41), (46), (47), (277), % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (278), (332), (334), (335), (371), (458), (539), % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (543), (544), (563), (633), (637), (783), (790), % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (795), (797), (810), (829), (832), (835), (865), % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (916), (917), (920), (921), (function-axioms) are % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | (928) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (928) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (929) all_56_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (838), (929) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (930) e3 = e0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (930) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (931) $false % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (931) is inconsistent. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_56_6 = e3 | all_56_12 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (932) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) all_56_6 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (933) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_52_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (934) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_52_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (935) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) ~ (all_52_14 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (936) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) ~ (all_52_14 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (935) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) ~ (all_10_2 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (938) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) ~ (all_10_2 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (935) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) ~ (all_6_2 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (940) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) ~ (all_6_2 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (634), (935) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) op(e1, e3) = all_58_14 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (935) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) op(e1, e3) = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_58_28 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (545), (939), (944) are inconsistent by sub-proof % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #783. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (945) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_58_29 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (946) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_8_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (947) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_8_2 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (948) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) ~ (all_52_9 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (948) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) ~ (all_52_13 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (948) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) op(e3, all_8_1) = all_8_0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (948) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) op(e3, e2) = all_8_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_56_9 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (953) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_52_12 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (954) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) ~ (all_52_4 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_14, e3, e1, simplifying with (942), (943) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_58_14 = e3 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_8_1, e2, e3, simplifying with (216), (952) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_52_4 = all_8_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (957) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) all_54_1 = all_8_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (957) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_56_1 = all_8_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (957) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) ~ (all_10_2 = all_8_1) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (960) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) ~ (all_10_2 = all_8_1) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (955), (957) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) ~ (all_8_1 = e3) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (626), (957) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) op(e3, all_8_1) = all_58_1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_1, all_8_1, e3, simplifying with (951), % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_58_1 = all_8_0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) all_56_0 = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) all_56_0 = e1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (965), (966) are inconsistent by sub-proof % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #796. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (817), (845), (850), (951), (953), % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959), (967), (function-axioms) are inconsistent % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #781. % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) ~ (all_56_0 = e2) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (968) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) ~ (all_10_2 = e2) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_56_1 = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (959), (970) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_8_1 = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (971) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_8_1 = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (962), (972) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) ~ (e3 = e2) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (951), (972) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) op(e3, e2) = all_8_0 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (952), (972) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) op(e3, e2) = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_56_0 = e1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (976) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) all_10_2 = e1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (977) implies: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_10_2 = e1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (978) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_58_28 = e1 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (969), (978) imply: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) ~ (e2 = e1) % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_58_28 = e2 % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (979), (981) are inconsistent by sub-proof % 146.50/21.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #856. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (982) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_58_29 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (946), (983) are inconsistent by sub-proof % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_58_30 = e2 | all_58_31 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) all_58_30 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (985) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) all_6_2 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (986) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) all_6_2 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (987) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) ~ (all_52_9 = e2) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (987) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) ~ (all_52_14 = e2) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_56_4 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (845), (990) are inconsistent by sub-proof % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #782. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (991) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_56_5 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (992) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_52_9 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (631), (993) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) op(e2, e1) = all_58_10 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (993) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) op(e2, e1) = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (860) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_10, e1, e2, simplifying with (994), (995) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) all_58_10 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (974), (975) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_8_0 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (964), (997) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_58_1 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (332), (810), (956), (996), (998) are inconsistent % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #778. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_54_11 = e3 | all_54_11 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (937), (989), (999) are inconsistent by % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #775. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) ~ (all_56_5 = e1) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (1000) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) ~ (all_52_9 = e1) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (867), (949), (988), (1001) are % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) all_58_31 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (797), (1002) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) e2 = e0 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1003) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) $false % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1004) is inconsistent. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (817), (845), (850), (951), (953), % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959), (1005), (function-axioms) are inconsistent % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #781. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) ~ (all_56_1 = e2) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (959), (1006) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) ~ (all_8_1 = e2) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_56_0 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1008) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_10_2 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1009) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) all_10_2 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (961), (1010) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) ~ (all_8_1 = e1) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1011) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) ~ (all_8_1 = e1) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (853) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) all_54_1 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (958), (1013) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) all_8_1 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1014) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) all_8_1 = e1 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1012), (1015) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) $false % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1016) is inconsistent. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) all_54_1 = e3 | all_54_1 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1017) gives: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) all_54_1 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (958), (1018) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) all_8_1 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1019) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) all_8_1 = e2 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1007), (1020) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) $false % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1021) is inconsistent. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) all_54_1 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (958), (1022) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) all_8_1 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1023) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) all_8_1 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (962), (1024) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) $false % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1025) is inconsistent. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) ~ (all_56_0 = e1) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (1026) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) ~ (all_10_2 = e1) % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (856), (939), (969), (1027) are % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #813. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (421), (427), (800), (937), (950), (1028) are % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #769. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) all_58_30 = e3 | all_58_31 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (543), (797), (941), (1029) are inconsistent % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #768. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) all_56_12 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1030) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) all_52_3 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1031) implies: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) all_52_3 = e3 % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (913), (1032) imply: % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) $false % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1033) is inconsistent. % 146.50/21.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | (1034) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (347), (419), (539), (790), (803), (843), (1034) % 146.50/21.38 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766. % 146.50/21.38 | | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | (1035) all_56_6 = e0 | all_56_12 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (371), (429), (801), (832), (1035) are % 146.50/21.38 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #765. % 146.50/21.38 | | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | (1036) all_56_8 = e0 | all_56_11 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (427), (539), (790), (804), (1036) are % 146.50/21.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #763. % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | (1037) all_32_1 = e0 % 146.50/21.38 | | | | | | | | | | | | | (1038) ~ (all_32_0 = e1) | ~ (all_32_2 = e2) % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | COMBINE_EQS: (696), (1037) imply: % 146.50/21.38 | | | | | | | | | | | | | (1039) all_10_1 = e0 % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | SIMP: (1039) implies: % 146.50/21.38 | | | | | | | | | | | | | (1040) all_10_1 = e0 % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | REDUCE: (53), (1040) imply: % 146.50/21.38 | | | | | | | | | | | | | (1041) op(all_10_2, e0) = all_10_0 % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | REDUCE: (52), (1040) imply: % 146.50/21.38 | | | | | | | | | | | | | (1042) op(all_10_2, e3) = e0 % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (43), (47), % 146.50/21.38 | | | | | | | | | | | | | (51), (127), (142), (156), (158), (159), (166), % 146.50/21.38 | | | | | | | | | | | | | (169), (172), (179), (180), (182), (185), (186), % 146.50/21.38 | | | | | | | | | | | | | (189), (190), (191), (192), (194), (206), (208), % 146.50/21.38 | | | | | | | | | | | | | (209), (210), (213), (214), (215), (216), (238), % 146.50/21.38 | | | | | | | | | | | | | (239), (243), (246), (248), (249), (250), (271), % 146.50/21.38 | | | | | | | | | | | | | (272), (275), (279), (281), (282), (287), (290), % 146.50/21.38 | | | | | | | | | | | | | (291), (293), (295), (296), (297), (298), (332), % 146.50/21.38 | | | | | | | | | | | | | (334), (335), (337), (347), (350), (360), (371), % 146.50/21.38 | | | | | | | | | | | | | (392), (411), (413), (417), (419), (421), (425), % 146.50/21.38 | | | | | | | | | | | | | (427), (429), (445), (447), (454), (467), (468), % 146.50/21.38 | | | | | | | | | | | | | (470), (509), (537), (539), (540), (541), (543), % 146.50/21.38 | | | | | | | | | | | | | (544), (545), (551), (555), (557), (559), (561), % 146.50/21.38 | | | | | | | | | | | | | (562), (563), (565), (574), (576), (577), (581), % 146.50/21.38 | | | | | | | | | | | | | (627), (629), (630), (635), (648), (727), (775), % 146.50/21.38 | | | | | | | | | | | | | (778), (783), (788), (790), (797), (800), (801), % 146.50/21.38 | | | | | | | | | | | | | (802), (803), (804), (810), (1038), (1041), % 146.50/21.38 | | | | | | | | | | | | | (1042), (function-axioms) are inconsistent by % 146.50/21.38 | | | | | | | | | | | | | sub-proof #734. % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | End of split % 146.50/21.38 | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | (1043) all_30_0 = e0 % 146.50/21.38 | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | COMBINE_EQS: (732), (1043) imply: % 146.50/21.38 | | | | | | | | | | | | (1044) all_8_0 = e0 % 146.50/21.38 | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | COMBINE_EQS: (777), (1044) imply: % 146.50/21.38 | | | | | | | | | | | | (1045) all_42_0 = e0 % 146.50/21.38 | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | BETA: splitting (108) gives: % 146.50/21.38 | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | Case 1: % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | (1046) ~ (all_32_1 = e0) % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | REDUCE: (696), (1046) imply: % 146.50/21.38 | | | | | | | | | | | | | (1047) ~ (all_10_1 = e0) % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | BETA: splitting (132) gives: % 146.50/21.38 | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | Case 1: % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | (1048) ~ (all_42_0 = e0) % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | REDUCE: (1045), (1048) imply: % 146.50/21.38 | | | | | | | | | | | | | | (1049) $false % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | CLOSE: (1049) is inconsistent. % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | (1050) ~ (all_42_1 = e1) | ~ (all_42_2 = e3) % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | BETA: splitting (275) gives: % 146.50/21.38 | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | Case 1: % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | (1051) all_56_6 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | COMBINE_EQS: (371), (1051) imply: % 146.50/21.38 | | | | | | | | | | | | | | | (1052) all_52_2 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | SIMP: (1052) implies: % 146.50/21.38 | | | | | | | | | | | | | | | (1053) all_52_2 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | REDUCE: (190), (1053) imply: % 146.50/21.38 | | | | | | | | | | | | | | | (1054) ~ (all_52_3 = e0) % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | REDUCE: (189), (1053) imply: % 146.50/21.38 | | | | | | | | | | | | | | | (1055) ~ (all_52_6 = e0) % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | SIMP: (1055) implies: % 146.50/21.38 | | | | | | | | | | | | | | | (1056) ~ (all_52_6 = e0) % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | REDUCE: (563), (1053) imply: % 146.50/21.38 | | | | | | | | | | | | | | | (1057) ~ (all_6_2 = e0) % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | REDUCE: (209), (1053) imply: % 146.50/21.38 | | | | | | | | | | | | | | | (1058) op(e1, e3) = e0 % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (42), (46), % 146.50/21.38 | | | | | | | | | | | | | | | (47), (48), (51), (52), (169), (172), (180), % 146.50/21.38 | | | | | | | | | | | | | | | (182), (185), (192), (208), (211), (213), (215), % 146.50/21.38 | | | | | | | | | | | | | | | (216), (241), (246), (248), (250), (269), (276), % 146.50/21.38 | | | | | | | | | | | | | | | (279), (280), (282), (286), (287), (293), (295), % 146.50/21.38 | | | | | | | | | | | | | | | (297), (298), (332), (334), (335), (337), (347), % 146.50/21.38 | | | | | | | | | | | | | | | (350), (411), (413), (417), (419), (425), (427), % 146.50/21.38 | | | | | | | | | | | | | | | (429), (447), (454), (459), (537), (539), (540), % 146.50/21.38 | | | | | | | | | | | | | | | (541), (543), (544), (545), (551), (555), (557), % 146.50/21.38 | | | | | | | | | | | | | | | (559), (562), (567), (571), (574), (576), (577), % 146.50/21.38 | | | | | | | | | | | | | | | (627), (629), (630), (633), (635), (637), (782), % 146.50/21.38 | | | | | | | | | | | | | | | (783), (790), (795), (797), (801), (802), (803), % 146.50/21.38 | | | | | | | | | | | | | | | (810), (1047), (1051), (1056), (1058), % 146.50/21.38 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.50/21.38 | | | | | | | | | | | | | | | #800. % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | Case 2: % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | (1059) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | BETA: splitting (1059) gives: % 146.50/21.38 | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | Case 1: % 146.50/21.38 | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | (1060) all_56_7 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (1060) imply: % 146.50/21.38 | | | | | | | | | | | | | | | | (1061) all_52_6 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | SIMP: (1061) implies: % 146.50/21.38 | | | | | | | | | | | | | | | | (1062) all_52_6 = e0 % 146.50/21.38 | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | REDUCE: (189), (1062) imply: % 146.50/21.38 | | | | | | | | | | | | | | | | (1063) ~ (all_52_2 = e0) % 146.50/21.38 | | | | | | | | | | | | | | | | % 146.50/21.38 | | | | | | | | | | | | | | | | REDUCE: (174), (1062) imply: % 146.50/21.39 | | | | | | | | | | | | | | | | (1064) ~ (all_52_7 = e0) % 146.50/21.39 | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | REDUCE: (574), (1062) imply: % 146.50/21.39 | | | | | | | | | | | | | | | | (1065) ~ (all_6_2 = e0) % 146.50/21.39 | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | REDUCE: (208), (1062) imply: % 146.50/21.39 | | | | | | | | | | | | | | | | (1066) op(e1, e2) = e0 % 146.50/21.39 | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 146.50/21.39 | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | Case 1: % 146.50/21.39 | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | (1067) all_56_0 = e0 % 146.50/21.39 | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (541), (788), (1067) are inconsistent by sub-proof % 146.50/21.39 | | | | | | | | | | | | | | | | | #799. % 146.50/21.39 | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | Case 2: % 146.50/21.39 | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | (1068) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 146.50/21.39 | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | BETA: splitting (1068) gives: % 146.50/21.39 | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | Case 1: % 146.50/21.39 | | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | | (1069) all_56_2 = e0 % 146.50/21.39 | | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (1069) imply: % 146.50/21.39 | | | | | | | | | | | | | | | | | | (1070) all_52_1 = e0 % 146.50/21.39 | | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | | REDUCE: (195), (1070) imply: % 146.50/21.39 | | | | | | | | | | | | | | | | | | (1071) ~ (all_52_2 = e0) % 146.50/21.39 | | | | | | | | | | | | | | | | | | % 146.50/21.39 | | | | | | | | | | | | | | | | | | REDUCE: (192), (1070) imply: % 146.50/21.39 | | | | | | | | | | | | | | | | | | (1072) ~ (all_52_9 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | SIMP: (1072) implies: % 146.89/21.39 | | | | | | | | | | | | | | | | | | (1073) ~ (all_52_9 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1074) all_56_4 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (1074) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1075) all_52_8 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | REDUCE: (180), (1075) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1076) ~ (all_52_4 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | REDUCE: (166), (1075) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1077) ~ (all_52_12 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | SIMP: (1077) implies: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1078) ~ (all_52_12 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1075) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1079) ~ (all_10_2 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | REDUCE: (215), (1075) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | (1080) op(e3, e1) = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | (1081) all_54_0 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (788), (1081) are inconsistent by sub-proof % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | #861. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | (1082) ~ (all_54_0 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | (1083) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | (1084) all_54_3 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (465), (1078), (1084) are inconsistent by % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | sub-proof #733. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | (1085) ~ (all_54_3 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | (1086) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | (1087) all_54_13 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (802), (1087) are inconsistent by sub-proof % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | #732. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | (1088) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | (1089) all_54_8 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (458), (1063), (1089) are inconsistent by % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #731. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | (1090) ~ (all_54_8 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | (1091) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | (1092) all_54_6 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (456), (1073), (1092) are inconsistent by % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #797. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | (1093) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1094) all_54_1 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (1076), (1094) are inconsistent by % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #798. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1095) ~ (all_54_1 = e0) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) all_56_0 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1097) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_10_2 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_58_28 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) ~ (all_52_2 = e1) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) ~ (all_52_4 = e1) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) ~ (all_52_12 = e1) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) op(e1, all_10_1) = all_10_0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) op(e1, e3) = all_10_1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (1098) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) op(e3, e1) = all_58_0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e3, e1, simplifying with (209), (1104) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_52_2 = all_10_1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_58_0, % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (1080), (1105) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_58_0 = e0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (1106) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_54_8 = all_10_1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (1106) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_56_6 = all_10_1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (1106) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) ~ (all_10_1 = all_6_2) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1100), (1106) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) ~ (all_10_1 = e1) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (634), (1106) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) op(e1, all_10_1) = all_58_14 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0, % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_14, all_10_1, e1, simplifying with (1103), % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_58_14 = all_10_0 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_56_0 = e3 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1097), (1114) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) e3 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1115) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) $false % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1116) is inconsistent. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) ~ (all_56_0 = e3) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1097), (1117) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) ~ (e3 = e1) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_58_28 = e3 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1099), (1120) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) e3 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1121) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) $false % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1122) is inconsistent. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_58_28 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1099), (1124) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) e2 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1125) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) $false % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1126) is inconsistent. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) all_56_9 = e3 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (1128) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) all_52_12 = e3 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (1129) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) ~ (all_52_4 = e3) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1096) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_54_1 = e1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (1101), (1131) are inconsistent by % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_54_1 = e3 | all_54_1 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1132) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_54_1 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (1133) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) all_52_4 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1134) implies: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) all_52_4 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1135) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) ~ (all_52_7 = e2) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1136) implies: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) ~ (all_52_7 = e2) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1130), (1135) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) ~ (e3 = e2) % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (626), (1135) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) op(e3, e2) = all_58_1 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (1135) imply: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) op(e3, e2) = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1127) gives: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) all_58_29 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (42), (543), (782), (797), (1080), % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105), (1123), (1141), (function-axioms) are % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #789. % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_58_30 = e2 | all_58_31 = e2 % 146.89/21.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (211), (278), (332), (456), (471), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543), (544), (569), (571), (577), (631), (790), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797), (810), (1047), (1088), (1091), (1093), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103), (1104), (1108), (1109), (1110), (1111), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113), (1123), (1137), (1139), (1140), (1142), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #724. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) all_54_1 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (1130), (1143) are inconsistent by % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #739. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) ~ (all_56_9 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1144) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) ~ (all_52_12 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (179), (411), (445), (465), (543), (544), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565), (782), (797), (1076), (1080), (1086), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096), (1101), (1102), (1105), (1118), (1123), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145), (function-axioms) are inconsistent by % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #720. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) ~ (all_56_0 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (1146) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) ~ (all_10_2 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) all_56_0 = e2 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1148) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_10_2 = e2 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1149) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_58_28 = e2 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (1149) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) ~ (all_52_2 = e2) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (1149) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) ~ (all_52_4 = e2) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (1149) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) op(e3, e2) = all_58_0 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_56_0 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1148), (1154) are inconsistent by sub-proof % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #719. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) all_56_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1069), (1156) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) e3 = e0 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1157) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) $false % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1158) is inconsistent. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) all_56_6 = e3 | all_56_12 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1159) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) all_56_6 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (1160) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) all_52_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (1161) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) ~ (all_6_2 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1162) implies: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) ~ (all_6_2 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) all_58_28 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1150), (1164) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) e3 = e2 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1165) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) $false % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1166) is inconsistent. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1167) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_58_29 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1168) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_8_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1169) implies: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) all_8_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (479), (1170) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) all_42_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (1170) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) ~ (all_52_4 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (1170) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) op(e3, e2) = all_8_1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) all_56_1 = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (1174) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_52_4 = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (1175) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) op(e3, e2) = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) ~ (all_42_1 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (653), (1177) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) ~ (all_8_1 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_0, e2, e3, simplifying with (1153), (1173) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) all_58_0 = all_8_1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_58_0, % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (1153), (1176) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) all_58_0 = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1179), (1180) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) all_8_1 = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1181) implies: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) all_8_1 = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1178), (1182) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) $false % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1183) is inconsistent. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) ~ (all_42_2 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1171), (1184) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) $false % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1185) is inconsistent. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) ~ (all_56_1 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (411), (1186) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) ~ (all_52_4 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (445), (1096), (1152), (1172), (1187) are % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) all_58_30 = e3 | all_58_31 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (543), (797), (1163), (1188) are inconsistent % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #768. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) all_56_12 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (47), (293), (334), (371), (543), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544), (563), (783), (797), (1063), (1066), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069), (1148), (1150), (1151), (1189), % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #791. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) ~ (all_56_0 = e2) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (1190) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) ~ (all_10_2 = e2) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1083) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_54_0 = e1 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (1147), (1192) are inconsistent by % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #841. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) ~ (all_54_0 = e1) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) all_54_0 = e3 | all_54_0 = e2 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1194) gives: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) all_54_0 = e2 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (1191), (1195) are inconsistent by % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #822. % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_54_0 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (1196) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) all_10_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1197) implies: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) all_10_2 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1198) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_58_28 = e3 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (1198) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) ~ (all_52_2 = e3) % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (1198) imply: % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) op(e3, e3) = all_58_0 % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (1198) imply: % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) op(e3, e3) = e3 % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (41), (46), (47), (277), % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (332), (334), (335), (371), (458), (539), % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543), (544), (563), (633), (637), (783), (790), % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795), (797), (810), (1060), (1063), (1066), % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091), (1199), (1200), (1201), (1202), % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #784. % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.41 | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | (1203) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 146.89/21.41 | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (347), (419), (539), (790), (803), (1073), (1203) % 146.89/21.41 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766. % 146.89/21.41 | | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.41 | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | (1204) all_56_6 = e0 | all_56_12 = e0 % 146.89/21.41 | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | | REF_CLOSE: (371), (429), (801), (1063), (1204) are % 146.89/21.41 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #765. % 146.89/21.41 | | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | Case 2: % 146.89/21.41 | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | (1205) all_56_8 = e0 | all_56_11 = e0 % 146.89/21.41 | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | | REF_CLOSE: (427), (539), (790), (804), (1205) are % 146.89/21.41 | | | | | | | | | | | | | | | | inconsistent by sub-proof #763. % 146.89/21.41 | | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | Case 2: % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | (1206) all_32_1 = e0 % 146.89/21.41 | | | | | | | | | | | | | (1207) ~ (all_32_0 = e1) | ~ (all_32_2 = e2) % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | COMBINE_EQS: (696), (1206) imply: % 146.89/21.41 | | | | | | | | | | | | | (1208) all_10_1 = e0 % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | REDUCE: (53), (1208) imply: % 146.89/21.41 | | | | | | | | | | | | | (1209) op(all_10_2, e0) = all_10_0 % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | REDUCE: (52), (1208) imply: % 146.89/21.41 | | | | | | | | | | | | | (1210) op(all_10_2, e3) = e0 % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (43), (47), % 146.89/21.41 | | | | | | | | | | | | | (51), (127), (142), (156), (158), (159), (166), % 146.89/21.41 | | | | | | | | | | | | | (169), (172), (179), (180), (182), (185), (186), % 146.89/21.41 | | | | | | | | | | | | | (189), (190), (191), (192), (194), (206), (208), % 146.89/21.41 | | | | | | | | | | | | | (209), (210), (213), (214), (215), (216), (238), % 146.89/21.41 | | | | | | | | | | | | | (239), (243), (246), (248), (249), (250), (271), % 146.89/21.41 | | | | | | | | | | | | | (272), (275), (279), (281), (282), (287), (290), % 146.89/21.41 | | | | | | | | | | | | | (291), (293), (295), (296), (297), (298), (332), % 146.89/21.41 | | | | | | | | | | | | | (334), (335), (337), (347), (350), (360), (371), % 146.89/21.41 | | | | | | | | | | | | | (392), (411), (413), (417), (419), (421), (425), % 146.89/21.41 | | | | | | | | | | | | | (427), (429), (445), (447), (454), (467), (468), % 146.89/21.41 | | | | | | | | | | | | | (470), (509), (537), (539), (540), (541), (543), % 146.89/21.41 | | | | | | | | | | | | | (544), (545), (551), (555), (557), (559), (561), % 146.89/21.41 | | | | | | | | | | | | | (562), (563), (565), (574), (576), (577), (581), % 146.89/21.41 | | | | | | | | | | | | | (627), (629), (630), (635), (648), (727), (775), % 146.89/21.41 | | | | | | | | | | | | | (778), (783), (788), (790), (797), (800), (801), % 146.89/21.41 | | | | | | | | | | | | | (802), (803), (804), (810), (1207), (1209), % 146.89/21.41 | | | | | | | | | | | | | (1210), (function-axioms) are inconsistent by % 146.89/21.41 | | | | | | | | | | | | | sub-proof #734. % 146.89/21.41 | | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | | % 146.89/21.41 | | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | | % 146.89/21.41 | | | | | | | | | End of split % 146.89/21.41 | | | | | | | | | % 146.89/21.41 | | | | | | | | End of split % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | Case 2: % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | (1211) all_18_2 = e0 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | COMBINE_EQS: (519), (1211) imply: % 146.89/21.41 | | | | | | | | (1212) all_6_2 = e0 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | COMBINE_EQS: (539), (1212) imply: % 146.89/21.41 | | | | | | | | (1213) all_56_8 = e0 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | COMBINE_EQS: (543), (1212) imply: % 146.89/21.41 | | | | | | | | (1214) all_58_30 = e0 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (563), (1212) imply: % 146.89/21.41 | | | | | | | | (1215) ~ (all_52_2 = e0) % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (574), (1212) imply: % 146.89/21.41 | | | | | | | | (1216) ~ (all_52_6 = e0) % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (576), (1212) imply: % 146.89/21.41 | | | | | | | | (1217) ~ (all_52_8 = e0) % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (577), (1212) imply: % 146.89/21.41 | | | | | | | | (1218) ~ (all_52_9 = e0) % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (579), (1212) imply: % 146.89/21.41 | | | | | | | | (1219) ~ (all_52_11 = e0) % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (581), (1212) imply: % 146.89/21.41 | | | | | | | | (1220) ~ (all_52_14 = e0) % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (43), (1212) imply: % 146.89/21.41 | | | | | | | | (1221) op(e0, all_6_1) = all_6_0 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (42), (1212) imply: % 146.89/21.41 | | | | | | | | (1222) op(e0, e1) = all_6_1 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (637), (1212) imply: % 146.89/21.41 | | | | | | | | (1223) op(e1, e0) = all_58_18 % 146.89/21.41 | | | | | | | | % 146.89/21.41 | | | | | | | | REDUCE: (41), (1212) imply: % 146.89/21.41 | | | | | | | | (1224) op(e1, e1) = e0 % 146.89/21.41 | | | | | | | | % 146.89/21.42 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (46), % 146.89/21.42 | | | | | | | | (47), (51), (52), (53), (79), (94), (113), (137), % 146.89/21.42 | | | | | | | | (156), (158), (159), (163), (164), (166), (167), % 146.89/21.42 | | | | | | | | (169), (171), (172), (174), (179), (180), (181), % 146.89/21.42 | | | | | | | | (182), (185), (186), (187), (189), (190), (191), % 146.89/21.42 | | | | | | | | (192), (194), (195), (203), (206), (208), (209), % 146.89/21.42 | | | | | | | | (210), (211), (214), (215), (216), (235), (238), % 146.89/21.42 | | | | | | | | (239), (241), (242), (243), (244), (245), (246), % 146.89/21.42 | | | | | | | | (247), (248), (249), (250), (268), (269), (270), % 146.89/21.42 | | | | | | | | (271), (272), (273), (274), (276), (277), (278), % 146.89/21.42 | | | | | | | | (280), (281), (282), (283), (284), (285), (286), % 146.89/21.42 | | | | | | | | (287), (288), (289), (290), (291), (292), (293), % 146.89/21.42 | | | | | | | | (294), (295), (296), (297), (298), (332), (334), % 146.89/21.42 | | | | | | | | (335), (336), (337), (338), (347), (350), (355), % 146.89/21.42 | | | | | | | | (358), (370), (371), (376), (379), (381), (391), % 146.89/21.42 | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 146.89/21.42 | | | | | | | | (421), (425), (427), (429), (445), (447), (454), % 146.89/21.42 | | | | | | | | (456), (458), (459), (465), (467), (468), (470), % 146.89/21.42 | | | | | | | | (527), (528), (529), (535), (537), (538), (540), % 146.89/21.42 | | | | | | | | (541), (542), (543), (544), (545), (546), (547), % 146.89/21.42 | | | | | | | | (548), (549), (551), (553), (555), (557), (559), % 146.89/21.42 | | | | | | | | (561), (562), (564), (565), (567), (569), (571), % 146.89/21.42 | | | | | | | | (573), (575), (579), (582), (583), (584), (585), % 146.89/21.42 | | | | | | | | (626), (628), (629), (630), (632), (633), (634), % 146.89/21.42 | | | | | | | | (635), (636), (638), (639), (640), (645), (671), % 146.89/21.42 | | | | | | | | (690), (697), (723), (748), (760), (774), (783), % 146.89/21.42 | | | | | | | | (786), (1213), (1214), (1215), (1216), (1217), % 146.89/21.42 | | | | | | | | (1218), (1219), (1220), (1221), (1222), (1223), % 146.89/21.42 | | | | | | | | (1224), (function-axioms) are inconsistent by % 146.89/21.42 | | | | | | | | sub-proof #518. % 146.89/21.42 | | | | | | | | % 146.89/21.42 | | | | | | | End of split % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | Case 2: % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | (1225) all_16_2 = e0 % 146.89/21.42 | | | | | | | (1226) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | COMBINE_EQS: (523), (1225) imply: % 146.89/21.42 | | | | | | | (1227) all_10_2 = e0 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | SIMP: (1227) implies: % 146.89/21.42 | | | | | | | (1228) all_10_2 = e0 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | COMBINE_EQS: (541), (1228) imply: % 146.89/21.42 | | | | | | | (1229) all_56_0 = e0 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | COMBINE_EQS: (545), (1228) imply: % 146.89/21.42 | | | | | | | (1230) all_58_28 = e0 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (551), (1228) imply: % 146.89/21.42 | | | | | | | (1231) ~ (all_52_1 = e0) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (553), (1228) imply: % 146.89/21.42 | | | | | | | (1232) ~ (all_52_2 = e0) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (555), (1228) imply: % 146.89/21.42 | | | | | | | (1233) ~ (all_52_3 = e0) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (557), (1228) imply: % 146.89/21.42 | | | | | | | (1234) ~ (all_52_4 = e0) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (559), (1228) imply: % 146.89/21.42 | | | | | | | (1235) ~ (all_52_8 = e0) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (561), (1228) imply: % 146.89/21.42 | | | | | | | (1236) ~ (all_52_12 = e0) % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (53), (1228) imply: % 146.89/21.42 | | | | | | | (1237) op(e0, all_10_1) = all_10_0 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (52), (1228) imply: % 146.89/21.42 | | | | | | | (1238) op(e0, e3) = all_10_1 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REDUCE: (629), (1228) imply: % 146.89/21.42 | | | | | | | (1239) op(e3, e0) = all_58_0 % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), % 146.89/21.42 | | | | | | | (42), (46), (47), (74), (79), (94), (156), (158), % 146.89/21.42 | | | | | | | (159), (163), (164), (166), (167), (169), (171), (172), % 146.89/21.42 | | | | | | | (174), (179), (180), (181), (182), (185), (186), (187), % 146.89/21.42 | | | | | | | (189), (190), (191), (192), (194), (195), (203), (205), % 146.89/21.42 | | | | | | | (206), (208), (210), (214), (215), (216), (235), (236), % 146.89/21.42 | | | | | | | (237), (238), (239), (240), (241), (242), (243), (245), % 146.89/21.42 | | | | | | | (246), (247), (248), (249), (268), (269), (270), (271), % 146.89/21.42 | | | | | | | (272), (273), (274), (275), (276), (277), (279), (280), % 146.89/21.42 | | | | | | | (281), (282), (283), (284), (285), (286), (287), (288), % 146.89/21.42 | | | | | | | (289), (290), (292), (293), (294), (297), (332), (334), % 146.89/21.42 | | | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 146.89/21.42 | | | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 146.89/21.42 | | | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 146.89/21.42 | | | | | | | (429), (445), (447), (454), (458), (459), (465), (467), % 146.89/21.42 | | | | | | | (468), (470), (471), (473), (519), (527), (535), (536), % 146.89/21.42 | | | | | | | (538), (539), (540), (541), (542), (543), (544), (545), % 146.89/21.42 | | | | | | | (546), (547), (548), (549), (562), (563), (564), (565), % 146.89/21.42 | | | | | | | (567), (569), (571), (573), (574), (575), (576), (577), % 146.89/21.42 | | | | | | | (579), (581), (582), (583), (584), (585), (626), (627), % 146.89/21.42 | | | | | | | (628), (631), (632), (633), (635), (636), (637), (638), % 146.89/21.42 | | | | | | | (639), (641), (671), (691), (771), (774), (781), (783), % 146.89/21.42 | | | | | | | (784), (1226), (1229), (1230), (1231), (1232), (1233), % 146.89/21.42 | | | | | | | (1234), (1235), (1236), (1237), (1238), (1239), % 146.89/21.42 | | | | | | | (function-axioms) are inconsistent by sub-proof #400. % 146.89/21.42 | | | | | | | % 146.89/21.42 | | | | | | End of split % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | Case 2: % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | (1240) all_14_2 = e0 % 146.89/21.42 | | | | | | (1241) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | COMBINE_EQS: (525), (1240) imply: % 146.89/21.42 | | | | | | (1242) all_8_2 = e0 % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | COMBINE_EQS: (540), (1242) imply: % 146.89/21.42 | | | | | | (1243) all_56_3 = e0 % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | COMBINE_EQS: (544), (1242) imply: % 146.89/21.42 | | | | | | (1244) all_58_29 = e0 % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (562), (1242) imply: % 146.89/21.42 | | | | | | (1245) ~ (all_52_1 = e0) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (565), (1242) imply: % 146.89/21.42 | | | | | | (1246) ~ (all_52_4 = e0) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (567), (1242) imply: % 146.89/21.42 | | | | | | (1247) ~ (all_52_6 = e0) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (569), (1242) imply: % 146.89/21.42 | | | | | | (1248) ~ (all_52_7 = e0) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (571), (1242) imply: % 146.89/21.42 | | | | | | (1249) ~ (all_52_9 = e0) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (573), (1242) imply: % 146.89/21.42 | | | | | | (1250) ~ (all_52_13 = e0) % 146.89/21.42 | | | | | | % 146.89/21.42 | | | | | | REDUCE: (48), (1242) imply: % 146.89/21.43 | | | | | | (1251) op(e0, all_8_1) = all_8_0 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (47), (1242) imply: % 146.89/21.43 | | | | | | (1252) op(e0, e2) = all_8_1 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (633), (1242) imply: % 146.89/21.43 | | | | | | (1253) op(e2, e0) = all_58_9 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, all_8_1, % 146.89/21.43 | | | | | | e2, e0, simplifying with (204), (1252) gives: % 146.89/21.43 | | | | | | (1254) all_52_7 = all_8_1 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 146.89/21.43 | | | | | | all_58_9, e0, e2, simplifying with (210), (1253) gives: % 146.89/21.43 | | | | | | (1255) all_58_9 = all_52_13 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | COMBINE_EQS: (471), (1254) imply: % 146.89/21.43 | | | | | | (1256) all_54_13 = all_8_1 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | COMBINE_EQS: (350), (1254) imply: % 146.89/21.43 | | | | | | (1257) all_56_13 = all_8_1 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | COMBINE_EQS: (547), (1254) imply: % 146.89/21.43 | | | | | | (1258) all_58_24 = all_8_1 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (186), (1254) imply: % 146.89/21.43 | | | | | | (1259) ~ (all_52_3 = all_8_1) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (181), (1254) imply: % 146.89/21.43 | | | | | | (1260) ~ (all_52_4 = all_8_1) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (174), (1254) imply: % 146.89/21.43 | | | | | | (1261) ~ (all_52_6 = all_8_1) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (171), (1254) imply: % 146.89/21.43 | | | | | | (1262) ~ (all_52_11 = all_8_1) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | SIMP: (1262) implies: % 146.89/21.43 | | | | | | (1263) ~ (all_52_11 = all_8_1) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (575), (1254) imply: % 146.89/21.43 | | | | | | (1264) ~ (all_8_1 = all_4_2) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (639), (1254) imply: % 146.89/21.43 | | | | | | (1265) op(e0, all_8_1) = all_58_23 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 146.89/21.43 | | | | | | all_58_23, all_8_1, e0, simplifying with (1251), (1265) % 146.89/21.43 | | | | | | gives: % 146.89/21.43 | | | | | | (1266) all_58_23 = all_8_0 % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), % 146.89/21.43 | | | | | | (51), (74), (79), (94), (137), (156), (158), (159), % 146.89/21.43 | | | | | | (163), (164), (166), (167), (169), (172), (179), (180), % 146.89/21.43 | | | | | | (182), (185), (187), (189), (190), (191), (192), (194), % 146.89/21.43 | | | | | | (195), (203), (206), (210), (211), (213), (214), (215), % 146.89/21.43 | | | | | | (235), (236), (237), (238), (239), (240), (241), (242), % 146.89/21.43 | | | | | | (243), (244), (246), (247), (248), (249), (250), (268), % 146.89/21.43 | | | | | | (269), (270), (271), (272), (273), (274), (275), (276), % 146.89/21.43 | | | | | | (277), (278), (279), (280), (281), (282), (284), (285), % 146.89/21.43 | | | | | | (286), (288), (289), (290), (291), (292), (293), (294), % 146.89/21.43 | | | | | | (295), (296), (297), (298), (332), (334), (335), (336), % 146.89/21.43 | | | | | | (337), (338), (347), (350), (355), (358), (370), (371), % 146.89/21.43 | | | | | | (376), (379), (391), (392), (397), (400), (411), (413), % 146.89/21.43 | | | | | | (417), (419), (421), (425), (427), (429), (445), (447), % 146.89/21.43 | | | | | | (454), (456), (458), (459), (465), (467), (468), (470), % 146.89/21.43 | | | | | | (473), (519), (529), (535), (536), (537), (538), (539), % 146.89/21.43 | | | | | | (541), (542), (543), (544), (545), (546), (548), (549), % 146.89/21.43 | | | | | | (551), (553), (555), (557), (559), (561), (563), (564), % 146.89/21.43 | | | | | | (574), (576), (577), (579), (581), (582), (583), (584), % 146.89/21.43 | | | | | | (585), (628), (629), (630), (631), (632), (634), (636), % 146.89/21.43 | | | | | | (637), (641), (645), (671), (693), (723), (772), (781), % 146.89/21.43 | | | | | | (783), (1241), (1243), (1244), (1245), (1246), (1247), % 146.89/21.43 | | | | | | (1248), (1249), (1250), (1251), (1252), (1255), (1256), % 146.89/21.43 | | | | | | (1257), (1258), (1259), (1260), (1261), (1263), (1264), % 146.89/21.43 | | | | | | (1266), (function-axioms) are inconsistent by sub-proof % 146.89/21.43 | | | | | | #254. % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | End of split % 146.89/21.43 | | | | | % 146.89/21.43 | | | | Case 2: % 146.89/21.43 | | | | | % 146.89/21.43 | | | | | (1267) all_10_0 = e0 % 146.89/21.43 | | | | | (1268) ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 146.89/21.43 | | | | | % 146.89/21.43 | | | | | COMBINE_EQS: (755), (1267) imply: % 146.89/21.43 | | | | | (1269) all_24_0 = e0 % 146.89/21.43 | | | | | % 146.89/21.43 | | | | | REDUCE: (53), (1267) imply: % 146.89/21.43 | | | | | (1270) op(all_10_2, all_10_1) = e0 % 146.89/21.43 | | | | | % 146.89/21.43 | | | | | BETA: splitting (64) gives: % 146.89/21.43 | | | | | % 146.89/21.43 | | | | | Case 1: % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | (1271) ~ (all_14_2 = e0) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | REDUCE: (525), (1271) imply: % 146.89/21.43 | | | | | | (1272) ~ (all_8_2 = e0) % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | BETA: splitting (74) gives: % 146.89/21.43 | | | | | | % 146.89/21.43 | | | | | | Case 1: % 146.89/21.43 | | | | | | | % 146.89/21.43 | | | | | | | (1273) ~ (all_18_2 = e0) % 146.89/21.43 | | | | | | | % 146.89/21.43 | | | | | | | REDUCE: (519), (1273) imply: % 146.89/21.43 | | | | | | | (1274) ~ (all_6_2 = e0) % 146.89/21.43 | | | | | | | % 146.89/21.43 | | | | | | | BETA: splitting (79) gives: % 146.89/21.43 | | | | | | | % 146.89/21.43 | | | | | | | Case 1: % 146.89/21.43 | | | | | | | | % 146.89/21.43 | | | | | | | | (1275) ~ (all_20_2 = e1) % 146.89/21.43 | | | | | | | | % 146.89/21.43 | | | | | | | | REDUCE: (338), (1275) imply: % 146.89/21.43 | | | | | | | | (1276) ~ (all_4_2 = e1) % 146.89/21.43 | | | | | | | | % 146.89/21.43 | | | | | | | | BETA: splitting (89) gives: % 146.89/21.43 | | | | | | | | % 146.89/21.43 | | | | | | | | Case 1: % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | | (1277) ~ (all_24_0 = e0) % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | | REDUCE: (1269), (1277) imply: % 146.89/21.43 | | | | | | | | | (1278) $false % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | | CLOSE: (1278) is inconsistent. % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | Case 2: % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | | (1279) ~ (all_24_1 = e1) | ~ (all_24_2 = e2) % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | | BETA: splitting (103) gives: % 146.89/21.43 | | | | | | | | | % 146.89/21.43 | | | | | | | | | Case 1: % 146.89/21.43 | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | (1280) ~ (all_30_0 = e0) % 146.89/21.43 | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | REDUCE: (732), (1280) imply: % 146.89/21.43 | | | | | | | | | | (1281) ~ (all_8_0 = e0) % 146.89/21.43 | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | BETA: splitting (268) gives: % 146.89/21.43 | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | Case 1: % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | (1282) all_56_15 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | COMBINE_EQS: (538), (1282) imply: % 146.89/21.43 | | | | | | | | | | | (1283) all_4_2 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | SIMP: (1283) implies: % 146.89/21.43 | | | | | | | | | | | (1284) all_4_2 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | COMBINE_EQS: (542), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1285) all_58_31 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (582), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1286) ~ (all_52_11 = e0) % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (583), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1287) ~ (all_52_12 = e0) % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (584), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1288) ~ (all_52_13 = e0) % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (585), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1289) ~ (all_52_14 = e0) % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (38), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1290) op(e0, all_4_1) = all_4_0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (37), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1291) op(e0, e0) = all_4_1 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (641), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1292) op(e0, e0) = all_58_27 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (36), (1284) imply: % 146.89/21.43 | | | | | | | | | | | (1293) op(e0, e0) = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 146.89/21.43 | | | | | | | | | | | all_58_27, e0, e0, simplifying with (1291), (1292) % 146.89/21.43 | | | | | | | | | | | gives: % 146.89/21.43 | | | | | | | | | | | (1294) all_58_27 = all_4_1 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 146.89/21.43 | | | | | | | | | | | all_58_27, e0, e0, simplifying with (1292), (1293) % 146.89/21.43 | | | | | | | | | | | gives: % 146.89/21.43 | | | | | | | | | | | (1295) all_58_27 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | COMBINE_EQS: (1294), (1295) imply: % 146.89/21.43 | | | | | | | | | | | (1296) all_4_1 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | SIMP: (1296) implies: % 146.89/21.43 | | | | | | | | | | | (1297) all_4_1 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (1290), (1297) imply: % 146.89/21.43 | | | | | | | | | | | (1298) op(e0, e0) = all_4_0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 146.89/21.43 | | | | | | | | | | | e0, e0, simplifying with (1293), (1298) gives: % 146.89/21.43 | | | | | | | | | | | (1299) all_4_0 = e0 % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | REDUCE: (781), (1299) imply: % 146.89/21.43 | | | | | | | | | | | (1300) ~ (e1 = e0) % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | BETA: splitting (275) gives: % 146.89/21.43 | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | Case 1: % 146.89/21.43 | | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | | (1301) all_56_6 = e0 % 146.89/21.43 | | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | | COMBINE_EQS: (371), (1301) imply: % 146.89/21.43 | | | | | | | | | | | | (1302) all_52_2 = e0 % 146.89/21.43 | | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | | SIMP: (1302) implies: % 146.89/21.43 | | | | | | | | | | | | (1303) all_52_2 = e0 % 146.89/21.43 | | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | | REDUCE: (195), (1303) imply: % 146.89/21.43 | | | | | | | | | | | | (1304) ~ (all_52_1 = e0) % 146.89/21.43 | | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | | REDUCE: (187), (1303) imply: % 146.89/21.43 | | | | | | | | | | | | (1305) ~ (all_52_14 = e0) % 146.89/21.43 | | | | | | | | | | | | % 146.89/21.43 | | | | | | | | | | | | REDUCE: (553), (1303) imply: % 146.89/21.44 | | | | | | | | | | | | (1306) ~ (all_10_2 = e0) % 146.89/21.44 | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | SIMP: (1306) implies: % 146.89/21.44 | | | | | | | | | | | | (1307) ~ (all_10_2 = e0) % 146.89/21.44 | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | REDUCE: (563), (1303) imply: % 146.89/21.44 | | | | | | | | | | | | (1308) ~ (all_6_2 = e0) % 146.89/21.44 | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | REDUCE: (634), (1303) imply: % 146.89/21.44 | | | | | | | | | | | | (1309) op(e1, e0) = all_58_14 % 146.89/21.44 | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | REDUCE: (209), (1303) imply: % 146.89/21.44 | | | | | | | | | | | | (1310) op(e1, e3) = e0 % 146.89/21.44 | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | BETA: splitting (287) gives: % 146.89/21.44 | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | (1311) all_56_1 = e0 % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | COMBINE_EQS: (411), (1311) imply: % 146.89/21.44 | | | | | | | | | | | | | (1312) all_52_4 = e0 % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | SIMP: (1312) implies: % 146.89/21.44 | | | | | | | | | | | | | (1313) all_52_4 = e0 % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | REDUCE: (182), (1313) imply: % 146.89/21.44 | | | | | | | | | | | | | (1314) ~ (all_52_6 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | SIMP: (1314) implies: % 146.89/21.44 | | | | | | | | | | | | | (1315) ~ (all_52_6 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | REDUCE: (181), (1313) imply: % 146.89/21.44 | | | | | | | | | | | | | (1316) ~ (all_52_7 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | SIMP: (1316) implies: % 146.89/21.44 | | | | | | | | | | | | | (1317) ~ (all_52_7 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | REDUCE: (180), (1313) imply: % 146.89/21.44 | | | | | | | | | | | | | (1318) ~ (all_52_8 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | SIMP: (1318) implies: % 146.89/21.44 | | | | | | | | | | | | | (1319) ~ (all_52_8 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | REDUCE: (179), (1313) imply: % 146.89/21.44 | | | | | | | | | | | | | (1320) ~ (all_52_12 = e0) % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | REDUCE: (626), (1313) imply: % 146.89/21.44 | | | | | | | | | | | | | (1321) op(e3, e0) = all_58_1 % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | BETA: splitting (279) gives: % 146.89/21.44 | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | (1322) all_56_4 = e0 % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | COMBINE_EQS: (413), (1322) imply: % 146.89/21.44 | | | | | | | | | | | | | | (1323) all_52_8 = e0 % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | REDUCE: (1319), (1323) imply: % 146.89/21.44 | | | | | | | | | | | | | | (1324) $false % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | CLOSE: (1324) is inconsistent. % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | (1325) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | BETA: splitting (1325) gives: % 146.89/21.44 | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | (1326) all_56_5 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1326) imply: % 146.89/21.44 | | | | | | | | | | | | | | | (1327) all_52_9 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | SIMP: (1327) implies: % 146.89/21.44 | | | | | | | | | | | | | | | (1328) all_52_9 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | REDUCE: (571), (1328) imply: % 146.89/21.44 | | | | | | | | | | | | | | | (1329) ~ (all_8_2 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | REDUCE: (631), (1328) imply: % 146.89/21.44 | | | | | | | | | | | | | | | (1330) op(e2, e0) = all_58_10 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 146.89/21.44 | | | | | | | | | | | | | | | all_58_14, e0, e1, simplifying with (206), (1309) % 146.89/21.44 | | | | | | | | | | | | | | | gives: % 146.89/21.44 | | | | | | | | | | | | | | | (1331) all_58_14 = all_52_14 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 146.89/21.44 | | | | | | | | | | | | | | | all_58_10, e0, e2, simplifying with (210), (1330) % 146.89/21.44 | | | | | | | | | | | | | | | gives: % 146.89/21.44 | | | | | | | | | | | | | | | (1332) all_58_10 = all_52_13 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 146.89/21.44 | | | | | | | | | | | | | | | all_58_1, e0, e3, simplifying with (214), (1321) % 146.89/21.44 | | | | | | | | | | | | | | | gives: % 146.89/21.44 | | | | | | | | | | | | | | | (1333) all_58_1 = all_52_12 % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 146.89/21.44 | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | (1334) all_54_13 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | REF_CLOSE: (471), (1317), (1334) are inconsistent by % 146.89/21.44 | | | | | | | | | | | | | | | | sub-proof #732. % 146.89/21.44 | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | (1335) ~ (all_54_13 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | | (1336) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | (1337) all_54_9 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (1315), (1337) are inconsistent by % 146.89/21.44 | | | | | | | | | | | | | | | | | sub-proof #572. % 146.89/21.44 | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | (1338) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | (1339) all_54_3 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (465), (1287), (1339) are inconsistent by % 146.89/21.44 | | | | | | | | | | | | | | | | | | sub-proof #733. % 146.89/21.44 | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | (1340) ~ (all_54_3 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | | | | (1341) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | (1342) all_54_4 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (447), (1304), (1342) are inconsistent by % 146.89/21.44 | | | | | | | | | | | | | | | | | | | sub-proof #859. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | (1343) ~ (all_54_4 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | (1344) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | (1345) all_54_2 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (1319), (1345) are inconsistent by % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | sub-proof #860. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | (1346) ~ (all_54_2 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | (1347) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | (1348) all_54_0 = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (1307), (1348) are inconsistent by % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | sub-proof #861. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | (1349) ~ (all_54_0 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | (1350) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1351) all_56_0 = e2 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1351) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1352) all_10_2 = e2 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (515), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1353) all_24_2 = e2 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1354) all_58_28 = e2 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1355) ~ (all_52_1 = e2) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1356) ~ (all_52_8 = e2) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1357) ~ (all_52_12 = e2) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1270), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1358) op(e2, all_10_1) = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1352) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | (1359) op(e2, e3) = all_10_1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1279) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1360) ~ (all_24_1 = e1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (657), (1360) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1361) ~ (all_10_1 = e1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e3, e2, simplifying with (213), (1359) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1362) all_52_1 = all_10_1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1363) all_56_2 = all_10_1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1364) ~ (all_52_3 = all_10_1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1364) implies: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1365) ~ (all_52_3 = all_10_1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1366) ~ (all_52_13 = all_10_1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1366) implies: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1367) ~ (all_52_13 = all_10_1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1368) ~ (all_10_1 = all_8_2) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1355), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1369) ~ (all_10_1 = e2) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1304), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1370) ~ (all_10_1 = e0) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (630), (1362) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | (1371) op(e2, all_10_1) = all_58_7 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_56_0 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1351), (1372) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (1373) e2 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1373) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (1374) $false % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1374) is inconsistent. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | (1375) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1375) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_56_2 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1363), (1376) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_10_1 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1377) implies: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1378) all_10_1 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1361), (1378) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1379) $false % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1379) is inconsistent. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1380) all_56_6 = e1 | all_56_12 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1380) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1381) all_56_6 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1301), (1381) are inconsistent by sub-proof % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | #253. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1382) all_56_12 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1382) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_52_3 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1383) implies: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_52_3 = e1 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1365), (1384) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1385) ~ (all_10_1 = e1) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1386) all_56_0 = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1351), (1386) are inconsistent by sub-proof % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | #719. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1387) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1387) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1388) all_56_2 = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1363), (1388) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1389) all_10_1 = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1389) implies: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1390) all_10_1 = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1367), (1390) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1391) ~ (all_52_13 = e3) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1368), (1390) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1392) ~ (all_8_2 = e3) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1392) implies: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1393) ~ (all_8_2 = e3) % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1371), (1390) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1394) op(e2, e3) = all_58_7 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1358), (1390) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395) op(e2, e3) = e0 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1359), (1390) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1396) op(e2, e3) = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) all_58_28 = e3 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1354), (1397) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) e3 = e2 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1388), (1398) imply: % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) all_56_2 = e2 % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (1301), (1382), (1387), (1399) are % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #837. % 146.89/21.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400) ~ (all_58_28 = e3) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1401) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1354), (1400) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1402) ~ (e3 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1401) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1403) all_58_29 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (1393), (1403) are inconsistent by % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #756. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1404) all_58_30 = e3 | all_58_31 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1404) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1405) all_58_30 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1405) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1406) all_6_2 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (1406) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) all_56_8 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (1406) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408) ~ (all_52_8 = e3) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (1406) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409) ~ (all_52_14 = e3) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1347) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1410) all_54_2 = e1 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (1410) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411) all_52_8 = e1 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1411) implies: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1412) all_52_8 = e1 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (1412) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1413) all_56_4 = e1 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (1412) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1414) ~ (all_52_12 = e1) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1414) implies: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415) ~ (all_52_12 = e1) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1408), (1412) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1416) ~ (e3 = e1) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1356), (1412) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1417) ~ (e2 = e1) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418) all_56_0 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1351), (1418) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) e3 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (1301), (1382), (1387), (1388), % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) are inconsistent by sub-proof #836. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1420) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1420) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421) all_56_1 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1311), (1421) are inconsistent by sub-proof % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #668. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422) ~ (all_56_1 = e3) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1423) all_56_4 = e3 | all_56_9 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1311), (1422) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) ~ (e3 = e0) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) all_56_4 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1413), (1425) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) e2 = e1 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1426) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) $false % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1427) is inconsistent. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) all_56_9 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (1429) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) all_52_12 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (413), (1301), (1326), (1382), % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1387), (1388), (1394), (1395), (1396), (1407), % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408), (1423), (1428), (1429), (function-axioms) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #750. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (421), (427), (1282), (1391), (1409), (1431) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #769. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) all_54_2 = e3 | all_54_2 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (454), (1356), (1408), (1432) are inconsistent by % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #555. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) all_58_31 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1285), (1433) are inconsistent by sub-proof % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #853. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) all_56_6 = e3 | all_56_12 = e3 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (1301), (1382), (1434) are inconsistent % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #838. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | (1435) ~ (all_24_2 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1353), (1435) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | (1436) $false % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1436) is inconsistent. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | (1437) ~ (all_56_0 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | (1438) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (1437) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | (1439) ~ (all_10_2 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1438) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | (1440) all_56_1 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1311), (1440) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | (1441) e2 = e0 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1441) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | (1442) $false % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1442) is inconsistent. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | (1443) all_56_4 = e2 | all_56_9 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1443) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_56_4 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (1444) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_52_8 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1445) implies: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1446) all_52_8 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (1446) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1447) ~ (all_52_11 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1447) implies: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1448) ~ (all_52_11 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1446) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1449) ~ (all_10_2 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (1446) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1450) ~ (all_6_2 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1450) implies: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1451) ~ (all_6_2 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (1446) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | (1452) op(e3, e1) = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (1453) all_58_28 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1453) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_10_2 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1439), (1454) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (1455) $false % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1455) is inconsistent. % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (1456) ~ (all_58_28 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1457) gives: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) all_58_29 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1458) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) all_8_2 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1459) implies: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_8_2 = e2 % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (1460) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) ~ (all_52_1 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1460) imply: % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) ~ (all_52_6 = e2) % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (1460) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) ~ (all_52_7 = e2) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (1460) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) op(e2, all_8_1) = all_8_0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (1460) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) op(e2, e2) = all_8_1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (633), (1460) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) op(e2, e2) = all_58_9 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (1460) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) op(e2, e2) = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_56_6 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1301), (1468) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) e2 = e0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1458), (1469) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_58_29 = e0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (52), (298), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (335), (337), (541), (543), (545), (629), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1285), (1307), (1470), (function-axioms) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #249. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1471) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) all_56_7 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (1472) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_52_6 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1462), (1473) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) $false % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1474) is inconsistent. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_56_8 = e2 | all_56_11 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_56_0 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1476) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_10_2 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1439), (1477) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) $false % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1478) is inconsistent. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1479) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) all_56_2 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (1480) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_52_1 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1481) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) all_52_1 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1461), (1482) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) $false % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1483) is inconsistent. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) all_56_6 = e2 | all_56_12 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) all_56_8 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (1485) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) all_6_2 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1451), (1486) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) $false % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1487) is inconsistent. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_56_11 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (1488) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) all_52_14 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1489) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) all_52_14 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (1490) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) ~ (all_52_12 = e2) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (1490) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) op(e1, e0) = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) all_56_12 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1493) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_52_3 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1494) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_52_3 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (1495) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) ~ (all_52_7 = e2) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_9, e2, e2, simplifying with (1465), (1466) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) all_58_9 = all_8_1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_58_9, % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (1466), (1467) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_58_9 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1497), (1498) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_8_1 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1464), (1499) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) op(e2, e2) = all_8_0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_8_0, % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (1467), (1500) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_8_0 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) all_56_6 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1301), (1502) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) e1 = e0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1503) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) $false % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1504) is inconsistent. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_56_9 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (1506) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) all_52_12 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1507) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_52_12 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1508) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) ~ (all_10_2 = e1) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1509) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) ~ (all_10_2 = e1) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (52), (298), (537), (541), (629), (1270), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307), (1350), (1439), (1510), (function-axioms) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #248. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) ~ (all_56_9 = e1) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1511) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) ~ (all_52_12 = e1) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) all_56_9 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (1513) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) all_52_12 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1514) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) all_52_12 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1333), (1515) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) all_58_1 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1515) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) ~ (all_10_2 = e3) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1517) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) ~ (all_10_2 = e3) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) all_56_0 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1519) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) all_10_2 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1520) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) all_10_2 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1521) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) all_58_28 = e1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1518), (1521) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) ~ (e3 = e1) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1439), (1521) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) ~ (e2 = e1) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1270), (1521) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) op(e1, all_10_1) = e0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1521) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) op(e1, e3) = all_10_1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (629), (1521) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) op(e3, e1) = all_58_0 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_58_28 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1522), (1528) are inconsistent by sub-proof % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #857. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) ~ (all_58_28 = e3) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1530) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) all_58_29 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1458), (1531) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) e3 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1532) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) e3 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1513), (1533) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) all_56_9 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1516), (1533) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_58_1 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (51), (52), (274), (284), (285), (298), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (335), (337), (413), (417), (421), (427), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447), (537), (540), (541), (543), (544), (545), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551), (559), (562), (573), (576), (629), (1270), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272), (1282), (1285), (1295), (1304), (1307), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311), (1319), (1326), (1331), (1332), (1344), % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350), (1439), (1534), (1535), (function-axioms) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #245. % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) all_58_30 = e3 | all_58_31 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1536) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) all_58_30 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (1537) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) all_6_2 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1538) implies: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) all_6_2 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (1539) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) ~ (all_52_6 = e3) % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1539) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) op(e3, e1) = all_6_1 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (637), (1539) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) op(e1, e3) = all_58_18 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) all_56_12 = e3 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1493), (1543) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) e3 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1513), (1544) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) all_56_9 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1516), (1544) imply: % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) all_58_1 = e2 % 146.89/21.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (51), (52), (274), (284), (285), (298), % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (335), (337), (413), (417), (421), (427), % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447), (537), (540), (541), (543), (544), (545), % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551), (559), (562), (573), (576), (629), (1270), % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272), (1282), (1285), (1295), (1304), (1307), % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311), (1319), (1326), (1331), (1332), (1344), % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350), (1439), (1545), (1546), (function-axioms) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #245. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1547) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) all_56_13 = e3 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (1548) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) all_52_7 = e3 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1549) implies: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_52_7 = e3 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) all_56_12 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1301), (1484), (1551) are inconsistent % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #327. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1552) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_56_13 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1548), (1553) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) e3 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1554) implies: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) e3 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1537), (1555) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_58_30 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (1285), (1536), (1556) are inconsistent % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #848. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_18, e3, e1, simplifying with (1310), (1542) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_58_18 = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_18, e3, e1, simplifying with (1526), (1542) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_58_18 = all_10_1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_58_0, % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (1452), (1527) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_58_0 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_0, e1, e3, simplifying with (1527), (1541) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_58_0 = all_6_1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1559), (1560) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_6_1 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1561) implies: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) all_6_1 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1557), (1558) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) all_10_1 = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1525), (1563) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) op(e1, e0) = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e0, e0, % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (1492), (1564) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) e2 = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1458), (1565) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_58_29 = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (1285), (1457), (1530), (1566) are % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #851. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) ~ (all_56_13 = e3) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (1567) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) ~ (all_52_7 = e3) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1505) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) all_56_7 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (1569) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_52_6 = e1 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (1570) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) ~ (all_52_7 = e1) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (471), (1336), (1463), (1568), (1571) are % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) ~ (all_56_7 = e1) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (1572) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) ~ (all_52_6 = e1) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (1338), (1462), (1540), (1573) are % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #619. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) all_58_31 = e3 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1285), (1574) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) e3 = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1575) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) $false % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1576) is inconsistent. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) ~ (all_56_0 = e1) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (1577) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) ~ (all_10_2 = e1) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (1350), (1439), (1518), (1578) are % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #813. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) ~ (all_56_9 = e3) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1579) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) ~ (all_52_12 = e3) % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (465), (1341), (1491), (1512), (1580) are % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #612. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1581) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) all_56_13 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (1582) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_52_7 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1463), (1583) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) $false % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1584) is inconsistent. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_56_14 = e2 | all_56_15 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1585) gives: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_56_14 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (1586) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) all_52_11 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1448), (1587) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) $false % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1588) is inconsistent. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) all_56_15 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1282), (1589) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1590) e2 = e0 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1590) imply: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1591) $false % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1591) is inconsistent. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_58_30 = e2 | all_58_31 = e2 % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (543), (1285), (1451), (1592) are % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #817. % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (1593) all_56_9 = e2 % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (1593) imply: % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (1594) all_52_12 = e2 % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1333), (1594) imply: % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (1595) all_58_1 = e2 % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (51), (52), (274), (284), (285), (298), % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (332), (335), (337), (413), (417), (421), (427), % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (447), (537), (540), (541), (543), (544), (545), % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (551), (559), (562), (573), (576), (629), (1270), % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (1272), (1282), (1285), (1295), (1304), (1307), % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (1311), (1319), (1326), (1331), (1332), (1344), % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | (1350), (1439), (1593), (1595), (function-axioms) % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #245. % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | Case 2: % 146.89/21.48 | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | (1596) all_56_8 = e0 | all_56_14 = e0 % 146.89/21.48 | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | | REF_CLOSE: (347), (539), (1274), (1286), (1596) are % 146.89/21.48 | | | | | | | | | | | | | | | inconsistent by sub-proof #805. % 146.89/21.48 | | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | Case 2: % 146.89/21.48 | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | (1597) ~ (all_56_1 = e0) % 146.89/21.48 | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | REDUCE: (411), (1597) imply: % 146.89/21.48 | | | | | | | | | | | | | (1598) ~ (all_52_4 = e0) % 146.89/21.48 | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (52), (169), % 146.89/21.48 | | | | | | | | | | | | | (283), (292), (298), (334), (335), (337), (392), % 146.89/21.48 | | | | | | | | | | | | | (411), (413), (417), (419), (421), (540), (541), % 146.89/21.48 | | | | | | | | | | | | | (543), (544), (545), (629), (1270), (1285), % 146.89/21.48 | | | | | | | | | | | | | (1287), (1288), (1304), (1307), (1598), % 146.89/21.48 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 146.89/21.48 | | | | | | | | | | | | | #243. % 146.89/21.48 | | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | Case 2: % 146.89/21.48 | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | (1599) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 146.89/21.48 | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (42), (47), % 146.89/21.48 | | | | | | | | | | | | (51), (52), (156), (164), (169), (174), (182), % 146.89/21.48 | | | | | | | | | | | | (190), (191), (194), (195), (203), (204), (205), % 146.89/21.48 | | | | | | | | | | | | (208), (209), (210), (213), (238), (243), (250), % 146.89/21.48 | | | | | | | | | | | | (269), (270), (277), (279), (283), (291), (292), % 146.89/21.48 | | | | | | | | | | | | (293), (295), (297), (298), (334), (335), (337), % 146.89/21.48 | | | | | | | | | | | | (347), (371), (392), (411), (413), (417), (419), % 146.89/21.48 | | | | | | | | | | | | (421), (425), (427), (429), (467), (470), (537), % 146.89/21.48 | | | | | | | | | | | | (539), (540), (541), (542), (543), (544), (545), % 146.89/21.48 | | | | | | | | | | | | (551), (553), (555), (559), (563), (573), (574), % 146.89/21.48 | | | | | | | | | | | | (629), (633), (637), (638), (782), (783), (1268), % 146.89/21.48 | | | | | | | | | | | | (1270), (1274), (1276), (1285), (1286), (1287), % 146.89/21.48 | | | | | | | | | | | | (1288), (1289), (1599), (function-axioms) are % 146.89/21.48 | | | | | | | | | | | | inconsistent by sub-proof #232. % 146.89/21.48 | | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | Case 2: % 146.89/21.48 | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | (1600) ~ (all_56_15 = e0) % 146.89/21.48 | | | | | | | | | | | (1601) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) % 146.89/21.48 | | | | | | | | | | | & (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = % 146.89/21.48 | | | | | | | | | | | e0) % 146.89/21.48 | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (156), (158), % 146.89/21.48 | | | | | | | | | | | (159), (163), (164), (166), (167), (171), (172), % 146.89/21.48 | | | | | | | | | | | (174), (179), (180), (181), (182), (185), (186), % 146.89/21.48 | | | | | | | | | | | (187), (190), (191), (203), (204), (205), (237), % 146.89/21.48 | | | | | | | | | | | (238), (245), (248), (249), (269), (270), (271), % 146.89/21.48 | | | | | | | | | | | (272), (274), (276), (279), (281), (282), (283), % 146.89/21.48 | | | | | | | | | | | (287), (288), (289), (290), (293), (294), (298), % 146.89/21.48 | | | | | | | | | | | (333), (334), (335), (336), (337), (347), (350), % 146.89/21.48 | | | | | | | | | | | (355), (358), (370), (371), (376), (379), (381), % 146.89/21.48 | | | | | | | | | | | (392), (397), (411), (413), (417), (419), (421), % 146.89/21.48 | | | | | | | | | | | (425), (427), (429), (445), (454), (470), (471), % 146.89/21.48 | | | | | | | | | | | (538), (539), (540), (541), (542), (543), (544), % 146.89/21.48 | | | | | | | | | | | (545), (546), (547), (548), (549), (551), (555), % 146.89/21.48 | | | | | | | | | | | (557), (559), (561), (563), (564), (565), (567), % 146.89/21.48 | | | | | | | | | | | (569), (571), (573), (575), (576), (579), (581), % 146.89/21.48 | | | | | | | | | | | (582), (583), (584), (585), (638), (1270), (1272), % 146.89/21.48 | | | | | | | | | | | (1274), (1276), (1600), (1601), (function-axioms) % 146.89/21.48 | | | | | | | | | | | are inconsistent by sub-proof #215. % 146.89/21.48 | | | | | | | | | | | % 146.89/21.48 | | | | | | | | | | End of split % 146.89/21.48 | | | | | | | | | | % 147.31/21.49 | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | (1602) all_30_0 = e0 % 147.31/21.49 | | | | | | | | | | (1603) ~ (all_30_1 = e3) | ~ (all_30_2 = e1) % 147.31/21.49 | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | COMBINE_EQS: (732), (1602) imply: % 147.31/21.49 | | | | | | | | | | (1604) all_8_0 = e0 % 147.31/21.49 | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | REDUCE: (48), (1604) imply: % 147.31/21.49 | | | | | | | | | | (1605) op(all_8_2, all_8_1) = e0 % 147.31/21.49 | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | BETA: splitting (268) gives: % 147.31/21.49 | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | (1606) all_56_15 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | COMBINE_EQS: (538), (1606) imply: % 147.31/21.49 | | | | | | | | | | | (1607) all_4_2 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | SIMP: (1607) implies: % 147.31/21.49 | | | | | | | | | | | (1608) all_4_2 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | COMBINE_EQS: (542), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1609) all_58_31 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (575), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1610) ~ (all_52_7 = e0) % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (582), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1611) ~ (all_52_11 = e0) % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (583), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1612) ~ (all_52_12 = e0) % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (584), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1613) ~ (all_52_13 = e0) % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (585), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1614) ~ (all_52_14 = e0) % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (38), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1615) op(e0, all_4_1) = all_4_0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (37), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1616) op(e0, e0) = all_4_1 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (641), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1617) op(e0, e0) = all_58_27 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (36), (1608) imply: % 147.31/21.49 | | | | | | | | | | | (1618) op(e0, e0) = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 147.31/21.49 | | | | | | | | | | | all_58_27, e0, e0, simplifying with (1616), (1617) % 147.31/21.49 | | | | | | | | | | | gives: % 147.31/21.49 | | | | | | | | | | | (1619) all_58_27 = all_4_1 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 147.31/21.49 | | | | | | | | | | | all_58_27, e0, e0, simplifying with (1617), (1618) % 147.31/21.49 | | | | | | | | | | | gives: % 147.31/21.49 | | | | | | | | | | | (1620) all_58_27 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | COMBINE_EQS: (1619), (1620) imply: % 147.31/21.49 | | | | | | | | | | | (1621) all_4_1 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | SIMP: (1621) implies: % 147.31/21.49 | | | | | | | | | | | (1622) all_4_1 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (1615), (1622) imply: % 147.31/21.49 | | | | | | | | | | | (1623) op(e0, e0) = all_4_0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 147.31/21.49 | | | | | | | | | | | e0, e0, simplifying with (1618), (1623) gives: % 147.31/21.49 | | | | | | | | | | | (1624) all_4_0 = e0 % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | REDUCE: (781), (1624) imply: % 147.31/21.49 | | | | | | | | | | | (1625) ~ (e1 = e0) % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | BETA: splitting (275) gives: % 147.31/21.49 | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | (1626) all_56_6 = e0 % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | COMBINE_EQS: (371), (1626) imply: % 147.31/21.49 | | | | | | | | | | | | (1627) all_52_2 = e0 % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | SIMP: (1627) implies: % 147.31/21.49 | | | | | | | | | | | | (1628) all_52_2 = e0 % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | REDUCE: (195), (1628) imply: % 147.31/21.49 | | | | | | | | | | | | (1629) ~ (all_52_1 = e0) % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | REDUCE: (190), (1628) imply: % 147.31/21.49 | | | | | | | | | | | | (1630) ~ (all_52_3 = e0) % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | SIMP: (1630) implies: % 147.31/21.49 | | | | | | | | | | | | (1631) ~ (all_52_3 = e0) % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | REDUCE: (187), (1628) imply: % 147.31/21.49 | | | | | | | | | | | | (1632) ~ (all_52_14 = e0) % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | REDUCE: (563), (1628) imply: % 147.31/21.49 | | | | | | | | | | | | (1633) ~ (all_6_2 = e0) % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | REDUCE: (634), (1628) imply: % 147.31/21.49 | | | | | | | | | | | | (1634) op(e1, e0) = all_58_14 % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | REDUCE: (209), (1628) imply: % 147.31/21.49 | | | | | | | | | | | | (1635) op(e1, e3) = e0 % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | BETA: splitting (287) gives: % 147.31/21.49 | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | (1636) all_56_1 = e0 % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | COMBINE_EQS: (411), (1636) imply: % 147.31/21.49 | | | | | | | | | | | | | (1637) all_52_4 = e0 % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | SIMP: (1637) implies: % 147.31/21.49 | | | | | | | | | | | | | (1638) all_52_4 = e0 % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | REDUCE: (182), (1638) imply: % 147.31/21.49 | | | | | | | | | | | | | (1639) ~ (all_52_6 = e0) % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | SIMP: (1639) implies: % 147.31/21.49 | | | | | | | | | | | | | (1640) ~ (all_52_6 = e0) % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | REDUCE: (557), (1638) imply: % 147.31/21.49 | | | | | | | | | | | | | (1641) ~ (all_10_2 = e0) % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | SIMP: (1641) implies: % 147.31/21.49 | | | | | | | | | | | | | (1642) ~ (all_10_2 = e0) % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | REDUCE: (216), (1638) imply: % 147.31/21.49 | | | | | | | | | | | | | (1643) op(e3, e2) = e0 % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | BETA: splitting (283) gives: % 147.31/21.49 | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | (1644) all_56_2 = e0 % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | COMBINE_EQS: (417), (1644) imply: % 147.31/21.49 | | | | | | | | | | | | | | (1645) all_52_1 = e0 % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | REDUCE: (1629), (1645) imply: % 147.31/21.49 | | | | | | | | | | | | | | (1646) $false % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | CLOSE: (1646) is inconsistent. % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | (1647) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | BETA: splitting (1647) gives: % 147.31/21.49 | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | (1648) all_56_3 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | COMBINE_EQS: (540), (1648) imply: % 147.31/21.49 | | | | | | | | | | | | | | | (1649) all_8_2 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1649) imply: % 147.31/21.49 | | | | | | | | | | | | | | | (1650) all_58_29 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (52), (298), % 147.31/21.49 | | | | | | | | | | | | | | | (334), (335), (337), (541), (543), (545), (629), % 147.31/21.49 | | | | | | | | | | | | | | | (1270), (1609), (1642), (1650), (function-axioms) % 147.31/21.49 | | | | | | | | | | | | | | | are inconsistent by sub-proof #249. % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | (1651) all_56_5 = e0 | all_56_10 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | BETA: splitting (1651) gives: % 147.31/21.49 | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | (1652) all_56_5 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (1652) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | (1653) all_52_9 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 147.31/21.49 | | | | | | | | | | | | | | | | all_58_14, e0, e1, simplifying with (206), (1634) % 147.31/21.49 | | | | | | | | | | | | | | | | gives: % 147.31/21.49 | | | | | | | | | | | | | | | | (1654) all_58_14 = all_52_14 % 147.31/21.49 | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | (1655) all_54_9 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | REF_CLOSE: (459), (1640), (1655) are inconsistent by % 147.31/21.49 | | | | | | | | | | | | | | | | | sub-proof #572. % 147.31/21.49 | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | (1656) ~ (all_54_9 = e0) % 147.31/21.49 | | | | | | | | | | | | | | | | | (1657) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | (1658) all_54_0 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (1642), (1658) are inconsistent by % 147.31/21.49 | | | | | | | | | | | | | | | | | | sub-proof #861. % 147.31/21.49 | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | (1659) ~ (all_54_0 = e0) % 147.31/21.49 | | | | | | | | | | | | | | | | | | (1660) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1661) all_56_12 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (1661) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1662) all_52_3 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | SIMP: (1662) implies: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1663) all_52_3 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | REDUCE: (186), (1663) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1664) ~ (all_52_7 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | SIMP: (1664) implies: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1665) ~ (all_52_7 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | REDUCE: (185), (1663) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1666) ~ (all_52_11 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | SIMP: (1666) implies: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | (1667) ~ (all_52_11 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1668) all_56_4 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (1668) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1669) all_52_8 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | SIMP: (1669) implies: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1670) all_52_8 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1670) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1671) ~ (all_10_2 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | SIMP: (1671) implies: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1672) ~ (all_10_2 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (576), (1670) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1673) ~ (all_6_2 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | SIMP: (1673) implies: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1674) ~ (all_6_2 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1675) all_58_28 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1675) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1676) all_10_2 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1672), (1676) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1677) $false % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1677) is inconsistent. % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1678) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1678) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1679) all_58_29 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (544), (1679) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1680) all_8_2 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (208), (459), (504), (567), (672), (1603), % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1605), (1640), (1657), (1680), (function-axioms) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #214. % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1681) all_58_30 = e1 | all_58_31 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (542), (543), (1276), (1674), (1681) are % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #673. % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | (1682) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1682) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1683) all_56_5 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1652), (1683) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1684) e1 = e0 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (1684) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1685) $false % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1685) is inconsistent. % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | (1686) all_56_8 = e1 | all_56_14 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1686) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1687) all_56_8 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (1687) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1688) all_6_2 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (574), (1688) imply: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | (1689) ~ (all_52_6 = e1) % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | (1690) all_56_1 = e1 % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1636), (1690) are inconsistent by sub-proof % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | #213. % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.49 | | | | | | | | | | | | | | | | | | | | | | | (1691) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1691) gives: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | (1692) all_56_3 = e1 % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (1692) imply: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | (1693) all_8_2 = e1 % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (208), (459), (504), (567), (672), (1603), % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | (1605), (1640), (1657), (1693), (function-axioms) % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #214. % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | (1694) all_56_7 = e1 | all_56_13 = e1 % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (350), (425), (1665), (1689), (1694) are % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | (1695) all_56_14 = e1 % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (347), (1667), (1695) are inconsistent by % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | sub-proof #811. % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | End of split % 147.31/21.50 | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | Case 2: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | (1696) ~ (all_56_12 = e1) % 147.31/21.50 | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | REDUCE: (429), (1696) imply: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | (1697) ~ (all_52_3 = e1) % 147.31/21.50 | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | Case 1: % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | % 147.31/21.50 | | | | | | | | | | | | | | | | | | | | (1698) all_56_0 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1698) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1699) all_10_2 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1270), (1699) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1700) op(e1, all_10_1) = e0 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1699) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1701) op(e1, e3) = all_10_1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_10_1, % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (1635), (1701) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1702) all_10_1 = e0 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1700), (1702) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1703) op(e1, e0) = e0 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (206), (1703) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1704) all_52_14 = e0 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1614), (1704) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1705) $false % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | CLOSE: (1705) is inconsistent. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | (1706) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1706) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1707) all_56_2 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (1707) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1708) all_52_1 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | SIMP: (1708) implies: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1709) all_52_1 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (1709) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1710) ~ (all_10_2 = e1) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | SIMP: (1710) implies: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1711) ~ (all_10_2 = e1) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (1709) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1712) ~ (all_8_2 = e1) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | SIMP: (1712) implies: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1713) ~ (all_8_2 = e1) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | (1714) all_58_28 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (1714) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | (1715) all_10_2 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1711), (1715) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | (1716) $false % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1716) is inconsistent. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | (1717) ~ (all_58_28 = e1) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | (1718) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1718) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | (1719) all_58_29 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (544), (1713), (1719) are inconsistent by % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #809. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | (1720) all_58_30 = e1 | all_58_31 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1720) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | (1721) all_58_30 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (1722) all_56_0 = e3 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (541), (1722) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (1723) all_10_2 = e3 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1723) implies: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (1724) all_10_2 = e3 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (52), (629), (1270), (1642), (1724), % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | #251. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (1725) ~ (all_56_0 = e3) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (1725) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (1726) ~ (all_10_2 = e3) % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (47), (295), (337), (537), (541), (544), % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (545), (629), (783), (1609), (1643), (1660), % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | (1711), (1721), (1726), (function-axioms) are % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #820. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | (1727) all_58_31 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1609), (1727) are inconsistent by sub-proof % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | #845. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | (1728) all_56_6 = e1 | all_56_12 = e1 % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (429), (1626), (1697), (1728) are % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #807. % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | (1729) all_56_10 = e0 % 147.36/21.50 | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (1729) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | (1730) all_52_13 = e0 % 147.36/21.50 | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | REDUCE: (1613), (1730) imply: % 147.36/21.50 | | | | | | | | | | | | | | | | (1731) $false % 147.36/21.50 | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | | CLOSE: (1731) is inconsistent. % 147.36/21.50 | | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | (1732) ~ (all_56_1 = e0) % 147.36/21.50 | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | REDUCE: (411), (1732) imply: % 147.36/21.50 | | | | | | | | | | | | | (1733) ~ (all_52_4 = e0) % 147.36/21.50 | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (52), (164), % 147.36/21.50 | | | | | | | | | | | | | (169), (203), (204), (205), (238), (269), (270), % 147.36/21.50 | | | | | | | | | | | | | (279), (283), (291), (292), (298), (334), (335), % 147.36/21.50 | | | | | | | | | | | | | (337), (347), (392), (411), (413), (417), (419), % 147.36/21.50 | | | | | | | | | | | | | (421), (429), (470), (539), (540), (541), (543), % 147.36/21.50 | | | | | | | | | | | | | (544), (545), (555), (559), (629), (638), (1270), % 147.36/21.50 | | | | | | | | | | | | | (1274), (1609), (1610), (1611), (1612), (1613), % 147.36/21.50 | | | | | | | | | | | | | (1629), (1733), (function-axioms) are inconsistent % 147.36/21.50 | | | | | | | | | | | | | by sub-proof #233. % 147.36/21.50 | | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | End of split % 147.36/21.50 | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | Case 2: % 147.36/21.50 | | | | | | | | | | | | % 147.36/21.50 | | | | | | | | | | | | (1734) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 147.36/21.50 | | | | | | | | | | | | % 147.36/21.51 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (42), (47), % 147.36/21.51 | | | | | | | | | | | | (51), (52), (156), (164), (169), (174), (182), % 147.36/21.51 | | | | | | | | | | | | (190), (191), (194), (195), (203), (204), (205), % 147.36/21.51 | | | | | | | | | | | | (208), (209), (210), (213), (238), (243), (250), % 147.36/21.51 | | | | | | | | | | | | (269), (270), (277), (279), (283), (291), (292), % 147.36/21.51 | | | | | | | | | | | | (293), (295), (297), (298), (334), (335), (337), % 147.36/21.51 | | | | | | | | | | | | (347), (371), (392), (411), (413), (417), (419), % 147.36/21.51 | | | | | | | | | | | | (421), (425), (427), (429), (467), (470), (537), % 147.36/21.51 | | | | | | | | | | | | (539), (540), (541), (542), (543), (544), (545), % 147.36/21.51 | | | | | | | | | | | | (551), (553), (555), (559), (563), (573), (574), % 147.36/21.51 | | | | | | | | | | | | (629), (633), (637), (638), (782), (783), (1268), % 147.36/21.51 | | | | | | | | | | | | (1270), (1274), (1276), (1609), (1611), (1612), % 147.36/21.51 | | | | | | | | | | | | (1613), (1614), (1734), (function-axioms) are % 147.36/21.51 | | | | | | | | | | | | inconsistent by sub-proof #232. % 147.36/21.51 | | | | | | | | | | | | % 147.36/21.51 | | | | | | | | | | | End of split % 147.36/21.51 | | | | | | | | | | | % 147.36/21.51 | | | | | | | | | | Case 2: % 147.36/21.51 | | | | | | | | | | | % 147.36/21.51 | | | | | | | | | | | (1735) ~ (all_56_15 = e0) % 147.36/21.51 | | | | | | | | | | | (1736) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) % 147.36/21.51 | | | | | | | | | | | & (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = % 147.36/21.51 | | | | | | | | | | | e0) % 147.36/21.51 | | | | | | | | | | | % 147.41/21.51 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (156), (158), % 147.41/21.51 | | | | | | | | | | | (159), (163), (164), (166), (167), (171), (172), % 147.41/21.51 | | | | | | | | | | | (174), (179), (180), (181), (182), (185), (186), % 147.41/21.51 | | | | | | | | | | | (187), (190), (191), (203), (204), (205), (237), % 147.41/21.51 | | | | | | | | | | | (238), (245), (248), (249), (269), (270), (271), % 147.41/21.51 | | | | | | | | | | | (272), (274), (276), (279), (281), (282), (283), % 147.41/21.51 | | | | | | | | | | | (287), (288), (289), (290), (293), (294), (298), % 147.41/21.51 | | | | | | | | | | | (333), (334), (335), (336), (337), (347), (350), % 147.41/21.51 | | | | | | | | | | | (355), (358), (370), (371), (376), (379), (381), % 147.41/21.51 | | | | | | | | | | | (392), (397), (411), (413), (417), (419), (421), % 147.41/21.51 | | | | | | | | | | | (425), (427), (429), (445), (454), (470), (471), % 147.41/21.51 | | | | | | | | | | | (538), (539), (540), (541), (542), (543), (544), % 147.41/21.51 | | | | | | | | | | | (545), (546), (547), (548), (549), (551), (555), % 147.41/21.51 | | | | | | | | | | | (557), (559), (561), (563), (564), (565), (567), % 147.41/21.51 | | | | | | | | | | | (569), (571), (573), (575), (576), (579), (581), % 147.41/21.51 | | | | | | | | | | | (582), (583), (584), (585), (638), (1270), (1272), % 147.41/21.51 | | | | | | | | | | | (1274), (1276), (1735), (1736), (function-axioms) % 147.41/21.51 | | | | | | | | | | | are inconsistent by sub-proof #215. % 147.41/21.51 | | | | | | | | | | | % 147.41/21.51 | | | | | | | | | | End of split % 147.41/21.51 | | | | | | | | | | % 147.41/21.51 | | | | | | | | | End of split % 147.41/21.51 | | | | | | | | | % 147.41/21.51 | | | | | | | | End of split % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | Case 2: % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | (1737) all_20_2 = e1 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | COMBINE_EQS: (338), (1737) imply: % 147.41/21.51 | | | | | | | | (1738) all_4_2 = e1 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | SIMP: (1738) implies: % 147.41/21.51 | | | | | | | | (1739) all_4_2 = e1 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | COMBINE_EQS: (538), (1739) imply: % 147.41/21.51 | | | | | | | | (1740) all_56_15 = e1 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | COMBINE_EQS: (542), (1739) imply: % 147.41/21.51 | | | | | | | | (1741) all_58_31 = e1 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REDUCE: (564), (1739) imply: % 147.41/21.51 | | | | | | | | (1742) ~ (all_52_3 = e1) % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REDUCE: (582), (1739) imply: % 147.41/21.51 | | | | | | | | (1743) ~ (all_52_11 = e1) % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REDUCE: (584), (1739) imply: % 147.41/21.51 | | | | | | | | (1744) ~ (all_52_13 = e1) % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REDUCE: (38), (1739) imply: % 147.41/21.51 | | | | | | | | (1745) op(e1, all_4_1) = all_4_0 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REDUCE: (37), (1739) imply: % 147.41/21.51 | | | | | | | | (1746) op(e1, e0) = all_4_1 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REDUCE: (641), (1739) imply: % 147.41/21.51 | | | | | | | | (1747) op(e0, e1) = all_58_27 % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (158), (159), % 147.41/21.51 | | | | | | | | (163), (164), (166), (167), (169), (171), (174), % 147.41/21.51 | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 147.41/21.51 | | | | | | | | (189), (190), (192), (194), (195), (203), (204), % 147.41/21.51 | | | | | | | | (205), (206), (236), (238), (242), (243), (245), % 147.41/21.51 | | | | | | | | (247), (249), (268), (269), (270), (271), (273), % 147.41/21.51 | | | | | | | | (274), (275), (276), (277), (278), (279), (280), % 147.41/21.51 | | | | | | | | (283), (284), (286), (288), (289), (292), (333), % 147.41/21.51 | | | | | | | | (334), (335), (336), (337), (347), (350), (355), % 147.41/21.51 | | | | | | | | (358), (370), (371), (376), (379), (381), (391), % 147.41/21.51 | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 147.41/21.51 | | | | | | | | (421), (425), (427), (429), (445), (458), (465), % 147.41/21.51 | | | | | | | | (467), (470), (473), (539), (540), (541), (543), % 147.41/21.51 | | | | | | | | (544), (545), (546), (547), (548), (549), (551), % 147.41/21.51 | | | | | | | | (553), (555), (559), (561), (562), (563), (565), % 147.41/21.51 | | | | | | | | (567), (573), (579), (581), (636), (638), (781), % 147.41/21.51 | | | | | | | | (1270), (1272), (1274), (1740), (1741), (1742), % 147.41/21.51 | | | | | | | | (1743), (1744), (1745), (1746), (1747), % 147.41/21.51 | | | | | | | | (function-axioms) are inconsistent by sub-proof #191. % 147.41/21.51 | | | | | | | | % 147.41/21.51 | | | | | | | End of split % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | Case 2: % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | (1748) all_18_2 = e0 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | COMBINE_EQS: (519), (1748) imply: % 147.41/21.51 | | | | | | | (1749) all_6_2 = e0 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | SIMP: (1749) implies: % 147.41/21.51 | | | | | | | (1750) all_6_2 = e0 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | COMBINE_EQS: (539), (1750) imply: % 147.41/21.51 | | | | | | | (1751) all_56_8 = e0 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | COMBINE_EQS: (543), (1750) imply: % 147.41/21.51 | | | | | | | (1752) all_58_30 = e0 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (574), (1750) imply: % 147.41/21.51 | | | | | | | (1753) ~ (all_52_6 = e0) % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (576), (1750) imply: % 147.41/21.51 | | | | | | | (1754) ~ (all_52_8 = e0) % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (577), (1750) imply: % 147.41/21.51 | | | | | | | (1755) ~ (all_52_9 = e0) % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (579), (1750) imply: % 147.41/21.51 | | | | | | | (1756) ~ (all_52_11 = e0) % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (581), (1750) imply: % 147.41/21.51 | | | | | | | (1757) ~ (all_52_14 = e0) % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (42), (1750) imply: % 147.41/21.51 | | | | | | | (1758) op(e0, e1) = all_6_1 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (637), (1750) imply: % 147.41/21.51 | | | | | | | (1759) op(e1, e0) = all_58_18 % 147.41/21.51 | | | | | | | % 147.41/21.51 | | | | | | | REDUCE: (41), (1750) imply: % 147.41/21.51 | | | | | | | (1760) op(e1, e1) = e0 % 147.41/21.51 | | | | | | | % 147.41/21.52 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (47), (51), % 147.41/21.52 | | | | | | | (52), (79), (156), (158), (159), (163), (164), (166), % 147.41/21.52 | | | | | | | (167), (169), (171), (172), (174), (179), (180), (181), % 147.41/21.52 | | | | | | | (182), (185), (186), (187), (189), (190), (191), (192), % 147.41/21.52 | | | | | | | (194), (195), (203), (206), (209), (210), (214), (216), % 147.41/21.52 | | | | | | | (238), (241), (242), (243), (244), (245), (246), (247), % 147.41/21.52 | | | | | | | (248), (249), (250), (268), (269), (270), (272), (273), % 147.41/21.52 | | | | | | | (274), (276), (277), (278), (280), (281), (282), (283), % 147.41/21.52 | | | | | | | (284), (285), (286), (287), (288), (290), (291), (292), % 147.41/21.52 | | | | | | | (293), (294), (295), (296), (297), (298), (332), (334), % 147.41/21.52 | | | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 147.41/21.52 | | | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 147.41/21.52 | | | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 147.41/21.52 | | | | | | | (429), (445), (447), (454), (456), (458), (459), (465), % 147.41/21.52 | | | | | | | (467), (470), (537), (538), (540), (541), (542), (543), % 147.41/21.52 | | | | | | | (544), (545), (546), (547), (548), (549), (551), (553), % 147.41/21.52 | | | | | | | (555), (557), (559), (561), (562), (564), (567), (569), % 147.41/21.52 | | | | | | | (571), (573), (575), (582), (583), (584), (585), (626), % 147.41/21.52 | | | | | | | (629), (632), (636), (638), (783), (1268), (1270), % 147.41/21.52 | | | | | | | (1272), (1751), (1752), (1753), (1754), (1755), (1756), % 147.41/21.52 | | | | | | | (1757), (1758), (1759), (1760), (function-axioms) are % 147.41/21.52 | | | | | | | inconsistent by sub-proof #174. % 147.41/21.52 | | | | | | | % 147.41/21.52 | | | | | | End of split % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | Case 2: % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | (1761) all_14_2 = e0 % 147.41/21.52 | | | | | | (1762) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | COMBINE_EQS: (525), (1761) imply: % 147.41/21.52 | | | | | | (1763) all_8_2 = e0 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | SIMP: (1763) implies: % 147.41/21.52 | | | | | | (1764) all_8_2 = e0 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | COMBINE_EQS: (540), (1764) imply: % 147.41/21.52 | | | | | | (1765) all_56_3 = e0 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | COMBINE_EQS: (544), (1764) imply: % 147.41/21.52 | | | | | | (1766) all_58_29 = e0 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (562), (1764) imply: % 147.41/21.52 | | | | | | (1767) ~ (all_52_1 = e0) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (565), (1764) imply: % 147.41/21.52 | | | | | | (1768) ~ (all_52_4 = e0) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (567), (1764) imply: % 147.41/21.52 | | | | | | (1769) ~ (all_52_6 = e0) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (569), (1764) imply: % 147.41/21.52 | | | | | | (1770) ~ (all_52_7 = e0) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (571), (1764) imply: % 147.41/21.52 | | | | | | (1771) ~ (all_52_9 = e0) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (573), (1764) imply: % 147.41/21.52 | | | | | | (1772) ~ (all_52_13 = e0) % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (48), (1764) imply: % 147.41/21.52 | | | | | | (1773) op(e0, all_8_1) = all_8_0 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (47), (1764) imply: % 147.41/21.52 | | | | | | (1774) op(e0, e2) = all_8_1 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REDUCE: (633), (1764) imply: % 147.41/21.52 | | | | | | (1775) op(e2, e0) = all_58_9 % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (37), (41), (51), (52), % 147.41/21.52 | | | | | | (74), (79), (156), (158), (159), (163), (164), (166), % 147.41/21.52 | | | | | | (167), (169), (171), (172), (174), (179), (180), (181), % 147.41/21.52 | | | | | | (182), (185), (186), (187), (189), (190), (191), (192), % 147.41/21.52 | | | | | | (194), (195), (203), (204), (206), (210), (211), (213), % 147.41/21.52 | | | | | | (214), (215), (235), (236), (237), (238), (239), (240), % 147.41/21.52 | | | | | | (241), (242), (243), (244), (246), (247), (248), (249), % 147.41/21.52 | | | | | | (250), (268), (269), (270), (271), (272), (273), (274), % 147.41/21.52 | | | | | | (275), (276), (277), (278), (279), (280), (281), (282), % 147.41/21.52 | | | | | | (284), (285), (286), (288), (290), (291), (292), (293), % 147.41/21.52 | | | | | | (294), (295), (296), (297), (298), (332), (334), (335), % 147.41/21.52 | | | | | | (336), (337), (338), (347), (350), (355), (358), (370), % 147.41/21.52 | | | | | | (371), (376), (379), (391), (392), (397), (400), (411), % 147.41/21.52 | | | | | | (413), (417), (419), (421), (425), (427), (429), (445), % 147.41/21.52 | | | | | | (447), (454), (456), (458), (459), (465), (467), (468), % 147.41/21.52 | | | | | | (470), (471), (473), (519), (535), (536), (537), (538), % 147.41/21.52 | | | | | | (539), (541), (542), (543), (544), (545), (546), (547), % 147.41/21.52 | | | | | | (548), (549), (551), (553), (555), (557), (559), (561), % 147.41/21.52 | | | | | | (563), (564), (574), (575), (576), (577), (579), (581), % 147.41/21.52 | | | | | | (582), (583), (584), (585), (628), (629), (630), (634), % 147.41/21.52 | | | | | | (636), (637), (639), (641), (693), (772), (1270), (1762), % 147.41/21.52 | | | | | | (1765), (1766), (1767), (1768), (1769), (1770), (1771), % 147.41/21.52 | | | | | | (1772), (1773), (1774), (1775), (function-axioms) are % 147.41/21.52 | | | | | | inconsistent by sub-proof #159. % 147.41/21.52 | | | | | | % 147.41/21.52 | | | | | End of split % 147.41/21.52 | | | | | % 147.41/21.52 | | | | End of split % 147.41/21.52 | | | | % 147.41/21.52 | | | Case 2: % 147.41/21.52 | | | | % 147.41/21.52 | | | | (1776) all_8_1 = e0 % 147.41/21.52 | | | | (1777) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 147.41/21.52 | | | | % 147.41/21.52 | | | | COMBINE_EQS: (686), (1776) imply: % 147.41/21.52 | | | | (1778) all_22_1 = e0 % 147.41/21.52 | | | | % 147.41/21.52 | | | | REDUCE: (48), (1776) imply: % 147.41/21.52 | | | | (1779) op(all_8_2, e0) = all_8_0 % 147.41/21.52 | | | | % 147.41/21.52 | | | | REDUCE: (47), (1776) imply: % 147.41/21.52 | | | | (1780) op(all_8_2, e2) = e0 % 147.41/21.52 | | | | % 147.41/21.53 | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), (42), % 147.41/21.53 | | | | (46), (51), (52), (53), (54), (69), (74), (79), (84), (108), % 147.41/21.53 | | | | (156), (158), (159), (163), (164), (166), (167), (169), % 147.41/21.53 | | | | (171), (172), (174), (179), (180), (181), (182), (185), % 147.41/21.53 | | | | (186), (187), (189), (190), (191), (192), (194), (195), % 147.41/21.53 | | | | (203), (204), (205), (206), (208), (209), (210), (211), % 147.41/21.53 | | | | (214), (215), (216), (236), (237), (238), (241), (242), % 147.41/21.53 | | | | (243), (244), (245), (246), (247), (248), (249), (250), % 147.41/21.53 | | | | (268), (269), (270), (271), (272), (273), (274), (275), % 147.41/21.53 | | | | (276), (277), (278), (279), (280), (281), (282), (283), % 147.41/21.53 | | | | (284), (285), (286), (287), (288), (289), (291), (292), % 147.41/21.53 | | | | (293), (294), (295), (296), (297), (298), (332), (333), % 147.41/21.53 | | | | (334), (335), (336), (337), (338), (347), (350), (355), % 147.41/21.53 | | | | (358), (370), (371), (376), (379), (381), (391), (392), % 147.41/21.53 | | | | (397), (400), (411), (413), (417), (419), (421), (425), % 147.41/21.53 | | | | (427), (429), (445), (447), (454), (456), (458), (459), % 147.41/21.53 | | | | (465), (467), (470), (471), (473), (517), (519), (523), % 147.41/21.53 | | | | (537), (538), (539), (540), (541), (542), (543), (544), % 147.41/21.53 | | | | (545), (546), (547), (548), (549), (551), (553), (555), % 147.41/21.53 | | | | (557), (559), (561), (562), (563), (564), (565), (567), % 147.41/21.53 | | | | (569), (571), (573), (574), (575), (576), (577), (579), % 147.41/21.53 | | | | (581), (582), (583), (584), (585), (626), (628), (629), % 147.41/21.53 | | | | (630), (631), (632), (633), (634), (635), (636), (637), % 147.41/21.53 | | | | (638), (641), (691), (696), (766), (771), (781), (1777), % 147.41/21.53 | | | | (1778), (1779), (1780), (function-axioms) are inconsistent by % 147.41/21.53 | | | | sub-proof #84. % 147.41/21.53 | | | | % 147.41/21.53 | | | End of split % 147.41/21.53 | | | % 147.41/21.53 | | Case 2: % 147.41/21.53 | | | % 147.41/21.53 | | | (1781) all_6_1 = e0 % 147.41/21.53 | | | (1782) ~ (all_6_0 = e2) | ~ (all_6_2 = e3) % 147.41/21.53 | | | % 147.41/21.53 | | | COMBINE_EQS: (666), (1781) imply: % 147.41/21.53 | | | (1783) all_36_1 = e0 % 147.41/21.53 | | | % 147.41/21.53 | | | REDUCE: (43), (1781) imply: % 147.41/21.53 | | | (1784) op(all_6_2, e0) = all_6_0 % 147.41/21.53 | | | % 147.41/21.53 | | | REDUCE: (42), (1781) imply: % 147.41/21.53 | | | (1785) op(all_6_2, e1) = e0 % 147.41/21.53 | | | % 147.41/21.53 | | | BETA: splitting (49) gives: % 147.41/21.53 | | | % 147.41/21.53 | | | Case 1: % 147.41/21.53 | | | | % 147.41/21.53 | | | | (1786) ~ (all_8_1 = e0) % 147.41/21.53 | | | | % 147.41/21.53 | | | | BETA: splitting (54) gives: % 147.41/21.53 | | | | % 147.41/21.53 | | | | Case 1: % 147.41/21.53 | | | | | % 147.41/21.53 | | | | | (1787) ~ (all_10_0 = e0) % 147.41/21.53 | | | | | % 147.41/21.53 | | | | | BETA: splitting (64) gives: % 147.41/21.53 | | | | | % 147.41/21.53 | | | | | Case 1: % 147.41/21.53 | | | | | | % 147.41/21.53 | | | | | | (1788) ~ (all_14_2 = e0) % 147.41/21.53 | | | | | | % 147.41/21.53 | | | | | | REDUCE: (525), (1788) imply: % 147.41/21.53 | | | | | | (1789) ~ (all_8_2 = e0) % 147.41/21.53 | | | | | | % 147.41/21.53 | | | | | | BETA: splitting (69) gives: % 147.41/21.53 | | | | | | % 147.41/21.53 | | | | | | Case 1: % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | (1790) ~ (all_16_2 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (523), (1790) imply: % 147.41/21.53 | | | | | | | (1791) ~ (all_10_2 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | BETA: splitting (79) gives: % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | Case 1: % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | (1792) ~ (all_20_2 = e1) % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | REDUCE: (338), (1792) imply: % 147.41/21.53 | | | | | | | | (1793) ~ (all_4_2 = e1) % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.41/21.53 | | | | | | | | (42), (43), (46), (47), (48), (51), (52), (53), % 147.41/21.53 | | | | | | | | (108), (118), (127), (142), (156), (158), (159), % 147.41/21.53 | | | | | | | | (164), (166), (167), (169), (172), (174), (179), % 147.41/21.53 | | | | | | | | (180), (181), (182), (185), (186), (187), (189), % 147.41/21.53 | | | | | | | | (190), (191), (192), (194), (195), (203), (206), % 147.41/21.53 | | | | | | | | (208), (209), (210), (211), (213), (214), (215), % 147.41/21.53 | | | | | | | | (216), (237), (238), (239), (241), (242), (243), % 147.41/21.53 | | | | | | | | (244), (246), (248), (249), (250), (268), (269), % 147.41/21.53 | | | | | | | | (271), (272), (273), (275), (276), (278), (279), % 147.41/21.53 | | | | | | | | (281), (282), (283), (284), (286), (287), (290), % 147.41/21.53 | | | | | | | | (291), (293), (294), (295), (296), (297), (298), % 147.41/21.53 | | | | | | | | (332), (333), (334), (335), (337), (347), (350), % 147.41/21.53 | | | | | | | | (360), (371), (392), (411), (413), (417), (419), % 147.41/21.53 | | | | | | | | (421), (425), (427), (429), (445), (447), (454), % 147.41/21.53 | | | | | | | | (456), (458), (459), (467), (468), (470), (471), % 147.41/21.53 | | | | | | | | (507), (509), (537), (538), (539), (540), (541), % 147.41/21.53 | | | | | | | | (542), (543), (544), (545), (551), (553), (555), % 147.41/21.53 | | | | | | | | (557), (559), (561), (562), (563), (564), (565), % 147.41/21.53 | | | | | | | | (567), (569), (571), (573), (574), (575), (576), % 147.41/21.53 | | | | | | | | (577), (579), (581), (582), (584), (585), (626), % 147.41/21.53 | | | | | | | | (627), (629), (630), (631), (633), (634), (635), % 147.41/21.53 | | | | | | | | (637), (641), (648), (696), (727), (775), (776), % 147.41/21.53 | | | | | | | | (778), (781), (1782), (1783), (1784), (1785), (1786), % 147.41/21.53 | | | | | | | | (1789), (1791), (1793), (function-axioms) are % 147.41/21.53 | | | | | | | | inconsistent by sub-proof #76. % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | Case 2: % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | (1794) all_20_2 = e1 % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | COMBINE_EQS: (338), (1794) imply: % 147.41/21.53 | | | | | | | | (1795) all_4_2 = e1 % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | SIMP: (1795) implies: % 147.41/21.53 | | | | | | | | (1796) all_4_2 = e1 % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | COMBINE_EQS: (542), (1796) imply: % 147.41/21.53 | | | | | | | | (1797) all_58_31 = e1 % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | | REF_CLOSE: (4), (203), (333), (543), (544), (545), (579), % 147.41/21.53 | | | | | | | | (1785), (1789), (1791), (1797), (function-axioms) are % 147.41/21.53 | | | | | | | | inconsistent by sub-proof #81. % 147.41/21.53 | | | | | | | | % 147.41/21.53 | | | | | | | End of split % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | Case 2: % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | (1798) all_16_2 = e0 % 147.41/21.53 | | | | | | | (1799) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | COMBINE_EQS: (523), (1798) imply: % 147.41/21.53 | | | | | | | (1800) all_10_2 = e0 % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | SIMP: (1800) implies: % 147.41/21.53 | | | | | | | (1801) all_10_2 = e0 % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | COMBINE_EQS: (541), (1801) imply: % 147.41/21.53 | | | | | | | (1802) all_56_0 = e0 % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | COMBINE_EQS: (545), (1801) imply: % 147.41/21.53 | | | | | | | (1803) all_58_28 = e0 % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (551), (1801) imply: % 147.41/21.53 | | | | | | | (1804) ~ (all_52_1 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (553), (1801) imply: % 147.41/21.53 | | | | | | | (1805) ~ (all_52_2 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (555), (1801) imply: % 147.41/21.53 | | | | | | | (1806) ~ (all_52_3 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (557), (1801) imply: % 147.41/21.53 | | | | | | | (1807) ~ (all_52_4 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (559), (1801) imply: % 147.41/21.53 | | | | | | | (1808) ~ (all_52_8 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (561), (1801) imply: % 147.41/21.53 | | | | | | | (1809) ~ (all_52_12 = e0) % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (53), (1801) imply: % 147.41/21.53 | | | | | | | (1810) op(e0, all_10_1) = all_10_0 % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (52), (1801) imply: % 147.41/21.53 | | | | | | | (1811) op(e0, e3) = all_10_1 % 147.41/21.53 | | | | | | | % 147.41/21.53 | | | | | | | REDUCE: (629), (1801) imply: % 147.41/21.53 | | | | | | | (1812) op(e3, e0) = all_58_0 % 147.41/21.53 | | | | | | | % 147.41/21.54 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.41/21.54 | | | | | | | (42), (46), (47), (74), (79), (94), (156), (158), % 147.41/21.54 | | | | | | | (159), (163), (164), (166), (167), (169), (171), (172), % 147.41/21.54 | | | | | | | (174), (179), (180), (181), (182), (185), (186), (187), % 147.41/21.54 | | | | | | | (189), (190), (191), (192), (194), (195), (203), (205), % 147.41/21.54 | | | | | | | (206), (208), (210), (214), (215), (216), (235), (236), % 147.41/21.54 | | | | | | | (237), (238), (239), (240), (241), (242), (243), (245), % 147.41/21.54 | | | | | | | (246), (247), (248), (249), (268), (269), (270), (271), % 147.41/21.54 | | | | | | | (272), (273), (274), (275), (276), (277), (279), (280), % 147.41/21.54 | | | | | | | (281), (282), (283), (284), (285), (286), (287), (288), % 147.41/21.54 | | | | | | | (289), (290), (292), (293), (294), (297), (332), (334), % 147.41/21.54 | | | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 147.41/21.54 | | | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 147.41/21.54 | | | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 147.41/21.54 | | | | | | | (429), (445), (447), (454), (458), (459), (465), (467), % 147.41/21.54 | | | | | | | (468), (470), (471), (473), (519), (527), (535), (536), % 147.41/21.54 | | | | | | | (538), (539), (540), (541), (542), (543), (544), (545), % 147.41/21.54 | | | | | | | (546), (547), (548), (549), (562), (563), (564), (565), % 147.41/21.54 | | | | | | | (567), (569), (571), (573), (574), (575), (576), (577), % 147.41/21.54 | | | | | | | (579), (581), (582), (583), (584), (585), (626), (627), % 147.41/21.54 | | | | | | | (628), (631), (632), (633), (635), (636), (637), (638), % 147.41/21.54 | | | | | | | (639), (641), (671), (691), (771), (774), (781), % 147.41/21.54 | | | | | | | (1786), (1787), (1799), (1802), (1803), (1804), (1805), % 147.41/21.54 | | | | | | | (1806), (1807), (1808), (1809), (1810), (1811), (1812), % 147.41/21.54 | | | | | | | (function-axioms) are inconsistent by sub-proof #400. % 147.41/21.54 | | | | | | | % 147.41/21.54 | | | | | | End of split % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | Case 2: % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | (1813) all_14_2 = e0 % 147.41/21.54 | | | | | | (1814) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | COMBINE_EQS: (525), (1813) imply: % 147.41/21.54 | | | | | | (1815) all_8_2 = e0 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | SIMP: (1815) implies: % 147.41/21.54 | | | | | | (1816) all_8_2 = e0 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | COMBINE_EQS: (540), (1816) imply: % 147.41/21.54 | | | | | | (1817) all_56_3 = e0 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | COMBINE_EQS: (544), (1816) imply: % 147.41/21.54 | | | | | | (1818) all_58_29 = e0 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (562), (1816) imply: % 147.41/21.54 | | | | | | (1819) ~ (all_52_1 = e0) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (565), (1816) imply: % 147.41/21.54 | | | | | | (1820) ~ (all_52_4 = e0) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (567), (1816) imply: % 147.41/21.54 | | | | | | (1821) ~ (all_52_6 = e0) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (569), (1816) imply: % 147.41/21.54 | | | | | | (1822) ~ (all_52_7 = e0) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (571), (1816) imply: % 147.41/21.54 | | | | | | (1823) ~ (all_52_9 = e0) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (573), (1816) imply: % 147.41/21.54 | | | | | | (1824) ~ (all_52_13 = e0) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (48), (1816) imply: % 147.41/21.54 | | | | | | (1825) op(e0, all_8_1) = all_8_0 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (47), (1816) imply: % 147.41/21.54 | | | | | | (1826) op(e0, e2) = all_8_1 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (633), (1816) imply: % 147.41/21.54 | | | | | | (1827) op(e2, e0) = all_58_9 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, all_8_1, % 147.41/21.54 | | | | | | e2, e0, simplifying with (204), (1826) gives: % 147.41/21.54 | | | | | | (1828) all_52_7 = all_8_1 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 147.41/21.54 | | | | | | all_58_9, e0, e2, simplifying with (210), (1827) gives: % 147.41/21.54 | | | | | | (1829) all_58_9 = all_52_13 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | COMBINE_EQS: (471), (1828) imply: % 147.41/21.54 | | | | | | (1830) all_54_13 = all_8_1 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | COMBINE_EQS: (350), (1828) imply: % 147.41/21.54 | | | | | | (1831) all_56_13 = all_8_1 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | COMBINE_EQS: (547), (1828) imply: % 147.41/21.54 | | | | | | (1832) all_58_24 = all_8_1 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (186), (1828) imply: % 147.41/21.54 | | | | | | (1833) ~ (all_52_3 = all_8_1) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (181), (1828) imply: % 147.41/21.54 | | | | | | (1834) ~ (all_52_4 = all_8_1) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (174), (1828) imply: % 147.41/21.54 | | | | | | (1835) ~ (all_52_6 = all_8_1) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (171), (1828) imply: % 147.41/21.54 | | | | | | (1836) ~ (all_52_11 = all_8_1) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | SIMP: (1836) implies: % 147.41/21.54 | | | | | | (1837) ~ (all_52_11 = all_8_1) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (575), (1828) imply: % 147.41/21.54 | | | | | | (1838) ~ (all_8_1 = all_4_2) % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | REDUCE: (639), (1828) imply: % 147.41/21.54 | | | | | | (1839) op(e0, all_8_1) = all_58_23 % 147.41/21.54 | | | | | | % 147.41/21.54 | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 147.41/21.54 | | | | | | all_58_23, all_8_1, e0, simplifying with (1825), (1839) % 147.41/21.54 | | | | | | gives: % 147.41/21.54 | | | | | | (1840) all_58_23 = all_8_0 % 147.41/21.54 | | | | | | % 147.41/21.55 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.41/21.55 | | | | | | (51), (74), (79), (94), (137), (156), (158), (159), % 147.41/21.55 | | | | | | (163), (164), (166), (167), (169), (172), (179), (180), % 147.41/21.55 | | | | | | (182), (185), (187), (189), (190), (191), (192), (194), % 147.41/21.55 | | | | | | (195), (203), (206), (210), (211), (213), (214), (215), % 147.41/21.55 | | | | | | (235), (236), (237), (238), (239), (240), (241), (242), % 147.41/21.55 | | | | | | (243), (244), (246), (247), (248), (249), (250), (268), % 147.41/21.55 | | | | | | (269), (270), (271), (272), (273), (274), (275), (276), % 147.41/21.55 | | | | | | (277), (278), (279), (280), (281), (282), (284), (285), % 147.41/21.55 | | | | | | (286), (288), (289), (290), (291), (292), (293), (294), % 147.41/21.55 | | | | | | (295), (296), (297), (298), (332), (334), (335), (336), % 147.41/21.55 | | | | | | (337), (338), (347), (350), (355), (358), (370), (371), % 147.41/21.55 | | | | | | (376), (379), (391), (392), (397), (400), (411), (413), % 147.41/21.55 | | | | | | (417), (419), (421), (425), (427), (429), (445), (447), % 147.41/21.55 | | | | | | (454), (456), (458), (459), (465), (467), (468), (470), % 147.41/21.55 | | | | | | (473), (519), (529), (535), (536), (537), (538), (539), % 147.41/21.55 | | | | | | (541), (542), (543), (544), (545), (546), (548), (549), % 147.41/21.55 | | | | | | (551), (553), (555), (557), (559), (561), (563), (564), % 147.41/21.55 | | | | | | (574), (576), (577), (579), (581), (582), (583), (584), % 147.41/21.55 | | | | | | (585), (628), (629), (630), (631), (632), (634), (636), % 147.41/21.55 | | | | | | (637), (641), (645), (671), (693), (723), (772), (781), % 147.41/21.55 | | | | | | (1786), (1814), (1817), (1818), (1819), (1820), (1821), % 147.41/21.55 | | | | | | (1822), (1823), (1824), (1825), (1826), (1829), (1830), % 147.41/21.55 | | | | | | (1831), (1832), (1833), (1834), (1835), (1837), (1838), % 147.41/21.55 | | | | | | (1840), (function-axioms) are inconsistent by sub-proof % 147.41/21.55 | | | | | | #254. % 147.41/21.55 | | | | | | % 147.41/21.55 | | | | | End of split % 147.41/21.55 | | | | | % 147.41/21.55 | | | | Case 2: % 147.41/21.55 | | | | | % 147.41/21.55 | | | | | (1841) all_10_0 = e0 % 147.41/21.55 | | | | | % 147.41/21.55 | | | | | REDUCE: (53), (1841) imply: % 147.41/21.55 | | | | | (1842) op(all_10_2, all_10_1) = e0 % 147.41/21.55 | | | | | % 147.41/21.55 | | | | | BETA: splitting (64) gives: % 147.41/21.55 | | | | | % 147.41/21.55 | | | | | Case 1: % 147.41/21.55 | | | | | | % 147.41/21.55 | | | | | | (1843) ~ (all_14_2 = e0) % 147.41/21.55 | | | | | | % 147.41/21.55 | | | | | | REDUCE: (525), (1843) imply: % 147.41/21.55 | | | | | | (1844) ~ (all_8_2 = e0) % 147.41/21.55 | | | | | | % 147.41/21.55 | | | | | | BETA: splitting (79) gives: % 147.41/21.55 | | | | | | % 147.41/21.55 | | | | | | Case 1: % 147.41/21.55 | | | | | | | % 147.41/21.55 | | | | | | | (1845) ~ (all_20_2 = e1) % 147.41/21.55 | | | | | | | % 147.41/21.55 | | | | | | | REDUCE: (338), (1845) imply: % 147.41/21.55 | | | | | | | (1846) ~ (all_4_2 = e1) % 147.41/21.55 | | | | | | | % 147.41/21.55 | | | | | | | BETA: splitting (268) gives: % 147.41/21.55 | | | | | | | % 147.41/21.55 | | | | | | | Case 1: % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | (1847) all_56_15 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | COMBINE_EQS: (538), (1847) imply: % 147.41/21.55 | | | | | | | | (1848) all_4_2 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | SIMP: (1848) implies: % 147.41/21.55 | | | | | | | | (1849) all_4_2 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | COMBINE_EQS: (542), (1849) imply: % 147.41/21.55 | | | | | | | | (1850) all_58_31 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (575), (1849) imply: % 147.41/21.55 | | | | | | | | (1851) ~ (all_52_7 = e0) % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (584), (1849) imply: % 147.41/21.55 | | | | | | | | (1852) ~ (all_52_13 = e0) % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (38), (1849) imply: % 147.41/21.55 | | | | | | | | (1853) op(e0, all_4_1) = all_4_0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (37), (1849) imply: % 147.41/21.55 | | | | | | | | (1854) op(e0, e0) = all_4_1 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (641), (1849) imply: % 147.41/21.55 | | | | | | | | (1855) op(e0, e0) = all_58_27 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (36), (1849) imply: % 147.41/21.55 | | | | | | | | (1856) op(e0, e0) = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, % 147.41/21.55 | | | | | | | | all_58_27, e0, e0, simplifying with (1854), (1855) % 147.41/21.55 | | | | | | | | gives: % 147.41/21.55 | | | | | | | | (1857) all_58_27 = all_4_1 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_58_27, % 147.41/21.55 | | | | | | | | e0, e0, simplifying with (1855), (1856) gives: % 147.41/21.55 | | | | | | | | (1858) all_58_27 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | COMBINE_EQS: (1857), (1858) imply: % 147.41/21.55 | | | | | | | | (1859) all_4_1 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | SIMP: (1859) implies: % 147.41/21.55 | | | | | | | | (1860) all_4_1 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (1853), (1860) imply: % 147.41/21.55 | | | | | | | | (1861) op(e0, e0) = all_4_0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_4_0, % 147.41/21.55 | | | | | | | | e0, e0, simplifying with (1856), (1861) gives: % 147.41/21.55 | | | | | | | | (1862) all_4_0 = e0 % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | REDUCE: (781), (1862) imply: % 147.41/21.55 | | | | | | | | (1863) ~ (e1 = e0) % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | BETA: splitting (283) gives: % 147.41/21.55 | | | | | | | | % 147.41/21.55 | | | | | | | | Case 1: % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | (1864) all_56_2 = e0 % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | COMBINE_EQS: (417), (1864) imply: % 147.41/21.55 | | | | | | | | | (1865) all_52_1 = e0 % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | REDUCE: (551), (1865) imply: % 147.41/21.55 | | | | | | | | | (1866) ~ (all_10_2 = e0) % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | SIMP: (1866) implies: % 147.41/21.55 | | | | | | | | | (1867) ~ (all_10_2 = e0) % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | REDUCE: (562), (1865) imply: % 147.41/21.55 | | | | | | | | | (1868) ~ (all_8_2 = e0) % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.41/21.55 | | | | | | | | | (42), (43), (46), (47), (48), (51), (52), (53), % 147.41/21.55 | | | | | | | | | (108), (118), (127), (142), (156), (158), (159), % 147.41/21.55 | | | | | | | | | (164), (166), (167), (169), (172), (174), (179), % 147.41/21.55 | | | | | | | | | (180), (181), (182), (185), (186), (187), (189), % 147.41/21.55 | | | | | | | | | (190), (191), (192), (194), (195), (203), (206), % 147.41/21.55 | | | | | | | | | (208), (209), (210), (211), (213), (214), (215), % 147.41/21.55 | | | | | | | | | (216), (237), (238), (239), (241), (242), (243), % 147.41/21.55 | | | | | | | | | (244), (246), (248), (249), (250), (268), (269), % 147.41/21.55 | | | | | | | | | (271), (272), (273), (275), (276), (278), (279), % 147.41/21.55 | | | | | | | | | (281), (282), (283), (284), (286), (287), (290), % 147.41/21.55 | | | | | | | | | (291), (293), (294), (295), (296), (297), (298), % 147.41/21.55 | | | | | | | | | (332), (333), (334), (335), (337), (347), (350), % 147.41/21.55 | | | | | | | | | (360), (371), (392), (411), (413), (417), (419), % 147.41/21.55 | | | | | | | | | (421), (425), (427), (429), (445), (447), (454), % 147.41/21.55 | | | | | | | | | (456), (458), (459), (467), (468), (470), (471), % 147.41/21.55 | | | | | | | | | (507), (509), (537), (538), (539), (540), (541), % 147.41/21.55 | | | | | | | | | (542), (543), (544), (545), (551), (553), (555), % 147.41/21.55 | | | | | | | | | (557), (559), (561), (562), (563), (564), (565), % 147.41/21.55 | | | | | | | | | (567), (569), (571), (573), (574), (575), (576), % 147.41/21.55 | | | | | | | | | (577), (579), (581), (582), (584), (585), (626), % 147.41/21.55 | | | | | | | | | (627), (629), (630), (631), (633), (634), (635), % 147.41/21.55 | | | | | | | | | (637), (641), (648), (696), (727), (775), (776), % 147.41/21.55 | | | | | | | | | (778), (781), (1782), (1783), (1784), (1785), % 147.41/21.55 | | | | | | | | | (1786), (1844), (1846), (1867), (function-axioms) % 147.41/21.55 | | | | | | | | | are inconsistent by sub-proof #76. % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | Case 2: % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | (1869) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | BETA: splitting (1869) gives: % 147.41/21.55 | | | | | | | | | % 147.41/21.55 | | | | | | | | | Case 1: % 147.41/21.55 | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | (1870) all_56_3 = e0 % 147.41/21.55 | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.41/21.55 | | | | | | | | | | (540), (543), (544), (1850), (1870) are % 147.41/21.55 | | | | | | | | | | inconsistent by sub-proof #804. % 147.41/21.55 | | | | | | | | | | % 147.41/21.55 | | | | | | | | | Case 2: % 147.41/21.55 | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | (1871) all_56_5 = e0 | all_56_10 = e0 % 147.41/21.55 | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | BETA: splitting (1871) gives: % 147.41/21.55 | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | Case 1: % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | (1872) all_56_5 = e0 % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | COMBINE_EQS: (419), (1872) imply: % 147.41/21.55 | | | | | | | | | | | (1873) all_52_9 = e0 % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | SIMP: (1873) implies: % 147.41/21.55 | | | | | | | | | | | (1874) all_52_9 = e0 % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | REDUCE: (164), (1874) imply: % 147.41/21.55 | | | | | | | | | | | (1875) ~ (all_52_11 = e0) % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | SIMP: (1875) implies: % 147.41/21.55 | | | | | | | | | | | (1876) ~ (all_52_11 = e0) % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | REDUCE: (571), (1874) imply: % 147.41/21.55 | | | | | | | | | | | (1877) ~ (all_8_2 = e0) % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | REDUCE: (577), (1874) imply: % 147.41/21.55 | | | | | | | | | | | (1878) ~ (all_6_2 = e0) % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | SIMP: (1878) implies: % 147.41/21.55 | | | | | | | | | | | (1879) ~ (all_6_2 = e0) % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | REDUCE: (631), (1874) imply: % 147.41/21.55 | | | | | | | | | | | (1880) op(e2, e0) = all_58_10 % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 147.41/21.55 | | | | | | | | | | | all_58_10, e0, e2, simplifying with (210), (1880) % 147.41/21.55 | | | | | | | | | | | gives: % 147.41/21.55 | | | | | | | | | | | (1881) all_58_10 = all_52_13 % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | BETA: splitting (291) gives: % 147.41/21.55 | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | Case 1: % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | (1882) all_56_0 = e0 % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | COMBINE_EQS: (541), (1882) imply: % 147.41/21.55 | | | | | | | | | | | | (1883) all_10_2 = e0 % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | SIMP: (1883) implies: % 147.41/21.55 | | | | | | | | | | | | (1884) all_10_2 = e0 % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | REDUCE: (555), (1884) imply: % 147.41/21.55 | | | | | | | | | | | | (1885) ~ (all_52_3 = e0) % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | REDUCE: (559), (1884) imply: % 147.41/21.55 | | | | | | | | | | | | (1886) ~ (all_52_8 = e0) % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | REDUCE: (1842), (1884) imply: % 147.41/21.55 | | | | | | | | | | | | (1887) op(e0, all_10_1) = e0 % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | REDUCE: (52), (1884) imply: % 147.41/21.55 | | | | | | | | | | | | (1888) op(e0, e3) = all_10_1 % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.55 | | | | | | | | | | | | REF_CLOSE: (164), (203), (204), (205), (238), (269), (270), % 147.41/21.55 | | | | | | | | | | | | (279), (347), (413), (419), (429), (470), (539), % 147.41/21.55 | | | | | | | | | | | | (638), (1851), (1876), (1879), (1885), (1886), % 147.41/21.55 | | | | | | | | | | | | (1887), (1888), (function-axioms) are inconsistent % 147.41/21.55 | | | | | | | | | | | | by sub-proof #234. % 147.41/21.55 | | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | Case 2: % 147.41/21.56 | | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | | (1889) ~ (all_56_0 = e0) % 147.41/21.56 | | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | | REDUCE: (541), (1889) imply: % 147.41/21.56 | | | | | | | | | | | | (1890) ~ (all_10_2 = e0) % 147.41/21.56 | | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.41/21.56 | | | | | | | | | | | | (42), (43), (46), (47), (48), (51), (52), (53), % 147.41/21.56 | | | | | | | | | | | | (108), (118), (127), (142), (156), (158), (159), % 147.41/21.56 | | | | | | | | | | | | (164), (166), (167), (169), (172), (174), (179), % 147.41/21.56 | | | | | | | | | | | | (180), (181), (182), (185), (186), (187), (189), % 147.41/21.56 | | | | | | | | | | | | (190), (191), (192), (194), (195), (203), (206), % 147.41/21.56 | | | | | | | | | | | | (208), (209), (210), (211), (213), (214), (215), % 147.41/21.56 | | | | | | | | | | | | (216), (237), (238), (239), (241), (242), (243), % 147.41/21.56 | | | | | | | | | | | | (244), (246), (248), (249), (250), (268), (269), % 147.41/21.56 | | | | | | | | | | | | (271), (272), (273), (275), (276), (278), (279), % 147.41/21.56 | | | | | | | | | | | | (281), (282), (283), (284), (286), (287), (290), % 147.41/21.56 | | | | | | | | | | | | (291), (293), (294), (295), (296), (297), (298), % 147.41/21.56 | | | | | | | | | | | | (332), (333), (334), (335), (337), (347), (350), % 147.41/21.56 | | | | | | | | | | | | (360), (371), (392), (411), (413), (417), (419), % 147.41/21.56 | | | | | | | | | | | | (421), (425), (427), (429), (445), (447), (454), % 147.41/21.56 | | | | | | | | | | | | (456), (458), (459), (467), (468), (470), (471), % 147.41/21.56 | | | | | | | | | | | | (507), (509), (537), (538), (539), (540), (541), % 147.41/21.56 | | | | | | | | | | | | (542), (543), (544), (545), (551), (553), (555), % 147.41/21.56 | | | | | | | | | | | | (557), (559), (561), (562), (563), (564), (565), % 147.41/21.56 | | | | | | | | | | | | (567), (569), (571), (573), (574), (575), (576), % 147.41/21.56 | | | | | | | | | | | | (577), (579), (581), (582), (584), (585), (626), % 147.41/21.56 | | | | | | | | | | | | (627), (629), (630), (631), (633), (634), (635), % 147.41/21.56 | | | | | | | | | | | | (637), (641), (648), (696), (727), (775), (776), % 147.41/21.56 | | | | | | | | | | | | (778), (781), (1782), (1783), (1784), (1785), % 147.41/21.56 | | | | | | | | | | | | (1786), (1844), (1846), (1890), (function-axioms) % 147.41/21.56 | | | | | | | | | | | | are inconsistent by sub-proof #76. % 147.41/21.56 | | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | End of split % 147.41/21.56 | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | Case 2: % 147.41/21.56 | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | (1891) all_56_10 = e0 % 147.41/21.56 | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | COMBINE_EQS: (421), (1891) imply: % 147.41/21.56 | | | | | | | | | | | (1892) all_52_13 = e0 % 147.41/21.56 | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | REDUCE: (1852), (1892) imply: % 147.41/21.56 | | | | | | | | | | | (1893) $false % 147.41/21.56 | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | | CLOSE: (1893) is inconsistent. % 147.41/21.56 | | | | | | | | | | | % 147.41/21.56 | | | | | | | | | | End of split % 147.41/21.56 | | | | | | | | | | % 147.41/21.56 | | | | | | | | | End of split % 147.41/21.56 | | | | | | | | | % 147.41/21.56 | | | | | | | | End of split % 147.41/21.56 | | | | | | | | % 147.41/21.56 | | | | | | | Case 2: % 147.41/21.56 | | | | | | | | % 147.41/21.56 | | | | | | | | (1894) ~ (all_56_15 = e0) % 147.41/21.56 | | | | | | | | (1895) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 147.41/21.56 | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 147.41/21.56 | | | | | | | | % 147.41/21.56 | | | | | | | | ALPHA: (1895) implies: % 147.41/21.56 | | | | | | | | (1896) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 147.41/21.56 | | | | | | | | (1897) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 147.41/21.56 | | | | | | | | % 147.41/21.56 | | | | | | | | REDUCE: (538), (1894) imply: % 147.41/21.56 | | | | | | | | (1898) ~ (all_4_2 = e0) % 147.41/21.56 | | | | | | | | % 147.41/21.56 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (79), (156), % 147.41/21.56 | | | | | | | | (158), (159), (163), (164), (166), (167), (171), % 147.41/21.56 | | | | | | | | (172), (174), (179), (180), (181), (182), (185), % 147.41/21.56 | | | | | | | | (186), (187), (190), (191), (203), (204), (205), % 147.41/21.56 | | | | | | | | (237), (238), (239), (241), (245), (248), (249), % 147.41/21.56 | | | | | | | | (269), (270), (271), (272), (274), (275), (276), % 147.41/21.56 | | | | | | | | (279), (281), (282), (283), (287), (288), (289), % 147.41/21.56 | | | | | | | | (290), (293), (294), (298), (333), (334), (335), % 147.41/21.56 | | | | | | | | (336), (337), (338), (347), (350), (355), (358), % 147.41/21.56 | | | | | | | | (370), (371), (376), (379), (381), (392), (397), % 147.41/21.56 | | | | | | | | (411), (413), (417), (419), (421), (425), (427), % 147.41/21.56 | | | | | | | | (429), (445), (454), (459), (468), (470), (471), % 147.41/21.56 | | | | | | | | (538), (539), (540), (541), (542), (543), (544), % 147.41/21.56 | | | | | | | | (545), (546), (547), (548), (549), (551), (553), % 147.41/21.56 | | | | | | | | (555), (557), (559), (561), (563), (564), (565), % 147.41/21.56 | | | | | | | | (567), (569), (571), (573), (574), (575), (576), % 147.41/21.56 | | | | | | | | (579), (581), (582), (583), (584), (585), (638), % 147.41/21.56 | | | | | | | | (1785), (1842), (1844), (1846), (1896), (1897), % 147.41/21.56 | | | | | | | | (1898), (function-axioms) are inconsistent by % 147.41/21.56 | | | | | | | | sub-proof #73. % 147.41/21.56 | | | | | | | | % 147.41/21.56 | | | | | | | End of split % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | Case 2: % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | (1899) all_20_2 = e1 % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | COMBINE_EQS: (338), (1899) imply: % 147.41/21.56 | | | | | | | (1900) all_4_2 = e1 % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | SIMP: (1900) implies: % 147.41/21.56 | | | | | | | (1901) all_4_2 = e1 % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | COMBINE_EQS: (538), (1901) imply: % 147.41/21.56 | | | | | | | (1902) all_56_15 = e1 % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | COMBINE_EQS: (542), (1901) imply: % 147.41/21.56 | | | | | | | (1903) all_58_31 = e1 % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | REDUCE: (564), (1901) imply: % 147.41/21.56 | | | | | | | (1904) ~ (all_52_3 = e1) % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | REDUCE: (582), (1901) imply: % 147.41/21.56 | | | | | | | (1905) ~ (all_52_11 = e1) % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | REDUCE: (583), (1901) imply: % 147.41/21.56 | | | | | | | (1906) ~ (all_52_12 = e1) % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | REDUCE: (584), (1901) imply: % 147.41/21.56 | | | | | | | (1907) ~ (all_52_13 = e1) % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | REDUCE: (38), (1901) imply: % 147.41/21.56 | | | | | | | (1908) op(e1, all_4_1) = all_4_0 % 147.41/21.56 | | | | | | | % 147.41/21.56 | | | | | | | REDUCE: (37), (1901) imply: % 147.41/21.56 | | | | | | | (1909) op(e1, e0) = all_4_1 % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | REDUCE: (641), (1901) imply: % 147.41/21.57 | | | | | | | (1910) op(e0, e1) = all_58_27 % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 147.41/21.57 | | | | | | | all_58_27, e1, e0, simplifying with (203), (1910) % 147.41/21.57 | | | | | | | gives: % 147.41/21.57 | | | | | | | (1911) all_58_27 = all_52_11 % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 147.41/21.57 | | | | | | | all_4_1, e0, e1, simplifying with (206), (1909) % 147.41/21.57 | | | | | | | gives: % 147.41/21.57 | | | | | | | (1912) all_52_14 = all_4_1 % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | REDUCE: (636), (1912) imply: % 147.41/21.57 | | | | | | | (1913) op(e1, all_4_1) = all_58_19 % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_0, % 147.41/21.57 | | | | | | | all_58_19, all_4_1, e1, simplifying with (1908), % 147.41/21.57 | | | | | | | (1913) gives: % 147.41/21.57 | | | | | | | (1914) all_58_19 = all_4_0 % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | BETA: splitting (243) gives: % 147.41/21.57 | | | | | | | % 147.41/21.57 | | | | | | | Case 1: % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | (1915) all_54_7 = e0 % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | COMBINE_EQS: (467), (1915) imply: % 147.41/21.57 | | | | | | | | (1916) all_52_13 = e0 % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | SIMP: (1916) implies: % 147.41/21.57 | | | | | | | | (1917) all_52_13 = e0 % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | REDUCE: (191), (1917) imply: % 147.41/21.57 | | | | | | | | (1918) ~ (all_52_1 = e0) % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | REDUCE: (163), (1917) imply: % 147.41/21.57 | | | | | | | | (1919) ~ (all_52_9 = e0) % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | REDUCE: (159), (1917) imply: % 147.41/21.57 | | | | | | | | (1920) ~ (all_52_12 = e0) % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | REDUCE: (573), (1917) imply: % 147.41/21.57 | | | | | | | | (1921) ~ (all_8_2 = e0) % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | REDUCE: (1907), (1917) imply: % 147.41/21.57 | | | | | | | | (1922) ~ (e1 = e0) % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | BETA: splitting (247) gives: % 147.41/21.57 | | | | | | | | % 147.41/21.57 | | | | | | | | Case 1: % 147.41/21.57 | | | | | | | | | % 147.41/21.57 | | | | | | | | | (1923) all_54_3 = e0 % 147.41/21.57 | | | | | | | | | % 147.41/21.57 | | | | | | | | | REF_CLOSE: (465), (1920), (1923) are inconsistent by sub-proof % 147.41/21.57 | | | | | | | | | #733. % 147.41/21.57 | | | | | | | | | % 147.41/21.57 | | | | | | | | Case 2: % 147.41/21.57 | | | | | | | | | % 147.41/21.57 | | | | | | | | | (1924) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 147.41/21.57 | | | | | | | | | % 147.41/21.57 | | | | | | | | | BETA: splitting (236) gives: % 147.41/21.57 | | | | | | | | | % 147.41/21.57 | | | | | | | | | Case 1: % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | (1925) all_54_14 = e0 % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | COMBINE_EQS: (473), (1925) imply: % 147.41/21.57 | | | | | | | | | | (1926) all_52_11 = e0 % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | SIMP: (1926) implies: % 147.41/21.57 | | | | | | | | | | (1927) all_52_11 = e0 % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | REDUCE: (579), (1927) imply: % 147.41/21.57 | | | | | | | | | | (1928) ~ (all_6_2 = e0) % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | SIMP: (1928) implies: % 147.41/21.57 | | | | | | | | | | (1929) ~ (all_6_2 = e0) % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (158), (159), % 147.41/21.57 | | | | | | | | | | (163), (164), (166), (167), (169), (171), (174), % 147.41/21.57 | | | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 147.41/21.57 | | | | | | | | | | (189), (190), (192), (194), (195), (203), (204), % 147.41/21.57 | | | | | | | | | | (205), (206), (236), (238), (242), (243), (245), % 147.41/21.57 | | | | | | | | | | (247), (249), (268), (269), (270), (271), (273), % 147.41/21.57 | | | | | | | | | | (274), (275), (276), (277), (278), (279), (280), % 147.41/21.57 | | | | | | | | | | (283), (284), (286), (288), (289), (292), (333), % 147.41/21.57 | | | | | | | | | | (334), (335), (336), (337), (347), (350), (355), % 147.41/21.57 | | | | | | | | | | (358), (370), (371), (376), (379), (381), (391), % 147.41/21.57 | | | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 147.41/21.57 | | | | | | | | | | (421), (425), (427), (429), (445), (458), (465), % 147.41/21.57 | | | | | | | | | | (467), (470), (473), (539), (540), (541), (543), % 147.41/21.57 | | | | | | | | | | (544), (545), (546), (547), (548), (549), (551), % 147.41/21.57 | | | | | | | | | | (553), (555), (559), (561), (562), (563), (565), % 147.41/21.57 | | | | | | | | | | (567), (573), (579), (581), (636), (638), (781), % 147.41/21.57 | | | | | | | | | | (1842), (1844), (1902), (1903), (1904), (1905), % 147.41/21.57 | | | | | | | | | | (1907), (1908), (1909), (1910), (1929), % 147.41/21.57 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.41/21.57 | | | | | | | | | | #191. % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | Case 2: % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | (1930) ~ (all_54_14 = e0) % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | REDUCE: (473), (1930) imply: % 147.41/21.57 | | | | | | | | | | (1931) ~ (all_52_11 = e0) % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | BETA: splitting (279) gives: % 147.41/21.57 | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | Case 1: % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | (1932) all_56_4 = e0 % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | COMBINE_EQS: (413), (1932) imply: % 147.41/21.57 | | | | | | | | | | | (1933) all_52_8 = e0 % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | REDUCE: (576), (1933) imply: % 147.41/21.57 | | | | | | | | | | | (1934) ~ (all_6_2 = e0) % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | SIMP: (1934) implies: % 147.41/21.57 | | | | | | | | | | | (1935) ~ (all_6_2 = e0) % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (158), (159), % 147.41/21.57 | | | | | | | | | | | (163), (164), (166), (167), (169), (171), (174), % 147.41/21.57 | | | | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 147.41/21.57 | | | | | | | | | | | (189), (190), (192), (194), (195), (203), (204), % 147.41/21.57 | | | | | | | | | | | (205), (206), (236), (238), (242), (243), (245), % 147.41/21.57 | | | | | | | | | | | (247), (249), (268), (269), (270), (271), (273), % 147.41/21.57 | | | | | | | | | | | (274), (275), (276), (277), (278), (279), (280), % 147.41/21.57 | | | | | | | | | | | (283), (284), (286), (288), (289), (292), (333), % 147.41/21.57 | | | | | | | | | | | (334), (335), (336), (337), (347), (350), (355), % 147.41/21.57 | | | | | | | | | | | (358), (370), (371), (376), (379), (381), (391), % 147.41/21.57 | | | | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 147.41/21.57 | | | | | | | | | | | (421), (425), (427), (429), (445), (458), (465), % 147.41/21.57 | | | | | | | | | | | (467), (470), (473), (539), (540), (541), (543), % 147.41/21.57 | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (551), % 147.41/21.57 | | | | | | | | | | | (553), (555), (559), (561), (562), (563), (565), % 147.41/21.57 | | | | | | | | | | | (567), (573), (579), (581), (636), (638), (781), % 147.41/21.57 | | | | | | | | | | | (1842), (1844), (1902), (1903), (1904), (1905), % 147.41/21.57 | | | | | | | | | | | (1907), (1908), (1909), (1910), (1935), % 147.41/21.57 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.41/21.57 | | | | | | | | | | | #191. % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | Case 2: % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | (1936) ~ (all_56_4 = e0) % 147.41/21.57 | | | | | | | | | | | (1937) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | REDUCE: (413), (1936) imply: % 147.41/21.57 | | | | | | | | | | | (1938) ~ (all_52_8 = e0) % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | BETA: splitting (1937) gives: % 147.41/21.57 | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | Case 1: % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | (1939) all_56_5 = e0 % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | COMBINE_EQS: (419), (1939) imply: % 147.41/21.57 | | | | | | | | | | | | (1940) all_52_9 = e0 % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | REDUCE: (1919), (1940) imply: % 147.41/21.57 | | | | | | | | | | | | (1941) $false % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | CLOSE: (1941) is inconsistent. % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | Case 2: % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | (1942) ~ (all_56_5 = e0) % 147.41/21.57 | | | | | | | | | | | | (1943) all_56_8 = e0 | all_56_14 = e0 % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | BETA: splitting (1943) gives: % 147.41/21.57 | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | Case 1: % 147.41/21.57 | | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | | (1944) all_56_8 = e0 % 147.41/21.57 | | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | | COMBINE_EQS: (539), (1944) imply: % 147.41/21.57 | | | | | | | | | | | | | (1945) all_6_2 = e0 % 147.41/21.57 | | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | | COMBINE_EQS: (543), (1945) imply: % 147.41/21.57 | | | | | | | | | | | | | (1946) all_58_30 = e0 % 147.41/21.57 | | | | | | | | | | | | | % 147.41/21.57 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (47), (51), (52), (159), % 147.41/21.57 | | | | | | | | | | | | | (179), (216), (273), (274), (283), (287), (292), % 147.41/21.57 | | | | | | | | | | | | | (335), (337), (392), (411), (413), (417), (419), % 147.41/21.57 | | | | | | | | | | | | | (421), (465), (540), (541), (544), (545), (557), % 147.41/21.57 | | | | | | | | | | | | | (561), (629), (1786), (1842), (1844), (1903), % 147.41/21.57 | | | | | | | | | | | | | (1906), (1918), (1919), (1924), (1938), (1946), % 147.41/21.57 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.41/21.57 | | | | | | | | | | | | | #175. % 147.41/21.57 | | | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | | Case 2: % 147.41/21.58 | | | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | | | (1947) all_56_14 = e0 % 147.41/21.58 | | | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | | | REF_CLOSE: (347), (1931), (1947) are inconsistent by % 147.41/21.58 | | | | | | | | | | | | | sub-proof #806. % 147.41/21.58 | | | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | | End of split % 147.41/21.58 | | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | End of split % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | End of split % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | End of split % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | End of split % 147.41/21.58 | | | | | | | | % 147.41/21.58 | | | | | | | Case 2: % 147.41/21.58 | | | | | | | | % 147.41/21.58 | | | | | | | | (1948) ~ (all_54_7 = e0) % 147.41/21.58 | | | | | | | | % 147.41/21.58 | | | | | | | | REDUCE: (467), (1948) imply: % 147.41/21.58 | | | | | | | | (1949) ~ (all_52_13 = e0) % 147.41/21.58 | | | | | | | | % 147.41/21.58 | | | | | | | | BETA: splitting (283) gives: % 147.41/21.58 | | | | | | | | % 147.41/21.58 | | | | | | | | Case 1: % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | (1950) all_56_2 = e0 % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | COMBINE_EQS: (417), (1950) imply: % 147.41/21.58 | | | | | | | | | (1951) all_52_1 = e0 % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | REDUCE: (551), (1951) imply: % 147.41/21.58 | | | | | | | | | (1952) ~ (all_10_2 = e0) % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | SIMP: (1952) implies: % 147.41/21.58 | | | | | | | | | (1953) ~ (all_10_2 = e0) % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | REDUCE: (562), (1951) imply: % 147.41/21.58 | | | | | | | | | (1954) ~ (all_8_2 = e0) % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | REF_CLOSE: (4), (203), (333), (543), (544), (545), (579), % 147.41/21.58 | | | | | | | | | (1785), (1844), (1903), (1953), (function-axioms) % 147.41/21.58 | | | | | | | | | are inconsistent by sub-proof #81. % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | Case 2: % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | (1955) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | BETA: splitting (1955) gives: % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | | Case 1: % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | (1956) all_56_3 = e0 % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | COMBINE_EQS: (540), (1956) imply: % 147.41/21.58 | | | | | | | | | | (1957) all_8_2 = e0 % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | REDUCE: (1844), (1957) imply: % 147.41/21.58 | | | | | | | | | | (1958) $false % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | CLOSE: (1958) is inconsistent. % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | Case 2: % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | (1959) all_56_5 = e0 | all_56_10 = e0 % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | BETA: splitting (1959) gives: % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | Case 1: % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | (1960) all_56_5 = e0 % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | COMBINE_EQS: (419), (1960) imply: % 147.41/21.58 | | | | | | | | | | | (1961) all_52_9 = e0 % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | REDUCE: (571), (1961) imply: % 147.41/21.58 | | | | | | | | | | | (1962) ~ (all_8_2 = e0) % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | REDUCE: (577), (1961) imply: % 147.41/21.58 | | | | | | | | | | | (1963) ~ (all_6_2 = e0) % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | SIMP: (1963) implies: % 147.41/21.58 | | | | | | | | | | | (1964) ~ (all_6_2 = e0) % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (52), (158), (159), % 147.41/21.58 | | | | | | | | | | | (163), (164), (166), (167), (169), (171), (174), % 147.41/21.58 | | | | | | | | | | | (179), (180), (181), (182), (185), (186), (187), % 147.41/21.58 | | | | | | | | | | | (189), (190), (192), (194), (195), (203), (204), % 147.41/21.58 | | | | | | | | | | | (205), (206), (236), (238), (242), (243), (245), % 147.41/21.58 | | | | | | | | | | | (247), (249), (268), (269), (270), (271), (273), % 147.41/21.58 | | | | | | | | | | | (274), (275), (276), (277), (278), (279), (280), % 147.41/21.58 | | | | | | | | | | | (283), (284), (286), (288), (289), (292), (333), % 147.41/21.58 | | | | | | | | | | | (334), (335), (336), (337), (347), (350), (355), % 147.41/21.58 | | | | | | | | | | | (358), (370), (371), (376), (379), (381), (391), % 147.41/21.58 | | | | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 147.41/21.58 | | | | | | | | | | | (421), (425), (427), (429), (445), (458), (465), % 147.41/21.58 | | | | | | | | | | | (467), (470), (473), (539), (540), (541), (543), % 147.41/21.58 | | | | | | | | | | | (544), (545), (546), (547), (548), (549), (551), % 147.41/21.58 | | | | | | | | | | | (553), (555), (559), (561), (562), (563), (565), % 147.41/21.58 | | | | | | | | | | | (567), (573), (579), (581), (636), (638), (781), % 147.41/21.58 | | | | | | | | | | | (1842), (1844), (1902), (1903), (1904), (1905), % 147.41/21.58 | | | | | | | | | | | (1907), (1908), (1909), (1910), (1964), % 147.41/21.58 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.41/21.58 | | | | | | | | | | | #191. % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | Case 2: % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | (1965) all_56_10 = e0 % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | | REF_CLOSE: (421), (1949), (1965) are inconsistent by % 147.41/21.58 | | | | | | | | | | | sub-proof #526. % 147.41/21.58 | | | | | | | | | | | % 147.41/21.58 | | | | | | | | | | End of split % 147.41/21.58 | | | | | | | | | | % 147.41/21.58 | | | | | | | | | End of split % 147.41/21.58 | | | | | | | | | % 147.41/21.58 | | | | | | | | End of split % 147.41/21.58 | | | | | | | | % 147.41/21.58 | | | | | | | End of split % 147.41/21.58 | | | | | | | % 147.41/21.58 | | | | | | End of split % 147.41/21.58 | | | | | | % 147.41/21.58 | | | | | Case 2: % 147.41/21.58 | | | | | | % 147.41/21.58 | | | | | | (1966) all_14_2 = e0 % 147.41/21.58 | | | | | | (1967) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 147.41/21.58 | | | | | | % 147.41/21.58 | | | | | | COMBINE_EQS: (525), (1966) imply: % 147.41/21.58 | | | | | | (1968) all_8_2 = e0 % 147.41/21.58 | | | | | | % 147.41/21.59 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (37), (41), (47), (48), % 147.41/21.59 | | | | | | (51), (52), (74), (79), (156), (158), (159), (163), % 147.41/21.59 | | | | | | (164), (166), (167), (169), (171), (172), (174), (179), % 147.41/21.59 | | | | | | (180), (181), (182), (185), (186), (187), (189), (190), % 147.41/21.59 | | | | | | (191), (192), (194), (195), (203), (204), (206), (210), % 147.41/21.59 | | | | | | (211), (213), (214), (215), (235), (236), (237), (238), % 147.41/21.59 | | | | | | (239), (240), (241), (242), (243), (244), (246), (247), % 147.41/21.59 | | | | | | (248), (249), (250), (268), (269), (270), (271), (272), % 147.41/21.59 | | | | | | (273), (274), (275), (276), (277), (278), (279), (280), % 147.41/21.59 | | | | | | (281), (282), (284), (285), (286), (288), (290), (291), % 147.41/21.59 | | | | | | (292), (293), (294), (295), (296), (297), (298), (332), % 147.41/21.59 | | | | | | (334), (335), (336), (337), (338), (347), (350), (355), % 147.41/21.59 | | | | | | (358), (370), (371), (376), (379), (391), (392), (397), % 147.41/21.59 | | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 147.41/21.59 | | | | | | (429), (445), (447), (454), (456), (458), (459), (465), % 147.41/21.59 | | | | | | (467), (468), (470), (471), (473), (519), (535), (536), % 147.41/21.59 | | | | | | (537), (538), (539), (540), (541), (542), (543), (544), % 147.41/21.59 | | | | | | (545), (546), (547), (548), (549), (551), (553), (555), % 147.41/21.59 | | | | | | (557), (559), (561), (562), (563), (564), (565), (567), % 147.41/21.59 | | | | | | (569), (571), (573), (574), (575), (576), (577), (579), % 147.41/21.59 | | | | | | (581), (582), (583), (584), (585), (628), (629), (630), % 147.41/21.59 | | | | | | (633), (634), (636), (637), (639), (641), (693), (772), % 147.41/21.59 | | | | | | (1842), (1967), (1968), (function-axioms) are % 147.41/21.59 | | | | | | inconsistent by sub-proof #72. % 147.41/21.59 | | | | | | % 147.41/21.59 | | | | | End of split % 147.41/21.59 | | | | | % 147.41/21.59 | | | | End of split % 147.41/21.59 | | | | % 147.41/21.59 | | | Case 2: % 147.41/21.59 | | | | % 147.41/21.59 | | | | (1969) all_8_1 = e0 % 147.41/21.59 | | | | (1970) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 147.41/21.59 | | | | % 147.41/21.59 | | | | COMBINE_EQS: (686), (1969) imply: % 147.41/21.59 | | | | (1971) all_22_1 = e0 % 147.41/21.59 | | | | % 147.41/21.59 | | | | REDUCE: (48), (1969) imply: % 147.41/21.59 | | | | (1972) op(all_8_2, e0) = all_8_0 % 147.41/21.59 | | | | % 147.41/21.59 | | | | REDUCE: (47), (1969) imply: % 147.41/21.59 | | | | (1973) op(all_8_2, e2) = e0 % 147.41/21.59 | | | | % 147.41/21.59 | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), (42), % 147.41/21.59 | | | | (46), (51), (52), (53), (54), (69), (74), (79), (84), (108), % 147.41/21.59 | | | | (156), (158), (159), (163), (164), (166), (167), (169), % 147.41/21.59 | | | | (171), (172), (174), (179), (180), (181), (182), (185), % 147.41/21.59 | | | | (186), (187), (189), (190), (191), (192), (194), (195), % 147.41/21.59 | | | | (203), (204), (205), (206), (208), (209), (210), (211), % 147.41/21.59 | | | | (214), (215), (216), (236), (237), (238), (241), (242), % 147.41/21.59 | | | | (243), (244), (245), (246), (247), (248), (249), (250), % 147.41/21.59 | | | | (268), (269), (270), (271), (272), (273), (274), (275), % 147.41/21.59 | | | | (276), (277), (278), (279), (280), (281), (282), (283), % 147.41/21.59 | | | | (284), (285), (286), (287), (288), (289), (291), (292), % 147.41/21.59 | | | | (293), (294), (295), (296), (297), (298), (332), (333), % 147.41/21.59 | | | | (334), (335), (336), (337), (338), (347), (350), (355), % 147.41/21.59 | | | | (358), (370), (371), (376), (379), (381), (391), (392), % 147.41/21.59 | | | | (397), (400), (411), (413), (417), (419), (421), (425), % 147.41/21.59 | | | | (427), (429), (445), (447), (454), (456), (458), (459), % 147.41/21.59 | | | | (465), (467), (470), (471), (473), (517), (519), (523), % 147.41/21.59 | | | | (537), (538), (539), (540), (541), (542), (543), (544), % 147.41/21.59 | | | | (545), (546), (547), (548), (549), (551), (553), (555), % 147.41/21.59 | | | | (557), (559), (561), (562), (563), (564), (565), (567), % 147.41/21.59 | | | | (569), (571), (573), (574), (575), (576), (577), (579), % 147.41/21.59 | | | | (581), (582), (583), (584), (585), (626), (628), (629), % 147.41/21.59 | | | | (630), (631), (632), (633), (634), (635), (636), (637), % 147.41/21.59 | | | | (638), (641), (691), (696), (766), (771), (781), (1970), % 147.41/21.59 | | | | (1971), (1972), (1973), (function-axioms) are inconsistent by % 147.41/21.59 | | | | sub-proof #84. % 147.41/21.59 | | | | % 147.41/21.59 | | | End of split % 147.41/21.59 | | | % 147.41/21.59 | | End of split % 147.41/21.59 | | % 147.41/21.59 | Case 2: % 147.41/21.59 | | % 147.41/21.59 | | (1974) all_4_0 = e1 % 147.41/21.59 | | % 147.41/21.59 | | COMBINE_EQS: (773), (1974) imply: % 147.41/21.59 | | (1975) all_12_0 = e1 % 147.41/21.59 | | % 147.41/21.59 | | REDUCE: (38), (1974) imply: % 147.41/21.59 | | (1976) op(all_4_2, all_4_1) = e1 % 147.41/21.59 | | % 147.41/21.59 | | BETA: splitting (44) gives: % 147.41/21.59 | | % 147.41/21.59 | | Case 1: % 147.41/21.59 | | | % 147.41/21.59 | | | (1977) ~ (all_6_1 = e0) % 147.41/21.59 | | | % 147.41/21.59 | | | BETA: splitting (49) gives: % 147.41/21.59 | | | % 147.41/21.59 | | | Case 1: % 147.41/21.59 | | | | % 147.41/21.59 | | | | (1978) ~ (all_8_1 = e0) % 147.41/21.59 | | | | % 147.41/21.59 | | | | BETA: splitting (54) gives: % 147.41/21.59 | | | | % 147.41/21.59 | | | | Case 1: % 147.41/21.59 | | | | | % 147.41/21.59 | | | | | (1979) ~ (all_10_0 = e0) % 147.41/21.59 | | | | | % 147.41/21.59 | | | | | BETA: splitting (64) gives: % 147.41/21.59 | | | | | % 147.41/21.59 | | | | | Case 1: % 147.41/21.59 | | | | | | % 147.41/21.59 | | | | | | (1980) ~ (all_14_2 = e0) % 147.41/21.59 | | | | | | % 147.41/21.59 | | | | | | REDUCE: (525), (1980) imply: % 147.41/21.59 | | | | | | (1981) ~ (all_8_2 = e0) % 147.41/21.59 | | | | | | % 147.41/21.60 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.41/21.60 | | | | | | (42), (43), (46), (47), (51), (52), (53), (69), (74), % 147.41/21.60 | | | | | | (79), (94), (113), (137), (152), (156), (158), (159), % 147.41/21.60 | | | | | | (163), (164), (166), (167), (169), (171), (172), (174), % 147.41/21.60 | | | | | | (179), (180), (181), (182), (185), (186), (187), (189), % 147.41/21.60 | | | | | | (190), (191), (192), (194), (195), (203), (204), (205), % 147.41/21.60 | | | | | | (206), (208), (209), (210), (211), (214), (215), (216), % 147.41/21.60 | | | | | | (235), (236), (237), (238), (239), (240), (241), (242), % 147.41/21.60 | | | | | | (243), (244), (245), (246), (247), (248), (249), (250), % 147.41/21.60 | | | | | | (268), (269), (270), (271), (272), (273), (274), (275), % 147.41/21.60 | | | | | | (276), (277), (278), (279), (280), (281), (282), (283), % 147.41/21.60 | | | | | | (284), (285), (286), (287), (288), (289), (290), (291), % 147.41/21.60 | | | | | | (292), (293), (294), (295), (296), (297), (298), (332), % 147.41/21.60 | | | | | | (333), (334), (335), (336), (337), (338), (347), (350), % 147.41/21.60 | | | | | | (355), (358), (370), (371), (376), (379), (381), (391), % 147.41/21.60 | | | | | | (392), (397), (400), (411), (413), (417), (419), (421), % 147.41/21.60 | | | | | | (425), (427), (429), (445), (447), (454), (456), (458), % 147.41/21.60 | | | | | | (459), (465), (467), (468), (470), (471), (473), (519), % 147.41/21.60 | | | | | | (523), (527), (528), (529), (531), (535), (536), (537), % 147.41/21.60 | | | | | | (538), (539), (540), (541), (542), (543), (544), (545), % 147.41/21.60 | | | | | | (546), (547), (548), (549), (551), (553), (555), (557), % 147.41/21.60 | | | | | | (559), (561), (562), (563), (564), (565), (567), (569), % 147.41/21.60 | | | | | | (571), (573), (574), (575), (576), (577), (579), (581), % 147.41/21.60 | | | | | | (582), (583), (584), (585), (626), (627), (628), (629), % 147.41/21.60 | | | | | | (630), (631), (632), (633), (634), (635), (636), (637), % 147.41/21.60 | | | | | | (638), (639), (640), (641), (645), (671), (690), (691), % 147.41/21.60 | | | | | | (697), (701), (723), (748), (760), (771), (774), (780), % 147.41/21.60 | | | | | | (1976), (1978), (1979), (1981), (function-axioms) are % 147.41/21.60 | | | | | | inconsistent by sub-proof #44. % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | Case 2: % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | (1982) all_14_2 = e0 % 147.41/21.60 | | | | | | (1983) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (525), (1982) imply: % 147.41/21.60 | | | | | | (1984) all_8_2 = e0 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (530), (1984) imply: % 147.41/21.60 | | | | | | (1985) all_48_2 = e0 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (540), (1984) imply: % 147.41/21.60 | | | | | | (1986) all_56_3 = e0 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (544), (1984) imply: % 147.41/21.60 | | | | | | (1987) all_58_29 = e0 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (562), (1984) imply: % 147.41/21.60 | | | | | | (1988) ~ (all_52_1 = e0) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (565), (1984) imply: % 147.41/21.60 | | | | | | (1989) ~ (all_52_4 = e0) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (569), (1984) imply: % 147.41/21.60 | | | | | | (1990) ~ (all_52_7 = e0) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (571), (1984) imply: % 147.41/21.60 | | | | | | (1991) ~ (all_52_9 = e0) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (573), (1984) imply: % 147.41/21.60 | | | | | | (1992) ~ (all_52_13 = e0) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (48), (1984) imply: % 147.41/21.60 | | | | | | (1993) op(e0, all_8_1) = all_8_0 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (47), (1984) imply: % 147.41/21.60 | | | | | | (1994) op(e0, e2) = all_8_1 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (633), (1984) imply: % 147.41/21.60 | | | | | | (1995) op(e2, e0) = all_58_9 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, all_8_1, % 147.41/21.60 | | | | | | e2, e0, simplifying with (204), (1994) gives: % 147.41/21.60 | | | | | | (1996) all_52_7 = all_8_1 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 147.41/21.60 | | | | | | all_58_9, e0, e2, simplifying with (210), (1995) gives: % 147.41/21.60 | | | | | | (1997) all_58_9 = all_52_13 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (471), (1996) imply: % 147.41/21.60 | | | | | | (1998) all_54_13 = all_8_1 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (350), (1996) imply: % 147.41/21.60 | | | | | | (1999) all_56_13 = all_8_1 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | COMBINE_EQS: (547), (1996) imply: % 147.41/21.60 | | | | | | (2000) all_58_24 = all_8_1 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (186), (1996) imply: % 147.41/21.60 | | | | | | (2001) ~ (all_52_3 = all_8_1) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (181), (1996) imply: % 147.41/21.60 | | | | | | (2002) ~ (all_52_4 = all_8_1) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (174), (1996) imply: % 147.41/21.60 | | | | | | (2003) ~ (all_52_6 = all_8_1) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (171), (1996) imply: % 147.41/21.60 | | | | | | (2004) ~ (all_52_11 = all_8_1) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | SIMP: (2004) implies: % 147.41/21.60 | | | | | | (2005) ~ (all_52_11 = all_8_1) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (575), (1996) imply: % 147.41/21.60 | | | | | | (2006) ~ (all_8_1 = all_4_2) % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | REDUCE: (639), (1996) imply: % 147.41/21.60 | | | | | | (2007) op(e0, all_8_1) = all_58_23 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 147.41/21.60 | | | | | | all_58_23, all_8_1, e0, simplifying with (1993), (2007) % 147.41/21.60 | | | | | | gives: % 147.41/21.60 | | | | | | (2008) all_58_23 = all_8_0 % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | BETA: splitting (74) gives: % 147.41/21.60 | | | | | | % 147.41/21.60 | | | | | | Case 1: % 147.41/21.60 | | | | | | | % 147.41/21.60 | | | | | | | (2009) ~ (all_18_2 = e0) % 147.41/21.60 | | | | | | | % 147.41/21.60 | | | | | | | REDUCE: (519), (2009) imply: % 147.41/21.60 | | | | | | | (2010) ~ (all_6_2 = e0) % 147.41/21.60 | | | | | | | % 147.41/21.60 | | | | | | | BETA: splitting (108) gives: % 147.41/21.60 | | | | | | | % 147.41/21.60 | | | | | | | Case 1: % 147.41/21.60 | | | | | | | | % 147.41/21.60 | | | | | | | | (2011) ~ (all_32_1 = e0) % 147.41/21.60 | | | | | | | | % 147.41/21.60 | | | | | | | | REDUCE: (696), (2011) imply: % 147.41/21.60 | | | | | | | | (2012) ~ (all_10_1 = e0) % 147.41/21.60 | | | | | | | | % 147.41/21.60 | | | | | | | | BETA: splitting (147) gives: % 147.41/21.60 | | | | | | | | % 147.41/21.60 | | | | | | | | Case 1: % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | | (2013) ~ (all_48_2 = e0) % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | | REDUCE: (1985), (2013) imply: % 147.41/21.60 | | | | | | | | | (2014) $false % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | | CLOSE: (2014) is inconsistent. % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | Case 2: % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | | (2015) ~ (all_48_0 = e1) | ~ (all_48_1 = e3) % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | | BETA: splitting (268) gives: % 147.41/21.60 | | | | | | | | | % 147.41/21.60 | | | | | | | | | Case 1: % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | (2016) all_56_15 = e0 % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | COMBINE_EQS: (538), (2016) imply: % 147.41/21.60 | | | | | | | | | | (2017) all_4_2 = e0 % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.41/21.60 | | | | | | | | | | (542), (543), (1987), (2017) are inconsistent by % 147.41/21.60 | | | | | | | | | | sub-proof #399. % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | Case 2: % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | (2018) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) % 147.41/21.60 | | | | | | | | | | & (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = % 147.41/21.60 | | | | | | | | | | e0) % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | ALPHA: (2018) implies: % 147.41/21.60 | | | | | | | | | | (2019) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 147.41/21.60 | | | | | | | | | | (2020) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | BETA: splitting (275) gives: % 147.41/21.60 | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | Case 1: % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | (2021) all_56_6 = e0 % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | COMBINE_EQS: (371), (2021) imply: % 147.41/21.60 | | | | | | | | | | | (2022) all_52_2 = e0 % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | COMBINE_EQS: (548), (2022) imply: % 147.41/21.60 | | | | | | | | | | | (2023) all_58_15 = e0 % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | REDUCE: (190), (2022) imply: % 147.41/21.60 | | | | | | | | | | | (2024) ~ (all_52_3 = e0) % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | SIMP: (2024) implies: % 147.41/21.60 | | | | | | | | | | | (2025) ~ (all_52_3 = e0) % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | REDUCE: (189), (2022) imply: % 147.41/21.60 | | | | | | | | | | | (2026) ~ (all_52_6 = e0) % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | SIMP: (2026) implies: % 147.41/21.60 | | | | | | | | | | | (2027) ~ (all_52_6 = e0) % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | REDUCE: (634), (2022) imply: % 147.41/21.60 | | | | | | | | | | | (2028) op(e1, e0) = all_58_14 % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | REDUCE: (209), (2022) imply: % 147.41/21.60 | | | | | | | | | | | (2029) op(e1, e3) = e0 % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (52), % 147.41/21.60 | | | | | | | | | | | (156), (158), (166), (167), (169), (172), (180), % 147.41/21.60 | | | | | | | | | | | (185), (192), (194), (205), (206), (213), (214), % 147.41/21.60 | | | | | | | | | | | (237), (238), (239), (246), (248), (250), (269), % 147.41/21.60 | | | | | | | | | | | (270), (276), (280), (284), (285), (286), (288), % 147.41/21.60 | | | | | | | | | | | (292), (294), (296), (332), (334), (335), (336), % 147.41/21.60 | | | | | | | | | | | (337), (347), (355), (358), (370), (379), (391), % 147.41/21.60 | | | | | | | | | | | (392), (397), (411), (413), (417), (419), (421), % 147.41/21.60 | | | | | | | | | | | (425), (429), (447), (454), (468), (470), (537), % 147.41/21.60 | | | | | | | | | | | (541), (542), (543), (545), (546), (549), (551), % 147.41/21.60 | | | | | | | | | | | (555), (557), (559), (564), (576), (577), (579), % 147.41/21.60 | | | | | | | | | | | (581), (583), (584), (585), (628), (630), (637), % 147.41/21.60 | | | | | | | | | | | (640), (700), (779), (1978), (1986), (1987), % 147.41/21.60 | | | | | | | | | | | (1988), (1989), (1993), (1994), (1997), (1998), % 147.41/21.60 | | | | | | | | | | | (1999), (2001), (2005), (2006), (2008), (2012), % 147.41/21.60 | | | | | | | | | | | (2015), (2019), (2021), (2023), (2025), (2027), % 147.41/21.60 | | | | | | | | | | | (2028), (2029), (function-axioms) are inconsistent % 147.41/21.60 | | | | | | | | | | | by sub-proof #37. % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | Case 2: % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | (2030) ~ (all_56_6 = e0) % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | REDUCE: (371), (2030) imply: % 147.41/21.60 | | | | | | | | | | | (2031) ~ (all_52_2 = e0) % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | BETA: splitting (291) gives: % 147.41/21.60 | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | Case 1: % 147.41/21.60 | | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | | (2032) all_56_0 = e0 % 147.41/21.60 | | | | | | | | | | | | % 147.41/21.60 | | | | | | | | | | | | COMBINE_EQS: (541), (2032) imply: % 147.41/21.60 | | | | | | | | | | | | (2033) all_10_2 = e0 % 147.41/21.60 | | | | | | | | | | | | % 147.41/21.61 | | | | | | | | | | | | COMBINE_EQS: (545), (2033) imply: % 147.41/21.61 | | | | | | | | | | | | (2034) all_58_28 = e0 % 147.41/21.61 | | | | | | | | | | | | % 147.41/21.61 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.41/21.61 | | | | | | | | | | | | (543), (1987), (2034) are inconsistent by % 147.41/21.61 | | | | | | | | | | | | sub-proof #483. % 147.41/21.61 | | | | | | | | | | | | % 147.41/21.61 | | | | | | | | | | | Case 2: % 147.41/21.61 | | | | | | | | | | | | % 147.41/21.61 | | | | | | | | | | | | (2035) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 147.41/21.61 | | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (51), % 147.85/21.61 | | | | | | | | | | | | (52), (79), (156), (158), (159), (163), (164), % 147.85/21.61 | | | | | | | | | | | | (166), (167), (169), (172), (179), (180), (182), % 147.85/21.61 | | | | | | | | | | | | (185), (187), (189), (191), (192), (194), (195), % 147.85/21.61 | | | | | | | | | | | | (203), (206), (209), (211), (214), (215), (236), % 147.85/21.61 | | | | | | | | | | | | (237), (240), (241), (242), (243), (244), (246), % 147.85/21.61 | | | | | | | | | | | | (247), (249), (250), (269), (271), (272), (273), % 147.85/21.61 | | | | | | | | | | | | (274), (276), (278), (279), (280), (282), (284), % 147.85/21.61 | | | | | | | | | | | | (285), (286), (288), (289), (290), (293), (295), % 147.85/21.61 | | | | | | | | | | | | (298), (332), (334), (335), (336), (337), (338), % 147.85/21.61 | | | | | | | | | | | | (347), (355), (358), (370), (371), (376), (379), % 147.85/21.61 | | | | | | | | | | | | (391), (392), (397), (400), (411), (413), (417), % 147.85/21.61 | | | | | | | | | | | | (419), (421), (425), (427), (429), (445), (447), % 147.85/21.61 | | | | | | | | | | | | (456), (458), (459), (465), (467), (473), (536), % 147.85/21.61 | | | | | | | | | | | | (537), (538), (539), (541), (542), (543), (544), % 147.85/21.61 | | | | | | | | | | | | (545), (546), (548), (549), (551), (553), (557), % 147.85/21.61 | | | | | | | | | | | | (561), (563), (565), (574), (577), (579), (582), % 147.85/21.61 | | | | | | | | | | | | (583), (584), (585), (627), (628), (629), (630), % 147.85/21.61 | | | | | | | | | | | | (631), (636), (638), (693), (772), (1977), (1983), % 147.85/21.61 | | | | | | | | | | | | (1986), (1987), (1988), (1991), (1992), (1993), % 147.85/21.61 | | | | | | | | | | | | (1994), (1997), (1998), (1999), (2000), (2001), % 147.85/21.61 | | | | | | | | | | | | (2002), (2003), (2005), (2006), (2008), (2010), % 147.85/21.61 | | | | | | | | | | | | (2020), (2031), (2035), (function-axioms) are % 147.85/21.61 | | | | | | | | | | | | inconsistent by sub-proof #30. % 147.85/21.61 | | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | End of split % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | End of split % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | End of split % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | End of split % 147.85/21.61 | | | | | | | | % 147.85/21.61 | | | | | | | Case 2: % 147.85/21.61 | | | | | | | | % 147.85/21.61 | | | | | | | | (2036) all_32_1 = e0 % 147.85/21.61 | | | | | | | | % 147.85/21.61 | | | | | | | | COMBINE_EQS: (696), (2036) imply: % 147.85/21.61 | | | | | | | | (2037) all_10_1 = e0 % 147.85/21.61 | | | | | | | | % 147.85/21.61 | | | | | | | | REDUCE: (52), (2037) imply: % 147.85/21.61 | | | | | | | | (2038) op(all_10_2, e3) = e0 % 147.85/21.61 | | | | | | | | % 147.85/21.61 | | | | | | | | BETA: splitting (268) gives: % 147.85/21.61 | | | | | | | | % 147.85/21.61 | | | | | | | | Case 1: % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | (2039) all_56_15 = e0 % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | COMBINE_EQS: (538), (2039) imply: % 147.85/21.61 | | | | | | | | | (2040) all_4_2 = e0 % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.85/21.61 | | | | | | | | | (542), (543), (1987), (2040) are inconsistent by % 147.85/21.61 | | | | | | | | | sub-proof #399. % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | Case 2: % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | (2041) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 147.85/21.61 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | ALPHA: (2041) implies: % 147.85/21.61 | | | | | | | | | (2042) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 147.85/21.61 | | | | | | | | | (2043) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | BETA: splitting (291) gives: % 147.85/21.61 | | | | | | | | | % 147.85/21.61 | | | | | | | | | Case 1: % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | (2044) all_56_0 = e0 % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | COMBINE_EQS: (541), (2044) imply: % 147.85/21.61 | | | | | | | | | | (2045) all_10_2 = e0 % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | COMBINE_EQS: (545), (2045) imply: % 147.85/21.61 | | | | | | | | | | (2046) all_58_28 = e0 % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.85/21.61 | | | | | | | | | | (543), (1987), (2046) are inconsistent by % 147.85/21.61 | | | | | | | | | | sub-proof #483. % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | Case 2: % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | (2047) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | BETA: splitting (275) gives: % 147.85/21.61 | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | Case 1: % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | (2048) all_56_6 = e0 % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | COMBINE_EQS: (371), (2048) imply: % 147.85/21.61 | | | | | | | | | | | (2049) all_52_2 = e0 % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | COMBINE_EQS: (548), (2049) imply: % 147.85/21.61 | | | | | | | | | | | (2050) all_58_15 = e0 % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | REDUCE: (190), (2049) imply: % 147.85/21.61 | | | | | | | | | | | (2051) ~ (all_52_3 = e0) % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | SIMP: (2051) implies: % 147.85/21.61 | | | | | | | | | | | (2052) ~ (all_52_3 = e0) % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | REDUCE: (187), (2049) imply: % 147.85/21.61 | | | | | | | | | | | (2053) ~ (all_52_14 = e0) % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | SIMP: (2053) implies: % 147.85/21.61 | | | | | | | | | | | (2054) ~ (all_52_14 = e0) % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (79), (158), % 147.85/21.61 | | | | | | | | | | | (159), (163), (164), (166), (169), (179), (180), % 147.85/21.61 | | | | | | | | | | | (185), (191), (194), (213), (238), (244), (248), % 147.85/21.61 | | | | | | | | | | | (250), (281), (285), (286), (289), (293), (295), % 147.85/21.61 | | | | | | | | | | | (296), (297), (298), (334), (335), (336), (337), % 147.85/21.61 | | | | | | | | | | | (338), (347), (355), (358), (376), (379), (391), % 147.85/21.61 | | | | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 147.85/21.61 | | | | | | | | | | | (421), (427), (429), (454), (456), (470), (537), % 147.85/21.61 | | | | | | | | | | | (541), (542), (543), (545), (546), (549), (551), % 147.85/21.61 | | | | | | | | | | | (555), (557), (559), (564), (576), (577), (579), % 147.85/21.61 | | | | | | | | | | | (584), (629), (1978), (1986), (1987), (1988), % 147.85/21.61 | | | | | | | | | | | (1992), (1999), (2000), (2002), (2038), (2042), % 147.85/21.61 | | | | | | | | | | | (2043), (2048), (2050), (2052), (2054), % 147.85/21.61 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.85/21.61 | | | | | | | | | | | #16. % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | Case 2: % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | (2055) ~ (all_56_6 = e0) % 147.85/21.61 | | | | | | | | | | | % 147.85/21.61 | | | | | | | | | | | REDUCE: (371), (2055) imply: % 147.85/21.61 | | | | | | | | | | | (2056) ~ (all_52_2 = e0) % 147.85/21.61 | | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (51), % 147.85/21.62 | | | | | | | | | | | (52), (79), (156), (158), (159), (163), (164), % 147.85/21.62 | | | | | | | | | | | (166), (167), (169), (172), (179), (180), (182), % 147.85/21.62 | | | | | | | | | | | (185), (187), (189), (191), (192), (194), (195), % 147.85/21.62 | | | | | | | | | | | (203), (206), (209), (211), (214), (215), (236), % 147.85/21.62 | | | | | | | | | | | (237), (240), (241), (242), (243), (244), (246), % 147.85/21.62 | | | | | | | | | | | (247), (249), (250), (269), (271), (272), (273), % 147.85/21.62 | | | | | | | | | | | (274), (276), (278), (279), (280), (282), (284), % 147.85/21.62 | | | | | | | | | | | (285), (286), (288), (289), (290), (293), (295), % 147.85/21.62 | | | | | | | | | | | (298), (332), (334), (335), (336), (337), (338), % 147.85/21.62 | | | | | | | | | | | (347), (355), (358), (370), (371), (376), (379), % 147.85/21.62 | | | | | | | | | | | (391), (392), (397), (400), (411), (413), (417), % 147.85/21.62 | | | | | | | | | | | (419), (421), (425), (427), (429), (445), (447), % 147.85/21.62 | | | | | | | | | | | (456), (458), (459), (465), (467), (473), (536), % 147.85/21.62 | | | | | | | | | | | (537), (538), (539), (541), (542), (543), (544), % 147.85/21.62 | | | | | | | | | | | (545), (546), (548), (549), (551), (553), (557), % 147.85/21.62 | | | | | | | | | | | (561), (563), (565), (574), (577), (579), (582), % 147.85/21.62 | | | | | | | | | | | (583), (584), (585), (627), (628), (629), (630), % 147.85/21.62 | | | | | | | | | | | (631), (636), (638), (693), (772), (1977), (1983), % 147.85/21.62 | | | | | | | | | | | (1986), (1987), (1988), (1991), (1992), (1993), % 147.85/21.62 | | | | | | | | | | | (1994), (1997), (1998), (1999), (2000), (2001), % 147.85/21.62 | | | | | | | | | | | (2002), (2003), (2005), (2006), (2008), (2010), % 147.85/21.62 | | | | | | | | | | | (2043), (2047), (2056), (function-axioms) are % 147.85/21.62 | | | | | | | | | | | inconsistent by sub-proof #30. % 147.85/21.62 | | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | End of split % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | End of split % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | End of split % 147.85/21.62 | | | | | | | | % 147.85/21.62 | | | | | | | End of split % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | Case 2: % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | (2057) all_18_2 = e0 % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | COMBINE_EQS: (519), (2057) imply: % 147.85/21.62 | | | | | | | (2058) all_6_2 = e0 % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | SIMP: (2058) implies: % 147.85/21.62 | | | | | | | (2059) all_6_2 = e0 % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | COMBINE_EQS: (543), (2059) imply: % 147.85/21.62 | | | | | | | (2060) all_58_30 = e0 % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (79), (334), (335), % 147.85/21.62 | | | | | | | (337), (338), (542), (545), (1987), (2060) are % 147.85/21.62 | | | | | | | inconsistent by sub-proof #691. % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | End of split % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | End of split % 147.85/21.62 | | | | | % 147.85/21.62 | | | | Case 2: % 147.85/21.62 | | | | | % 147.85/21.62 | | | | | (2061) all_10_0 = e0 % 147.85/21.62 | | | | | (2062) ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 147.85/21.62 | | | | | % 147.85/21.62 | | | | | REDUCE: (53), (2061) imply: % 147.85/21.62 | | | | | (2063) op(all_10_2, all_10_1) = e0 % 147.85/21.62 | | | | | % 147.85/21.62 | | | | | BETA: splitting (59) gives: % 147.85/21.62 | | | | | % 147.85/21.62 | | | | | Case 1: % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | | (2064) ~ (all_12_0 = e1) % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | | REDUCE: (1975), (2064) imply: % 147.85/21.62 | | | | | | (2065) $false % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | | CLOSE: (2065) is inconsistent. % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | Case 2: % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | | (2066) ~ (all_12_1 = e2) | ~ (all_12_2 = e3) % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | | BETA: splitting (64) gives: % 147.85/21.62 | | | | | | % 147.85/21.62 | | | | | | Case 1: % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | (2067) ~ (all_14_2 = e0) % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | REDUCE: (525), (2067) imply: % 147.85/21.62 | | | | | | | (2068) ~ (all_8_2 = e0) % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | BETA: splitting (74) gives: % 147.85/21.62 | | | | | | | % 147.85/21.62 | | | | | | | Case 1: % 147.85/21.62 | | | | | | | | % 147.85/21.62 | | | | | | | | (2069) ~ (all_18_2 = e0) % 147.85/21.62 | | | | | | | | % 147.85/21.62 | | | | | | | | REDUCE: (519), (2069) imply: % 147.85/21.62 | | | | | | | | (2070) ~ (all_6_2 = e0) % 147.85/21.62 | | | | | | | | % 147.85/21.62 | | | | | | | | BETA: splitting (268) gives: % 147.85/21.62 | | | | | | | | % 147.85/21.62 | | | | | | | | Case 1: % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | (2071) all_56_15 = e0 % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | COMBINE_EQS: (538), (2071) imply: % 147.85/21.62 | | | | | | | | | (2072) all_4_2 = e0 % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | SIMP: (2072) implies: % 147.85/21.62 | | | | | | | | | (2073) all_4_2 = e0 % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | REF_CLOSE: (4), (36), (37), (641), (1976), (2073), % 147.85/21.62 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 147.85/21.62 | | | | | | | | | #70. % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | Case 2: % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | (2074) ~ (all_56_15 = e0) % 147.85/21.62 | | | | | | | | | (2075) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 147.85/21.62 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | ALPHA: (2075) implies: % 147.85/21.62 | | | | | | | | | (2076) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | REDUCE: (538), (2074) imply: % 147.85/21.62 | | | | | | | | | (2077) ~ (all_4_2 = e0) % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | BETA: splitting (333) gives: % 147.85/21.62 | | | | | | | | | % 147.85/21.62 | | | | | | | | | Case 1: % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | (2078) all_58_28 = e0 % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | COMBINE_EQS: (545), (2078) imply: % 147.85/21.62 | | | | | | | | | | (2079) all_10_2 = e0 % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | COMBINE_EQS: (541), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2080) all_56_0 = e0 % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (551), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2081) ~ (all_52_1 = e0) % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (553), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2082) ~ (all_52_2 = e0) % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (555), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2083) ~ (all_52_3 = e0) % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (557), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2084) ~ (all_52_4 = e0) % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (559), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2085) ~ (all_52_8 = e0) % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (561), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2086) ~ (all_52_12 = e0) % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (2063), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2087) op(e0, all_10_1) = e0 % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (52), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2088) op(e0, e3) = all_10_1 % 147.85/21.62 | | | | | | | | | | % 147.85/21.62 | | | | | | | | | | REDUCE: (629), (2079) imply: % 147.85/21.62 | | | | | | | | | | (2089) op(e3, e0) = all_58_0 % 147.85/21.62 | | | | | | | | | | % 147.85/21.63 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (37), (42), (156), % 147.85/21.63 | | | | | | | | | | (158), (159), (163), (164), (166), (167), (169), % 147.85/21.63 | | | | | | | | | | (171), (172), (174), (179), (180), (181), (182), % 147.85/21.63 | | | | | | | | | | (185), (186), (187), (189), (190), (192), (194), % 147.85/21.63 | | | | | | | | | | (195), (203), (204), (205), (211), (214), (236), % 147.85/21.63 | | | | | | | | | | (238), (239), (241), (242), (245), (246), (247), % 147.85/21.63 | | | | | | | | | | (248), (249), (269), (270), (271), (272), (273), % 147.85/21.63 | | | | | | | | | | (274), (275), (276), (277), (278), (279), (280), % 147.85/21.63 | | | | | | | | | | (281), (283), (284), (286), (287), (288), (289), % 147.85/21.63 | | | | | | | | | | (290), (292), (294), (296), (297), (334), (335), % 147.85/21.63 | | | | | | | | | | (336), (337), (347), (350), (355), (358), (370), % 147.85/21.63 | | | | | | | | | | (371), (376), (379), (381), (391), (392), (397), % 147.85/21.63 | | | | | | | | | | (400), (411), (413), (417), (419), (421), (425), % 147.85/21.63 | | | | | | | | | | (427), (429), (445), (447), (454), (458), (459), % 147.85/21.63 | | | | | | | | | | (465), (468), (470), (473), (526), (538), (539), % 147.85/21.63 | | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 147.85/21.63 | | | | | | | | | | (547), (548), (549), (562), (563), (564), (565), % 147.85/21.63 | | | | | | | | | | (567), (571), (573), (574), (575), (576), (577), % 147.85/21.63 | | | | | | | | | | (579), (581), (582), (584), (585), (638), (695), % 147.85/21.63 | | | | | | | | | | (1977), (2066), (2070), (2076), (2078), (2080), % 147.85/21.63 | | | | | | | | | | (2081), (2082), (2083), (2084), (2085), (2086), % 147.85/21.63 | | | | | | | | | | (2087), (2088), (2089), (function-axioms) are % 147.85/21.63 | | | | | | | | | | inconsistent by sub-proof #11. % 147.85/21.63 | | | | | | | | | | % 147.85/21.63 | | | | | | | | | Case 2: % 147.85/21.63 | | | | | | | | | | % 147.85/21.63 | | | | | | | | | | (2090) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 147.85/21.63 | | | | | | | | | | % 147.85/21.63 | | | | | | | | | | REF_CLOSE: (542), (543), (544), (2068), (2070), (2077), % 147.85/21.63 | | | | | | | | | | (2090) are inconsistent by sub-proof #216. % 147.85/21.63 | | | | | | | | | | % 147.85/21.63 | | | | | | | | | End of split % 147.85/21.63 | | | | | | | | | % 147.85/21.63 | | | | | | | | End of split % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | Case 2: % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | (2091) all_18_2 = e0 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | COMBINE_EQS: (519), (2091) imply: % 147.85/21.63 | | | | | | | | (2092) all_6_2 = e0 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | SIMP: (2092) implies: % 147.85/21.63 | | | | | | | | (2093) all_6_2 = e0 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | COMBINE_EQS: (539), (2093) imply: % 147.85/21.63 | | | | | | | | (2094) all_56_8 = e0 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | COMBINE_EQS: (543), (2093) imply: % 147.85/21.63 | | | | | | | | (2095) all_58_30 = e0 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (574), (2093) imply: % 147.85/21.63 | | | | | | | | (2096) ~ (all_52_6 = e0) % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (576), (2093) imply: % 147.85/21.63 | | | | | | | | (2097) ~ (all_52_8 = e0) % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (577), (2093) imply: % 147.85/21.63 | | | | | | | | (2098) ~ (all_52_9 = e0) % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (579), (2093) imply: % 147.85/21.63 | | | | | | | | (2099) ~ (all_52_11 = e0) % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (581), (2093) imply: % 147.85/21.63 | | | | | | | | (2100) ~ (all_52_14 = e0) % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (42), (2093) imply: % 147.85/21.63 | | | | | | | | (2101) op(e0, e1) = all_6_1 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (637), (2093) imply: % 147.85/21.63 | | | | | | | | (2102) op(e1, e0) = all_58_18 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REDUCE: (41), (2093) imply: % 147.85/21.63 | | | | | | | | (2103) op(e1, e1) = e0 % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (47), (51), % 147.85/21.63 | | | | | | | | (52), (79), (156), (158), (159), (163), (164), (166), % 147.85/21.63 | | | | | | | | (167), (169), (171), (172), (174), (179), (180), % 147.85/21.63 | | | | | | | | (181), (182), (185), (186), (187), (189), (190), % 147.85/21.63 | | | | | | | | (191), (192), (194), (195), (203), (206), (209), % 147.85/21.63 | | | | | | | | (210), (214), (216), (238), (241), (242), (243), % 147.85/21.63 | | | | | | | | (244), (245), (246), (247), (248), (249), (250), % 147.85/21.63 | | | | | | | | (268), (269), (270), (272), (273), (274), (276), % 147.85/21.63 | | | | | | | | (277), (278), (280), (281), (282), (283), (284), % 147.85/21.63 | | | | | | | | (285), (286), (287), (288), (290), (291), (292), % 147.85/21.63 | | | | | | | | (293), (294), (295), (296), (297), (298), (332), % 147.85/21.63 | | | | | | | | (334), (335), (336), (337), (338), (347), (350), % 147.85/21.63 | | | | | | | | (355), (358), (370), (371), (376), (379), (381), % 147.85/21.63 | | | | | | | | (391), (392), (397), (400), (411), (413), (417), % 147.85/21.63 | | | | | | | | (419), (421), (425), (427), (429), (445), (447), % 147.85/21.63 | | | | | | | | (454), (456), (458), (459), (465), (467), (470), % 147.85/21.63 | | | | | | | | (537), (538), (540), (541), (542), (543), (544), % 147.85/21.63 | | | | | | | | (545), (546), (547), (548), (549), (551), (553), % 147.85/21.63 | | | | | | | | (555), (557), (559), (561), (562), (564), (567), % 147.85/21.63 | | | | | | | | (569), (571), (573), (575), (582), (583), (584), % 147.85/21.63 | | | | | | | | (585), (626), (629), (632), (636), (638), (1978), % 147.85/21.63 | | | | | | | | (2062), (2063), (2068), (2094), (2095), (2096), % 147.85/21.63 | | | | | | | | (2097), (2098), (2099), (2100), (2101), (2102), % 147.85/21.63 | | | | | | | | (2103), (function-axioms) are inconsistent by % 147.85/21.63 | | | | | | | | sub-proof #174. % 147.85/21.63 | | | | | | | | % 147.85/21.63 | | | | | | | End of split % 147.85/21.63 | | | | | | | % 147.85/21.63 | | | | | | Case 2: % 147.85/21.63 | | | | | | | % 147.85/21.63 | | | | | | | (2104) all_14_2 = e0 % 147.85/21.63 | | | | | | | (2105) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 147.85/21.63 | | | | | | | % 147.85/21.63 | | | | | | | COMBINE_EQS: (525), (2104) imply: % 147.85/21.63 | | | | | | | (2106) all_8_2 = e0 % 147.85/21.63 | | | | | | | % 147.85/21.63 | | | | | | | SIMP: (2106) implies: % 147.85/21.63 | | | | | | | (2107) all_8_2 = e0 % 147.85/21.63 | | | | | | | % 147.85/21.64 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (37), (41), (47), (48), % 147.85/21.64 | | | | | | | (51), (52), (74), (79), (156), (158), (159), (163), % 147.85/21.64 | | | | | | | (164), (166), (167), (169), (171), (172), (174), (179), % 147.85/21.64 | | | | | | | (180), (181), (182), (185), (186), (187), (189), (190), % 147.85/21.64 | | | | | | | (191), (192), (194), (195), (203), (204), (206), (210), % 147.85/21.64 | | | | | | | (211), (213), (214), (215), (235), (236), (237), (238), % 147.85/21.64 | | | | | | | (239), (240), (241), (242), (243), (244), (246), (247), % 147.85/21.64 | | | | | | | (248), (249), (250), (268), (269), (270), (271), (272), % 147.85/21.64 | | | | | | | (273), (274), (275), (276), (277), (278), (279), (280), % 147.85/21.64 | | | | | | | (281), (282), (284), (285), (286), (288), (290), (291), % 147.85/21.64 | | | | | | | (292), (293), (294), (295), (296), (297), (298), (332), % 147.85/21.64 | | | | | | | (334), (335), (336), (337), (338), (347), (350), (355), % 147.85/21.64 | | | | | | | (358), (370), (371), (376), (379), (391), (392), (397), % 147.85/21.64 | | | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 147.85/21.64 | | | | | | | (429), (445), (447), (454), (456), (458), (459), (465), % 147.85/21.64 | | | | | | | (467), (468), (470), (471), (473), (519), (535), (536), % 147.85/21.64 | | | | | | | (537), (538), (539), (540), (541), (542), (543), (544), % 147.85/21.64 | | | | | | | (545), (546), (547), (548), (549), (551), (553), (555), % 147.85/21.64 | | | | | | | (557), (559), (561), (562), (563), (564), (565), (567), % 147.85/21.64 | | | | | | | (569), (571), (573), (574), (575), (576), (577), (579), % 147.85/21.64 | | | | | | | (581), (582), (583), (584), (585), (628), (629), (630), % 147.85/21.64 | | | | | | | (633), (634), (636), (637), (639), (641), (693), (772), % 147.85/21.64 | | | | | | | (2063), (2105), (2107), (function-axioms) are % 147.85/21.64 | | | | | | | inconsistent by sub-proof #72. % 147.85/21.64 | | | | | | | % 147.85/21.64 | | | | | | End of split % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | End of split % 147.85/21.64 | | | | | % 147.85/21.64 | | | | End of split % 147.85/21.64 | | | | % 147.85/21.64 | | | Case 2: % 147.85/21.64 | | | | % 147.85/21.64 | | | | (2108) all_8_1 = e0 % 147.85/21.64 | | | | (2109) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 147.85/21.64 | | | | % 147.85/21.64 | | | | COMBINE_EQS: (686), (2108) imply: % 147.85/21.64 | | | | (2110) all_22_1 = e0 % 147.85/21.64 | | | | % 147.85/21.64 | | | | REDUCE: (48), (2108) imply: % 147.85/21.64 | | | | (2111) op(all_8_2, e0) = all_8_0 % 147.85/21.64 | | | | % 147.85/21.64 | | | | REDUCE: (47), (2108) imply: % 147.85/21.64 | | | | (2112) op(all_8_2, e2) = e0 % 147.85/21.64 | | | | % 147.85/21.64 | | | | BETA: splitting (54) gives: % 147.85/21.64 | | | | % 147.85/21.64 | | | | Case 1: % 147.85/21.64 | | | | | % 147.85/21.64 | | | | | (2113) ~ (all_10_0 = e0) % 147.85/21.64 | | | | | % 147.85/21.64 | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (41), (42), (46), % 147.85/21.64 | | | | | (51), (52), (53), (69), (74), (79), (84), (108), (152), % 147.85/21.64 | | | | | (156), (158), (159), (163), (164), (166), (167), (169), % 147.85/21.64 | | | | | (171), (172), (174), (179), (180), (181), (182), (185), % 147.85/21.64 | | | | | (186), (187), (189), (190), (191), (192), (194), (195), % 147.85/21.64 | | | | | (203), (204), (205), (206), (208), (209), (210), (214), % 147.85/21.64 | | | | | (215), (216), (236), (238), (240), (241), (243), (244), % 147.85/21.64 | | | | | (245), (246), (247), (248), (249), (250), (268), (269), % 147.85/21.64 | | | | | (270), (271), (272), (273), (274), (275), (276), (277), % 147.85/21.64 | | | | | (278), (279), (280), (281), (282), (283), (284), (285), % 147.85/21.64 | | | | | (286), (287), (288), (289), (290), (291), (292), (293), % 147.85/21.64 | | | | | (294), (295), (296), (297), (298), (332), (333), (334), % 147.85/21.64 | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 147.85/21.64 | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 147.85/21.64 | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 147.85/21.64 | | | | | (429), (445), (447), (454), (456), (459), (465), (467), % 147.85/21.64 | | | | | (470), (473), (517), (519), (523), (531), (536), (537), % 147.85/21.64 | | | | | (538), (539), (540), (541), (542), (543), (544), (545), % 147.85/21.64 | | | | | (546), (547), (548), (549), (551), (553), (555), (557), % 147.85/21.64 | | | | | (559), (561), (562), (563), (564), (565), (567), (569), % 147.85/21.64 | | | | | (571), (573), (574), (575), (576), (577), (579), (581), % 147.85/21.64 | | | | | (582), (583), (584), (585), (626), (627), (628), (629), % 147.85/21.64 | | | | | (630), (631), (632), (633), (634), (635), (636), (637), % 147.85/21.64 | | | | | (638), (639), (641), (691), (696), (701), (766), (771), % 147.85/21.64 | | | | | (780), (1976), (2109), (2110), (2111), (2112), (2113), % 147.85/21.64 | | | | | (function-axioms) are inconsistent by sub-proof #9. % 147.85/21.64 | | | | | % 147.85/21.64 | | | | Case 2: % 147.85/21.64 | | | | | % 147.85/21.64 | | | | | (2114) all_10_0 = e0 % 147.85/21.64 | | | | | % 147.85/21.64 | | | | | REDUCE: (53), (2114) imply: % 147.85/21.64 | | | | | (2115) op(all_10_2, all_10_1) = e0 % 147.85/21.64 | | | | | % 147.85/21.64 | | | | | BETA: splitting (59) gives: % 147.85/21.64 | | | | | % 147.85/21.64 | | | | | Case 1: % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | | (2116) ~ (all_12_0 = e1) % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | | REDUCE: (1975), (2116) imply: % 147.85/21.64 | | | | | | (2117) $false % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | | CLOSE: (2117) is inconsistent. % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | Case 2: % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | | (2118) ~ (all_12_1 = e2) | ~ (all_12_2 = e3) % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | | BETA: splitting (74) gives: % 147.85/21.64 | | | | | | % 147.85/21.64 | | | | | | Case 1: % 147.85/21.64 | | | | | | | % 147.85/21.64 | | | | | | | (2119) ~ (all_18_2 = e0) % 147.85/21.64 | | | | | | | % 147.85/21.64 | | | | | | | REDUCE: (519), (2119) imply: % 147.85/21.64 | | | | | | | (2120) ~ (all_6_2 = e0) % 147.85/21.64 | | | | | | | % 147.85/21.64 | | | | | | | BETA: splitting (268) gives: % 147.85/21.64 | | | | | | | % 147.85/21.64 | | | | | | | Case 1: % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | (2121) all_56_15 = e0 % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | COMBINE_EQS: (538), (2121) imply: % 147.85/21.64 | | | | | | | | (2122) all_4_2 = e0 % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | SIMP: (2122) implies: % 147.85/21.64 | | | | | | | | (2123) all_4_2 = e0 % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | REF_CLOSE: (4), (36), (37), (641), (1976), (2123), % 147.85/21.64 | | | | | | | | (function-axioms) are inconsistent by sub-proof #70. % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | Case 2: % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | (2124) ~ (all_56_15 = e0) % 147.85/21.64 | | | | | | | | (2125) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 147.85/21.64 | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | ALPHA: (2125) implies: % 147.85/21.64 | | | | | | | | (2126) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | REDUCE: (538), (2124) imply: % 147.85/21.64 | | | | | | | | (2127) ~ (all_4_2 = e0) % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | BETA: splitting (333) gives: % 147.85/21.64 | | | | | | | | % 147.85/21.64 | | | | | | | | Case 1: % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | (2128) all_58_28 = e0 % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | COMBINE_EQS: (545), (2128) imply: % 147.85/21.64 | | | | | | | | | (2129) all_10_2 = e0 % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | COMBINE_EQS: (541), (2129) imply: % 147.85/21.64 | | | | | | | | | (2130) all_56_0 = e0 % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (551), (2129) imply: % 147.85/21.64 | | | | | | | | | (2131) ~ (all_52_1 = e0) % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (553), (2129) imply: % 147.85/21.64 | | | | | | | | | (2132) ~ (all_52_2 = e0) % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (555), (2129) imply: % 147.85/21.64 | | | | | | | | | (2133) ~ (all_52_3 = e0) % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (557), (2129) imply: % 147.85/21.64 | | | | | | | | | (2134) ~ (all_52_4 = e0) % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (559), (2129) imply: % 147.85/21.64 | | | | | | | | | (2135) ~ (all_52_8 = e0) % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (561), (2129) imply: % 147.85/21.64 | | | | | | | | | (2136) ~ (all_52_12 = e0) % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (2115), (2129) imply: % 147.85/21.64 | | | | | | | | | (2137) op(e0, all_10_1) = e0 % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (52), (2129) imply: % 147.85/21.64 | | | | | | | | | (2138) op(e0, e3) = all_10_1 % 147.85/21.64 | | | | | | | | | % 147.85/21.64 | | | | | | | | | REDUCE: (629), (2129) imply: % 147.85/21.64 | | | | | | | | | (2139) op(e3, e0) = all_58_0 % 147.85/21.64 | | | | | | | | | % 147.85/21.65 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (37), (42), (156), % 147.85/21.65 | | | | | | | | | (158), (159), (163), (164), (166), (167), (169), % 147.85/21.65 | | | | | | | | | (171), (172), (174), (179), (180), (181), (182), % 147.85/21.65 | | | | | | | | | (185), (186), (187), (189), (190), (192), (194), % 147.85/21.65 | | | | | | | | | (195), (203), (204), (205), (211), (214), (236), % 147.85/21.65 | | | | | | | | | (238), (239), (241), (242), (245), (246), (247), % 147.85/21.65 | | | | | | | | | (248), (249), (269), (270), (271), (272), (273), % 147.85/21.65 | | | | | | | | | (274), (275), (276), (277), (278), (279), (280), % 147.85/21.65 | | | | | | | | | (281), (283), (284), (286), (287), (288), (289), % 147.85/21.65 | | | | | | | | | (290), (292), (294), (296), (297), (334), (335), % 147.85/21.65 | | | | | | | | | (336), (337), (347), (350), (355), (358), (370), % 147.85/21.65 | | | | | | | | | (371), (376), (379), (381), (391), (392), (397), % 147.85/21.65 | | | | | | | | | (400), (411), (413), (417), (419), (421), (425), % 147.85/21.65 | | | | | | | | | (427), (429), (445), (447), (454), (458), (459), % 147.85/21.65 | | | | | | | | | (465), (468), (470), (473), (526), (538), (539), % 147.85/21.65 | | | | | | | | | (540), (541), (542), (543), (544), (545), (546), % 147.85/21.65 | | | | | | | | | (547), (548), (549), (562), (563), (564), (565), % 147.85/21.65 | | | | | | | | | (567), (571), (573), (574), (575), (576), (577), % 147.85/21.65 | | | | | | | | | (579), (581), (582), (584), (585), (638), (695), % 147.85/21.65 | | | | | | | | | (1977), (2118), (2120), (2126), (2128), (2130), % 147.85/21.65 | | | | | | | | | (2131), (2132), (2133), (2134), (2135), (2136), % 147.85/21.65 | | | | | | | | | (2137), (2138), (2139), (function-axioms) are % 147.85/21.65 | | | | | | | | | inconsistent by sub-proof #11. % 147.85/21.65 | | | | | | | | | % 147.85/21.65 | | | | | | | | Case 2: % 147.85/21.65 | | | | | | | | | % 147.85/21.65 | | | | | | | | | (2140) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 147.85/21.65 | | | | | | | | | % 147.85/21.65 | | | | | | | | | REF_CLOSE: (204), (542), (543), (544), (569), (2112), (2120), % 147.85/21.65 | | | | | | | | | (2127), (2140), (function-axioms) are inconsistent % 147.85/21.65 | | | | | | | | | by sub-proof #133. % 147.85/21.65 | | | | | | | | | % 147.85/21.65 | | | | | | | | End of split % 147.85/21.65 | | | | | | | | % 147.85/21.65 | | | | | | | End of split % 147.85/21.65 | | | | | | | % 147.85/21.65 | | | | | | Case 2: % 147.85/21.65 | | | | | | | % 147.85/21.65 | | | | | | | (2141) all_18_2 = e0 % 147.85/21.65 | | | | | | | % 147.85/21.65 | | | | | | | COMBINE_EQS: (519), (2141) imply: % 147.85/21.65 | | | | | | | (2142) all_6_2 = e0 % 147.85/21.65 | | | | | | | % 147.85/21.65 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (41), (42), % 147.85/21.65 | | | | | | | (46), (52), (79), (156), (158), (159), (163), (164), % 147.85/21.65 | | | | | | | (166), (167), (169), (171), (172), (174), (179), (180), % 147.85/21.65 | | | | | | | (181), (182), (185), (186), (187), (189), (190), (191), % 147.85/21.65 | | | | | | | (192), (194), (195), (203), (204), (206), (208), (209), % 147.85/21.65 | | | | | | | (210), (214), (216), (236), (238), (241), (243), (244), % 147.85/21.65 | | | | | | | (245), (246), (247), (248), (249), (250), (268), (269), % 147.85/21.65 | | | | | | | (271), (272), (273), (274), (276), (277), (278), (280), % 147.85/21.65 | | | | | | | (281), (282), (283), (284), (286), (287), (288), (289), % 147.85/21.65 | | | | | | | (291), (292), (293), (294), (295), (296), (297), (298), % 147.85/21.65 | | | | | | | (332), (334), (335), (336), (337), (338), (347), (350), % 147.85/21.65 | | | | | | | (355), (358), (370), (371), (376), (379), (381), (391), % 147.85/21.65 | | | | | | | (392), (397), (400), (411), (413), (417), (419), (421), % 147.85/21.65 | | | | | | | (425), (427), (429), (445), (447), (454), (456), (459), % 147.85/21.65 | | | | | | | (465), (467), (470), (473), (537), (538), (539), (540), % 147.85/21.65 | | | | | | | (541), (542), (543), (544), (545), (546), (547), (548), % 147.85/21.65 | | | | | | | (549), (551), (553), (555), (557), (559), (561), (562), % 147.85/21.65 | | | | | | | (563), (564), (565), (567), (569), (571), (573), (574), % 147.85/21.65 | | | | | | | (575), (576), (577), (579), (581), (582), (583), (584), % 147.85/21.65 | | | | | | | (585), (626), (632), (633), (635), (636), (637), (638), % 147.85/21.65 | | | | | | | (2109), (2111), (2112), (2142), (function-axioms) are % 147.85/21.65 | | | | | | | inconsistent by sub-proof #10. % 147.85/21.65 | | | | | | | % 147.85/21.65 | | | | | | End of split % 147.85/21.65 | | | | | | % 147.85/21.65 | | | | | End of split % 147.85/21.65 | | | | | % 147.85/21.65 | | | | End of split % 147.85/21.65 | | | | % 147.85/21.65 | | | End of split % 147.85/21.65 | | | % 147.85/21.65 | | Case 2: % 147.85/21.65 | | | % 147.85/21.65 | | | (2143) all_6_1 = e0 % 147.85/21.65 | | | % 147.85/21.65 | | | REDUCE: (42), (2143) imply: % 147.85/21.65 | | | (2144) op(all_6_2, e1) = e0 % 147.85/21.65 | | | % 147.85/21.65 | | | BETA: splitting (49) gives: % 147.85/21.65 | | | % 147.85/21.65 | | | Case 1: % 147.85/21.65 | | | | % 147.85/21.65 | | | | (2145) ~ (all_8_1 = e0) % 147.85/21.65 | | | | % 147.85/21.65 | | | | BETA: splitting (54) gives: % 147.85/21.65 | | | | % 147.85/21.65 | | | | Case 1: % 147.85/21.65 | | | | | % 147.85/21.65 | | | | | (2146) ~ (all_10_0 = e0) % 147.85/21.65 | | | | | % 147.85/21.65 | | | | | BETA: splitting (64) gives: % 147.85/21.65 | | | | | % 147.85/21.65 | | | | | Case 1: % 147.85/21.65 | | | | | | % 147.85/21.65 | | | | | | (2147) ~ (all_14_2 = e0) % 147.85/21.65 | | | | | | % 147.85/21.65 | | | | | | REDUCE: (525), (2147) imply: % 147.85/21.65 | | | | | | (2148) ~ (all_8_2 = e0) % 147.85/21.65 | | | | | | % 147.85/21.66 | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41), % 147.85/21.66 | | | | | | (42), (43), (46), (47), (51), (52), (53), (69), (74), % 147.85/21.66 | | | | | | (79), (94), (113), (137), (152), (156), (158), (159), % 147.85/21.66 | | | | | | (163), (164), (166), (167), (169), (171), (172), (174), % 147.85/21.66 | | | | | | (179), (180), (181), (182), (185), (186), (187), (189), % 147.85/21.66 | | | | | | (190), (191), (192), (194), (195), (203), (204), (205), % 147.85/21.66 | | | | | | (206), (208), (209), (210), (211), (214), (215), (216), % 147.85/21.66 | | | | | | (235), (236), (237), (238), (239), (240), (241), (242), % 147.85/21.66 | | | | | | (243), (244), (245), (246), (247), (248), (249), (250), % 147.85/21.66 | | | | | | (268), (269), (270), (271), (272), (273), (274), (275), % 147.85/21.66 | | | | | | (276), (277), (278), (279), (280), (281), (282), (283), % 147.85/21.66 | | | | | | (284), (285), (286), (287), (288), (289), (290), (291), % 147.85/21.66 | | | | | | (292), (293), (294), (295), (296), (297), (298), (332), % 147.85/21.66 | | | | | | (333), (334), (335), (336), (337), (338), (347), (350), % 147.85/21.66 | | | | | | (355), (358), (370), (371), (376), (379), (381), (391), % 147.85/21.66 | | | | | | (392), (397), (400), (411), (413), (417), (419), (421), % 147.85/21.66 | | | | | | (425), (427), (429), (445), (447), (454), (456), (458), % 147.85/21.66 | | | | | | (459), (465), (467), (468), (470), (471), (473), (519), % 147.85/21.66 | | | | | | (523), (527), (528), (529), (531), (535), (536), (537), % 147.85/21.66 | | | | | | (538), (539), (540), (541), (542), (543), (544), (545), % 147.85/21.66 | | | | | | (546), (547), (548), (549), (551), (553), (555), (557), % 147.85/21.66 | | | | | | (559), (561), (562), (563), (564), (565), (567), (569), % 147.85/21.66 | | | | | | (571), (573), (574), (575), (576), (577), (579), (581), % 147.85/21.66 | | | | | | (582), (583), (584), (585), (626), (627), (628), (629), % 147.85/21.66 | | | | | | (630), (631), (632), (633), (634), (635), (636), (637), % 147.85/21.66 | | | | | | (638), (639), (640), (641), (645), (671), (690), (691), % 147.85/21.66 | | | | | | (697), (701), (723), (748), (760), (771), (774), (780), % 147.85/21.66 | | | | | | (1976), (2145), (2146), (2148), (function-axioms) are % 147.85/21.66 | | | | | | inconsistent by sub-proof #44. % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | Case 2: % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | (2149) all_14_2 = e0 % 147.85/21.66 | | | | | | (2150) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (525), (2149) imply: % 147.85/21.66 | | | | | | (2151) all_8_2 = e0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | SIMP: (2151) implies: % 147.85/21.66 | | | | | | (2152) all_8_2 = e0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (530), (2152) imply: % 147.85/21.66 | | | | | | (2153) all_48_2 = e0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (540), (2152) imply: % 147.85/21.66 | | | | | | (2154) all_56_3 = e0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (544), (2152) imply: % 147.85/21.66 | | | | | | (2155) all_58_29 = e0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (562), (2152) imply: % 147.85/21.66 | | | | | | (2156) ~ (all_52_1 = e0) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (565), (2152) imply: % 147.85/21.66 | | | | | | (2157) ~ (all_52_4 = e0) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (567), (2152) imply: % 147.85/21.66 | | | | | | (2158) ~ (all_52_6 = e0) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (569), (2152) imply: % 147.85/21.66 | | | | | | (2159) ~ (all_52_7 = e0) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (571), (2152) imply: % 147.85/21.66 | | | | | | (2160) ~ (all_52_9 = e0) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (573), (2152) imply: % 147.85/21.66 | | | | | | (2161) ~ (all_52_13 = e0) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (48), (2152) imply: % 147.85/21.66 | | | | | | (2162) op(e0, all_8_1) = all_8_0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (47), (2152) imply: % 147.85/21.66 | | | | | | (2163) op(e0, e2) = all_8_1 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (633), (2152) imply: % 147.85/21.66 | | | | | | (2164) op(e2, e0) = all_58_9 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, all_8_1, % 147.85/21.66 | | | | | | e2, e0, simplifying with (204), (2163) gives: % 147.85/21.66 | | | | | | (2165) all_52_7 = all_8_1 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 147.85/21.66 | | | | | | all_58_9, e0, e2, simplifying with (210), (2164) gives: % 147.85/21.66 | | | | | | (2166) all_58_9 = all_52_13 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (471), (2165) imply: % 147.85/21.66 | | | | | | (2167) all_54_13 = all_8_1 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (350), (2165) imply: % 147.85/21.66 | | | | | | (2168) all_56_13 = all_8_1 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | COMBINE_EQS: (547), (2165) imply: % 147.85/21.66 | | | | | | (2169) all_58_24 = all_8_1 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (186), (2165) imply: % 147.85/21.66 | | | | | | (2170) ~ (all_52_3 = all_8_1) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (181), (2165) imply: % 147.85/21.66 | | | | | | (2171) ~ (all_52_4 = all_8_1) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (174), (2165) imply: % 147.85/21.66 | | | | | | (2172) ~ (all_52_6 = all_8_1) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (171), (2165) imply: % 147.85/21.66 | | | | | | (2173) ~ (all_52_11 = all_8_1) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | SIMP: (2173) implies: % 147.85/21.66 | | | | | | (2174) ~ (all_52_11 = all_8_1) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (575), (2165) imply: % 147.85/21.66 | | | | | | (2175) ~ (all_8_1 = all_4_2) % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | REDUCE: (639), (2165) imply: % 147.85/21.66 | | | | | | (2176) op(e0, all_8_1) = all_58_23 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 147.85/21.66 | | | | | | all_58_23, all_8_1, e0, simplifying with (2162), (2176) % 147.85/21.66 | | | | | | gives: % 147.85/21.66 | | | | | | (2177) all_58_23 = all_8_0 % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | BETA: splitting (108) gives: % 147.85/21.66 | | | | | | % 147.85/21.66 | | | | | | Case 1: % 147.85/21.66 | | | | | | | % 147.85/21.66 | | | | | | | (2178) ~ (all_32_1 = e0) % 147.85/21.66 | | | | | | | % 147.85/21.66 | | | | | | | REDUCE: (696), (2178) imply: % 147.85/21.66 | | | | | | | (2179) ~ (all_10_1 = e0) % 147.85/21.66 | | | | | | | % 147.85/21.66 | | | | | | | BETA: splitting (147) gives: % 147.85/21.66 | | | | | | | % 147.85/21.66 | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | | (2180) ~ (all_48_2 = e0) % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | | REDUCE: (2153), (2180) imply: % 147.85/21.66 | | | | | | | | (2181) $false % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | | CLOSE: (2181) is inconsistent. % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | | (2182) ~ (all_48_0 = e1) | ~ (all_48_1 = e3) % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | | BETA: splitting (268) gives: % 147.85/21.66 | | | | | | | | % 147.85/21.66 | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | (2183) all_56_15 = e0 % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | COMBINE_EQS: (538), (2183) imply: % 147.85/21.66 | | | | | | | | | (2184) all_4_2 = e0 % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.85/21.66 | | | | | | | | | (542), (543), (2155), (2184) are inconsistent by % 147.85/21.66 | | | | | | | | | sub-proof #399. % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | (2185) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 147.85/21.66 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | ALPHA: (2185) implies: % 147.85/21.66 | | | | | | | | | (2186) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | BETA: splitting (292) gives: % 147.85/21.66 | | | | | | | | | % 147.85/21.66 | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | (2187) all_56_0 = e0 % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | COMBINE_EQS: (541), (2187) imply: % 147.85/21.66 | | | | | | | | | | (2188) all_10_2 = e0 % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | COMBINE_EQS: (545), (2188) imply: % 147.85/21.66 | | | | | | | | | | (2189) all_58_28 = e0 % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.85/21.66 | | | | | | | | | | (543), (2155), (2189) are inconsistent by % 147.85/21.66 | | | | | | | | | | sub-proof #483. % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | (2190) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | BETA: splitting (237) gives: % 147.85/21.66 | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | (2191) all_54_13 = e0 % 147.85/21.66 | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | REF_CLOSE: (2145), (2167), (2191) are inconsistent by % 147.85/21.66 | | | | | | | | | | | sub-proof #397. % 147.85/21.66 | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | (2192) ~ (all_54_13 = e0) % 147.85/21.66 | | | | | | | | | | | (2193) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 147.85/21.66 | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | BETA: splitting (243) gives: % 147.85/21.66 | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | (2194) all_54_7 = e0 % 147.85/21.66 | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | REF_CLOSE: (467), (2161), (2194) are inconsistent by % 147.85/21.66 | | | | | | | | | | | | sub-proof #742. % 147.85/21.66 | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | (2195) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 147.85/21.66 | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | BETA: splitting (244) gives: % 147.85/21.66 | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | (2196) all_54_6 = e0 % 147.85/21.66 | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | REF_CLOSE: (456), (2160), (2196) are inconsistent by % 147.85/21.66 | | | | | | | | | | | | | sub-proof #797. % 147.85/21.66 | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | (2197) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 147.85/21.66 | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | BETA: splitting (241) gives: % 147.85/21.66 | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | (2198) all_54_9 = e0 % 147.85/21.66 | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | REF_CLOSE: (459), (2158), (2198) are inconsistent by % 147.85/21.66 | | | | | | | | | | | | | | sub-proof #572. % 147.85/21.66 | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | (2199) ~ (all_54_9 = e0) % 147.85/21.66 | | | | | | | | | | | | | | (2200) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 147.85/21.66 | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | BETA: splitting (246) gives: % 147.85/21.66 | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | (2201) all_54_4 = e0 % 147.85/21.66 | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | REF_CLOSE: (447), (2156), (2201) are inconsistent by % 147.85/21.66 | | | | | | | | | | | | | | | sub-proof #859. % 147.85/21.66 | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | (2202) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 147.85/21.66 | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 147.85/21.66 | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | | (2203) all_54_0 = e0 % 147.85/21.66 | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.85/21.66 | | | | | | | | | | | | | | | | (537), (543), (545), (2155), (2203) are % 147.85/21.66 | | | | | | | | | | | | | | | | inconsistent by sub-proof #395. % 147.85/21.66 | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | Case 2: % 147.85/21.66 | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | | (2204) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 147.85/21.66 | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 147.85/21.66 | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | | Case 1: % 147.85/21.66 | | | | | | | | | | | | | | | | | % 147.85/21.66 | | | | | | | | | | | | | | | | | (2205) all_54_15 = e0 % 147.85/21.66 | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (2205) imply: % 147.85/21.67 | | | | | | | | | | | | | | | | | (2206) all_4_2 = e0 % 147.85/21.67 | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 147.85/21.67 | | | | | | | | | | | | | | | | | (542), (543), (2155), (2206) are inconsistent by % 147.85/21.67 | | | | | | | | | | | | | | | | | sub-proof #399. % 147.85/21.67 | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | Case 2: % 147.85/21.67 | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | (2207) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 147.85/21.67 | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 147.85/21.67 | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | Case 1: % 147.85/21.67 | | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | | (2208) all_54_2 = e0 % 147.85/21.67 | | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2208) imply: % 147.85/21.67 | | | | | | | | | | | | | | | | | | (2209) all_52_8 = e0 % 147.85/21.67 | | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | | SIMP: (2209) implies: % 147.85/21.67 | | | | | | | | | | | | | | | | | | (2210) all_52_8 = e0 % 147.85/21.67 | | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (2210) imply: % 147.85/21.67 | | | | | | | | | | | | | | | | | | (2211) all_56_4 = e0 % 147.85/21.67 | | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (2210) imply: % 147.85/21.67 | | | | | | | | | | | | | | | | | | (2212) all_58_4 = e0 % 147.85/21.67 | | | | | | | | | | | | | | | | | | % 147.85/21.67 | | | | | | | | | | | | | | | | | | REDUCE: (169), (2210) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2213) ~ (all_52_9 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | REDUCE: (167), (2210) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2214) ~ (all_52_11 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | SIMP: (2214) implies: % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2215) ~ (all_52_11 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | REDUCE: (627), (2210) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2216) op(e3, e0) = all_58_3 % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | REDUCE: (215), (2210) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2217) op(e3, e1) = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (79), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (156), (158), (159), (163), (164), (172), (179), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (182), (185), (187), (189), (190), (191), (192), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (194), (195), (203), (206), (211), (214), (236), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (240), (242), (246), (247), (249), (269), (271), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (272), (273), (274), (275), (276), (277), (278), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (280), (284), (285), (286), (288), (289), (290), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (293), (294), (295), (296), (298), (332), (334), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (335), (336), (337), (338), (347), (350), (355), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (358), (370), (371), (376), (379), (391), (392), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (400), (411), (417), (419), (421), (425), (427), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (429), (445), (447), (456), (458), (459), (465), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (467), (473), (535), (536), (537), (538), (539), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (541), (542), (543), (545), (546), (548), (549), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (551), (553), (555), (557), (561), (563), (574), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (577), (579), (582), (583), (584), (585), (628), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (629), (630), (631), (636), (638), (693), (772), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2150), (2154), (2155), (2157), (2158), (2159), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2160), (2162), (2163), (2166), (2167), (2168), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2169), (2170), (2171), (2172), (2174), (2175), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2177), (2186), (2193), (2195), (2197), (2200), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2202), (2204), (2207), (2211), (2212), (2215), % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2216), (2217), (function-axioms) are inconsistent % 148.30/21.72 | | | | | | | | | | | | | | | | | | by sub-proof #4. % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2218) ~ (all_54_2 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | REDUCE: (454), (2218) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | (2219) ~ (all_52_8 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | BETA: splitting (2190) gives: % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | (2220) all_56_1 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (2220) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | (2221) all_52_4 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | REDUCE: (2157), (2221) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | (2222) $false % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | CLOSE: (2222) is inconsistent. % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | (2223) all_56_4 = e0 | all_56_9 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (2223) gives: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2224) all_56_4 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (2224) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2225) all_52_8 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (2219), (2225) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2226) $false % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | CLOSE: (2226) is inconsistent. % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2227) all_56_9 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (2227) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2228) all_52_12 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (2228) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2229) ~ (all_52_14 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | SIMP: (2229) implies: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | (2230) ~ (all_52_14 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2231) all_56_6 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (2231) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2232) all_52_2 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2232) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2233) all_58_15 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (2232) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2234) ~ (all_52_3 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | SIMP: (2234) implies: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2235) ~ (all_52_3 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (2232) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2236) ~ (all_52_6 = e0) % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (634), (2232) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2237) op(e1, e0) = all_58_14 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (2232) imply: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2238) op(e1, e3) = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (52), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (156), (158), (166), (167), (169), (172), (180), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (185), (192), (194), (205), (206), (213), (214), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (246), (248), (250), (269), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (270), (276), (280), (284), (285), (286), (288), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (292), (294), (296), (332), (334), (335), (336), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (337), (347), (355), (358), (370), (379), (391), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (392), (397), (411), (413), (417), (419), (421), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (425), (429), (447), (454), (468), (470), (537), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (541), (542), (543), (545), (546), (549), (551), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (555), (557), (559), (564), (576), (577), (579), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (581), (583), (584), (585), (628), (630), (637), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (640), (700), (779), (2145), (2154), (2155), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2156), (2157), (2158), (2162), (2163), (2166), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2167), (2168), (2170), (2174), (2175), (2177), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2179), (2182), (2186), (2231), (2233), (2235), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2237), (2238), (function-axioms) are inconsistent % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | by sub-proof #37. % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (2239) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (79), (334), (335), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (337), (338), (425), (427), (539), (542), (543), % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | (545), (2155), (2158), (2230), (2239) are % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | | % 148.30/21.72 | | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | | % 148.30/21.72 | | | | | | | | | End of split % 148.30/21.72 | | | | | | | | | % 148.30/21.72 | | | | | | | | End of split % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | End of split % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | Case 2: % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | | (2240) all_32_1 = e0 % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | | COMBINE_EQS: (696), (2240) imply: % 148.30/21.72 | | | | | | | (2241) all_10_1 = e0 % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | | SIMP: (2241) implies: % 148.30/21.72 | | | | | | | (2242) all_10_1 = e0 % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | | REDUCE: (52), (2242) imply: % 148.30/21.72 | | | | | | | (2243) op(all_10_2, e3) = e0 % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | | BETA: splitting (268) gives: % 148.30/21.72 | | | | | | | % 148.30/21.72 | | | | | | | Case 1: % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | | (2244) all_56_15 = e0 % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | | COMBINE_EQS: (538), (2244) imply: % 148.30/21.72 | | | | | | | | (2245) all_4_2 = e0 % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 148.30/21.72 | | | | | | | | (542), (543), (2155), (2245) are inconsistent by % 148.30/21.72 | | | | | | | | sub-proof #399. % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | Case 2: % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | | (2246) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 148.30/21.72 | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 148.30/21.72 | | | | | | | | % 148.30/21.72 | | | | | | | | ALPHA: (2246) implies: % 148.30/21.72 | | | | | | | | (2247) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 148.30/21.72 | | | | | | | | (2248) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 148.30/21.72 | | | | | | | | % 148.30/21.73 | | | | | | | | BETA: splitting (292) gives: % 148.30/21.73 | | | | | | | | % 148.30/21.73 | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | (2249) all_56_0 = e0 % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | COMBINE_EQS: (541), (2249) imply: % 148.30/21.73 | | | | | | | | | (2250) all_10_2 = e0 % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | COMBINE_EQS: (545), (2250) imply: % 148.30/21.73 | | | | | | | | | (2251) all_58_28 = e0 % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 148.30/21.73 | | | | | | | | | (543), (2155), (2251) are inconsistent by sub-proof % 148.30/21.73 | | | | | | | | | #483. % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | (2252) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | BETA: splitting (237) gives: % 148.30/21.73 | | | | | | | | | % 148.30/21.73 | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | (2253) all_54_13 = e0 % 148.30/21.73 | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | REF_CLOSE: (2145), (2167), (2253) are inconsistent by % 148.30/21.73 | | | | | | | | | | sub-proof #397. % 148.30/21.73 | | | | | | | | | | % 148.30/21.73 | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | (2254) ~ (all_54_13 = e0) % 148.30/21.73 | | | | | | | | | | (2255) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 148.30/21.73 | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | BETA: splitting (243) gives: % 148.30/21.73 | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | (2256) all_54_7 = e0 % 148.30/21.73 | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | REF_CLOSE: (467), (2161), (2256) are inconsistent by % 148.30/21.73 | | | | | | | | | | | sub-proof #742. % 148.30/21.73 | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | (2257) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 148.30/21.73 | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | BETA: splitting (244) gives: % 148.30/21.73 | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | (2258) all_54_6 = e0 % 148.30/21.73 | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | REF_CLOSE: (456), (2160), (2258) are inconsistent by % 148.30/21.73 | | | | | | | | | | | | sub-proof #797. % 148.30/21.73 | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | (2259) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 148.30/21.73 | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | BETA: splitting (241) gives: % 148.30/21.73 | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | (2260) all_54_9 = e0 % 148.30/21.73 | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | REF_CLOSE: (459), (2158), (2260) are inconsistent by % 148.30/21.73 | | | | | | | | | | | | | sub-proof #572. % 148.30/21.73 | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | (2261) ~ (all_54_9 = e0) % 148.30/21.73 | | | | | | | | | | | | | (2262) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 148.30/21.73 | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | BETA: splitting (246) gives: % 148.30/21.73 | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | (2263) all_54_4 = e0 % 148.30/21.73 | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | REF_CLOSE: (447), (2156), (2263) are inconsistent by % 148.30/21.73 | | | | | | | | | | | | | | sub-proof #859. % 148.30/21.73 | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | (2264) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 148.30/21.73 | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | BETA: splitting (250) gives: % 148.30/21.73 | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | (2265) all_54_0 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 148.30/21.73 | | | | | | | | | | | | | | | (537), (543), (545), (2155), (2265) are % 148.30/21.73 | | | | | | | | | | | | | | | inconsistent by sub-proof #395. % 148.30/21.73 | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | (2266) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 148.30/21.73 | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 148.30/21.73 | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | (2267) all_54_15 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (2267) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | (2268) all_4_2 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (334), (335), (337), % 148.30/21.73 | | | | | | | | | | | | | | | | (542), (543), (2155), (2268) are inconsistent by % 148.30/21.73 | | | | | | | | | | | | | | | | sub-proof #399. % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | (2269) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 148.30/21.73 | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | (2270) all_54_2 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (2270) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2271) all_52_8 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | SIMP: (2271) implies: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2272) all_52_8 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (2272) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2273) all_56_4 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (397), (2272) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2274) all_58_4 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | REDUCE: (169), (2272) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2275) ~ (all_52_9 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | REDUCE: (167), (2272) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2276) ~ (all_52_11 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | SIMP: (2276) implies: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2277) ~ (all_52_11 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | REDUCE: (627), (2272) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2278) op(e3, e0) = all_58_3 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | REDUCE: (215), (2272) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2279) op(e3, e1) = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (79), % 148.30/21.73 | | | | | | | | | | | | | | | | | (156), (158), (159), (163), (164), (172), (179), % 148.30/21.73 | | | | | | | | | | | | | | | | | (182), (185), (187), (189), (190), (191), (192), % 148.30/21.73 | | | | | | | | | | | | | | | | | (194), (195), (203), (206), (211), (214), (236), % 148.30/21.73 | | | | | | | | | | | | | | | | | (240), (242), (246), (247), (249), (269), (271), % 148.30/21.73 | | | | | | | | | | | | | | | | | (272), (273), (274), (275), (276), (277), (278), % 148.30/21.73 | | | | | | | | | | | | | | | | | (280), (284), (285), (286), (288), (289), (290), % 148.30/21.73 | | | | | | | | | | | | | | | | | (293), (294), (295), (296), (298), (332), (334), % 148.30/21.73 | | | | | | | | | | | | | | | | | (335), (336), (337), (338), (347), (350), (355), % 148.30/21.73 | | | | | | | | | | | | | | | | | (358), (370), (371), (376), (379), (391), (392), % 148.30/21.73 | | | | | | | | | | | | | | | | | (400), (411), (417), (419), (421), (425), (427), % 148.30/21.73 | | | | | | | | | | | | | | | | | (429), (445), (447), (456), (458), (459), (465), % 148.30/21.73 | | | | | | | | | | | | | | | | | (467), (473), (535), (536), (537), (538), (539), % 148.30/21.73 | | | | | | | | | | | | | | | | | (541), (542), (543), (545), (546), (548), (549), % 148.30/21.73 | | | | | | | | | | | | | | | | | (551), (553), (555), (557), (561), (563), (574), % 148.30/21.73 | | | | | | | | | | | | | | | | | (577), (579), (582), (583), (584), (585), (628), % 148.30/21.73 | | | | | | | | | | | | | | | | | (629), (630), (631), (636), (638), (693), (772), % 148.30/21.73 | | | | | | | | | | | | | | | | | (2150), (2154), (2155), (2157), (2158), (2159), % 148.30/21.73 | | | | | | | | | | | | | | | | | (2160), (2162), (2163), (2166), (2167), (2168), % 148.30/21.73 | | | | | | | | | | | | | | | | | (2169), (2170), (2171), (2172), (2174), (2175), % 148.30/21.73 | | | | | | | | | | | | | | | | | (2177), (2247), (2255), (2257), (2259), (2262), % 148.30/21.73 | | | | | | | | | | | | | | | | | (2264), (2266), (2269), (2273), (2274), (2277), % 148.30/21.73 | | | | | | | | | | | | | | | | | (2278), (2279), (function-axioms) are inconsistent % 148.30/21.73 | | | | | | | | | | | | | | | | | by sub-proof #4. % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | (2280) ~ (all_54_2 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | REDUCE: (454), (2280) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | (2281) ~ (all_52_8 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | BETA: splitting (2252) gives: % 148.30/21.73 | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | (2282) all_56_1 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (2282) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | (2283) all_52_4 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | REDUCE: (2157), (2283) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | (2284) $false % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | CLOSE: (2284) is inconsistent. % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | (2285) all_56_4 = e0 | all_56_9 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | BETA: splitting (2285) gives: % 148.30/21.73 | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2286) all_56_4 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (2286) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2287) all_52_8 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | REDUCE: (2281), (2287) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2288) $false % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | CLOSE: (2288) is inconsistent. % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2289) all_56_9 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (2289) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2290) all_52_12 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | REDUCE: (159), (2290) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2291) ~ (all_52_13 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | REDUCE: (158), (2290) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2292) ~ (all_52_14 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | SIMP: (2292) implies: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | (2293) ~ (all_52_14 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | (2294) all_56_6 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (2294) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | (2295) all_52_2 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (2295) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | (2296) all_58_15 = e0 % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (2295) imply: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | (2297) ~ (all_52_3 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | SIMP: (2297) implies: % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | (2298) ~ (all_52_3 = e0) % 148.30/21.73 | | | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (79), (158), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (166), (169), (179), (180), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (185), (191), (194), (213), (238), (244), (248), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (250), (281), (285), (286), (289), (293), (295), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (296), (297), (298), (334), (335), (336), (337), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (338), (347), (355), (358), (376), (379), (391), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (392), (397), (400), (411), (413), (417), (419), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (421), (427), (429), (454), (456), (470), (537), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (541), (542), (543), (545), (546), (549), (551), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (555), (557), (559), (564), (576), (577), (579), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (584), (629), (2145), (2154), (2155), (2156), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (2161), (2168), (2169), (2171), (2243), (2247), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (2248), (2293), (2294), (2296), (2298), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | #16. % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (2299) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (79), (334), (335), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (337), (338), (425), (427), (539), (542), (543), % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | (545), (2155), (2158), (2293), (2299) are % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 148.30/21.74 | | | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | | % 148.30/21.74 | | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | | % 148.30/21.74 | | | | | | | | | End of split % 148.30/21.74 | | | | | | | | | % 148.30/21.74 | | | | | | | | End of split % 148.30/21.74 | | | | | | | | % 148.30/21.74 | | | | | | | End of split % 148.30/21.74 | | | | | | | % 148.30/21.74 | | | | | | End of split % 148.30/21.74 | | | | | | % 148.30/21.74 | | | | | End of split % 148.30/21.74 | | | | | % 148.30/21.74 | | | | Case 2: % 148.30/21.74 | | | | | % 148.30/21.74 | | | | | (2300) all_10_0 = e0 % 148.30/21.74 | | | | | % 148.30/21.74 | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (41), (47), (48), % 148.30/21.74 | | | | | (51), (52), (53), (64), (74), (79), (156), (158), (159), % 148.30/21.74 | | | | | (163), (164), (166), (167), (169), (171), (172), (174), % 148.30/21.74 | | | | | (179), (180), (181), (182), (185), (186), (187), (189), % 148.30/21.74 | | | | | (190), (191), (192), (194), (195), (203), (204), (205), % 148.30/21.74 | | | | | (206), (210), (211), (213), (214), (215), (235), (236), % 148.30/21.74 | | | | | (237), (238), (239), (240), (241), (242), (243), (244), % 148.30/21.74 | | | | | (245), (246), (247), (248), (249), (250), (268), (269), % 148.30/21.74 | | | | | (270), (271), (272), (273), (274), (275), (276), (277), % 148.30/21.74 | | | | | (278), (279), (280), (281), (282), (283), (284), (285), % 148.30/21.74 | | | | | (286), (287), (288), (289), (290), (291), (292), (293), % 148.30/21.74 | | | | | (294), (295), (296), (297), (298), (332), (333), (334), % 148.30/21.74 | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 148.30/21.74 | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 148.30/21.74 | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 148.30/21.74 | | | | | (429), (445), (447), (454), (456), (458), (459), (465), % 148.30/21.74 | | | | | (467), (468), (470), (471), (473), (519), (525), (535), % 148.30/21.74 | | | | | (536), (537), (538), (539), (540), (541), (542), (543), % 148.30/21.74 | | | | | (544), (545), (546), (547), (548), (549), (551), (553), % 148.30/21.74 | | | | | (555), (557), (559), (561), (562), (563), (564), (565), % 148.30/21.74 | | | | | (567), (569), (571), (573), (574), (575), (576), (577), % 148.30/21.74 | | | | | (579), (581), (582), (583), (584), (585), (628), (629), % 148.30/21.74 | | | | | (630), (633), (634), (636), (637), (638), (639), (641), % 148.30/21.74 | | | | | (693), (772), (1976), (2144), (2300), (function-axioms) are % 148.30/21.74 | | | | | inconsistent by sub-proof #1. % 148.30/21.74 | | | | | % 148.30/21.74 | | | | End of split % 148.30/21.74 | | | | % 148.30/21.74 | | | Case 2: % 148.30/21.74 | | | | % 148.30/21.74 | | | | (2301) all_8_1 = e0 % 148.30/21.74 | | | | (2302) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 148.30/21.74 | | | | % 148.30/21.74 | | | | COMBINE_EQS: (686), (2301) imply: % 148.30/21.74 | | | | (2303) all_22_1 = e0 % 148.30/21.74 | | | | % 148.30/21.74 | | | | REDUCE: (48), (2301) imply: % 148.30/21.74 | | | | (2304) op(all_8_2, e0) = all_8_0 % 148.30/21.74 | | | | % 148.30/21.74 | | | | REDUCE: (47), (2301) imply: % 148.30/21.74 | | | | (2305) op(all_8_2, e2) = e0 % 148.30/21.74 | | | | % 148.30/21.74 | | | | BETA: splitting (54) gives: % 148.30/21.74 | | | | % 148.30/21.74 | | | | Case 1: % 148.30/21.74 | | | | | % 148.30/21.74 | | | | | (2306) ~ (all_10_0 = e0) % 148.30/21.74 | | | | | % 148.30/21.75 | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (41), (42), (46), % 148.30/21.75 | | | | | (51), (52), (53), (69), (74), (79), (84), (108), (152), % 148.30/21.75 | | | | | (156), (158), (159), (163), (164), (166), (167), (169), % 148.30/21.75 | | | | | (171), (172), (174), (179), (180), (181), (182), (185), % 148.30/21.75 | | | | | (186), (187), (189), (190), (191), (192), (194), (195), % 148.30/21.75 | | | | | (203), (204), (205), (206), (208), (209), (210), (214), % 148.30/21.75 | | | | | (215), (216), (236), (238), (240), (241), (243), (244), % 148.30/21.75 | | | | | (245), (246), (247), (248), (249), (250), (268), (269), % 148.30/21.75 | | | | | (270), (271), (272), (273), (274), (275), (276), (277), % 148.30/21.75 | | | | | (278), (279), (280), (281), (282), (283), (284), (285), % 148.30/21.75 | | | | | (286), (287), (288), (289), (290), (291), (292), (293), % 148.30/21.75 | | | | | (294), (295), (296), (297), (298), (332), (333), (334), % 148.30/21.75 | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 148.30/21.75 | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 148.30/21.75 | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 148.30/21.75 | | | | | (429), (445), (447), (454), (456), (459), (465), (467), % 148.30/21.75 | | | | | (470), (473), (517), (519), (523), (531), (536), (537), % 148.30/21.75 | | | | | (538), (539), (540), (541), (542), (543), (544), (545), % 148.30/21.75 | | | | | (546), (547), (548), (549), (551), (553), (555), (557), % 148.30/21.75 | | | | | (559), (561), (562), (563), (564), (565), (567), (569), % 148.30/21.75 | | | | | (571), (573), (574), (575), (576), (577), (579), (581), % 148.30/21.75 | | | | | (582), (583), (584), (585), (626), (627), (628), (629), % 148.30/21.75 | | | | | (630), (631), (632), (633), (634), (635), (636), (637), % 148.30/21.75 | | | | | (638), (639), (641), (691), (696), (701), (766), (771), % 148.30/21.75 | | | | | (780), (1976), (2302), (2303), (2304), (2305), (2306), % 148.30/21.75 | | | | | (function-axioms) are inconsistent by sub-proof #9. % 148.30/21.75 | | | | | % 148.30/21.75 | | | | Case 2: % 148.30/21.75 | | | | | % 148.30/21.75 | | | | | (2307) all_10_0 = e0 % 148.30/21.75 | | | | | % 148.30/21.75 | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (41), (47), (48), % 148.30/21.75 | | | | | (51), (52), (53), (64), (74), (79), (156), (158), (159), % 148.30/21.75 | | | | | (163), (164), (166), (167), (169), (171), (172), (174), % 148.30/21.75 | | | | | (179), (180), (181), (182), (185), (186), (187), (189), % 148.30/21.75 | | | | | (190), (191), (192), (194), (195), (203), (204), (205), % 148.30/21.75 | | | | | (206), (210), (211), (213), (214), (215), (235), (236), % 148.30/21.75 | | | | | (237), (238), (239), (240), (241), (242), (243), (244), % 148.30/21.75 | | | | | (245), (246), (247), (248), (249), (250), (268), (269), % 148.30/21.75 | | | | | (270), (271), (272), (273), (274), (275), (276), (277), % 148.30/21.75 | | | | | (278), (279), (280), (281), (282), (283), (284), (285), % 148.30/21.75 | | | | | (286), (287), (288), (289), (290), (291), (292), (293), % 148.30/21.75 | | | | | (294), (295), (296), (297), (298), (332), (333), (334), % 148.30/21.75 | | | | | (335), (336), (337), (338), (347), (350), (355), (358), % 148.30/21.75 | | | | | (370), (371), (376), (379), (381), (391), (392), (397), % 148.30/21.75 | | | | | (400), (411), (413), (417), (419), (421), (425), (427), % 148.30/21.75 | | | | | (429), (445), (447), (454), (456), (458), (459), (465), % 148.30/21.75 | | | | | (467), (468), (470), (471), (473), (519), (525), (535), % 148.30/21.75 | | | | | (536), (537), (538), (539), (540), (541), (542), (543), % 148.30/21.75 | | | | | (544), (545), (546), (547), (548), (549), (551), (553), % 148.30/21.75 | | | | | (555), (557), (559), (561), (562), (563), (564), (565), % 148.30/21.75 | | | | | (567), (569), (571), (573), (574), (575), (576), (577), % 148.30/21.75 | | | | | (579), (581), (582), (583), (584), (585), (628), (629), % 148.30/21.75 | | | | | (630), (633), (634), (636), (637), (638), (639), (641), % 148.30/21.75 | | | | | (693), (772), (1976), (2144), (2307), (function-axioms) are % 148.30/21.75 | | | | | inconsistent by sub-proof #1. % 148.30/21.75 | | | | | % 148.30/21.75 | | | | End of split % 148.30/21.75 | | | | % 148.30/21.75 | | | End of split % 148.30/21.75 | | | % 148.30/21.75 | | End of split % 148.30/21.75 | | % 148.30/21.75 | End of split % 148.30/21.75 | % 148.30/21.75 End of proof % 148.30/21.75 % 148.30/21.75 Sub-proof #1 shows that the following formulas are inconsistent: % 148.30/21.75 ---------------------------------------------------------------- % 148.30/21.75 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 148.30/21.75 (2) all_58_31 = all_4_2 % 148.30/21.75 (3) ~ (all_52_8 = all_52_9) % 148.30/21.75 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 148.30/21.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 148.30/21.75 (5) all_54_13 = all_52_7 % 148.30/21.75 (6) ~ (all_52_2 = all_52_3) % 148.30/21.75 (7) all_58_11 = all_52_9 % 148.30/21.75 (8) all_56_15 = all_4_2 % 148.30/21.75 (9) all_56_7 = all_52_6 % 148.30/21.75 (10) ~ (all_52_6 = all_6_2) % 148.30/21.75 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.30/21.75 (12) all_54_2 = all_52_8 % 148.30/21.75 (13) all_14_2 = all_8_2 % 148.30/21.75 (14) all_54_8 = all_52_2 % 148.30/21.75 (15) op(e1, all_6_2) = all_58_18 % 148.30/21.75 (16) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 148.30/21.75 (17) op(all_8_2, all_8_1) = all_8_0 % 148.30/21.75 (18) ~ (all_52_8 = all_10_2) % 148.30/21.75 (19) all_58_15 = all_52_2 % 148.30/21.75 (20) all_58_26 = all_52_11 % 148.30/21.75 (21) op(e1, all_52_14) = all_58_19 % 148.30/21.75 (22) ~ (all_52_8 = all_52_11) % 148.30/21.75 (23) ~ (all_52_11 = all_4_2) % 148.30/21.75 (24) all_54_7 = all_52_13 % 148.30/21.75 (25) all_58_6 = all_52_12 % 148.30/21.75 (26) ~ (all_52_6 = all_8_2) % 148.30/21.75 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 148.30/21.75 (28) all_56_4 = all_52_8 % 148.30/21.75 (29) ~ (all_52_4 = all_8_2) % 148.30/21.75 (30) all_54_3 = all_52_12 % 148.30/21.75 (31) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.30/21.75 (32) all_54_1 = all_52_4 % 148.30/21.75 (33) op(e0, all_4_2) = all_58_27 % 148.30/21.75 (34) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 148.30/21.75 (35) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 148.30/21.75 (36) ~ (all_52_4 = all_52_6) % 148.30/21.75 (37) all_58_13 = all_52_13 % 148.30/21.76 (38) op(e0, e1) = all_52_11 % 148.30/21.76 (39) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 148.30/21.76 (40) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 148.30/21.76 (41) ~ (all_52_6 = all_52_7) % 148.30/21.76 (42) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 148.30/21.76 (43) op(all_10_2, all_10_1) = all_10_0 % 148.30/21.76 (44) all_54_11 = all_52_14 % 148.30/21.76 (45) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 148.30/21.76 (46) all_58_20 = all_52_14 % 148.30/21.76 (47) ~ (all_52_8 = all_6_2) % 148.30/21.76 (48) op(e2, e3) = all_52_1 % 148.30/21.76 (49) ~ (all_52_12 = all_52_13) % 148.30/21.76 (50) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 148.30/21.76 (51) all_54_10 = all_6_2 % 148.30/21.76 (52) op(e0, all_52_3) = all_58_21 % 148.30/21.76 (53) op(e0, all_52_7) = all_58_23 % 148.30/21.76 (54) all_54_5 = all_8_2 % 148.30/21.76 (55) ~ (all_52_6 = all_52_14) % 148.30/21.76 (56) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 148.30/21.76 (57) all_54_6 = all_52_9 % 148.30/21.76 (58) all_54_15 = all_4_2 % 148.30/21.76 (59) ~ (all_52_4 = all_52_7) % 148.30/21.76 (60) ~ (all_52_2 = all_6_2) % 148.30/21.76 (61) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 148.30/21.76 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 148.30/21.76 (62) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 148.30/21.76 (63) op(e3, e3) = all_10_2 % 148.30/21.76 (64) ~ (all_52_8 = all_52_12) % 148.30/21.76 (65) all_54_9 = all_52_6 % 148.30/21.76 (66) ~ (all_52_13 = all_4_2) % 148.30/21.76 (67) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 148.30/21.76 (68) ~ (all_52_13 = all_8_2) % 148.30/21.76 (69) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 148.30/21.76 (70) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 148.30/21.76 (71) ~ (e3 = e1) % 148.30/21.76 (72) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 148.30/21.76 (73) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 148.30/21.76 (74) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 148.30/21.76 (75) ~ (all_52_1 = all_52_13) % 148.30/21.76 (76) all_56_5 = all_52_9 % 148.30/21.76 (77) all_54_14 = all_52_11 % 148.30/21.76 (78) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 148.30/21.76 (79) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 148.30/21.76 (80) all_56_12 = all_52_3 % 148.30/21.76 (81) ~ (all_52_3 = all_52_7) % 148.30/21.76 (82) all_58_2 = all_52_4 % 148.30/21.76 (83) all_20_2 = all_4_2 % 148.30/21.76 (84) all_56_11 = all_52_14 % 148.30/21.76 (85) all_56_1 = all_52_4 % 148.30/21.76 (86) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 148.30/21.76 (87) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 148.30/21.76 (88) ~ (all_52_3 = all_4_2) % 148.30/21.76 (89) op(e1, e0) = all_52_14 % 148.30/21.76 (90) ~ (all_52_9 = all_52_11) % 148.30/21.76 (91) ~ (all_52_1 = all_8_2) % 148.30/21.76 (92) all_56_3 = all_8_2 % 148.30/21.76 (93) all_58_24 = all_52_7 % 148.30/21.76 (94) ~ (all_52_13 = all_52_14) % 148.30/21.76 (95) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 148.30/21.76 (96) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 148.30/21.76 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 148.30/21.76 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 148.30/21.76 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 148.30/21.76 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 148.30/21.76 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 148.30/21.76 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 148.30/21.76 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 148.30/21.76 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 148.30/21.76 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 148.30/21.76 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 148.30/21.76 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 148.30/21.76 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 148.30/21.76 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.30/21.76 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 148.30/21.76 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 148.30/21.76 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.30/21.76 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 148.30/21.76 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.30/21.76 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 148.30/21.76 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 148.30/21.76 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 148.30/21.76 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 148.30/21.76 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 148.30/21.76 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 148.30/21.76 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 148.30/21.76 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 148.30/21.76 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 148.30/21.76 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 148.30/21.76 e0) % 148.30/21.76 (97) ~ (all_52_4 = all_52_8) % 148.30/21.76 (98) op(e1, all_52_2) = all_58_14 % 148.30/21.76 (99) all_10_0 = e0 % 148.30/21.76 (100) op(e2, e1) = all_52_9 % 148.30/21.76 (101) all_56_9 = all_52_12 % 148.30/21.76 (102) all_58_29 = all_8_2 % 148.30/21.76 (103) ~ (all_52_12 = all_52_14) % 148.30/21.76 (104) all_58_8 = all_52_1 % 148.30/21.76 (105) ~ (e2 = e1) % 148.30/21.76 (106) op(e3, e0) = all_52_12 % 148.30/21.76 (107) all_56_6 = all_52_2 % 148.30/21.76 (108) ~ (all_52_2 = all_52_6) % 148.30/21.76 (109) all_18_2 = all_6_2 % 148.30/21.76 (110) all_56_13 = all_52_7 % 148.30/21.76 (111) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 148.30/21.76 (112) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 148.30/21.76 (113) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 148.30/21.76 (114) op(all_6_2, e1) = e0 % 148.30/21.76 (115) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 148.30/21.76 (116) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 148.30/21.76 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 148.30/21.76 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 148.30/21.76 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 148.30/21.76 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 148.30/21.76 (all_58_27 = e0)) % 148.30/21.76 (117) ~ (all_52_9 = all_52_13) % 148.30/21.76 (118) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 148.30/21.76 (119) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 148.30/21.76 (120) ~ (all_52_11 = all_6_2) % 148.30/21.76 (121) op(e3, all_10_2) = all_58_0 % 148.30/21.76 (122) ~ (e3 = e0) % 148.30/21.76 (123) all_56_2 = all_52_1 % 148.30/21.76 (124) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.30/21.76 (125) op(e0, e3) = all_52_3 % 148.30/21.76 (126) op(e3, all_52_12) = all_58_5 % 148.30/21.76 (127) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 148.30/21.76 (128) all_56_10 = all_52_13 % 148.30/21.76 (129) ~ (all_52_12 = all_10_2) % 148.30/21.76 (130) ~ (all_52_1 = all_52_3) % 148.30/21.76 (131) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.30/21.76 (132) ~ (all_52_9 = all_8_2) % 148.30/21.76 (133) all_56_14 = all_52_11 % 148.30/21.76 (134) all_58_28 = all_10_2 % 148.30/21.77 (135) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 148.30/21.77 (136) all_58_17 = all_52_6 % 148.30/21.77 (137) ~ (all_52_1 = all_52_9) % 148.30/21.77 (138) op(e3, e1) = all_52_8 % 148.30/21.77 (139) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 148.30/21.77 (140) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 148.30/21.77 (141) ~ (all_52_7 = all_52_11) % 148.30/21.77 (142) op(all_8_2, e2) = all_8_1 % 148.30/21.77 (143) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 148.30/21.77 (144) all_14_0 = all_8_0 % 148.30/21.77 (145) ~ (e2 = e0) % 148.30/21.77 (146) ~ (all_52_9 = all_6_2) % 148.30/21.77 (147) ~ (all_52_2 = all_10_2) % 148.30/21.77 (148) all_56_0 = all_10_2 % 148.30/21.77 (149) op(e0, e0) = all_4_2 % 148.30/21.77 (150) ~ (all_52_3 = all_52_11) % 148.30/21.77 (151) all_58_22 = all_52_3 % 148.30/21.77 (152) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 148.30/21.77 (153) ~ (all_52_12 = all_4_2) % 148.30/21.77 (154) ~ (all_52_3 = all_10_2) % 148.30/21.77 (155) all_56_8 = all_6_2 % 148.30/21.77 (156) op(e1, e1) = all_6_2 % 148.30/21.77 (157) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 148.30/21.77 (158) ~ (all_52_1 = all_52_2) % 148.30/21.77 (159) ~ (all_52_7 = all_8_2) % 148.30/21.77 (160) op(e2, e0) = all_52_13 % 148.30/21.77 (161) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 148.30/21.77 (162) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 148.30/21.77 (163) all_58_4 = all_52_8 % 148.30/21.77 (164) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 148.30/21.77 (165) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 148.30/21.77 (166) all_54_0 = all_10_2 % 148.30/21.77 (167) ~ (all_52_2 = all_52_14) % 148.30/21.77 (168) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.30/21.77 (169) all_14_1 = all_8_1 % 148.30/21.77 (170) ~ (all_52_14 = all_4_2) % 148.30/21.77 (171) ~ (e1 = e0) % 148.30/21.77 (172) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 148.30/21.77 (173) ~ (all_52_7 = all_4_2) % 148.30/21.77 (174) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 148.30/21.77 (175) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 148.30/21.77 (176) op(all_4_2, all_4_1) = e1 % 148.30/21.77 (177) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) | ~ (all_14_2 = e0) % 148.30/21.77 (178) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 148.30/21.77 (179) op(e0, e2) = all_52_7 % 148.30/21.77 (180) ~ (all_52_4 = all_10_2) % 148.30/21.77 (181) all_58_30 = all_6_2 % 148.30/21.77 (182) op(e2, all_52_1) = all_58_7 % 148.30/21.77 (183) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.30/21.77 (184) ~ (e3 = e2) % 148.30/21.77 (185) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 148.30/21.77 (186) ~ (all_52_14 = all_6_2) % 148.30/21.77 (187) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 148.30/21.77 (188) op(all_4_2, e0) = all_4_1 % 148.30/21.77 (189) op(all_10_2, e3) = all_10_1 % 148.30/21.77 (190) ~ (all_52_4 = all_52_12) % 148.30/21.77 (191) all_54_12 = all_52_3 % 148.30/21.77 (192) op(e2, all_8_2) = all_58_9 % 148.30/21.77 (193) all_54_4 = all_52_1 % 148.30/21.77 (194) ~ (all_52_1 = all_10_2) % 148.30/21.77 % 148.30/21.77 Begin of proof % 148.30/21.77 | % 148.30/21.77 | REDUCE: (43), (99) imply: % 148.30/21.77 | (195) op(all_10_2, all_10_1) = e0 % 148.30/21.77 | % 148.30/21.77 | BETA: splitting (177) gives: % 148.30/21.77 | % 148.30/21.77 | Case 1: % 148.30/21.77 | | % 148.30/21.77 | | (196) ~ (all_14_2 = e0) % 148.30/21.77 | | % 148.30/21.77 | | REDUCE: (13), (196) imply: % 148.30/21.77 | | (197) ~ (all_8_2 = e0) % 148.30/21.77 | | % 148.30/21.77 | | BETA: splitting (61) gives: % 148.30/21.77 | | % 148.30/21.77 | | Case 1: % 148.30/21.77 | | | % 148.30/21.77 | | | (198) all_56_15 = e0 % 148.30/21.77 | | | % 148.30/21.77 | | | COMBINE_EQS: (8), (198) imply: % 148.30/21.77 | | | (199) all_4_2 = e0 % 148.30/21.77 | | | % 148.30/21.77 | | | SIMP: (199) implies: % 148.30/21.77 | | | (200) all_4_2 = e0 % 148.30/21.77 | | | % 148.30/21.77 | | | REF_CLOSE: (4), (33), (149), (171), (176), (188), (200) are inconsistent % 148.30/21.77 | | | by sub-proof #70. % 148.30/21.77 | | | % 148.30/21.77 | | Case 2: % 148.30/21.77 | | | % 148.30/21.77 | | | (201) ~ (all_56_15 = e0) % 148.30/21.77 | | | (202) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 = % 148.30/21.77 | | | e0 | all_56_13 = e0 | all_56_14 = e0) % 148.30/21.77 | | | % 148.30/21.77 | | | ALPHA: (202) implies: % 148.30/21.77 | | | (203) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 148.30/21.77 | | | (204) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 148.30/21.77 | | | % 148.30/21.77 | | | REDUCE: (8), (201) imply: % 148.30/21.77 | | | (205) ~ (all_4_2 = e0) % 148.30/21.77 | | | % 148.30/21.77 | | | BETA: splitting (62) gives: % 148.30/21.77 | | | % 148.30/21.77 | | | Case 1: % 148.30/21.77 | | | | % 148.30/21.77 | | | | (206) all_58_28 = e0 % 148.30/21.77 | | | | % 148.30/21.77 | | | | COMBINE_EQS: (134), (206) imply: % 148.30/21.77 | | | | (207) all_10_2 = e0 % 148.30/21.77 | | | | % 148.30/21.77 | | | | COMBINE_EQS: (148), (207) imply: % 148.30/21.77 | | | | (208) all_56_0 = e0 % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (194), (207) imply: % 148.30/21.77 | | | | (209) ~ (all_52_1 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (147), (207) imply: % 148.30/21.77 | | | | (210) ~ (all_52_2 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (154), (207) imply: % 148.30/21.77 | | | | (211) ~ (all_52_3 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (180), (207) imply: % 148.30/21.77 | | | | (212) ~ (all_52_4 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (18), (207) imply: % 148.30/21.77 | | | | (213) ~ (all_52_8 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (129), (207) imply: % 148.30/21.77 | | | | (214) ~ (all_52_12 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (195), (207) imply: % 148.30/21.77 | | | | (215) op(e0, all_10_1) = e0 % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (189), (207) imply: % 148.30/21.77 | | | | (216) op(e0, e3) = all_10_1 % 148.30/21.77 | | | | % 148.30/21.77 | | | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, % 148.30/21.77 | | | | simplifying with (125), (216) gives: % 148.30/21.77 | | | | (217) all_52_3 = all_10_1 % 148.30/21.77 | | | | % 148.30/21.77 | | | | COMBINE_EQS: (191), (217) imply: % 148.30/21.77 | | | | (218) all_54_12 = all_10_1 % 148.30/21.77 | | | | % 148.30/21.77 | | | | COMBINE_EQS: (80), (217) imply: % 148.30/21.77 | | | | (219) all_56_12 = all_10_1 % 148.30/21.77 | | | | % 148.30/21.77 | | | | COMBINE_EQS: (151), (217) imply: % 148.30/21.77 | | | | (220) all_58_22 = all_10_1 % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (130), (217) imply: % 148.30/21.77 | | | | (221) ~ (all_52_1 = all_10_1) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (6), (217) imply: % 148.30/21.77 | | | | (222) ~ (all_52_2 = all_10_1) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (81), (217) imply: % 148.30/21.77 | | | | (223) ~ (all_52_7 = all_10_1) % 148.30/21.77 | | | | % 148.30/21.77 | | | | SIMP: (223) implies: % 148.30/21.77 | | | | (224) ~ (all_52_7 = all_10_1) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (150), (217) imply: % 148.30/21.77 | | | | (225) ~ (all_52_11 = all_10_1) % 148.30/21.77 | | | | % 148.30/21.77 | | | | SIMP: (225) implies: % 148.30/21.77 | | | | (226) ~ (all_52_11 = all_10_1) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (88), (217) imply: % 148.30/21.77 | | | | (227) ~ (all_10_1 = all_4_2) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (211), (217) imply: % 148.30/21.77 | | | | (228) ~ (all_10_1 = e0) % 148.30/21.77 | | | | % 148.30/21.77 | | | | REDUCE: (52), (217) imply: % 148.30/21.77 | | | | (229) op(e0, all_10_1) = all_58_21 % 148.30/21.77 | | | | % 148.30/21.77 | | | | GROUND_INST: instantiating (4) with e0, all_58_21, all_10_1, e0, % 148.30/21.77 | | | | simplifying with (215), (229) gives: % 148.30/21.77 | | | | (230) all_58_21 = e0 % 148.30/21.77 | | | | % 148.30/21.77 | | | | BETA: splitting (34) gives: % 148.30/21.77 | | | | % 148.30/21.77 | | | | Case 1: % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | (231) all_56_2 = e0 % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | COMBINE_EQS: (123), (231) imply: % 148.30/21.77 | | | | | (232) all_52_1 = e0 % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | REDUCE: (209), (232) imply: % 148.30/21.77 | | | | | (233) $false % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | CLOSE: (233) is inconsistent. % 148.30/21.77 | | | | | % 148.30/21.77 | | | | Case 2: % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | (234) ~ (all_56_2 = e0) % 148.30/21.77 | | | | | (235) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | BETA: splitting (112) gives: % 148.30/21.77 | | | | | % 148.30/21.77 | | | | | Case 1: % 148.30/21.77 | | | | | | % 148.30/21.77 | | | | | | (236) all_54_4 = e0 % 148.30/21.77 | | | | | | % 148.30/21.77 | | | | | | REF_CLOSE: (193), (209), (236) are inconsistent by sub-proof #859. % 148.30/21.77 | | | | | | % 148.30/21.77 | | | | | Case 2: % 148.30/21.77 | | | | | | % 148.30/21.77 | | | | | | (237) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 148.30/21.77 | | | | | | % 148.30/21.77 | | | | | | BETA: splitting (35) gives: % 148.30/21.77 | | | | | | % 148.30/21.77 | | | | | | Case 1: % 148.30/21.77 | | | | | | | % 148.30/21.77 | | | | | | | (238) all_54_8 = e0 % 148.30/21.77 | | | | | | | % 148.30/21.77 | | | | | | | REF_CLOSE: (14), (210), (238) are inconsistent by sub-proof #731. % 148.30/21.77 | | | | | | | % 148.30/21.77 | | | | | | Case 2: % 148.30/21.77 | | | | | | | % 148.30/21.77 | | | | | | | (239) ~ (all_54_8 = e0) % 148.30/21.77 | | | | | | | (240) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 148.30/21.77 | | | | | | | % 148.30/21.77 | | | | | | | BETA: splitting (11) gives: % 148.30/21.77 | | | | | | | % 148.30/21.77 | | | | | | | Case 1: % 148.30/21.77 | | | | | | | | % 148.30/21.77 | | | | | | | | (241) all_54_3 = e0 % 148.30/21.77 | | | | | | | | % 148.30/21.77 | | | | | | | | REF_CLOSE: (30), (214), (241) are inconsistent by sub-proof % 148.30/21.77 | | | | | | | | #733. % 148.30/21.77 | | | | | | | | % 148.30/21.77 | | | | | | | Case 2: % 148.30/21.77 | | | | | | | | % 148.30/21.77 | | | | | | | | (242) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 148.30/21.77 | | | | | | | | % 148.30/21.77 | | | | | | | | BETA: splitting (127) gives: % 148.30/21.77 | | | | | | | | % 148.30/21.77 | | | | | | | | Case 1: % 148.30/21.77 | | | | | | | | | % 148.30/21.77 | | | | | | | | | (243) all_54_12 = e0 % 148.30/21.77 | | | | | | | | | % 148.30/21.77 | | | | | | | | | REF_CLOSE: (218), (228), (243) are inconsistent by sub-proof % 148.30/21.77 | | | | | | | | | #459. % 148.30/21.77 | | | | | | | | | % 148.30/21.77 | | | | | | | | Case 2: % 148.30/21.77 | | | | | | | | | % 148.30/21.77 | | | | | | | | | (244) ~ (all_54_12 = e0) % 148.30/21.77 | | | | | | | | | (245) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 148.30/21.77 | | | | | | | | | % 148.30/21.77 | | | | | | | | | BETA: splitting (161) gives: % 148.30/21.77 | | | | | | | | | % 148.30/21.77 | | | | | | | | | Case 1: % 148.30/21.77 | | | | | | | | | | % 148.30/21.77 | | | | | | | | | | (246) all_54_1 = e0 % 148.30/21.77 | | | | | | | | | | % 148.30/21.77 | | | | | | | | | | REF_CLOSE: (32), (212), (246) are inconsistent by sub-proof % 148.30/21.77 | | | | | | | | | | #798. % 148.30/21.77 | | | | | | | | | | % 148.30/21.77 | | | | | | | | | Case 2: % 148.30/21.77 | | | | | | | | | | % 148.30/21.77 | | | | | | | | | | (247) ~ (all_54_1 = e0) % 148.30/21.78 | | | | | | | | | | (248) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 148.30/21.78 | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | BETA: splitting (174) gives: % 148.30/21.78 | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | (249) all_54_2 = e0 % 148.30/21.78 | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | REF_CLOSE: (12), (213), (249) are inconsistent by sub-proof % 148.30/21.78 | | | | | | | | | | | #860. % 148.30/21.78 | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | (250) ~ (all_54_2 = e0) % 148.30/21.78 | | | | | | | | | | | (251) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 148.30/21.78 | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | BETA: splitting (168) gives: % 148.30/21.78 | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | (252) all_56_6 = e0 % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | COMBINE_EQS: (107), (252) imply: % 148.30/21.78 | | | | | | | | | | | | (253) all_52_2 = e0 % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | REDUCE: (210), (253) imply: % 148.30/21.78 | | | | | | | | | | | | (254) $false % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | CLOSE: (254) is inconsistent. % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | (255) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | BETA: splitting (56) gives: % 148.30/21.78 | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | (256) all_54_11 = e0 % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | COMBINE_EQS: (44), (256) imply: % 148.30/21.78 | | | | | | | | | | | | | (257) all_52_14 = e0 % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | SIMP: (257) implies: % 148.30/21.78 | | | | | | | | | | | | | (258) all_52_14 = e0 % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | COMBINE_EQS: (84), (258) imply: % 148.30/21.78 | | | | | | | | | | | | | (259) all_56_11 = e0 % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | COMBINE_EQS: (46), (258) imply: % 148.30/21.78 | | | | | | | | | | | | | (260) all_58_20 = e0 % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | REDUCE: (55), (258) imply: % 148.30/21.78 | | | | | | | | | | | | | (261) ~ (all_52_6 = e0) % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | REDUCE: (94), (258) imply: % 148.30/21.78 | | | | | | | | | | | | | (262) ~ (all_52_13 = e0) % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | REDUCE: (186), (258) imply: % 148.30/21.78 | | | | | | | | | | | | | (263) ~ (all_6_2 = e0) % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | SIMP: (263) implies: % 148.30/21.78 | | | | | | | | | | | | | (264) ~ (all_6_2 = e0) % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | BETA: splitting (235) gives: % 148.30/21.78 | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | (265) all_56_3 = e0 % 148.30/21.78 | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | REF_CLOSE: (9), (28), (31), (71), (78), (84), (85), (92), % 148.30/21.78 | | | | | | | | | | | | | | (101), (102), (103), (105), (122), (134), (145), % 148.30/21.78 | | | | | | | | | | | | | | (148), (155), (164), (171), (181), (183), (184), % 148.30/21.78 | | | | | | | | | | | | | | (212), (213), (255), (261), (264), (265) are % 148.30/21.78 | | | | | | | | | | | | | | inconsistent by sub-proof #480. % 148.30/21.78 | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | (266) all_56_5 = e0 | all_56_10 = e0 % 148.30/21.78 | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | BETA: splitting (266) gives: % 148.30/21.78 | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | (267) all_56_5 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | COMBINE_EQS: (76), (267) imply: % 148.30/21.78 | | | | | | | | | | | | | | | (268) all_52_9 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | COMBINE_EQS: (7), (268) imply: % 148.30/21.78 | | | | | | | | | | | | | | | (269) all_58_11 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | REDUCE: (90), (268) imply: % 148.30/21.78 | | | | | | | | | | | | | | | (270) ~ (all_52_11 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | SIMP: (270) implies: % 148.30/21.78 | | | | | | | | | | | | | | | (271) ~ (all_52_11 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | REDUCE: (117), (268) imply: % 148.30/21.78 | | | | | | | | | | | | | | | (272) ~ (all_52_13 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 148.30/21.78 | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | (273) all_56_12 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | REF_CLOSE: (219), (228), (273) are inconsistent by sub-proof % 148.30/21.78 | | | | | | | | | | | | | | | | #230. % 148.30/21.78 | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | (274) all_56_13 = e0 | all_56_14 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | (275) all_56_13 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (275) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | (276) all_52_7 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | SIMP: (276) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | (277) all_52_7 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (277) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | (278) all_58_24 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | REDUCE: (224), (277) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | (279) ~ (all_10_1 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | REDUCE: (159), (277) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | (280) ~ (all_8_2 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | REDUCE: (173), (277) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | (281) ~ (all_4_2 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | (282) all_54_14 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (271), (282) are inconsistent by sub-proof % 148.30/21.78 | | | | | | | | | | | | | | | | | | #517. % 148.30/21.78 | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | (283) ~ (all_54_14 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | | | | (284) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | (285) all_54_9 = e0 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (261), (285) are inconsistent by sub-proof % 148.30/21.78 | | | | | | | | | | | | | | | | | | | #572. % 148.30/21.78 | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | (286) ~ (all_54_9 = e0) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | (287) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | (288) all_56_6 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (288) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | (289) all_52_2 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (289) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | (290) ~ (all_6_2 = e1) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | SIMP: (290) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | (291) ~ (all_6_2 = e1) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (292) all_56_4 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (14), (16), (19), (20), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (22), (23), (25), (26), (28), (29), (30), (31), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (32), (35), (36), (37), (38), (49), (50), (54), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (66), (68), (69), (71), (73), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (77), (78), (79), (82), (84), (85), (87), (91), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (92), (95), (96), (97), (101), (102), (103), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (104), (105), (107), (108), (113), (115), (119), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (120), (122), (123), (128), (133), (134), (136), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (140), (143), (145), (148), (155), (157), (158), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (162), (163), (164), (165), (175), (181), (183), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (184), (185), (190), (193), (197), (205), (206), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (208), (209), (210), (212), (213), (214), (215), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (221), (222), (226), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (227), (228), (237), (242), (245), (248), (255), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (259), (260), (261), (262), (264), (267), (269), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (271), (275), (278), (284), (287), (292) are % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #14. % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (293) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | (294) all_56_5 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (267), (294) are inconsistent by sub-proof % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | #305. % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | (295) all_56_8 = e1 | all_56_14 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (296) all_56_8 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (291), (296) are inconsistent by sub-proof % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | #353. % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (297) all_56_14 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (297) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (298) all_52_11 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (299) all_52_11 = e1 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (299) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (300) ~ (all_4_2 = e1) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (301) ~ (all_4_2 = e1) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (12), (18), (19), (20), (22), (23), (25), (26), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (28), (29), (31), (32), (34), (36), (37), (38), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (44), (46), (47), (49), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (52), (54), (55), (56), (59), (60), (62), (64), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (65), (66), (68), (69), (71), (72), (75), (76), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (79), (80), (81), (83), (84), (85), (86), (88), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (90), (92), (93), (94), (95), (96), (97), (101), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (102), (103), (105), (107), (110), (111), (113), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (114), (115), (117), (118), (119), (120), (122), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (123), (125), (127), (128), (129), (132), (133), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (134), (136), (139), (140), (141), (143), (145), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (147), (148), (150), (151), (153), (154), (155), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (157), (159), (161), (162), (163), (164), (167), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (168), (170), (171), (172), (173), (174), (179), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (180), (181), (183), (184), (186), (189), (190), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (191), (194), (195), (197), (203), (204), (205), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (301) are inconsistent by sub-proof #73. % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | End of split % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | End of split % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | (302) ~ (all_56_6 = e1) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (302) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | (303) ~ (all_52_2 = e1) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (304) all_56_4 = e2 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (10), (26), (28), (31), (38), (47), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (102), (107), (143), (155), (181), (185), (206), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (222), (227), % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (228), (245), (259), (261), (271), (304) are % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (305) ~ (all_56_4 = e2) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (305) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | (306) ~ (all_52_8 = e2) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | (307) all_56_4 = e3 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (307) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | (308) all_52_8 = e3 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (308) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | (309) ~ (all_52_11 = e3) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | SIMP: (309) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | (310) ~ (all_52_11 = e3) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (311) all_56_6 = e3 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (311) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (312) all_52_2 = e3 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (313) all_52_2 = e3 % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (313) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_52_1 = e3) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (313) imply: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_10_1 = e3) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies: % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | (316) ~ (all_10_1 = e3) % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.78 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (313) imply: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_6_2 = e3) % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (317) implies: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_6_2 = e3) % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | (319) all_56_12 = e3 % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (219), (316), (319) are inconsistent by sub-proof % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | #48. % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | (320) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_56_2 = e3 % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (321) imply: % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_52_1 = e3 % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.30/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (314), (322) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | (323) $false % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (323) is inconsistent. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_28 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (206), (325) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | #689. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_58_28 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (326) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (328) ~ (e3 = e0) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_29 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (28), (31), (71), (78), (84), (85), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (101), (103), (105), (122), (133), (134), (145), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (148), (155), (164), (171), (181), (183), (184), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (212), (213), (255), (261), (264), (275), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (310), (320), (329) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | #2. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_30 = e3 | all_58_31 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_56_3 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (331) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_8_2 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (332) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_58_29 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (28), (31), (71), (78), (84), (85), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (101), (103), (105), (122), (133), (134), (145), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (148), (155), (164), (171), (181), (183), (184), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (212), (213), (255), (261), (264), (275), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310), (320), (333) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #2. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_56_5 = e3 | all_56_10 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_56_5 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (267), (335) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #79. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_56_10 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (336) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_52_13 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (337) implies: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_52_13 = e3 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (338) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (all_4_2 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) ~ (all_4_2 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (181), (318), (330), (340) are inconsistent % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #47. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (341) ~ (all_56_6 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (341) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (342) ~ (all_52_2 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (38), (107), (143), (185), (215), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (222), (228), (240), (245), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (271), (303), (342) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | #209. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_56_4 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (343) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_52_8 = e3) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (345) all_54_2 = e1 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (345) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (346) all_52_8 = e1 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (346) implies: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (347) all_52_8 = e1 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (347) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_52_4 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (347) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_52_11 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (349) implies: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_52_11 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (347) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_52_12 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (351) implies: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (352) ~ (all_52_12 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (347) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (353) ~ (e3 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (306), (347) imply: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (e2 = e1) % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (14), (16), (19), (20), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (25), (26), (28), (29), (30), (31), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (32), (35), (36), (37), (38), (49), (50), (54), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (60), (64), (65), (66), (68), (69), (71), (73), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (77), (78), (79), (82), (84), (85), (87), (91), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (92), (95), (96), (97), (101), (102), (103), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (104), (105), (107), (108), (113), (115), (119), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (120), (122), (123), (128), (133), (134), (136), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (140), (143), (145), (148), (155), (157), (158), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (162), (163), (164), (165), (175), (181), (183), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (184), (185), (190), (193), (197), (205), (206), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (210), (212), (213), (214), (215), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (221), (222), (226), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (237), (242), (245), (248), (255), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (259), (260), (261), (262), (264), (267), (269), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (271), (275), (278), (284), (287), (347), (348), % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (350), (352) are inconsistent by sub-proof #15. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | (355) all_54_2 = e3 | all_54_2 = e2 % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (306), (344), (355) are inconsistent by % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #555. % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | (356) all_56_14 = e0 % 148.74/21.79 | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (271), (356) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | | | #806. % 148.74/21.79 | | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | (357) all_56_10 = e0 % 148.74/21.79 | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | | REF_CLOSE: (128), (262), (357) are inconsistent by sub-proof % 148.74/21.79 | | | | | | | | | | | | | | | #526. % 148.74/21.79 | | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | End of split % 148.74/21.79 | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | (358) ~ (all_54_11 = e0) % 148.74/21.79 | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | REDUCE: (44), (358) imply: % 148.74/21.79 | | | | | | | | | | | | | (359) ~ (all_52_14 = e0) % 148.74/21.79 | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | BETA: splitting (72) gives: % 148.74/21.79 | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | Case 1: % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | (360) all_54_9 = e0 % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | COMBINE_EQS: (65), (360) imply: % 148.74/21.79 | | | | | | | | | | | | | | (361) all_52_6 = e0 % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | SIMP: (361) implies: % 148.74/21.79 | | | | | | | | | | | | | | (362) all_52_6 = e0 % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | REDUCE: (55), (362) imply: % 148.74/21.79 | | | | | | | | | | | | | | (363) ~ (all_52_14 = e0) % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | REDUCE: (10), (362) imply: % 148.74/21.79 | | | | | | | | | | | | | | (364) ~ (all_6_2 = e0) % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | SIMP: (364) implies: % 148.74/21.79 | | | | | | | | | | | | | | (365) ~ (all_6_2 = e0) % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (19), (20), (26), (28), (29), % 148.74/21.79 | | | | | | | | | | | | | | (31), (37), (41), (46), (49), (66), (68), (71), % 148.74/21.79 | | | | | | | | | | | | | | (76), (84), (85), (90), (92), (93), (94), (96), % 148.74/21.79 | | | | | | | | | | | | | | (101), (102), (103), (105), (107), (110), (111), % 148.74/21.79 | | | | | | | | | | | | | | (113), (119), (122), (128), (133), (136), (140), % 148.74/21.79 | | | | | | | | | | | | | | (141), (143), (145), (155), (162), (163), (164), % 148.74/21.79 | | | | | | | | | | | | | | (167), (170), (179), (181), (183), (184), (186), % 148.74/21.79 | | | | | | | | | | | | | | (190), (203), (206), (208), (215), (216), (218), % 148.74/21.79 | | | | | | | | | | | | | | (219), (220), (222), (224), (226), (227), (228), % 148.74/21.79 | | | | | | | | | | | | | | (235), (245), (255), (359), (365) are inconsistent % 148.74/21.79 | | | | | | | | | | | | | | by sub-proof #12. % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | Case 2: % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | (366) ~ (all_54_9 = e0) % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | REDUCE: (65), (366) imply: % 148.74/21.79 | | | | | | | | | | | | | | (367) ~ (all_52_6 = e0) % 148.74/21.79 | | | | | | | | | | | | | | % 148.74/21.79 | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (31), (71), (83), (84), (102), (105), % 148.74/21.79 | | | | | | | | | | | | | | (122), (139), (145), (155), (164), (171), (181), % 148.74/21.79 | | | | | | | | | | | | | | (183), (184), (206), (255), (359), (367) are % 148.74/21.80 | | | | | | | | | | | | | | inconsistent by sub-proof #74. % 148.74/21.80 | | | | | | | | | | | | | | % 148.74/21.80 | | | | | | | | | | | | | End of split % 148.74/21.80 | | | | | | | | | | | | | % 148.74/21.80 | | | | | | | | | | | | End of split % 148.74/21.80 | | | | | | | | | | | | % 148.74/21.80 | | | | | | | | | | | End of split % 148.74/21.80 | | | | | | | | | | | % 148.74/21.80 | | | | | | | | | | End of split % 148.74/21.80 | | | | | | | | | | % 148.74/21.80 | | | | | | | | | End of split % 148.74/21.80 | | | | | | | | | % 148.74/21.80 | | | | | | | | End of split % 148.74/21.80 | | | | | | | | % 148.74/21.80 | | | | | | | End of split % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | End of split % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | End of split % 148.74/21.80 | | | | | % 148.74/21.80 | | | | End of split % 148.74/21.80 | | | | % 148.74/21.80 | | | Case 2: % 148.74/21.80 | | | | % 148.74/21.80 | | | | (368) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 148.74/21.80 | | | | % 148.74/21.80 | | | | REF_CLOSE: (2), (4), (38), (102), (114), (120), (181), (197), (205), % 148.74/21.80 | | | | (368) are inconsistent by sub-proof #78. % 148.74/21.80 | | | | % 148.74/21.80 | | | End of split % 148.74/21.80 | | | % 148.74/21.80 | | End of split % 148.74/21.80 | | % 148.74/21.80 | Case 2: % 148.74/21.80 | | % 148.74/21.80 | | (369) all_14_2 = e0 % 148.74/21.80 | | (370) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 148.74/21.80 | | % 148.74/21.80 | | COMBINE_EQS: (13), (369) imply: % 148.74/21.80 | | (371) all_8_2 = e0 % 148.74/21.80 | | % 148.74/21.80 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 148.74/21.80 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 148.74/21.80 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), % 148.74/21.80 | | (37), (38), (39), (40), (41), (42), (44), (45), (46), (47), (48), % 148.74/21.80 | | (49), (50), (51), (53), (55), (56), (57), (58), (59), (60), (61), % 148.74/21.80 | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 148.74/21.80 | | (74), (75), (76), (77), (78), (80), (81), (82), (83), (84), (85), % 148.74/21.80 | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), % 148.74/21.80 | | (97), (98), (100), (101), (102), (103), (104), (105), (106), % 148.74/21.80 | | (107), (108), (109), (110), (111), (112), (113), (115), (116), % 148.74/21.80 | | (117), (119), (120), (121), (122), (123), (124), (126), (127), % 148.74/21.80 | | (128), (129), (130), (131), (132), (133), (134), (135), (136), % 148.74/21.80 | | (137), (138), (139), (140), (141), (142), (143), (144), (145), % 148.74/21.80 | | (146), (147), (148), (150), (151), (152), (153), (154), (155), % 148.74/21.80 | | (156), (158), (159), (160), (161), (162), (163), (164), (165), % 148.74/21.80 | | (166), (167), (168), (169), (170), (171), (172), (173), (174), % 148.74/21.80 | | (175), (178), (179), (180), (181), (182), (183), (184), (185), % 148.74/21.80 | | (186), (187), (188), (189), (190), (191), (192), (193), (194), % 148.74/21.80 | | (195), (370), (371) are inconsistent by sub-proof #72. % 148.74/21.80 | | % 148.74/21.80 | End of split % 148.74/21.80 | % 148.74/21.80 End of proof % 148.74/21.80 % 148.74/21.80 Sub-proof #2 shows that the following formulas are inconsistent: % 148.74/21.80 ---------------------------------------------------------------- % 148.74/21.80 (1) all_58_31 = all_4_2 % 148.74/21.80 (2) all_58_28 = e0 % 148.74/21.80 (3) all_56_15 = all_4_2 % 148.74/21.80 (4) all_56_7 = all_52_6 % 148.74/21.80 (5) all_56_4 = all_52_8 % 148.74/21.80 (6) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.74/21.80 (7) ~ (all_6_2 = e0) % 148.74/21.80 (8) all_56_13 = e0 % 148.74/21.80 (9) ~ (e3 = e1) % 148.74/21.80 (10) ~ (all_52_6 = e0) % 148.74/21.80 (11) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 148.74/21.80 (12) all_56_11 = all_52_14 % 148.74/21.80 (13) all_56_1 = all_52_4 % 148.74/21.80 (14) all_56_9 = all_52_12 % 148.74/21.80 (15) all_58_29 = e3 % 148.74/21.80 (16) ~ (all_52_12 = all_52_14) % 148.74/21.80 (17) ~ (e2 = e1) % 148.74/21.80 (18) ~ (all_52_4 = e0) % 148.74/21.80 (19) ~ (e3 = e0) % 148.74/21.80 (20) all_56_14 = all_52_11 % 148.74/21.80 (21) all_58_28 = all_10_2 % 148.74/21.80 (22) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.74/21.80 (23) ~ (e2 = e0) % 148.74/21.80 (24) all_56_0 = all_10_2 % 148.74/21.80 (25) all_56_8 = all_6_2 % 148.74/21.80 (26) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 148.74/21.80 (27) ~ (e1 = e0) % 148.74/21.80 (28) ~ (all_52_11 = e3) % 148.74/21.80 (29) ~ (all_52_8 = e0) % 148.74/21.80 (30) all_58_30 = all_6_2 % 148.74/21.80 (31) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.74/21.80 (32) ~ (e3 = e2) % 148.74/21.80 (33) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 148.74/21.80 % 148.74/21.80 Begin of proof % 148.74/21.80 | % 148.74/21.80 | BETA: splitting (33) gives: % 148.74/21.80 | % 148.74/21.80 | Case 1: % 148.74/21.80 | | % 148.74/21.80 | | (34) all_56_13 = e3 % 148.74/21.80 | | % 148.74/21.80 | | COMBINE_EQS: (8), (34) imply: % 148.74/21.80 | | (35) e3 = e0 % 148.74/21.80 | | % 148.74/21.80 | | COMBINE_EQS: (15), (35) imply: % 148.74/21.80 | | (36) all_58_29 = e0 % 148.74/21.80 | | % 148.74/21.80 | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), (16), % 148.74/21.80 | | (17), (18), (19), (21), (22), (23), (24), (25), (26), (27), (29), % 148.74/21.80 | | (30), (31), (32), (36) are inconsistent by sub-proof #481. % 148.74/21.80 | | % 148.74/21.80 | Case 2: % 148.74/21.80 | | % 148.74/21.80 | | (37) all_56_14 = e3 | all_56_15 = e3 % 148.74/21.80 | | % 148.74/21.80 | | BETA: splitting (37) gives: % 148.74/21.80 | | % 148.74/21.80 | | Case 1: % 148.74/21.80 | | | % 148.74/21.80 | | | (38) all_56_14 = e3 % 148.74/21.80 | | | % 148.74/21.80 | | | REF_CLOSE: (20), (28), (38) are inconsistent by sub-proof #759. % 148.74/21.80 | | | % 148.74/21.80 | | Case 2: % 148.74/21.80 | | | % 148.74/21.80 | | | (39) all_56_15 = e3 % 148.74/21.80 | | | % 148.74/21.80 | | | COMBINE_EQS: (3), (39) imply: % 148.74/21.80 | | | (40) all_4_2 = e3 % 148.74/21.80 | | | % 148.74/21.80 | | | SIMP: (40) implies: % 148.74/21.80 | | | (41) all_4_2 = e3 % 148.74/21.80 | | | % 148.74/21.80 | | | COMBINE_EQS: (1), (41) imply: % 148.74/21.80 | | | (42) all_58_31 = e3 % 148.74/21.80 | | | % 148.74/21.80 | | | BETA: splitting (31) gives: % 148.74/21.80 | | | % 148.74/21.80 | | | Case 1: % 148.74/21.80 | | | | % 148.74/21.80 | | | | (43) all_58_28 = e1 % 148.74/21.80 | | | | % 148.74/21.80 | | | | REF_CLOSE: (2), (27), (43) are inconsistent by sub-proof #690. % 148.74/21.80 | | | | % 148.74/21.80 | | | Case 2: % 148.74/21.80 | | | | % 148.74/21.80 | | | | (44) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.74/21.80 | | | | % 148.74/21.80 | | | | BETA: splitting (44) gives: % 148.74/21.80 | | | | % 148.74/21.80 | | | | Case 1: % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | (45) all_58_29 = e1 % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | COMBINE_EQS: (15), (45) imply: % 148.74/21.80 | | | | | (46) e3 = e1 % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | REDUCE: (9), (46) imply: % 148.74/21.80 | | | | | (47) $false % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | CLOSE: (47) is inconsistent. % 148.74/21.80 | | | | | % 148.74/21.80 | | | | Case 2: % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | (48) ~ (all_58_29 = e1) % 148.74/21.80 | | | | | (49) all_58_30 = e1 | all_58_31 = e1 % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | BETA: splitting (6) gives: % 148.74/21.80 | | | | | % 148.74/21.80 | | | | | Case 1: % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | | (50) all_58_28 = e2 % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | | REF_CLOSE: (2), (23), (50) are inconsistent by sub-proof #688. % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | Case 2: % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | | (51) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | | BETA: splitting (51) gives: % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | | Case 1: % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | | (52) all_58_29 = e2 % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | | COMBINE_EQS: (15), (52) imply: % 148.74/21.80 | | | | | | | (53) e3 = e2 % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | | REDUCE: (32), (53) imply: % 148.74/21.80 | | | | | | | (54) $false % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | | CLOSE: (54) is inconsistent. % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | Case 2: % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | | (55) all_58_30 = e2 | all_58_31 = e2 % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | | REF_CLOSE: (9), (17), (32), (42), (49), (55) are inconsistent by % 148.74/21.80 | | | | | | | sub-proof #457. % 148.74/21.80 | | | | | | | % 148.74/21.80 | | | | | | End of split % 148.74/21.80 | | | | | | % 148.74/21.80 | | | | | End of split % 148.74/21.80 | | | | | % 148.74/21.80 | | | | End of split % 148.74/21.80 | | | | % 148.74/21.80 | | | End of split % 148.74/21.80 | | | % 148.74/21.80 | | End of split % 148.74/21.80 | | % 148.74/21.80 | End of split % 148.74/21.80 | % 148.74/21.80 End of proof % 148.74/21.80 % 148.74/21.80 Sub-proof #3 shows that the following formulas are inconsistent: % 148.74/21.80 ---------------------------------------------------------------- % 148.74/21.80 (1) all_58_31 = all_4_2 % 148.74/21.80 (2) all_56_7 = all_52_6 % 148.74/21.80 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.74/21.80 (4) ~ (e3 = e1) % 148.74/21.80 (5) ~ (all_52_6 = e0) % 148.74/21.80 (6) all_20_2 = all_4_2 % 148.74/21.80 (7) all_56_11 = all_52_14 % 148.74/21.80 (8) all_58_29 = e0 % 148.74/21.80 (9) ~ (e2 = e1) % 148.74/21.80 (10) ~ (e3 = e0) % 148.74/21.80 (11) all_58_28 = all_10_2 % 148.74/21.80 (12) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.74/21.80 (13) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 148.74/21.80 (14) ~ (e2 = e0) % 148.74/21.80 (15) all_56_8 = all_6_2 % 148.74/21.80 (16) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 148.74/21.80 (17) ~ (e1 = e0) % 148.74/21.80 (18) ~ (all_52_14 = e0) % 148.74/21.80 (19) all_58_30 = all_6_2 % 148.74/21.80 (20) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.74/21.80 (21) ~ (e3 = e2) % 148.74/21.80 % 148.74/21.80 Begin of proof % 148.74/21.80 | % 148.74/21.80 | BETA: splitting (12) gives: % 148.74/21.80 | % 148.74/21.80 | Case 1: % 148.74/21.80 | | % 148.74/21.80 | | (22) all_56_7 = e0 % 148.74/21.80 | | % 148.74/21.80 | | COMBINE_EQS: (2), (22) imply: % 148.74/21.80 | | (23) all_52_6 = e0 % 148.74/21.80 | | % 148.74/21.80 | | REDUCE: (5), (23) imply: % 148.74/21.80 | | (24) $false % 148.74/21.80 | | % 148.74/21.80 | | CLOSE: (24) is inconsistent. % 148.74/21.80 | | % 148.74/21.80 | Case 2: % 148.74/21.80 | | % 148.74/21.80 | | (25) all_56_8 = e0 | all_56_11 = e0 % 148.74/21.80 | | % 148.74/21.80 | | BETA: splitting (25) gives: % 148.74/21.80 | | % 148.74/21.80 | | Case 1: % 148.74/21.80 | | | % 148.74/21.80 | | | (26) all_56_8 = e0 % 148.74/21.80 | | | % 148.74/21.80 | | | COMBINE_EQS: (15), (26) imply: % 148.74/21.80 | | | (27) all_6_2 = e0 % 148.74/21.80 | | | % 148.74/21.80 | | | COMBINE_EQS: (19), (27) imply: % 148.74/21.80 | | | (28) all_58_30 = e0 % 148.74/21.80 | | | % 148.74/21.80 | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (13), (14), (16), % 148.74/21.80 | | | (17), (20), (21), (28) are inconsistent by sub-proof #691. % 148.74/21.80 | | | % 148.74/21.80 | | Case 2: % 148.74/21.80 | | | % 148.74/21.80 | | | (29) all_56_11 = e0 % 148.74/21.80 | | | % 148.74/21.80 | | | REF_CLOSE: (7), (18), (29) are inconsistent by sub-proof #220. % 148.74/21.80 | | | % 148.74/21.80 | | End of split % 148.74/21.80 | | % 148.74/21.80 | End of split % 148.74/21.80 | % 148.74/21.80 End of proof % 148.74/21.80 % 148.74/21.80 Sub-proof #4 shows that the following formulas are inconsistent: % 148.74/21.80 ---------------------------------------------------------------- % 148.74/21.80 (1) all_58_23 = all_8_0 % 148.74/21.80 (2) all_58_31 = all_4_2 % 148.74/21.80 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 148.74/21.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 148.74/21.80 (4) ~ (all_52_2 = all_52_3) % 148.74/21.80 (5) all_58_11 = all_52_9 % 148.74/21.80 (6) all_56_15 = all_4_2 % 148.74/21.80 (7) all_56_7 = all_52_6 % 148.74/21.80 (8) ~ (all_52_6 = all_6_2) % 148.74/21.81 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 148.74/21.81 (10) all_54_8 = all_52_2 % 148.74/21.81 (11) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 148.74/21.81 (12) all_58_15 = all_52_2 % 148.74/21.81 (13) all_58_26 = all_52_11 % 148.74/21.81 (14) op(e1, all_52_14) = all_58_19 % 148.74/21.81 (15) all_56_3 = e0 % 148.74/21.81 (16) all_58_24 = all_8_1 % 148.74/21.81 (17) ~ (all_52_11 = all_4_2) % 148.74/21.81 (18) all_54_7 = all_52_13 % 148.74/21.81 (19) all_58_6 = all_52_12 % 148.74/21.81 (20) all_58_4 = e0 % 148.74/21.81 (21) ~ (all_52_6 = all_8_1) % 148.74/21.81 (22) all_54_3 = all_52_12 % 148.74/21.81 (23) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.74/21.81 (24) all_54_1 = all_52_4 % 148.74/21.81 (25) op(e0, e2) = all_8_1 % 148.74/21.81 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 148.74/21.81 (27) ~ (all_52_4 = all_52_6) % 148.74/21.81 (28) all_58_13 = all_52_13 % 148.74/21.81 (29) op(e0, e1) = all_52_11 % 148.74/21.81 (30) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 148.74/21.81 (31) all_56_13 = all_8_1 % 148.74/21.81 (32) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 148.74/21.81 (33) all_58_20 = all_52_14 % 148.74/21.81 (34) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 148.74/21.81 (35) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 148.74/21.81 (36) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 148.74/21.81 (37) ~ (all_52_12 = all_52_13) % 148.74/21.81 (38) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 148.74/21.81 (39) all_54_10 = all_6_2 % 148.74/21.81 (40) op(e0, all_52_3) = all_58_21 % 148.74/21.81 (41) ~ (all_52_6 = all_52_14) % 148.74/21.81 (42) all_54_6 = all_52_9 % 148.74/21.81 (43) all_54_15 = all_4_2 % 148.74/21.81 (44) ~ (all_52_2 = all_6_2) % 148.74/21.81 (45) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 148.74/21.81 (46) op(e3, e3) = all_10_2 % 148.74/21.81 (47) all_54_9 = all_52_6 % 148.74/21.81 (48) ~ (all_52_13 = all_4_2) % 148.74/21.81 (49) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 148.74/21.81 (50) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 148.74/21.81 (51) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 148.74/21.81 (52) ~ (e3 = e1) % 148.74/21.81 (53) ~ (all_52_6 = e0) % 148.74/21.81 (54) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 148.74/21.81 (55) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 148.74/21.81 (56) ~ (all_52_1 = all_52_13) % 148.74/21.81 (57) all_56_5 = all_52_9 % 148.74/21.81 (58) all_54_14 = all_52_11 % 148.74/21.81 (59) op(e0, all_8_1) = all_8_0 % 148.74/21.81 (60) all_56_12 = all_52_3 % 148.74/21.81 (61) all_58_2 = all_52_4 % 148.74/21.81 (62) all_20_2 = all_4_2 % 148.74/21.81 (63) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 148.74/21.81 (64) all_56_11 = all_52_14 % 148.74/21.81 (65) all_56_1 = all_52_4 % 148.74/21.81 (66) all_58_9 = all_52_13 % 148.74/21.81 (67) ~ (all_52_4 = all_8_1) % 148.74/21.81 (68) op(e1, e0) = all_52_14 % 148.74/21.81 (69) ~ (all_52_9 = all_52_11) % 148.74/21.81 (70) ~ (all_52_9 = e0) % 148.74/21.81 (71) ~ (all_52_13 = all_52_14) % 148.74/21.81 (72) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 148.74/21.81 (73) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 148.74/21.81 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 148.74/21.81 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 148.74/21.81 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 148.74/21.81 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 148.74/21.81 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 148.74/21.81 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 148.74/21.81 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 148.74/21.81 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 148.74/21.81 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 148.74/21.81 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 148.74/21.81 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 148.74/21.81 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 148.74/21.81 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.74/21.81 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 148.74/21.81 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 148.74/21.81 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.74/21.81 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 148.74/21.81 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.74/21.81 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 148.74/21.81 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 148.74/21.81 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 148.74/21.81 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 148.74/21.81 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 148.74/21.81 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 148.74/21.81 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 148.74/21.81 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 148.74/21.81 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 148.74/21.81 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 148.74/21.81 e0) % 148.74/21.81 (74) all_58_29 = e0 % 148.74/21.81 (75) op(e2, e1) = all_52_9 % 148.74/21.81 (76) all_56_9 = all_52_12 % 148.74/21.81 (77) ~ (all_52_12 = all_52_14) % 148.74/21.81 (78) all_58_8 = all_52_1 % 148.74/21.81 (79) ~ (e2 = e1) % 148.74/21.81 (80) op(e3, e0) = all_52_12 % 148.74/21.81 (81) all_56_6 = all_52_2 % 148.74/21.81 (82) ~ (all_52_2 = all_52_6) % 148.74/21.81 (83) all_56_13 = all_52_7 % 148.74/21.81 (84) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 148.74/21.81 (85) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 148.74/21.81 (86) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 148.74/21.81 (87) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 148.74/21.81 (88) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 148.74/21.81 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 148.74/21.81 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 148.74/21.81 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 148.74/21.81 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 148.74/21.81 (all_58_27 = e0)) % 148.74/21.81 (89) ~ (all_52_9 = all_52_13) % 148.74/21.81 (90) ~ (all_52_11 = all_8_1) % 148.74/21.81 (91) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 148.74/21.81 (92) all_54_13 = all_8_1 % 148.74/21.81 (93) ~ (all_52_4 = e0) % 148.74/21.81 (94) op(e2, all_52_9) = all_58_10 % 148.74/21.81 (95) ~ (all_52_11 = all_6_2) % 148.74/21.81 (96) op(e3, all_10_2) = all_58_0 % 148.74/21.81 (97) ~ (e3 = e0) % 148.74/21.81 (98) all_56_2 = all_52_1 % 148.74/21.81 (99) all_56_4 = e0 % 148.74/21.81 (100) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 148.74/21.81 (101) ~ (all_52_11 = e0) % 148.74/21.81 (102) op(e3, all_52_12) = all_58_5 % 148.74/21.81 (103) all_56_10 = all_52_13 % 148.74/21.81 (104) ~ (all_52_3 = all_8_1) % 148.74/21.81 (105) ~ (all_52_12 = all_10_2) % 148.74/21.81 (106) ~ (all_52_1 = all_52_3) % 148.74/21.81 (107) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 148.74/21.81 (108) all_56_14 = all_52_11 % 148.74/21.81 (109) all_58_28 = all_10_2 % 148.74/21.81 (110) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 148.74/21.81 (111) all_58_17 = all_52_6 % 148.74/21.81 (112) ~ (all_52_1 = all_52_9) % 148.74/21.81 (113) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 148.74/21.81 (114) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 148.74/21.81 (115) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 148.74/21.81 (116) all_14_0 = all_8_0 % 148.74/21.81 (117) ~ (e2 = e0) % 148.74/21.81 (118) ~ (all_52_9 = all_6_2) % 148.74/21.81 (119) ~ (all_8_1 = all_4_2) % 148.74/21.81 (120) ~ (all_52_2 = all_10_2) % 148.74/21.81 (121) all_56_0 = all_10_2 % 148.74/21.81 (122) op(e0, e0) = all_4_2 % 148.74/21.81 (123) ~ (all_52_3 = all_52_11) % 148.74/21.81 (124) all_58_22 = all_52_3 % 148.74/21.81 (125) ~ (all_52_12 = all_4_2) % 148.74/21.81 (126) ~ (all_52_3 = all_10_2) % 148.74/21.81 (127) all_56_8 = all_6_2 % 148.74/21.82 (128) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 148.74/21.82 (129) ~ (all_52_1 = all_52_2) % 148.74/21.82 (130) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 148.74/21.82 (131) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 148.74/21.82 (132) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 148.74/21.82 (133) all_54_0 = all_10_2 % 148.74/21.82 (134) ~ (all_52_2 = all_52_14) % 148.74/21.82 (135) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.74/21.82 (136) all_14_1 = all_8_1 % 148.74/21.82 (137) ~ (all_52_7 = e0) % 148.74/21.82 (138) ~ (all_52_14 = all_4_2) % 148.74/21.82 (139) ~ (e1 = e0) % 148.74/21.82 (140) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 148.74/21.82 (141) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 148.74/21.82 (142) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 148.74/21.82 (143) ~ (all_52_4 = all_10_2) % 148.74/21.82 (144) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 148.74/21.82 (145) all_58_30 = all_6_2 % 148.74/21.82 (146) op(e2, all_52_1) = all_58_7 % 148.74/21.82 (147) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.74/21.82 (148) ~ (e3 = e2) % 148.74/21.82 (149) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 148.74/21.82 (150) op(e3, e0) = all_58_3 % 148.74/21.82 (151) ~ (all_52_4 = all_52_12) % 148.74/21.82 (152) all_54_4 = all_52_1 % 148.74/21.82 (153) ~ (all_52_1 = all_10_2) % 148.74/21.82 (154) op(e3, e1) = e0 % 148.74/21.82 % 148.74/21.82 Begin of proof % 148.74/21.82 | % 148.74/21.82 | BETA: splitting (144) gives: % 148.74/21.82 | % 148.74/21.82 | Case 1: % 148.74/21.82 | | % 148.74/21.82 | | (155) all_56_12 = e0 % 148.74/21.82 | | % 148.74/21.82 | | COMBINE_EQS: (60), (155) imply: % 148.74/21.82 | | (156) all_52_3 = e0 % 148.74/21.82 | | % 148.74/21.82 | | SIMP: (156) implies: % 148.74/21.82 | | (157) all_52_3 = e0 % 148.74/21.82 | | % 148.74/21.82 | | COMBINE_EQS: (124), (157) imply: % 148.74/21.82 | | (158) all_58_22 = e0 % 148.74/21.82 | | % 148.74/21.82 | | REDUCE: (106), (157) imply: % 148.74/21.82 | | (159) ~ (all_52_1 = e0) % 148.74/21.82 | | % 148.74/21.82 | | REDUCE: (4), (157) imply: % 148.74/21.82 | | (160) ~ (all_52_2 = e0) % 148.74/21.82 | | % 148.74/21.82 | | REDUCE: (123), (157) imply: % 148.74/21.82 | | (161) ~ (all_52_11 = e0) % 148.74/21.82 | | % 148.74/21.82 | | REDUCE: (126), (157) imply: % 148.74/21.82 | | (162) ~ (all_10_2 = e0) % 148.74/21.82 | | % 148.74/21.82 | | SIMP: (162) implies: % 148.74/21.82 | | (163) ~ (all_10_2 = e0) % 148.74/21.82 | | % 148.74/21.82 | | REDUCE: (104), (157) imply: % 148.74/21.82 | | (164) ~ (all_8_1 = e0) % 148.74/21.82 | | % 148.74/21.82 | | SIMP: (164) implies: % 148.74/21.82 | | (165) ~ (all_8_1 = e0) % 148.74/21.82 | | % 148.74/21.82 | | REDUCE: (40), (157) imply: % 148.74/21.82 | | (166) op(e0, e0) = all_58_21 % 148.74/21.82 | | % 148.74/21.82 | | BETA: splitting (135) gives: % 148.74/21.82 | | % 148.74/21.82 | | Case 1: % 148.74/21.82 | | | % 148.74/21.82 | | | (167) all_56_6 = e0 % 148.74/21.82 | | | % 148.74/21.82 | | | COMBINE_EQS: (81), (167) imply: % 148.74/21.82 | | | (168) all_52_2 = e0 % 148.74/21.82 | | | % 148.74/21.82 | | | REDUCE: (160), (168) imply: % 148.74/21.82 | | | (169) $false % 148.74/21.82 | | | % 148.74/21.82 | | | CLOSE: (169) is inconsistent. % 148.74/21.82 | | | % 148.74/21.82 | | Case 2: % 148.74/21.82 | | | % 148.74/21.82 | | | (170) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 148.74/21.82 | | | % 148.74/21.82 | | | BETA: splitting (170) gives: % 148.74/21.82 | | | % 148.74/21.82 | | | Case 1: % 148.74/21.82 | | | | % 148.74/21.82 | | | | (171) all_56_7 = e0 % 148.74/21.82 | | | | % 148.74/21.82 | | | | COMBINE_EQS: (7), (171) imply: % 148.74/21.82 | | | | (172) all_52_6 = e0 % 148.74/21.82 | | | | % 148.74/21.82 | | | | REDUCE: (53), (172) imply: % 148.74/21.82 | | | | (173) $false % 148.74/21.82 | | | | % 148.74/21.82 | | | | CLOSE: (173) is inconsistent. % 148.74/21.82 | | | | % 148.74/21.82 | | | Case 2: % 148.74/21.82 | | | | % 148.74/21.82 | | | | (174) all_56_8 = e0 | all_56_11 = e0 % 148.74/21.82 | | | | % 148.74/21.82 | | | | BETA: splitting (174) gives: % 148.74/21.82 | | | | % 148.74/21.82 | | | | Case 1: % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | (175) all_56_8 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | COMBINE_EQS: (127), (175) imply: % 148.74/21.82 | | | | | (176) all_6_2 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | COMBINE_EQS: (145), (176) imply: % 148.74/21.82 | | | | | (177) all_58_30 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), (113), % 148.74/21.82 | | | | | (117), (131), (139), (147), (148), (177) are inconsistent % 148.74/21.82 | | | | | by sub-proof #691. % 148.74/21.82 | | | | | % 148.74/21.82 | | | | Case 2: % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | (178) all_56_11 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | COMBINE_EQS: (64), (178) imply: % 148.74/21.82 | | | | | (179) all_52_14 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | SIMP: (179) implies: % 148.74/21.82 | | | | | (180) all_52_14 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | COMBINE_EQS: (33), (180) imply: % 148.74/21.82 | | | | | (181) all_58_20 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | REDUCE: (77), (180) imply: % 148.74/21.82 | | | | | (182) ~ (all_52_12 = e0) % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | REDUCE: (71), (180) imply: % 148.74/21.82 | | | | | (183) ~ (all_52_13 = e0) % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | REDUCE: (138), (180) imply: % 148.74/21.82 | | | | | (184) ~ (all_4_2 = e0) % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | SIMP: (184) implies: % 148.74/21.82 | | | | | (185) ~ (all_4_2 = e0) % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | REDUCE: (14), (180) imply: % 148.74/21.82 | | | | | (186) op(e1, e0) = all_58_19 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | REDUCE: (68), (180) imply: % 148.74/21.82 | | | | | (187) op(e1, e0) = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | GROUND_INST: instantiating (3) with all_4_2, all_58_21, e0, e0, % 148.74/21.82 | | | | | simplifying with (122), (166) gives: % 148.74/21.82 | | | | | (188) all_58_21 = all_4_2 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | GROUND_INST: instantiating (3) with e0, all_58_19, e0, e1, simplifying % 148.74/21.82 | | | | | with (186), (187) gives: % 148.74/21.82 | | | | | (189) all_58_19 = e0 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | GROUND_INST: instantiating (3) with all_52_12, all_58_3, e0, e3, % 148.74/21.82 | | | | | simplifying with (80), (150) gives: % 148.74/21.82 | | | | | (190) all_58_3 = all_52_12 % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | BETA: splitting (26) gives: % 148.74/21.82 | | | | | % 148.74/21.82 | | | | | Case 1: % 148.74/21.82 | | | | | | % 148.74/21.82 | | | | | | (191) all_54_8 = e0 % 148.74/21.82 | | | | | | % 148.74/21.82 | | | | | | REF_CLOSE: (10), (160), (191) are inconsistent by sub-proof #731. % 148.74/21.82 | | | | | | % 148.74/21.82 | | | | | Case 2: % 148.74/21.82 | | | | | | % 148.74/21.82 | | | | | | (192) ~ (all_54_8 = e0) % 148.74/21.82 | | | | | | (193) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 148.74/21.82 | | | | | | % 148.74/21.82 | | | | | | BETA: splitting (107) gives: % 148.74/21.82 | | | | | | % 148.74/21.82 | | | | | | Case 1: % 148.74/21.82 | | | | | | | % 148.74/21.82 | | | | | | | (194) all_54_14 = e0 % 148.74/21.82 | | | | | | | % 148.74/21.82 | | | | | | | REF_CLOSE: (58), (101), (194) are inconsistent by sub-proof #517. % 148.74/21.82 | | | | | | | % 148.74/21.82 | | | | | | Case 2: % 148.74/21.82 | | | | | | | % 148.74/21.82 | | | | | | | (195) ~ (all_54_14 = e0) % 148.74/21.82 | | | | | | | (196) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 148.74/21.82 | | | | | | | % 148.74/21.82 | | | | | | | BETA: splitting (100) gives: % 148.74/21.82 | | | | | | | % 148.74/21.82 | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | | (197) all_54_10 = e0 % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | | REF_CLOSE: (2), (23), (39), (52), (62), (74), (79), (97), (109), % 148.74/21.82 | | | | | | | | (113), (117), (131), (139), (145), (147), (148), % 148.74/21.82 | | | | | | | | (197) are inconsistent by sub-proof #36. % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | | (198) ~ (all_54_10 = e0) % 148.74/21.82 | | | | | | | | (199) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | | REDUCE: (39), (198) imply: % 148.74/21.82 | | | | | | | | (200) ~ (all_6_2 = e0) % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | | BETA: splitting (9) gives: % 148.74/21.82 | | | | | | | | % 148.74/21.82 | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | % 148.74/21.82 | | | | | | | | | (201) all_54_3 = e0 % 148.74/21.82 | | | | | | | | | % 148.74/21.82 | | | | | | | | | REF_CLOSE: (22), (182), (201) are inconsistent by sub-proof % 148.74/21.82 | | | | | | | | | #733. % 148.74/21.82 | | | | | | | | | % 148.74/21.82 | | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | | % 148.74/21.82 | | | | | | | | | (202) ~ (all_54_3 = e0) % 148.74/21.82 | | | | | | | | | (203) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 148.74/21.82 | | | | | | | | | % 148.74/21.82 | | | | | | | | | BETA: splitting (11) gives: % 148.74/21.82 | | | | | | | | | % 148.74/21.82 | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | (204) all_56_9 = e2 % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | COMBINE_EQS: (76), (204) imply: % 148.74/21.82 | | | | | | | | | | (205) all_52_12 = e2 % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | SIMP: (205) implies: % 148.74/21.82 | | | | | | | | | | (206) all_52_12 = e2 % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | COMBINE_EQS: (19), (206) imply: % 148.74/21.82 | | | | | | | | | | (207) all_58_6 = e2 % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | REDUCE: (151), (206) imply: % 148.74/21.82 | | | | | | | | | | (208) ~ (all_52_4 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | REDUCE: (37), (206) imply: % 148.74/21.82 | | | | | | | | | | (209) ~ (all_52_13 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | SIMP: (209) implies: % 148.74/21.82 | | | | | | | | | | (210) ~ (all_52_13 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | REDUCE: (105), (206) imply: % 148.74/21.82 | | | | | | | | | | (211) ~ (all_10_2 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | SIMP: (211) implies: % 148.74/21.82 | | | | | | | | | | (212) ~ (all_10_2 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | REDUCE: (125), (206) imply: % 148.74/21.82 | | | | | | | | | | (213) ~ (all_4_2 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | SIMP: (213) implies: % 148.74/21.82 | | | | | | | | | | (214) ~ (all_4_2 = e2) % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | BETA: splitting (23) gives: % 148.74/21.82 | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | (215) all_58_28 = e2 % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | COMBINE_EQS: (109), (215) imply: % 148.74/21.82 | | | | | | | | | | | (216) all_10_2 = e2 % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | REDUCE: (212), (216) imply: % 148.74/21.82 | | | | | | | | | | | (217) $false % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | CLOSE: (217) is inconsistent. % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | (218) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | BETA: splitting (218) gives: % 148.74/21.82 | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | (219) all_58_29 = e2 % 148.74/21.82 | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | REF_CLOSE: (74), (117), (219) are inconsistent by sub-proof % 148.74/21.82 | | | | | | | | | | | | #706. % 148.74/21.82 | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | (220) all_58_30 = e2 | all_58_31 = e2 % 148.74/21.82 | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | BETA: splitting (220) gives: % 148.74/21.82 | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | (221) all_58_30 = e2 % 148.74/21.82 | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | COMBINE_EQS: (145), (221) imply: % 148.74/21.82 | | | | | | | | | | | | | (222) all_6_2 = e2 % 148.74/21.82 | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | REDUCE: (8), (222) imply: % 148.74/21.82 | | | | | | | | | | | | | (223) ~ (all_52_6 = e2) % 148.74/21.82 | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | REDUCE: (118), (222) imply: % 148.74/21.82 | | | | | | | | | | | | | (224) ~ (all_52_9 = e2) % 148.74/21.82 | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | BETA: splitting (128) gives: % 148.74/21.82 | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | (225) all_56_1 = e2 % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | COMBINE_EQS: (65), (225) imply: % 148.74/21.82 | | | | | | | | | | | | | | (226) all_52_4 = e2 % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | REDUCE: (208), (226) imply: % 148.74/21.82 | | | | | | | | | | | | | | (227) $false % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | (228) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | BETA: splitting (228) gives: % 148.74/21.82 | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | (229) all_56_3 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (23), (52), (62), (74), (79), (97), % 148.74/21.82 | | | | | | | | | | | | | | | (109), (113), (117), (131), (139), (147), (148), % 148.74/21.82 | | | | | | | | | | | | | | | (221), (229) are inconsistent by sub-proof #22. % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | (230) ~ (all_56_3 = e2) % 148.74/21.82 | | | | | | | | | | | | | | | (231) all_56_7 = e2 | all_56_13 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | REDUCE: (15), (230) imply: % 148.74/21.82 | | | | | | | | | | | | | | | (232) ~ (e2 = e0) % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | BETA: splitting (49) gives: % 148.74/21.82 | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | (233) all_56_2 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (233) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | (234) all_52_1 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (234) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | (235) all_58_8 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | REDUCE: (129), (234) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | (236) ~ (all_52_2 = e2) % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | SIMP: (236) implies: % 148.74/21.82 | | | | | | | | | | | | | | | | (237) ~ (all_52_2 = e2) % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 148.74/21.82 | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | (238) all_56_7 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (238) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | | (239) all_52_6 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | REDUCE: (223), (239) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | | (240) $false % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent. % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | Case 2: % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | (241) all_56_13 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (241) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | | (242) all_8_1 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | SIMP: (242) implies: % 148.74/21.82 | | | | | | | | | | | | | | | | | (243) all_8_1 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (243) imply: % 148.74/21.82 | | | | | | | | | | | | | | | | | (244) all_58_24 = e2 % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 148.74/21.82 | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.82 | | | | | | | | | | | | | | | | | | % 148.74/21.82 | | | | | | | | | | | | | | | | | | (245) all_58_31 = e0 % 148.74/21.82 | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (52), (74), (79), (97), (117), (131), (139), % 148.74/21.83 | | | | | | | | | | | | | | | | | | (145), (147), (148), (245) are inconsistent by % 148.74/21.83 | | | | | | | | | | | | | | | | | | sub-proof #844. % 148.74/21.83 | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.83 | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | (246) ~ (all_58_31 = e0) % 148.74/21.83 | | | | | | | | | | | | | | | | | | (247) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 148.74/21.83 | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | e0) % 148.74/21.83 | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 148.74/21.83 | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | (248) all_58_30 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (79), (214), (220), (248) are inconsistent by % 148.74/21.83 | | | | | | | | | | | | | | | | | | | sub-proof #45. % 148.74/21.83 | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | (249) ~ (all_58_30 = e1) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | (250) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (251) all_58_29 = e2 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (251) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (252) e2 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (253) e2 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (253) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (254) all_58_30 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (254) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (255) ~ (all_58_29 = e2) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (256) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | e0) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | (257) all_58_28 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (257) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | (258) all_10_2 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (258) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | (259) all_56_0 = e3 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | (260) all_58_28 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (260) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | (261) e3 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (261) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | (262) $false % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | (263) ~ (all_58_28 = e1) % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | (264) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | (265) all_56_0 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (265) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | (266) e3 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (266) imply: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | (267) $false % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent. % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | (268) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 148.74/21.83 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (13), (15), (17), (18), (19), (20), (21), (22), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (23), (25), (29), (30), (31), (35), (37), (38), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (44), (46), (47), (48), (50), (52), (53), (54), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (55), (56), (57), (58), (59), (61), (62), (63), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (65), (66), (70), (72), (73), (74), (75), (76), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (81), (82), (86), (88), (89), (90), (91), (92), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (93), (94), (96), (97), (98), (99), (101), (102), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (103), (105), (107), (108), (109), (110), (111), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (112), (113), (114), (115), (116), (117), (119), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (125), (127), (128), (129), (131), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (132), (133), (136), (139), (141), (142), (145), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (153), (154), (155), (158), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (159), (160), (163), (181), (182), (185), (188), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (189), (190), (193), (200), (203), (237), (264), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (268) are inconsistent by sub-proof #8. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | (269) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | e0) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | (270) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | = e0) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | (271) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_4 = e1 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (139), (274) are inconsistent by sub-proof % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | #165. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_6 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (277) imply: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (278) e2 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (278) imply: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_30 = e0 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (279) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_8 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (235), (281) are inconsistent by sub-proof % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | #347. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | (282) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | (283) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_8 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (235), (285) are inconsistent by sub-proof % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | #347. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_4 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (97), (287) are inconsistent by sub-proof % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | (288) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_22 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_6 = e3 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (158), % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (221), (290), (291) are inconsistent by % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_58_2 = e2 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (293) imply: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_52_4 = e2 % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (294) imply: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.84 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | (296) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (297) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (298) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_24 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (300) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (301) e2 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (301) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_30 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (302) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (304) e3 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (304) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (305) $false % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (306) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_6 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (308) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (309) e2 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (309) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_30 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (310) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_58_4 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (97), (312) are inconsistent by sub-proof % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (313) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (314) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_20 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (316) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (317) e1 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (317) imply: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (318) $false % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (318) is inconsistent. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (319) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_22 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_6 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (158), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (221), (320), (321) are inconsistent by % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_4 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (139), (324) are inconsistent by sub-proof % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | #165. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_4 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (139), (326) are inconsistent by sub-proof % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | #165. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (327) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | (328) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (329) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_58_4 = e1 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (139), (331) are inconsistent by sub-proof % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | #165. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | (332) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_22 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_58_6 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (158), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (221), (334), (335) are inconsistent by % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_22 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_6 = e3 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (158), % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (221), (337), (338) are inconsistent by % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (339) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (340) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_58_6 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (342) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (343) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (343) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_30 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (344) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_6 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (346) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (347) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (347) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_58_30 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (348) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (349) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_6 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (351) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (352) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (352) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_30 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (353) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_24 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (355) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (356) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (356) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (357) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (357) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_30 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (358) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | (359) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (359) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | (360) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (361) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (362) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_58_20 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (363) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) e1 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (364) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) $false % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_13 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (367) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_52_13 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (368) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) $false % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (369) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (370) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_58_26 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (101), (372) are inconsistent by sub-proof % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | #273. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (374) e2 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (374) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_30 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (79), (214), (220), (375) are inconsistent by % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #45. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | (376) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (377) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_58_13 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (379) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_52_13 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (380) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (381) $false % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (381) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_58_24 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (383) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (384) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (384) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_58_30 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (385) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (386) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (387) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_58_24 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (388) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (389) e2 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (389) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_58_30 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (23), (52), (62), (74), (79), (97), (109), % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (117), (131), (139), (147), (148), (390) % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (392) e1 = e0 % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (392) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (393) $false % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (393) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | (394) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | BETA: splitting (394) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | (395) all_56_3 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (23), (52), (62), (74), (79), (97), % 148.74/21.86 | | | | | | | | | | | | | | | | | (109), (113), (117), (131), (139), (147), (148), % 148.74/21.86 | | | | | | | | | | | | | | | | | (221), (395) are inconsistent by sub-proof #22. % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | (396) all_56_5 = e2 | all_56_10 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | BETA: splitting (396) gives: % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | (397) all_56_5 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (397) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | (398) all_52_9 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | REDUCE: (224), (398) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | (399) $false % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | (400) all_56_10 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (400) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | (401) all_52_13 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | SIMP: (401) implies: % 148.74/21.86 | | | | | | | | | | | | | | | | | | (402) all_52_13 = e2 % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | REDUCE: (210), (402) imply: % 148.74/21.86 | | | | | | | | | | | | | | | | | | (403) $false % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | | CLOSE: (403) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | (404) all_58_31 = e2 % 148.74/21.86 | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | COMBINE_EQS: (2), (404) imply: % 148.74/21.86 | | | | | | | | | | | | | (405) all_4_2 = e2 % 148.74/21.86 | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | REDUCE: (214), (405) imply: % 148.74/21.86 | | | | | | | | | | | | | (406) $false % 148.74/21.86 | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | | CLOSE: (406) is inconsistent. % 148.74/21.86 | | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | End of split % 148.74/21.86 | | | | | | | | | | % 148.74/21.86 | | | | | | | | | Case 2: % 148.74/21.86 | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | (407) ~ (all_56_9 = e2) % 148.74/21.86 | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | REDUCE: (76), (407) imply: % 148.74/21.86 | | | | | | | | | | (408) ~ (all_52_12 = e2) % 148.74/21.86 | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | BETA: splitting (32) gives: % 148.74/21.86 | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | Case 1: % 148.74/21.86 | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | (409) all_56_0 = e2 % 148.74/21.86 | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | COMBINE_EQS: (121), (409) imply: % 148.74/21.86 | | | | | | | | | | | (410) all_10_2 = e2 % 148.74/21.86 | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | COMBINE_EQS: (109), (410) imply: % 148.74/21.86 | | | | | | | | | | | (411) all_58_28 = e2 % 148.74/21.86 | | | | | | | | | | | % 148.74/21.86 | | | | | | | | | | | REDUCE: (120), (410) imply: % 148.74/21.87 | | | | | | | | | | | (412) ~ (all_52_2 = e2) % 148.74/21.87 | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | BETA: splitting (30) gives: % 148.74/21.87 | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | (413) all_56_0 = e1 % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | COMBINE_EQS: (409), (413) imply: % 148.74/21.87 | | | | | | | | | | | | (414) e2 = e1 % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | REDUCE: (79), (414) imply: % 148.74/21.87 | | | | | | | | | | | | (415) $false % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | CLOSE: (415) is inconsistent. % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | (416) ~ (all_56_0 = e1) % 148.74/21.87 | | | | | | | | | | | | (417) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | BETA: splitting (147) gives: % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | (418) all_58_28 = e1 % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | COMBINE_EQS: (411), (418) imply: % 148.74/21.87 | | | | | | | | | | | | | (419) e2 = e1 % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | REDUCE: (79), (419) imply: % 148.74/21.87 | | | | | | | | | | | | | (420) $false % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | CLOSE: (420) is inconsistent. % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | (421) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), % 148.74/21.87 | | | | | | | | | | | | | (13), (15), (17), (18), (19), (20), (21), (22), % 148.74/21.87 | | | | | | | | | | | | | (23), (25), (29), (30), (31), (35), (37), (38), % 148.74/21.87 | | | | | | | | | | | | | (44), (46), (47), (48), (50), (52), (53), (54), % 148.74/21.87 | | | | | | | | | | | | | (55), (56), (57), (58), (59), (61), (62), (63), % 148.74/21.87 | | | | | | | | | | | | | (65), (66), (70), (72), (73), (74), (75), (76), % 148.74/21.87 | | | | | | | | | | | | | (81), (82), (86), (88), (89), (90), (91), (92), % 148.74/21.87 | | | | | | | | | | | | | (93), (94), (96), (97), (98), (99), (101), (102), % 148.74/21.87 | | | | | | | | | | | | | (103), (105), (107), (108), (109), (110), (111), % 148.74/21.87 | | | | | | | | | | | | | (112), (113), (114), (115), (116), (117), (119), % 148.74/21.87 | | | | | | | | | | | | | (120), (121), (125), (127), (128), (129), (131), % 148.74/21.87 | | | | | | | | | | | | | (132), (133), (136), (139), (141), (142), (145), % 148.74/21.87 | | | | | | | | | | | | | (146), (147), (148), (153), (154), (155), (158), % 148.74/21.87 | | | | | | | | | | | | | (159), (160), (163), (181), (182), (185), (188), % 148.74/21.87 | | | | | | | | | | | | | (189), (190), (193), (200), (203), (412), (417), % 148.74/21.87 | | | | | | | | | | | | | (421) are inconsistent by sub-proof #8. % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | End of split % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | End of split % 148.74/21.87 | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | (422) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 148.74/21.87 | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | BETA: splitting (422) gives: % 148.74/21.87 | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | (423) all_56_1 = e2 % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | COMBINE_EQS: (65), (423) imply: % 148.74/21.87 | | | | | | | | | | | | (424) all_52_4 = e2 % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | COMBINE_EQS: (61), (424) imply: % 148.74/21.87 | | | | | | | | | | | | (425) all_58_2 = e2 % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | REDUCE: (151), (424) imply: % 148.74/21.87 | | | | | | | | | | | | (426) ~ (all_52_12 = e2) % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | REDUCE: (143), (424) imply: % 148.74/21.87 | | | | | | | | | | | | (427) ~ (all_10_2 = e2) % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | SIMP: (427) implies: % 148.74/21.87 | | | | | | | | | | | | (428) ~ (all_10_2 = e2) % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | REDUCE: (67), (424) imply: % 148.74/21.87 | | | | | | | | | | | | (429) ~ (all_8_1 = e2) % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | SIMP: (429) implies: % 148.74/21.87 | | | | | | | | | | | | (430) ~ (all_8_1 = e2) % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | BETA: splitting (140) gives: % 148.74/21.87 | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | (431) all_56_0 = e3 % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | COMBINE_EQS: (121), (431) imply: % 148.74/21.87 | | | | | | | | | | | | | (432) all_10_2 = e3 % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | REDUCE: (105), (432) imply: % 148.74/21.87 | | | | | | | | | | | | | (433) ~ (all_52_12 = e3) % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | BETA: splitting (84) gives: % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | (434) all_56_0 = e1 % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | COMBINE_EQS: (431), (434) imply: % 148.74/21.87 | | | | | | | | | | | | | | (435) e3 = e1 % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | REDUCE: (52), (435) imply: % 148.74/21.87 | | | | | | | | | | | | | | (436) $false % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | CLOSE: (436) is inconsistent. % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | (437) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | BETA: splitting (437) gives: % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | (438) all_56_1 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | COMBINE_EQS: (423), (438) imply: % 148.74/21.87 | | | | | | | | | | | | | | | (439) e2 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | REDUCE: (79), (439) imply: % 148.74/21.87 | | | | | | | | | | | | | | | (440) $false % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent. % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | (441) all_56_4 = e1 | all_56_9 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | BETA: splitting (441) gives: % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | (442) all_56_4 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REF_CLOSE: (99), (139), (442) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | | | #782. % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | (443) all_56_9 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (443) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (444) all_52_12 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | SIMP: (444) implies: % 148.74/21.87 | | | | | | | | | | | | | | | | (445) all_52_12 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REDUCE: (125), (445) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (446) ~ (all_4_2 = e1) % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | SIMP: (446) implies: % 148.74/21.87 | | | | | | | | | | | | | | | | (447) ~ (all_4_2 = e1) % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REDUCE: (433), (445) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (448) ~ (e3 = e1) % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REDUCE: (408), (445) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (449) ~ (e2 = e1) % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), % 148.74/21.87 | | | | | | | | | | | | | | | | (12), (13), (15), (16), (17), (19), (20), (22), % 148.74/21.87 | | | | | | | | | | | | | | | | (23), (24), (26), (27), (28), (29), (30), (31), % 148.74/21.87 | | | | | | | | | | | | | | | | (32), (34), (35), (37), (38), (39), (42), (43), % 148.74/21.87 | | | | | | | | | | | | | | | | (44), (45), (47), (48), (49), (50), (51), (52), % 148.74/21.87 | | | | | | | | | | | | | | | | (53), (54), (56), (57), (58), (59), (61), (63), % 148.74/21.87 | | | | | | | | | | | | | | | | (65), (67), (70), (72), (73), (74), (75), (76), % 148.74/21.87 | | | | | | | | | | | | | | | | (78), (79), (81), (82), (85), (86), (87), (88), % 148.74/21.87 | | | | | | | | | | | | | | | | (89), (90), (91), (92), (93), (95), (97), (98), % 148.74/21.87 | | | | | | | | | | | | | | | | (99), (100), (101), (102), (103), (105), (107), % 148.74/21.87 | | | | | | | | | | | | | | | | (108), (109), (111), (112), (114), (116), (117), % 148.74/21.87 | | | | | | | | | | | | | | | | (118), (120), (121), (125), (127), (128), (129), % 148.74/21.87 | | | | | | | | | | | | | | | | (130), (131), (132), (133), (136), (139), (141), % 148.74/21.87 | | | | | | | | | | | | | | | | (142), (143), (145), (146), (147), (149), (151), % 148.74/21.87 | | | | | | | | | | | | | | | | (152), (153), (154), (155), (158), (159), (160), % 148.74/21.87 | | | | | | | | | | | | | | | | (163), (165), (178), (181), (182), (183), (185), % 148.74/21.87 | | | | | | | | | | | | | | | | (189), (193), (196), (199), (200), (203), (447) % 148.74/21.87 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #333. % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | End of split % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | End of split % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | End of split % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | (450) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | BETA: splitting (450) gives: % 148.74/21.87 | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | (451) all_56_1 = e3 % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | REF_CLOSE: (148), (423), (451) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | #568. % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | (452) all_56_4 = e3 | all_56_9 = e3 % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | BETA: splitting (452) gives: % 148.74/21.87 | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | (453) all_56_4 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | REF_CLOSE: (97), (99), (453) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | | #33. % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | (454) all_56_9 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | COMBINE_EQS: (76), (454) imply: % 148.74/21.87 | | | | | | | | | | | | | | | (455) all_52_12 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | SIMP: (455) implies: % 148.74/21.87 | | | | | | | | | | | | | | | (456) all_52_12 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | COMBINE_EQS: (19), (456) imply: % 148.74/21.87 | | | | | | | | | | | | | | | (457) all_58_6 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | REDUCE: (105), (456) imply: % 148.74/21.87 | | | | | | | | | | | | | | | (458) ~ (all_10_2 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | SIMP: (458) implies: % 148.74/21.87 | | | | | | | | | | | | | | | (459) ~ (all_10_2 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | REDUCE: (125), (456) imply: % 148.74/21.87 | | | | | | | | | | | | | | | (460) ~ (all_4_2 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | SIMP: (460) implies: % 148.74/21.87 | | | | | | | | | | | | | | | (461) ~ (all_4_2 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | BETA: splitting (84) gives: % 148.74/21.87 | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | (462) all_56_0 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (462) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (463) all_10_2 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (463) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (464) all_58_28 = e1 % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REDUCE: (120), (463) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (465) ~ (all_52_2 = e1) % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | REDUCE: (459), (463) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | (466) ~ (e3 = e1) % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | (467) all_58_28 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (464), (467) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | | | | #857. % 148.74/21.87 | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | (468) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | BETA: splitting (468) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | (469) all_58_29 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (97), (469) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | | | | | #707. % 148.74/21.87 | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | (470) all_58_30 = e3 | all_58_31 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | (471) all_58_30 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (471) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | (472) all_6_2 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (472) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | (473) ~ (all_52_2 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | REDUCE: (8), (472) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | (474) ~ (all_52_6 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (475) all_56_6 = e2 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (475) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (476) all_52_2 = e2 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (476) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (477) all_58_15 = e2 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (476) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (478) ~ (all_52_1 = e2) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (476) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (479) ~ (all_52_6 = e2) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | SIMP: (479) implies: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (480) ~ (all_52_6 = e2) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (473), (476) imply: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | (481) ~ (e3 = e2) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | (482) all_56_1 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (423), (482) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | #568. % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | (483) ~ (all_56_1 = e3) % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | (484) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | (485) all_56_3 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (74), (79), (97), (117), (148), (464), % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | (468), (471), (485) are inconsistent by sub-proof % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | #28. % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | (486) all_56_7 = e3 | all_56_13 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | | (487) all_56_2 = e3 % 148.74/21.87 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (487) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | (488) all_52_1 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (488) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | (489) all_58_8 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (488) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | (490) ~ (all_52_9 = e3) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (490) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | (491) ~ (all_52_9 = e3) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (488) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | (492) ~ (all_52_13 = e3) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (492) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | (493) ~ (all_52_13 = e3) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_28 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (79), (464), (494) are inconsistent by sub-proof % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | #856. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | (495) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_29 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (117), (496) are inconsistent by sub-proof % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | #706. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_58_30 = e2 | all_58_31 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_54_9 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (498) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_52_6 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (499) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_52_6 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (500) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_56_7 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (500) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_58_17 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (480), (500) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (503) ~ (e2 = e1) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_56_7 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (501), (504) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) e3 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (505) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_58_30 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (74), (79), (97), (148), (468), (497), (506) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #662. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_56_13 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (507) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_8_1 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (508) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_8_1 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (509) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_58_24 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (509) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) ~ (all_52_11 = e3) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (497) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_58_30 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (471), (512) are inconsistent by sub-proof % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #659. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_58_31 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (513) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_4_2 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (514) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_4_2 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (515) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) ~ (all_52_11 = e2) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (515) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) ~ (all_52_13 = e2) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_54_7 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (518) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_52_13 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (519) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_52_13 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (520) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_58_13 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (520) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) ~ (all_52_9 = e1) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_58_31 = e0 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (117), (148), (470), (497), (523) are % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #852. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_54_6 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (522), (525) are inconsistent by sub-proof % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_54_6 = e3 | all_54_6 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_54_14 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (527) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_52_11 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (528) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_52_11 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (529) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_26 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_54_6 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (531) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_52_9 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (532) implies: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_52_9 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (533) imply: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_58_11 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (524) gives: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_58_30 = e1 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (74), (97), (131), (148), (464), (513), % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) are inconsistent by sub-proof #355. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (52), (74), (79), (97), (117), (139), (148), % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (181), (425), (457), (464), (471), (477), % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489), (495), (497), (502), (510), (513), (521), % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530), (534), (536) are inconsistent by sub-proof % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #342. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_54_6 = e3 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (491), (537) are inconsistent by sub-proof % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #772. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_54_14 = e3 | all_54_14 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (511), (516), (538) are inconsistent by % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #358. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_54_7 = e3 | all_54_7 = e2 % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (493), (517), (539) are inconsistent by % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #602. % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_54_9 = e3 | all_54_9 = e2 % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (474), (480), (540) are inconsistent by % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #559. % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | (541) ~ (all_56_2 = e3) % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (541) imply: % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | (542) ~ (all_52_1 = e3) % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (36), (133), (152), (153), (428), (459), % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | (478), (542) are inconsistent by sub-proof #745. % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | End of split % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | Case 2: % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | (543) ~ (all_56_6 = e2) % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (543) imply: % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | (544) ~ (all_52_2 = e2) % 148.74/21.89 | | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (193), (465), (473), (544) are inconsistent % 149.13/21.89 | | | | | | | | | | | | | | | | | | | | by sub-proof #416. % 149.13/21.89 | | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | Case 2: % 149.13/21.89 | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | | (545) all_58_31 = e3 % 149.13/21.89 | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (545) imply: % 149.13/21.89 | | | | | | | | | | | | | | | | | | | (546) all_4_2 = e3 % 149.13/21.89 | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | | REDUCE: (461), (546) imply: % 149.13/21.89 | | | | | | | | | | | | | | | | | | | (547) $false % 149.13/21.89 | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | | CLOSE: (547) is inconsistent. % 149.13/21.89 | | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | Case 2: % 149.13/21.89 | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | (548) ~ (all_56_0 = e1) % 149.13/21.89 | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | REDUCE: (121), (548) imply: % 149.13/21.89 | | | | | | | | | | | | | | | | (549) ~ (all_10_2 = e1) % 149.13/21.89 | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (133), (428), (459), (549) are inconsistent % 149.13/21.89 | | | | | | | | | | | | | | | | by sub-proof #813. % 149.13/21.89 | | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | Case 2: % 149.13/21.89 | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | (550) all_56_4 = e2 | all_56_9 = e2 % 149.13/21.89 | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | BETA: splitting (550) gives: % 149.13/21.89 | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | Case 1: % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | (551) all_56_4 = e2 % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | COMBINE_EQS: (99), (551) imply: % 149.13/21.89 | | | | | | | | | | | | | (552) e2 = e0 % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | SIMP: (552) implies: % 149.13/21.89 | | | | | | | | | | | | | (553) e2 = e0 % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | REDUCE: (117), (553) imply: % 149.13/21.89 | | | | | | | | | | | | | (554) $false % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | CLOSE: (554) is inconsistent. % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | Case 2: % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | (555) all_56_9 = e2 % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | | REF_CLOSE: (76), (408), (555) are inconsistent by sub-proof % 149.13/21.89 | | | | | | | | | | | | | #431. % 149.13/21.89 | | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | | % 149.13/21.89 | | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | | % 149.13/21.89 | | | | | | | | | End of split % 149.13/21.89 | | | | | | | | | % 149.13/21.89 | | | | | | | | End of split % 149.13/21.89 | | | | | | | | % 149.13/21.89 | | | | | | | End of split % 149.13/21.89 | | | | | | | % 149.13/21.89 | | | | | | End of split % 149.13/21.89 | | | | | | % 149.13/21.89 | | | | | End of split % 149.13/21.89 | | | | | % 149.13/21.89 | | | | End of split % 149.13/21.89 | | | | % 149.13/21.89 | | | End of split % 149.13/21.89 | | | % 149.13/21.89 | | End of split % 149.13/21.89 | | % 149.13/21.89 | Case 2: % 149.13/21.89 | | % 149.13/21.89 | | (556) all_56_13 = e0 | all_56_14 = e0 % 149.13/21.89 | | % 149.13/21.89 | | REF_CLOSE: (83), (101), (108), (137), (556) are inconsistent by sub-proof % 149.13/21.89 | | #609. % 149.13/21.89 | | % 149.13/21.89 | End of split % 149.13/21.89 | % 149.13/21.89 End of proof % 149.13/21.89 % 149.13/21.89 Sub-proof #5 shows that the following formulas are inconsistent: % 149.13/21.89 ---------------------------------------------------------------- % 149.13/21.89 (1) all_58_31 = all_4_2 % 149.13/21.89 (2) all_58_22 = e0 % 149.13/21.89 (3) all_58_6 = e2 % 149.13/21.89 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.13/21.89 (5) all_58_30 = e2 % 149.13/21.89 (6) ~ (e3 = e1) % 149.13/21.89 (7) all_20_2 = all_4_2 % 149.13/21.89 (8) all_58_29 = e0 % 149.13/21.89 (9) ~ (e2 = e1) % 149.13/21.89 (10) ~ (e3 = e0) % 149.13/21.89 (11) all_58_6 = e3 % 149.13/21.89 (12) all_58_28 = all_10_2 % 149.13/21.89 (13) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.13/21.89 (14) ~ (e2 = e0) % 149.13/21.89 (15) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.13/21.89 (16) ~ (e1 = e0) % 149.13/21.89 (17) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.13/21.89 (18) ~ (e3 = e2) % 149.13/21.89 (19) all_58_22 = e3 % 149.13/21.89 % 149.13/21.89 Begin of proof % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (3), (11) imply: % 149.13/21.89 | (20) e3 = e2 % 149.13/21.89 | % 149.13/21.89 | SIMP: (20) implies: % 149.13/21.89 | (21) e3 = e2 % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (2), (19) imply: % 149.13/21.89 | (22) e3 = e0 % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (21), (22) imply: % 149.13/21.89 | (23) e2 = e0 % 149.13/21.89 | % 149.13/21.89 | SIMP: (23) implies: % 149.13/21.89 | (24) e2 = e0 % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (5), (24) imply: % 149.13/21.89 | (25) all_58_30 = e0 % 149.13/21.89 | % 149.13/21.89 | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15), (16), % 149.13/21.89 | (17), (18), (25) are inconsistent by sub-proof #691. % 149.13/21.89 | % 149.13/21.89 End of proof % 149.13/21.89 % 149.13/21.89 Sub-proof #6 shows that the following formulas are inconsistent: % 149.13/21.89 ---------------------------------------------------------------- % 149.13/21.89 (1) all_58_31 = all_4_2 % 149.13/21.89 (2) all_58_22 = e0 % 149.13/21.89 (3) all_58_6 = e2 % 149.13/21.89 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.13/21.89 (5) all_58_30 = e2 % 149.13/21.89 (6) ~ (e3 = e1) % 149.13/21.89 (7) all_20_2 = all_4_2 % 149.13/21.89 (8) all_58_29 = e0 % 149.13/21.89 (9) ~ (e2 = e1) % 149.13/21.89 (10) ~ (e3 = e0) % 149.13/21.89 (11) all_58_6 = e3 % 149.13/21.89 (12) all_58_28 = all_10_2 % 149.13/21.89 (13) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.13/21.89 (14) ~ (e2 = e0) % 149.13/21.89 (15) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.13/21.89 (16) ~ (e1 = e0) % 149.13/21.89 (17) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.13/21.89 (18) ~ (e3 = e2) % 149.13/21.89 (19) all_58_22 = e3 % 149.13/21.89 % 149.13/21.89 Begin of proof % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (3), (11) imply: % 149.13/21.89 | (20) e3 = e2 % 149.13/21.89 | % 149.13/21.89 | SIMP: (20) implies: % 149.13/21.89 | (21) e3 = e2 % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (2), (19) imply: % 149.13/21.89 | (22) e3 = e0 % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (21), (22) imply: % 149.13/21.89 | (23) e2 = e0 % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (5), (23) imply: % 149.13/21.89 | (24) all_58_30 = e0 % 149.13/21.89 | % 149.13/21.89 | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15), (16), % 149.13/21.89 | (17), (18), (24) are inconsistent by sub-proof #691. % 149.13/21.89 | % 149.13/21.89 End of proof % 149.13/21.89 % 149.13/21.89 Sub-proof #7 shows that the following formulas are inconsistent: % 149.13/21.89 ---------------------------------------------------------------- % 149.13/21.89 (1) all_58_4 = e3 % 149.13/21.89 (2) all_58_4 = e0 % 149.13/21.89 (3) ~ (e3 = e0) % 149.13/21.89 % 149.13/21.89 Begin of proof % 149.13/21.89 | % 149.13/21.89 | COMBINE_EQS: (1), (2) imply: % 149.13/21.89 | (4) e3 = e0 % 149.13/21.89 | % 149.13/21.89 | SIMP: (4) implies: % 149.13/21.89 | (5) e3 = e0 % 149.13/21.89 | % 149.13/21.89 | REDUCE: (3), (5) imply: % 149.13/21.89 | (6) $false % 149.13/21.89 | % 149.13/21.89 | CLOSE: (6) is inconsistent. % 149.13/21.89 | % 149.13/21.89 End of proof % 149.13/21.89 % 149.13/21.89 Sub-proof #8 shows that the following formulas are inconsistent: % 149.13/21.89 ---------------------------------------------------------------- % 149.13/21.89 (1) all_58_23 = all_8_0 % 149.13/21.89 (2) all_58_31 = all_4_2 % 149.13/21.89 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.13/21.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.13/21.89 (4) all_58_11 = all_52_9 % 149.13/21.89 (5) all_56_15 = all_4_2 % 149.13/21.89 (6) all_56_7 = all_52_6 % 149.13/21.89 (7) ~ (all_52_6 = all_6_2) % 149.13/21.89 (8) all_58_22 = e0 % 149.13/21.89 (9) ~ (all_52_2 = e0) % 149.13/21.89 (10) all_54_8 = all_52_2 % 149.13/21.89 (11) all_58_15 = all_52_2 % 149.13/21.89 (12) all_58_26 = all_52_11 % 149.13/21.89 (13) all_56_3 = e0 % 149.13/21.89 (14) ~ (all_52_11 = all_4_2) % 149.13/21.89 (15) all_54_7 = all_52_13 % 149.13/21.89 (16) all_58_6 = all_52_12 % 149.13/21.89 (17) all_58_4 = e0 % 149.13/21.89 (18) ~ (all_52_6 = all_8_1) % 149.13/21.89 (19) all_54_3 = all_52_12 % 149.13/21.89 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.13/21.89 (21) op(e0, e2) = all_8_1 % 149.13/21.89 (22) ~ (all_6_2 = e0) % 149.13/21.89 (23) op(e0, e1) = all_52_11 % 149.13/21.89 (24) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.13/21.89 (25) all_56_13 = all_8_1 % 149.13/21.89 (26) all_58_20 = e0 % 149.13/21.89 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 149.13/21.89 (28) ~ (all_52_12 = all_52_13) % 149.13/21.89 (29) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.13/21.89 (30) ~ (all_10_2 = e0) % 149.13/21.89 (31) ~ (all_52_2 = all_6_2) % 149.13/21.89 (32) op(e3, e3) = all_10_2 % 149.13/21.89 (33) all_54_9 = all_52_6 % 149.13/21.89 (34) ~ (all_52_13 = all_4_2) % 149.13/21.89 (35) all_58_19 = e0 % 149.13/21.89 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 149.13/21.89 (37) ~ (e3 = e1) % 149.13/21.89 (38) ~ (all_52_6 = e0) % 149.13/21.89 (39) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.13/21.90 (40) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 149.13/21.90 (41) ~ (all_52_1 = all_52_13) % 149.13/21.90 (42) all_56_5 = all_52_9 % 149.13/21.90 (43) all_54_14 = all_52_11 % 149.13/21.90 (44) op(e0, all_8_1) = all_8_0 % 149.13/21.90 (45) ~ (all_52_12 = e0) % 149.13/21.90 (46) all_58_2 = all_52_4 % 149.13/21.90 (47) all_20_2 = all_4_2 % 149.13/21.90 (48) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 149.13/21.90 (49) all_56_1 = all_52_4 % 149.13/21.90 (50) all_58_9 = all_52_13 % 149.13/21.90 (51) ~ (all_52_9 = e0) % 149.13/21.90 (52) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 149.13/21.90 (53) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/21.90 (54) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.18/21.90 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.18/21.90 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.18/21.90 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.18/21.90 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.18/21.90 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.18/21.90 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.18/21.90 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.18/21.90 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.18/21.90 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.18/21.90 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.18/21.90 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.18/21.90 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.18/21.90 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.18/21.90 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.90 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.90 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.18/21.90 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.18/21.90 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.18/21.90 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.18/21.90 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.18/21.90 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.18/21.90 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.18/21.90 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.18/21.90 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.18/21.90 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.18/21.90 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.18/21.90 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.18/21.90 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.18/21.90 e0) % 149.18/21.90 (55) all_58_29 = e0 % 149.18/21.90 (56) op(e2, e1) = all_52_9 % 149.18/21.90 (57) all_56_9 = all_52_12 % 149.18/21.90 (58) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/21.90 (59) all_56_6 = all_52_2 % 149.18/21.90 (60) ~ (all_52_2 = all_52_6) % 149.18/21.90 (61) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.18/21.90 (62) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 149.18/21.90 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 149.18/21.90 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 149.18/21.90 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 149.18/21.90 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 149.18/21.90 (all_58_27 = e0)) % 149.18/21.90 (63) ~ (all_52_9 = all_52_13) % 149.18/21.90 (64) ~ (all_52_11 = all_8_1) % 149.18/21.90 (65) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.18/21.90 (66) all_54_13 = all_8_1 % 149.18/21.90 (67) ~ (all_52_4 = e0) % 149.18/21.90 (68) op(e2, all_52_9) = all_58_10 % 149.18/21.90 (69) op(e3, all_10_2) = all_58_0 % 149.18/21.90 (70) ~ (e3 = e0) % 149.18/21.90 (71) all_56_2 = all_52_1 % 149.18/21.90 (72) all_56_4 = e0 % 149.18/21.90 (73) ~ (all_52_11 = e0) % 149.18/21.90 (74) op(e3, all_52_12) = all_58_5 % 149.18/21.90 (75) all_56_10 = all_52_13 % 149.18/21.90 (76) ~ (all_52_12 = all_10_2) % 149.18/21.90 (77) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.18/21.90 (78) all_56_14 = all_52_11 % 149.18/21.90 (79) all_58_28 = all_10_2 % 149.18/21.90 (80) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 149.18/21.90 (81) all_58_21 = all_4_2 % 149.18/21.90 (82) all_58_17 = all_52_6 % 149.18/21.90 (83) ~ (all_52_1 = all_52_9) % 149.18/21.90 (84) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.18/21.90 (85) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/21.90 (86) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/21.90 (87) all_14_0 = all_8_0 % 149.18/21.90 (88) ~ (e2 = e0) % 149.18/21.90 (89) ~ (all_4_2 = e0) % 149.18/21.90 (90) ~ (all_8_1 = all_4_2) % 149.18/21.90 (91) all_56_12 = e0 % 149.18/21.90 (92) ~ (all_52_2 = all_10_2) % 149.18/21.90 (93) all_56_0 = all_10_2 % 149.18/21.90 (94) ~ (all_52_1 = e0) % 149.18/21.90 (95) ~ (all_52_12 = all_4_2) % 149.18/21.90 (96) all_56_8 = all_6_2 % 149.18/21.90 (97) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.18/21.90 (98) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.18/21.90 (99) ~ (all_52_1 = all_52_2) % 149.18/21.90 (100) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 149.18/21.90 (101) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/21.90 (102) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.18/21.90 (103) all_54_0 = all_10_2 % 149.18/21.90 (104) all_14_1 = all_8_1 % 149.18/21.90 (105) ~ (e1 = e0) % 149.18/21.90 (106) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.18/21.90 (107) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 149.18/21.90 (108) all_58_3 = all_52_12 % 149.18/21.90 (109) all_58_30 = all_6_2 % 149.18/21.90 (110) op(e2, all_52_1) = all_58_7 % 149.18/21.90 (111) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/21.90 (112) ~ (e3 = e2) % 149.18/21.90 (113) ~ (all_52_2 = e2) % 149.18/21.90 (114) ~ (all_52_1 = all_10_2) % 149.18/21.90 (115) op(e3, e1) = e0 % 149.18/21.90 % 149.18/21.90 Begin of proof % 149.18/21.90 | % 149.18/21.90 | BETA: splitting (85) gives: % 149.18/21.90 | % 149.18/21.90 | Case 1: % 149.18/21.90 | | % 149.18/21.90 | | (116) all_56_6 = e1 % 149.18/21.90 | | % 149.18/21.90 | | COMBINE_EQS: (59), (116) imply: % 149.18/21.90 | | (117) all_52_2 = e1 % 149.18/21.90 | | % 149.18/21.90 | | SIMP: (117) implies: % 149.18/21.90 | | (118) all_52_2 = e1 % 149.18/21.90 | | % 149.18/21.90 | | REDUCE: (31), (118) imply: % 149.18/21.90 | | (119) ~ (all_6_2 = e1) % 149.18/21.90 | | % 149.18/21.90 | | SIMP: (119) implies: % 149.18/21.90 | | (120) ~ (all_6_2 = e1) % 149.18/21.90 | | % 149.18/21.90 | | REDUCE: (113), (118) imply: % 149.18/21.90 | | (121) ~ (e2 = e1) % 149.18/21.90 | | % 149.18/21.90 | | SIMP: (121) implies: % 149.18/21.90 | | (122) ~ (e2 = e1) % 149.18/21.90 | | % 149.18/21.90 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 149.18/21.90 | | (16), (17), (20), (21), (22), (24), (25), (26), (29), (32), (34), % 149.18/21.90 | | (35), (37), (38), (39), (42), (44), (45), (46), (49), (51), (54), % 149.18/21.90 | | (55), (56), (58), (59), (60), (61), (62), (63), (67), (68), (69), % 149.18/21.90 | | (70), (71), (72), (73), (75), (78), (79), (82), (83), (88), (89), % 149.18/21.90 | | (90), (91), (93), (96), (98), (101), (105), (109), (111), (112), % 149.18/21.90 | | (120), (122) are inconsistent by sub-proof #35. % 149.18/21.90 | | % 149.18/21.90 | Case 2: % 149.18/21.90 | | % 149.18/21.90 | | (123) ~ (all_56_6 = e1) % 149.18/21.90 | | % 149.18/21.90 | | REDUCE: (59), (123) imply: % 149.18/21.90 | | (124) ~ (all_52_2 = e1) % 149.18/21.90 | | % 149.18/21.90 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 149.18/21.90 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 149.18/21.90 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 149.18/21.90 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 149.18/21.90 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 149.18/21.90 | | (57), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 149.18/21.90 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 149.18/21.90 | | (80), (81), (82), (83), (84), (86), (87), (89), (90), (91), (92), % 149.18/21.90 | | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102), % 149.18/21.90 | | (103), (104), (105), (106), (107), (108), (109), (110), (111), % 149.18/21.90 | | (112), (114), (115), (124) are inconsistent by sub-proof #31. % 149.18/21.90 | | % 149.18/21.90 | End of split % 149.18/21.90 | % 149.18/21.90 End of proof % 149.18/21.90 % 149.18/21.90 Sub-proof #9 shows that the following formulas are inconsistent: % 149.18/21.90 ---------------------------------------------------------------- % 149.18/21.90 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 149.18/21.90 (2) all_58_31 = all_4_2 % 149.18/21.90 (3) ~ (all_52_8 = all_52_9) % 149.18/21.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/21.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/21.91 (5) ~ (all_52_2 = all_52_3) % 149.18/21.91 (6) all_58_11 = all_52_9 % 149.18/21.91 (7) all_56_15 = all_4_2 % 149.18/21.91 (8) all_56_7 = all_52_6 % 149.18/21.91 (9) ~ (all_52_6 = all_6_2) % 149.18/21.91 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 149.18/21.91 (11) all_54_2 = all_52_8 % 149.18/21.91 (12) all_22_0 = all_8_0 % 149.18/21.91 (13) op(e1, all_6_2) = all_58_18 % 149.18/21.91 (14) op(e3, all_52_4) = all_58_1 % 149.18/21.91 (15) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 149.18/21.91 (16) ~ (all_52_8 = all_10_2) % 149.18/21.91 (17) all_58_15 = all_52_2 % 149.18/21.91 (18) all_58_26 = all_52_11 % 149.18/21.91 (19) op(e1, all_52_14) = all_58_19 % 149.18/21.91 (20) ~ (all_52_8 = all_52_11) % 149.18/21.91 (21) ~ (all_52_11 = all_4_2) % 149.18/21.91 (22) all_54_7 = all_52_13 % 149.18/21.91 (23) all_58_6 = all_52_12 % 149.18/21.91 (24) ~ (all_52_6 = all_8_2) % 149.18/21.91 (25) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) | ~ (all_16_2 = e0) % 149.18/21.91 (26) all_56_4 = all_52_8 % 149.18/21.91 (27) ~ (all_52_4 = all_8_2) % 149.18/21.91 (28) all_54_3 = all_52_12 % 149.18/21.91 (29) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/21.91 (30) all_54_1 = all_52_4 % 149.18/21.91 (31) op(e0, all_4_2) = all_58_27 % 149.18/21.91 (32) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 149.18/21.91 (33) ~ (all_52_4 = all_52_6) % 149.18/21.91 (34) all_58_13 = all_52_13 % 149.18/21.91 (35) op(e2, e2) = all_8_2 % 149.18/21.91 (36) op(e0, e1) = all_52_11 % 149.18/21.91 (37) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 149.18/21.91 (38) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.18/21.91 (39) ~ (all_52_6 = all_52_7) % 149.18/21.91 (40) all_50_2 = all_10_2 % 149.18/21.91 (41) op(all_10_2, all_10_1) = all_10_0 % 149.18/21.91 (42) op(e3, e2) = all_52_4 % 149.18/21.91 (43) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 149.18/21.91 (44) all_58_20 = all_52_14 % 149.18/21.91 (45) ~ (all_52_8 = all_6_2) % 149.18/21.91 (46) ~ (all_52_12 = all_52_13) % 149.18/21.91 (47) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.18/21.91 (48) all_54_10 = all_6_2 % 149.18/21.91 (49) op(e0, all_52_3) = all_58_21 % 149.18/21.91 (50) all_16_2 = all_10_2 % 149.18/21.91 (51) op(e0, all_52_7) = all_58_23 % 149.18/21.91 (52) all_54_5 = all_8_2 % 149.18/21.91 (53) ~ (all_52_6 = all_52_14) % 149.18/21.91 (54) all_54_6 = all_52_9 % 149.18/21.91 (55) ~ (all_52_4 = all_52_7) % 149.18/21.91 (56) ~ (all_52_2 = all_6_2) % 149.18/21.91 (57) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 149.18/21.91 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 149.18/21.91 (58) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 149.18/21.91 (59) op(e3, e3) = all_10_2 % 149.18/21.91 (60) op(e3, all_52_8) = all_58_3 % 149.18/21.91 (61) ~ (all_52_8 = all_52_12) % 149.18/21.91 (62) all_54_9 = all_52_6 % 149.18/21.91 (63) ~ (all_52_13 = all_4_2) % 149.18/21.91 (64) op(e1, e2) = all_52_6 % 149.18/21.91 (65) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 149.18/21.91 (66) ~ (all_52_13 = all_8_2) % 149.18/21.91 (67) op(e1, all_52_6) = all_58_16 % 149.18/21.91 (68) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 149.18/21.91 (69) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 149.18/21.91 (70) ~ (e3 = e1) % 149.18/21.91 (71) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.18/21.91 (72) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.18/21.91 (73) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.18/21.91 (74) ~ (all_52_1 = all_52_13) % 149.18/21.91 (75) all_56_5 = all_52_9 % 149.18/21.91 (76) all_54_14 = all_52_11 % 149.18/21.91 (77) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 149.18/21.91 (78) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.18/21.91 (79) all_56_12 = all_52_3 % 149.18/21.91 (80) ~ (all_52_3 = all_52_7) % 149.18/21.91 (81) all_58_2 = all_52_4 % 149.18/21.91 (82) all_20_2 = all_4_2 % 149.18/21.91 (83) all_56_11 = all_52_14 % 149.18/21.91 (84) all_56_1 = all_52_4 % 149.18/21.91 (85) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 149.18/21.91 (86) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.18/21.91 (87) ~ (all_52_3 = all_4_2) % 149.18/21.91 (88) op(e1, e3) = all_52_2 % 149.18/21.91 (89) op(e1, e0) = all_52_14 % 149.18/21.91 (90) ~ (all_52_9 = all_52_11) % 149.18/21.91 (91) ~ (all_52_1 = all_8_2) % 149.18/21.91 (92) all_56_3 = all_8_2 % 149.18/21.91 (93) all_58_24 = all_52_7 % 149.18/21.91 (94) ~ (all_52_13 = all_52_14) % 149.18/21.91 (95) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/21.91 (96) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.18/21.91 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.18/21.91 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.18/21.91 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.18/21.91 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.18/21.91 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.18/21.91 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.18/21.91 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.18/21.91 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.18/21.91 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.18/21.91 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.18/21.91 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.18/21.91 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.18/21.91 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.18/21.91 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.91 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.91 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.18/21.91 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.18/21.91 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.18/21.91 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.18/21.91 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.18/21.91 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.18/21.91 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.18/21.91 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.18/21.91 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.18/21.91 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.18/21.91 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.18/21.91 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.18/21.91 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.18/21.91 e0) % 149.18/21.91 (97) ~ (all_52_4 = all_52_8) % 149.18/21.91 (98) all_50_0 = all_10_0 % 149.18/21.91 (99) ~ (all_50_0 = e1) | ~ (all_50_1 = e2) | ~ (all_50_2 = e0) % 149.18/21.91 (100) op(e1, all_52_2) = all_58_14 % 149.18/21.91 (101) ~ (all_10_0 = e0) % 149.18/21.91 (102) all_56_9 = all_52_12 % 149.18/21.91 (103) all_58_29 = all_8_2 % 149.18/21.91 (104) ~ (all_52_12 = all_52_14) % 149.18/21.91 (105) all_58_8 = all_52_1 % 149.18/21.91 (106) ~ (e2 = e1) % 149.18/21.91 (107) op(e3, e0) = all_52_12 % 149.18/21.91 (108) all_56_6 = all_52_2 % 149.18/21.91 (109) ~ (all_52_2 = all_52_6) % 149.18/21.91 (110) all_18_2 = all_6_2 % 149.18/21.91 (111) op(all_8_2, e2) = e0 % 149.18/21.91 (112) all_56_13 = all_52_7 % 149.18/21.91 (113) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 149.18/21.92 (114) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.18/21.92 (115) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.18/21.92 (116) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.18/21.92 (117) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 149.18/21.92 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 149.18/21.92 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 149.18/21.92 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 149.18/21.92 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 149.18/21.92 (all_58_27 = e0)) % 149.18/21.92 (118) ~ (all_52_9 = all_52_13) % 149.18/21.92 (119) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 149.18/21.92 (120) op(all_6_2, e1) = all_6_1 % 149.18/21.92 (121) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.18/21.92 (122) op(e2, all_52_9) = all_58_10 % 149.18/21.92 (123) ~ (all_52_11 = all_6_2) % 149.18/21.92 (124) op(e3, all_10_2) = all_58_0 % 149.18/21.92 (125) ~ (e3 = e0) % 149.18/21.92 (126) all_56_2 = all_52_1 % 149.18/21.92 (127) ~ (all_32_0 = e1) | ~ (all_32_1 = e0) | ~ (all_32_2 = e2) % 149.18/21.92 (128) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.18/21.92 (129) op(e0, e3) = all_52_3 % 149.18/21.92 (130) op(e3, all_52_12) = all_58_5 % 149.18/21.92 (131) all_22_1 = e0 % 149.18/21.92 (132) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.18/21.92 (133) all_56_10 = all_52_13 % 149.18/21.92 (134) ~ (all_52_12 = all_10_2) % 149.18/21.92 (135) ~ (all_52_1 = all_52_3) % 149.18/21.92 (136) all_32_1 = all_10_1 % 149.18/21.92 (137) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.18/21.92 (138) ~ (all_52_9 = all_8_2) % 149.18/21.92 (139) all_56_14 = all_52_11 % 149.18/21.92 (140) all_58_28 = all_10_2 % 149.18/21.92 (141) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 149.18/21.92 (142) op(all_8_2, e0) = all_8_0 % 149.18/21.92 (143) all_58_17 = all_52_6 % 149.18/21.92 (144) ~ (all_52_1 = all_52_9) % 149.18/21.92 (145) op(e3, e1) = all_52_8 % 149.18/21.92 (146) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.18/21.92 (147) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/21.92 (148) ~ (all_52_7 = all_52_11) % 149.18/21.92 (149) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/21.92 (150) ~ (e2 = e0) % 149.18/21.92 (151) ~ (all_52_9 = all_6_2) % 149.18/21.92 (152) ~ (all_52_2 = all_10_2) % 149.18/21.92 (153) all_56_0 = all_10_2 % 149.18/21.92 (154) op(e0, e0) = all_4_2 % 149.18/21.92 (155) ~ (all_22_0 = e3) | ~ (all_22_1 = e0) | ~ (all_22_2 = e1) % 149.18/21.92 (156) ~ (all_52_3 = all_52_11) % 149.18/21.92 (157) all_58_22 = all_52_3 % 149.18/21.92 (158) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 149.18/21.92 (159) ~ (all_52_12 = all_4_2) % 149.18/21.92 (160) all_50_1 = all_10_1 % 149.18/21.92 (161) ~ (all_52_3 = all_10_2) % 149.18/21.92 (162) all_56_8 = all_6_2 % 149.18/21.92 (163) op(e1, e1) = all_6_2 % 149.18/21.92 (164) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.18/21.92 (165) ~ (all_52_1 = all_52_2) % 149.18/21.92 (166) ~ (all_52_7 = all_8_2) % 149.18/21.92 (167) op(e2, e0) = all_52_13 % 149.18/21.92 (168) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.18/21.92 (169) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 149.18/21.92 (170) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 149.18/21.92 (171) op(e2, all_52_13) = all_58_12 % 149.18/21.92 (172) all_58_4 = all_52_8 % 149.18/21.92 (173) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/21.92 (174) all_16_1 = all_10_1 % 149.18/21.92 (175) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.18/21.92 (176) all_16_0 = all_10_0 % 149.18/21.92 (177) all_54_0 = all_10_2 % 149.18/21.92 (178) ~ (all_52_2 = all_52_14) % 149.18/21.92 (179) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.18/21.92 (180) ~ (all_52_14 = all_4_2) % 149.18/21.92 (181) all_22_2 = all_8_2 % 149.18/21.92 (182) ~ (e1 = e0) % 149.18/21.92 (183) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 149.18/21.92 (184) ~ (all_52_7 = all_4_2) % 149.18/21.92 (185) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.18/21.92 (186) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.18/21.92 (187) op(all_4_2, all_4_1) = e1 % 149.18/21.92 (188) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.18/21.92 (189) op(e0, e2) = all_52_7 % 149.18/21.92 (190) ~ (all_52_4 = all_10_2) % 149.18/21.92 (191) all_58_30 = all_6_2 % 149.18/21.92 (192) op(e2, all_52_1) = all_58_7 % 149.18/21.92 (193) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/21.92 (194) ~ (e3 = e2) % 149.18/21.92 (195) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.18/21.92 (196) ~ (all_52_14 = all_6_2) % 149.18/21.92 (197) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 149.18/21.92 (198) op(all_4_2, e0) = all_4_1 % 149.18/21.92 (199) op(all_10_2, e3) = all_10_1 % 149.18/21.92 (200) ~ (all_52_4 = all_52_12) % 149.18/21.92 (201) all_54_12 = all_52_3 % 149.18/21.92 (202) op(e2, all_8_2) = all_58_9 % 149.18/21.92 (203) all_54_4 = all_52_1 % 149.18/21.92 (204) ~ (all_52_1 = all_10_2) % 149.18/21.92 % 149.18/21.92 Begin of proof % 149.18/21.92 | % 149.18/21.92 | BETA: splitting (25) gives: % 149.18/21.92 | % 149.18/21.92 | Case 1: % 149.18/21.92 | | % 149.18/21.92 | | (205) ~ (all_16_2 = e0) % 149.18/21.92 | | % 149.18/21.92 | | REDUCE: (50), (205) imply: % 149.18/21.92 | | (206) ~ (all_10_2 = e0) % 149.18/21.92 | | % 149.18/21.92 | | BETA: splitting (69) gives: % 149.18/21.92 | | % 149.18/21.92 | | Case 1: % 149.18/21.92 | | | % 149.18/21.92 | | | (207) ~ (all_18_2 = e0) % 149.18/21.92 | | | % 149.18/21.92 | | | REDUCE: (110), (207) imply: % 149.18/21.92 | | | (208) ~ (all_6_2 = e0) % 149.18/21.92 | | | % 149.18/21.92 | | | BETA: splitting (155) gives: % 149.18/21.92 | | | % 149.18/21.92 | | | Case 1: % 149.18/21.92 | | | | % 149.18/21.92 | | | | (209) ~ (all_22_1 = e0) % 149.18/21.92 | | | | % 149.18/21.92 | | | | REDUCE: (131), (209) imply: % 149.18/21.92 | | | | (210) $false % 149.18/21.92 | | | | % 149.18/21.92 | | | | CLOSE: (210) is inconsistent. % 149.18/21.92 | | | | % 149.18/21.92 | | | Case 2: % 149.18/21.92 | | | | % 149.18/21.92 | | | | (211) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 149.18/21.92 | | | | % 149.18/21.92 | | | | BETA: splitting (127) gives: % 149.18/21.92 | | | | % 149.18/21.92 | | | | Case 1: % 149.18/21.92 | | | | | % 149.18/21.92 | | | | | (212) ~ (all_32_1 = e0) % 149.18/21.92 | | | | | % 149.18/21.92 | | | | | REDUCE: (136), (212) imply: % 149.18/21.92 | | | | | (213) ~ (all_10_1 = e0) % 149.18/21.92 | | | | | % 149.18/21.92 | | | | | BETA: splitting (57) gives: % 149.18/21.92 | | | | | % 149.18/21.92 | | | | | Case 1: % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | (214) all_56_15 = e0 % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | COMBINE_EQS: (7), (214) imply: % 149.18/21.92 | | | | | | (215) all_4_2 = e0 % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | SIMP: (215) implies: % 149.18/21.92 | | | | | | (216) all_4_2 = e0 % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | COMBINE_EQS: (2), (216) imply: % 149.18/21.92 | | | | | | (217) all_58_31 = e0 % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | REDUCE: (184), (216) imply: % 149.18/21.92 | | | | | | (218) ~ (all_52_7 = e0) % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | REDUCE: (159), (216) imply: % 149.18/21.92 | | | | | | (219) ~ (all_52_12 = e0) % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | REDUCE: (63), (216) imply: % 149.18/21.92 | | | | | | (220) ~ (all_52_13 = e0) % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | REDUCE: (180), (216) imply: % 149.18/21.92 | | | | | | (221) ~ (all_52_14 = e0) % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | REDUCE: (31), (216) imply: % 149.18/21.92 | | | | | | (222) op(e0, e0) = all_58_27 % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | REDUCE: (154), (216) imply: % 149.18/21.92 | | | | | | (223) op(e0, e0) = e0 % 149.18/21.92 | | | | | | % 149.18/21.92 | | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, % 149.18/21.92 | | | | | | simplifying with (222), (223) gives: % 149.18/21.92 | | | | | | (224) all_58_27 = e0 % 149.18/21.92 | | | | | | % 149.18/21.93 | | | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (12), (13), (14), (16), % 149.18/21.93 | | | | | | (22), (24), (26), (27), (28), (29), (30), (32), (33), % 149.18/21.93 | | | | | | (35), (38), (41), (42), (45), (46), (47), (52), (56), % 149.18/21.93 | | | | | | (59), (61), (62), (64), (66), (67), (70), (71), (72), % 149.18/21.93 | | | | | | (73), (75), (77), (78), (79), (80), (83), (84), (86), % 149.18/21.93 | | | | | | (88), (89), (91), (92), (97), (100), (101), (102), (103), % 149.18/21.93 | | | | | | (106), (107), (108), (109), (111), (112), (113), (114), % 149.18/21.93 | | | | | | (115), (116), (117), (118), (119), (121), (122), (124), % 149.18/21.93 | | | | | | (125), (126), (130), (133), (134), (135), (138), (139), % 149.18/21.93 | | | | | | (140), (141), (142), (144), (145), (149), (150), (152), % 149.18/21.93 | | | | | | (153), (156), (162), (163), (164), (165), (166), (167), % 149.18/21.93 | | | | | | (168), (170), (173), (177), (178), (179), (181), (182), % 149.18/21.93 | | | | | | (183), (185), (186), (189), (190), (191), (192), (193), % 149.18/21.93 | | | | | | (194), (195), (196), (197), (199), (200), (202), (203), % 149.18/21.93 | | | | | | (204), (206), (208), (211), (213), (214), (217), (218), % 149.18/21.93 | | | | | | (219), (220), (221), (224) are inconsistent by sub-proof % 149.18/21.93 | | | | | | #134. % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | Case 2: % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | (225) ~ (all_56_15 = e0) % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REF_CLOSE: (2), (4), (7), (58), (103), (111), (140), (166), (189), % 149.18/21.93 | | | | | | (191), (206), (208), (225) are inconsistent by sub-proof % 149.18/21.93 | | | | | | #132. % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | End of split % 149.18/21.93 | | | | | % 149.18/21.93 | | | | Case 2: % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | (226) all_32_1 = e0 % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | COMBINE_EQS: (136), (226) imply: % 149.18/21.93 | | | | | (227) all_10_1 = e0 % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | REDUCE: (41), (227) imply: % 149.18/21.93 | | | | | (228) op(all_10_2, e0) = all_10_0 % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | BETA: splitting (57) gives: % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | Case 1: % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | (229) all_56_15 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | COMBINE_EQS: (7), (229) imply: % 149.18/21.93 | | | | | | (230) all_4_2 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | SIMP: (230) implies: % 149.18/21.93 | | | | | | (231) all_4_2 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | COMBINE_EQS: (2), (231) imply: % 149.18/21.93 | | | | | | (232) all_58_31 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (184), (231) imply: % 149.18/21.93 | | | | | | (233) ~ (all_52_7 = e0) % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (159), (231) imply: % 149.18/21.93 | | | | | | (234) ~ (all_52_12 = e0) % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (63), (231) imply: % 149.18/21.93 | | | | | | (235) ~ (all_52_13 = e0) % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (180), (231) imply: % 149.18/21.93 | | | | | | (236) ~ (all_52_14 = e0) % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (31), (231) imply: % 149.18/21.93 | | | | | | (237) op(e0, e0) = all_58_27 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (154), (231) imply: % 149.18/21.93 | | | | | | (238) op(e0, e0) = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, % 149.18/21.93 | | | | | | simplifying with (237), (238) gives: % 149.18/21.93 | | | | | | (239) all_58_27 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (12), (13), (14), (15), % 149.18/21.93 | | | | | | (16), (22), (24), (26), (27), (28), (29), (30), (32), % 149.18/21.93 | | | | | | (33), (35), (38), (41), (42), (45), (46), (47), (52), % 149.18/21.93 | | | | | | (56), (59), (61), (62), (64), (66), (67), (70), (71), % 149.18/21.93 | | | | | | (72), (73), (75), (77), (78), (79), (80), (83), (84), % 149.18/21.93 | | | | | | (86), (89), (91), (92), (97), (100), (101), (102), (103), % 149.18/21.93 | | | | | | (106), (107), (108), (109), (111), (112), (113), (114), % 149.18/21.93 | | | | | | (115), (116), (117), (118), (119), (121), (122), (124), % 149.18/21.93 | | | | | | (125), (126), (130), (133), (134), (135), (138), (139), % 149.18/21.93 | | | | | | (140), (141), (142), (144), (145), (149), (150), (152), % 149.18/21.93 | | | | | | (153), (156), (162), (163), (164), (165), (166), (167), % 149.18/21.93 | | | | | | (168), (170), (173), (177), (178), (179), (181), (182), % 149.18/21.93 | | | | | | (183), (185), (186), (189), (190), (191), (192), (193), % 149.18/21.93 | | | | | | (194), (195), (196), (197), (199), (200), (202), (203), % 149.18/21.93 | | | | | | (204), (206), (208), (211), (228), (229), (232), (233), % 149.18/21.93 | | | | | | (234), (235), (236), (239) are inconsistent by sub-proof % 149.18/21.93 | | | | | | #130. % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | Case 2: % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | (240) ~ (all_56_15 = e0) % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REF_CLOSE: (2), (4), (7), (58), (103), (111), (140), (166), (189), % 149.18/21.93 | | | | | | (191), (206), (208), (240) are inconsistent by sub-proof % 149.18/21.93 | | | | | | #132. % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | End of split % 149.18/21.93 | | | | | % 149.18/21.93 | | | | End of split % 149.18/21.93 | | | | % 149.18/21.93 | | | End of split % 149.18/21.93 | | | % 149.18/21.93 | | Case 2: % 149.18/21.93 | | | % 149.18/21.93 | | | (241) all_18_2 = e0 % 149.18/21.93 | | | % 149.18/21.93 | | | COMBINE_EQS: (110), (241) imply: % 149.18/21.93 | | | (242) all_6_2 = e0 % 149.18/21.93 | | | % 149.18/21.93 | | | SIMP: (242) implies: % 149.18/21.93 | | | (243) all_6_2 = e0 % 149.18/21.93 | | | % 149.18/21.93 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 149.18/21.93 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 149.18/21.93 | | | (24), (26), (27), (28), (29), (30), (32), (33), (34), (35), % 149.18/21.93 | | | (36), (37), (38), (39), (42), (43), (44), (45), (46), (47), % 149.18/21.93 | | | (49), (52), (53), (54), (55), (56), (57), (61), (62), (63), % 149.18/21.93 | | | (64), (66), (67), (70), (71), (72), (73), (74), (75), (76), % 149.18/21.93 | | | (77), (78), (79), (80), (81), (82), (83), (84), (86), (87), % 149.18/21.93 | | | (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), % 149.18/21.93 | | | (102), (103), (104), (105), (106), (107), (108), (109), (111), % 149.18/21.93 | | | (112), (113), (114), (115), (116), (117), (118), (119), (120), % 149.18/21.93 | | | (121), (123), (125), (126), (132), (133), (134), (135), (137), % 149.18/21.93 | | | (138), (139), (140), (141), (142), (143), (144), (146), (147), % 149.18/21.93 | | | (148), (149), (150), (151), (152), (153), (154), (156), (157), % 149.18/21.93 | | | (158), (159), (161), (162), (163), (164), (165), (166), (167), % 149.18/21.93 | | | (168), (170), (171), (172), (173), (175), (177), (178), (180), % 149.18/21.93 | | | (182), (183), (184), (185), (186), (188), (189), (190), (191), % 149.18/21.93 | | | (193), (194), (195), (196), (197), (198), (199), (200), (201), % 149.18/21.93 | | | (202), (203), (204), (243) are inconsistent by sub-proof #10. % 149.18/21.93 | | | % 149.18/21.93 | | End of split % 149.18/21.93 | | % 149.18/21.93 | Case 2: % 149.18/21.93 | | % 149.18/21.93 | | (244) all_16_2 = e0 % 149.18/21.93 | | (245) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (50), (244) imply: % 149.18/21.93 | | (246) all_10_2 = e0 % 149.18/21.93 | | % 149.18/21.93 | | SIMP: (246) implies: % 149.18/21.93 | | (247) all_10_2 = e0 % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (40), (247) imply: % 149.18/21.93 | | (248) all_50_2 = e0 % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (153), (247) imply: % 149.18/21.93 | | (249) all_56_0 = e0 % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (140), (247) imply: % 149.18/21.93 | | (250) all_58_28 = e0 % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (204), (247) imply: % 149.18/21.93 | | (251) ~ (all_52_1 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (152), (247) imply: % 149.18/21.93 | | (252) ~ (all_52_2 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (161), (247) imply: % 149.18/21.93 | | (253) ~ (all_52_3 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (190), (247) imply: % 149.18/21.93 | | (254) ~ (all_52_4 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (16), (247) imply: % 149.18/21.93 | | (255) ~ (all_52_8 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (134), (247) imply: % 149.18/21.93 | | (256) ~ (all_52_12 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (41), (247) imply: % 149.18/21.93 | | (257) op(e0, all_10_1) = all_10_0 % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (199), (247) imply: % 149.18/21.93 | | (258) op(e0, e3) = all_10_1 % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (124), (247) imply: % 149.18/21.93 | | (259) op(e3, e0) = all_58_0 % 149.18/21.93 | | % 149.18/21.93 | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, simplifying % 149.18/21.93 | | with (129), (258) gives: % 149.18/21.93 | | (260) all_52_3 = all_10_1 % 149.18/21.93 | | % 149.18/21.93 | | GROUND_INST: instantiating (4) with all_52_12, all_58_0, e0, e3, simplifying % 149.18/21.93 | | with (107), (259) gives: % 149.18/21.93 | | (261) all_58_0 = all_52_12 % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (201), (260) imply: % 149.18/21.93 | | (262) all_54_12 = all_10_1 % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (79), (260) imply: % 149.18/21.93 | | (263) all_56_12 = all_10_1 % 149.18/21.93 | | % 149.18/21.93 | | COMBINE_EQS: (157), (260) imply: % 149.18/21.93 | | (264) all_58_22 = all_10_1 % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (135), (260) imply: % 149.18/21.93 | | (265) ~ (all_52_1 = all_10_1) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (5), (260) imply: % 149.18/21.93 | | (266) ~ (all_52_2 = all_10_1) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (80), (260) imply: % 149.18/21.93 | | (267) ~ (all_52_7 = all_10_1) % 149.18/21.93 | | % 149.18/21.93 | | SIMP: (267) implies: % 149.18/21.93 | | (268) ~ (all_52_7 = all_10_1) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (156), (260) imply: % 149.18/21.93 | | (269) ~ (all_52_11 = all_10_1) % 149.18/21.93 | | % 149.18/21.93 | | SIMP: (269) implies: % 149.18/21.93 | | (270) ~ (all_52_11 = all_10_1) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (87), (260) imply: % 149.18/21.93 | | (271) ~ (all_10_1 = all_4_2) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (253), (260) imply: % 149.18/21.93 | | (272) ~ (all_10_1 = e0) % 149.18/21.93 | | % 149.18/21.93 | | REDUCE: (49), (260) imply: % 149.18/21.93 | | (273) op(e0, all_10_1) = all_58_21 % 149.18/21.93 | | % 149.18/21.93 | | GROUND_INST: instantiating (4) with all_10_0, all_58_21, all_10_1, e0, % 149.18/21.93 | | simplifying with (257), (273) gives: % 149.18/21.93 | | (274) all_58_21 = all_10_0 % 149.18/21.93 | | % 149.18/21.93 | | BETA: splitting (99) gives: % 149.18/21.93 | | % 149.18/21.93 | | Case 1: % 149.18/21.93 | | | % 149.18/21.93 | | | (275) ~ (all_50_2 = e0) % 149.18/21.93 | | | % 149.18/21.93 | | | REDUCE: (248), (275) imply: % 149.18/21.93 | | | (276) $false % 149.18/21.93 | | | % 149.18/21.93 | | | CLOSE: (276) is inconsistent. % 149.18/21.93 | | | % 149.18/21.93 | | Case 2: % 149.18/21.93 | | | % 149.18/21.93 | | | (277) ~ (all_50_0 = e1) | ~ (all_50_1 = e2) % 149.18/21.93 | | | % 149.18/21.93 | | | BETA: splitting (57) gives: % 149.18/21.93 | | | % 149.18/21.93 | | | Case 1: % 149.18/21.93 | | | | % 149.18/21.93 | | | | (278) all_56_15 = e0 % 149.18/21.93 | | | | % 149.18/21.93 | | | | REF_CLOSE: (2), (4), (7), (29), (31), (70), (84), (92), (103), (106), % 149.18/21.93 | | | | (112), (119), (125), (150), (154), (173), (182), (184), % 149.18/21.93 | | | | (187), (191), (193), (194), (198), (254), (278) are % 149.18/21.93 | | | | inconsistent by sub-proof #69. % 149.18/21.93 | | | | % 149.18/21.93 | | | Case 2: % 149.18/21.93 | | | | % 149.18/21.93 | | | | (279) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 % 149.18/21.93 | | | | = e0 | all_56_13 = e0 | all_56_14 = e0) % 149.18/21.93 | | | | % 149.18/21.93 | | | | ALPHA: (279) implies: % 149.18/21.93 | | | | (280) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 149.18/21.93 | | | | % 149.18/21.93 | | | | BETA: splitting (179) gives: % 149.18/21.93 | | | | % 149.18/21.93 | | | | Case 1: % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | (281) all_56_6 = e0 % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | COMBINE_EQS: (108), (281) imply: % 149.18/21.93 | | | | | (282) all_52_2 = e0 % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | REDUCE: (252), (282) imply: % 149.18/21.93 | | | | | (283) $false % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | CLOSE: (283) is inconsistent. % 149.18/21.93 | | | | | % 149.18/21.93 | | | | Case 2: % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | (284) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | BETA: splitting (85) gives: % 149.18/21.93 | | | | | % 149.18/21.93 | | | | | Case 1: % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | (285) all_56_4 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | COMBINE_EQS: (26), (285) imply: % 149.18/21.93 | | | | | | (286) all_52_8 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | REDUCE: (255), (286) imply: % 149.18/21.93 | | | | | | (287) $false % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | CLOSE: (287) is inconsistent. % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | Case 2: % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | (288) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | BETA: splitting (114) gives: % 149.18/21.93 | | | | | | % 149.18/21.93 | | | | | | Case 1: % 149.18/21.93 | | | | | | | % 149.18/21.93 | | | | | | | (289) all_54_4 = e0 % 149.18/21.93 | | | | | | | % 149.18/21.93 | | | | | | | REF_CLOSE: (203), (251), (289) are inconsistent by sub-proof #859. % 149.18/21.93 | | | | | | | % 149.18/21.93 | | | | | | Case 2: % 149.18/21.93 | | | | | | | % 149.18/21.94 | | | | | | | (290) ~ (all_54_4 = e0) % 149.18/21.94 | | | | | | | (291) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 149.18/21.94 | | | | | | | % 149.18/21.94 | | | | | | | BETA: splitting (10) gives: % 149.18/21.94 | | | | | | | % 149.18/21.94 | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | % 149.18/21.94 | | | | | | | | (292) all_54_3 = e0 % 149.18/21.94 | | | | | | | | % 149.18/21.94 | | | | | | | | REF_CLOSE: (28), (256), (292) are inconsistent by sub-proof % 149.18/21.94 | | | | | | | | #733. % 149.18/21.94 | | | | | | | | % 149.18/21.94 | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | % 149.18/21.94 | | | | | | | | (293) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 149.18/21.94 | | | | | | | | % 149.18/21.94 | | | | | | | | BETA: splitting (128) gives: % 149.18/21.94 | | | | | | | | % 149.18/21.94 | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | % 149.18/21.94 | | | | | | | | | (294) all_54_10 = e0 % 149.18/21.94 | | | | | | | | | % 149.18/21.94 | | | | | | | | | REF_CLOSE: (2), (29), (48), (70), (82), (103), (106), (125), % 149.18/21.94 | | | | | | | | | (146), (150), (173), (182), (191), (193), (194), % 149.18/21.94 | | | | | | | | | (250), (294) are inconsistent by sub-proof #68. % 149.18/21.94 | | | | | | | | | % 149.18/21.94 | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | % 149.18/21.94 | | | | | | | | | (295) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 149.18/21.94 | | | | | | | | | % 149.18/21.94 | | | | | | | | | BETA: splitting (168) gives: % 149.18/21.94 | | | | | | | | | % 149.18/21.94 | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | (296) all_54_1 = e0 % 149.18/21.94 | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | REF_CLOSE: (30), (254), (296) are inconsistent by sub-proof % 149.18/21.94 | | | | | | | | | | #798. % 149.18/21.94 | | | | | | | | | | % 149.18/21.94 | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | (297) ~ (all_54_1 = e0) % 149.18/21.94 | | | | | | | | | | (298) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 149.18/21.94 | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | BETA: splitting (132) gives: % 149.18/21.94 | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | (299) all_54_12 = e0 % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | COMBINE_EQS: (262), (299) imply: % 149.18/21.94 | | | | | | | | | | | (300) all_10_1 = e0 % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | REDUCE: (272), (300) imply: % 149.18/21.94 | | | | | | | | | | | (301) $false % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | CLOSE: (301) is inconsistent. % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | (302) ~ (all_54_12 = e0) % 149.18/21.94 | | | | | | | | | | | (303) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | BETA: splitting (137) gives: % 149.18/21.94 | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | (304) all_54_14 = e0 % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | COMBINE_EQS: (76), (304) imply: % 149.18/21.94 | | | | | | | | | | | | (305) all_52_11 = e0 % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | SIMP: (305) implies: % 149.18/21.94 | | | | | | | | | | | | (306) all_52_11 = e0 % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | COMBINE_EQS: (139), (306) imply: % 149.18/21.94 | | | | | | | | | | | | (307) all_56_14 = e0 % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | REDUCE: (148), (306) imply: % 149.18/21.94 | | | | | | | | | | | | (308) ~ (all_52_7 = e0) % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | REDUCE: (90), (306) imply: % 149.18/21.94 | | | | | | | | | | | | (309) ~ (all_52_9 = e0) % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | REDUCE: (270), (306) imply: % 149.18/21.94 | | | | | | | | | | | | (310) ~ (all_10_1 = e0) % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | REDUCE: (36), (306) imply: % 149.18/21.94 | | | | | | | | | | | | (311) op(e0, e1) = e0 % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | BETA: splitting (32) gives: % 149.18/21.94 | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | (312) all_56_2 = e0 % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | COMBINE_EQS: (126), (312) imply: % 149.18/21.94 | | | | | | | | | | | | | (313) all_52_1 = e0 % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | REDUCE: (251), (313) imply: % 149.18/21.94 | | | | | | | | | | | | | (314) $false % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | (315) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | BETA: splitting (119) gives: % 149.18/21.94 | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | (316) all_56_1 = e0 % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | COMBINE_EQS: (84), (316) imply: % 149.18/21.94 | | | | | | | | | | | | | | (317) all_52_4 = e0 % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | REDUCE: (254), (317) imply: % 149.18/21.94 | | | | | | | | | | | | | | (318) $false % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | CLOSE: (318) is inconsistent. % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | (319) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | BETA: splitting (71) gives: % 149.18/21.94 | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | (320) all_54_9 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | COMBINE_EQS: (62), (320) imply: % 149.18/21.94 | | | | | | | | | | | | | | | (321) all_52_6 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | SIMP: (321) implies: % 149.18/21.94 | | | | | | | | | | | | | | | (322) all_52_6 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | COMBINE_EQS: (8), (322) imply: % 149.18/21.94 | | | | | | | | | | | | | | | (323) all_56_7 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | REDUCE: (39), (322) imply: % 149.18/21.94 | | | | | | | | | | | | | | | (324) ~ (all_52_7 = e0) % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | REDUCE: (9), (322) imply: % 149.18/21.94 | | | | | | | | | | | | | | | (325) ~ (all_6_2 = e0) % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | SIMP: (325) implies: % 149.18/21.94 | | | | | | | | | | | | | | | (326) ~ (all_6_2 = e0) % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | BETA: splitting (315) gives: % 149.18/21.94 | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | (327) all_56_3 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (327) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | (328) all_8_2 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (328) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | (329) all_58_29 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | REF_CLOSE: (29), (70), (106), (125), (150), (173), (182), % 149.18/21.94 | | | | | | | | | | | | | | | | (191), (193), (194), (250), (329) are inconsistent % 149.18/21.94 | | | | | | | | | | | | | | | | by sub-proof #483. % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | (330) all_56_5 = e0 | all_56_10 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | (331) all_56_5 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (331) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | (332) all_52_9 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | REDUCE: (309), (332) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | (333) $false % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | (334) all_56_10 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (334) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | (335) all_52_13 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | REDUCE: (94), (335) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | (336) ~ (all_52_14 = e0) % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | (337) ~ (all_52_14 = e0) % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | (338) all_56_12 = e1 % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (338) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | (339) all_10_1 = e1 % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | SIMP: (339) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | (340) all_10_1 = e1 % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (101), (257), (311), (340) are inconsistent % 149.18/21.94 | | | | | | | | | | | | | | | | | | by sub-proof #491. % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | (341) ~ (all_56_12 = e1) % 149.18/21.94 | | | | | | | | | | | | | | | | | | (342) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | REDUCE: (263), (341) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | (343) ~ (all_10_1 = e1) % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (344) all_56_12 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (344) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (345) all_10_1 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | SIMP: (345) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (346) all_10_1 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | REDUCE: (268), (346) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (347) ~ (all_52_7 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | REDUCE: (271), (346) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (348) ~ (all_4_2 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (349) ~ (all_4_2 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | REDUCE: (257), (346) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (350) op(e0, e3) = all_10_0 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | REDUCE: (258), (346) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (351) op(e0, e3) = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e3, all_10_0, e3, e0, % 149.18/21.94 | | | | | | | | | | | | | | | | | | | simplifying with (350), (351) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (352) all_10_0 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (353) all_56_1 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (353) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (354) all_52_4 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (354) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (355) ~ (all_52_12 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | SIMP: (355) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (356) ~ (all_52_12 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (354) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (357) ~ (all_8_2 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | SIMP: (357) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (358) ~ (all_8_2 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (359) all_56_9 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (359) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (360) all_52_12 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (361) all_52_12 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (361) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (362) $false % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | CLOSE: (362) is inconsistent. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (363) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | (364) all_56_10 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (364) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | (365) e3 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (365) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | (366) $false % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (366) is inconsistent. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | (367) all_56_11 = e3 | all_56_15 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | (368) all_56_11 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (368) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | (369) all_52_14 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (369) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | (370) all_52_14 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (370) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | (371) ~ (all_6_2 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (371) implies: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | (372) ~ (all_6_2 = e3) % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | (373) all_58_28 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (250), (373) are inconsistent by sub-proof % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | #689. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_29 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (358), (375) are inconsistent by sub-proof % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | #756. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_58_30 = e3 | all_58_31 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (191), (349), (372), (376) are inconsistent % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #47. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | (377) all_56_15 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (349), (377) are inconsistent by sub-proof % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | #392. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | (378) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (379) all_56_3 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (379) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (380) all_8_2 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (380) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (381) op(e3, e2) = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_4, e0, e2, e3, % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | simplifying with (42), (381) gives: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (382) all_52_4 = e0 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (382) imply: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (383) $false % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | (384) all_56_7 = e3 | all_56_13 = e3 % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (125), (323), (347), (384) are inconsistent % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | by sub-proof #49. % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.94 | | | | | | | | | | | | | | | | | | | % 149.18/21.94 | | | | | | | | | | | | | | | | | | | (385) ~ (all_56_12 = e3) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (386) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | REDUCE: (263), (385) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (387) ~ (all_10_1 = e3) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | (388) all_54_12 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (262), (343), (388) are inconsistent by sub-proof % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | #514. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | (389) all_54_12 = e3 | all_54_12 = e2 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (390) all_54_12 = e2 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (390) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (391) all_10_1 = e2 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | SIMP: (391) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (392) all_10_1 = e2 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (392) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (393) all_50_1 = e2 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (392) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_52_7 = e2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (392) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_4_2 = e2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | SIMP: (395) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_4_2 = e2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (392) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (397) op(e0, e2) = all_10_0 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (398) ~ (all_50_0 = e1) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (398) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (399) ~ (all_10_0 = e1) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_7, all_10_0, e2, e0, % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | simplifying with (189), (397) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (400) all_52_7 = all_10_0 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (400) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (401) all_56_13 = all_10_0 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (400) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_10_0 = all_8_2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (400) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (403) ~ (all_10_0 = all_4_2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (400) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (404) ~ (all_10_0 = e2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | (405) all_56_13 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (405) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | (406) all_10_0 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (406) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | (407) all_10_0 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (399), (407) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | (408) $false % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (408) is inconsistent. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | (409) all_56_14 = e1 | all_56_15 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (410) all_56_14 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (410) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (411) e1 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (411) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (412) $false % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (412) is inconsistent. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (413) all_56_15 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (413) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (414) all_4_2 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (414) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (415) all_4_2 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (415) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (416) all_58_31 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (415) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | (417) ~ (e2 = e1) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_56_13 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (418) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_10_0 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (419) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_10_0 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (402), (420) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (421) ~ (all_8_2 = e3) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (421) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (422) ~ (all_8_2 = e3) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (29), (35), (70), (103), (106), (111), (125), % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (150), (173), (191), (194), (202), (250), (307), % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (326), (386), (413), (416), (418), (422) are % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #94. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_56_14 = e3 | all_56_15 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (125), (307), (413), (423) are inconsistent % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #434. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (424) ~ (all_50_1 = e2) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (424) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | (425) $false % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (425) is inconsistent. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (426) all_54_12 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (426) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (427) all_10_1 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | SIMP: (427) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (428) all_10_1 = e3 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (428) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | (429) $false % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | CLOSE: (429) is inconsistent. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | (430) ~ (all_54_9 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | REDUCE: (62), (430) imply: % 149.18/21.95 | | | | | | | | | | | | | | | (431) ~ (all_52_6 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (92), (111), (112), (166), (189), (308), % 149.18/21.95 | | | | | | | | | | | | | | | (319), (431) are inconsistent by sub-proof #148. % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | End of split % 149.18/21.95 | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | (432) ~ (all_54_14 = e0) % 149.18/21.95 | | | | | | | | | | | | (433) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 149.18/21.95 | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | REDUCE: (76), (432) imply: % 149.18/21.95 | | | | | | | | | | | | (434) ~ (all_52_11 = e0) % 149.18/21.95 | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | BETA: splitting (280) gives: % 149.18/21.95 | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | (435) all_56_12 = e0 % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | REF_CLOSE: (263), (272), (435) are inconsistent by sub-proof % 149.18/21.95 | | | | | | | | | | | | | #230. % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | (436) all_56_13 = e0 | all_56_14 = e0 % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | BETA: splitting (436) gives: % 149.18/21.95 | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | (437) all_56_13 = e0 % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | COMBINE_EQS: (112), (437) imply: % 149.18/21.95 | | | | | | | | | | | | | | (438) all_52_7 = e0 % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | SIMP: (438) implies: % 149.18/21.95 | | | | | | | | | | | | | | (439) all_52_7 = e0 % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | COMBINE_EQS: (93), (439) imply: % 149.18/21.95 | | | | | | | | | | | | | | (440) all_58_24 = e0 % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | REDUCE: (39), (439) imply: % 149.18/21.95 | | | | | | | | | | | | | | (441) ~ (all_52_6 = e0) % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | REDUCE: (148), (439) imply: % 149.18/21.95 | | | | | | | | | | | | | | (442) ~ (all_52_11 = e0) % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | REDUCE: (268), (439) imply: % 149.18/21.95 | | | | | | | | | | | | | | (443) ~ (all_10_1 = e0) % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | REDUCE: (51), (439) imply: % 149.18/21.95 | | | | | | | | | | | | | | (444) op(e0, e0) = all_58_23 % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | BETA: splitting (284) gives: % 149.18/21.95 | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | (445) all_56_7 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | COMBINE_EQS: (8), (445) imply: % 149.18/21.95 | | | | | | | | | | | | | | | (446) all_52_6 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | REDUCE: (441), (446) imply: % 149.18/21.95 | | | | | | | | | | | | | | | (447) $false % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | CLOSE: (447) is inconsistent. % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | (448) ~ (all_56_7 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | (449) all_56_8 = e0 | all_56_11 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | BETA: splitting (449) gives: % 149.18/21.95 | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | (450) all_56_8 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (450) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (451) all_6_2 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (451) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (452) all_58_30 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (29), (64), (70), (82), (103), (106), % 149.18/21.95 | | | | | | | | | | | | | | | | (111), (125), (146), (150), (173), (182), (193), % 149.18/21.95 | | | | | | | | | | | | | | | | (194), (250), (441), (452) are inconsistent by % 149.18/21.95 | | | | | | | | | | | | | | | | sub-proof #85. % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | (453) all_56_11 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (453) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (454) all_52_14 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (454) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (455) all_58_20 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | REDUCE: (196), (454) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (456) ~ (all_6_2 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | SIMP: (456) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | (457) ~ (all_6_2 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | REDUCE: (180), (454) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (458) ~ (all_4_2 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | SIMP: (458) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | (459) ~ (all_4_2 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | REDUCE: (19), (454) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (460) op(e1, e0) = all_58_19 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | REDUCE: (89), (454) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | (461) op(e1, e0) = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | (462) all_56_5 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (462) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | (463) all_52_9 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | SIMP: (463) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | (464) all_52_9 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (464) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | (465) all_58_11 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | REDUCE: (118), (464) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | (466) ~ (all_52_13 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | SIMP: (466) implies: % 149.18/21.95 | | | | | | | | | | | | | | | | | (467) ~ (all_52_13 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | REDUCE: (122), (464) imply: % 149.18/21.95 | | | | | | | | | | | | | | | | | (468) op(e2, e0) = all_58_10 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_23, e0, e0, % 149.18/21.95 | | | | | | | | | | | | | | | | | simplifying with (154), (444) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | (469) all_58_23 = all_4_2 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_19, e0, e1, % 149.18/21.95 | | | | | | | | | | | | | | | | | simplifying with (460), (461) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | (470) all_58_19 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, all_58_10, e0, % 149.18/21.95 | | | | | | | | | | | | | | | | | e2, simplifying with (167), (468) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | (471) all_58_10 = all_52_13 % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | (472) all_54_9 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (441), (472) are inconsistent by sub-proof % 149.18/21.95 | | | | | | | | | | | | | | | | | | #572. % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | (473) ~ (all_54_9 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | | | (474) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 149.18/21.95 | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (475) all_54_5 = e0 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (26), (29), (52), (70), (77), (83), (84), % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (102), (103), (104), (106), (125), (140), (150), % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (153), (162), (173), (182), (191), (193), (194), % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (254), (255), (284), (441), (457), (475) are % 149.18/21.95 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211. % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (476) ~ (all_54_5 = e0) % 149.18/21.95 | | | | | | | | | | | | | | | | | | | (477) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 149.18/21.95 | | | | | | | | | | | | | | | | | | | % 149.18/21.95 | | | | | | | | | | | | | | | | | | | REDUCE: (52), (476) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | (478) ~ (all_8_2 = e0) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | (479) all_54_7 = e0 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (467), (479) are inconsistent by sub-proof % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | #742. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | (480) ~ (all_54_7 = e0) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | (481) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (482) all_56_12 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (482) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (483) all_10_1 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | SIMP: (483) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (484) all_10_1 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (484) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (485) ~ (all_4_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | SIMP: (485) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (486) ~ (all_4_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (17), (18), (20), (21), (22), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (23), (24), (26), (27), (29), (34), (36), (46), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (48), (63), (66), (70), (76), (84), (96), (102), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (103), (106), (108), (113), (116), (117), (123), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (125), (133), (137), (139), (147), (149), (150), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (162), (169), (172), (173), (174), (176), (182), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (191), (193), (194), (245), (249), (250), (252), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (257), (261), (263), (270), (295), (434), (437), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (440), (453), (455), (459), (465), (467), (469), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (470), (471), (478), (481), (486) are inconsistent % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | by sub-proof #464. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (487) ~ (all_56_12 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (488) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (487) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_10_1 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | (490) all_56_0 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (249), (490) are inconsistent by sub-proof % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | #516. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | (491) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (492) all_56_6 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (492) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (493) all_52_2 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (493) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_15 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (493) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (495) ~ (all_52_6 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (495) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (496) ~ (all_52_6 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (493) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (497) ~ (all_10_1 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (493) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (498) ~ (all_6_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (498) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (499) ~ (all_6_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (500) all_56_4 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (500) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (501) all_52_8 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (501) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (502) ~ (all_52_4 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (501) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (503) ~ (all_52_11 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (503) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (504) ~ (all_52_11 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (501) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (505) ~ (all_52_12 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (505) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (506) ~ (all_52_12 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (8), (9), (15), (18), (23), (24), (26), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (33), (34), (46), (62), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (66), (68), (70), (76), (77), (81), (83), (84), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (86), (91), (92), (95), (96), (102), (103), (104), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (105), (106), (115), (116), (123), (125), (126), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (133), (139), (140), (143), (150), (153), (162), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (164), (169), (173), (182), (191), (193), (194), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (200), (203), (249), (250), (254), (255), (256), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (263), (264), (265), (270), (272), (284), (291), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (293), (298), (433), (434), (437), (440), (441), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (453), (455), (457), (465), (467), (474), (478), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (488), (489), (494), (496), (502), (504), (506) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #67. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (507) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_56_5 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (462), (508) are inconsistent by sub-proof % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | #305. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_56_8 = e1 | all_56_14 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (509) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_56_8 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (499), (510) are inconsistent by sub-proof % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_56_14 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (511) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_52_11 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (512) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_52_11 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (513) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (514) ~ (all_4_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (514) implies: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (515) ~ (all_4_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (64), (103), (111), (182), (191), (193), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (441), (499), (515) are inconsistent by % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #98. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (516) ~ (all_56_6 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (517) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (516) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | (518) ~ (all_52_2 = e1) % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (519) all_56_2 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (519) imply: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (520) all_52_1 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (9), (17), (18), (20), (21), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (24), (26), (27), (28), (29), (30), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (35), (37), (45), (46), (47), (52), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (60), (61), (63), (65), (66), (68), (70), (74), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (76), (81), (82), (84), (91), (92), (95), (96), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (97), (102), (103), (105), (106), (109), (115), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (116), (117), (121), (123), (125), (133), (139), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (143), (145), (146), (150), (162), (164), (172), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (173), (191), (193), (194), (200), (202), (250), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (251), (254), (255), (256), (257), (258), (262), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (263), (270), (271), (272), (274), (293), (298), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (303), (433), (434), (437), (440), (441), (453), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (455), (457), (459), (462), (465), (467), (470), % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (477), (478), (481), (517), (519), (520) are % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | (521) all_56_6 = e1 | all_56_12 = e1 % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (263), (489), (518), (521) are inconsistent % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #404. % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | (522) all_56_8 = e0 | all_56_14 = e0 % 149.18/21.96 | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (162), (434), (457), (522) are inconsistent % 149.18/21.96 | | | | | | | | | | | | | | | | | by sub-proof #805. % 149.18/21.96 | | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | Case 2: % 149.18/21.96 | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | (523) all_56_14 = e0 % 149.18/21.96 | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | | REF_CLOSE: (139), (434), (523) are inconsistent by sub-proof % 149.18/21.96 | | | | | | | | | | | | | | #806. % 149.18/21.96 | | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | | % 149.18/21.96 | | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | | % 149.18/21.96 | | | | | | | | | End of split % 149.18/21.96 | | | | | | | | | % 149.18/21.96 | | | | | | | | End of split % 149.18/21.96 | | | | | | | | % 149.18/21.96 | | | | | | | End of split % 149.18/21.96 | | | | | | | % 149.18/21.96 | | | | | | End of split % 149.18/21.96 | | | | | | % 149.18/21.96 | | | | | End of split % 149.18/21.96 | | | | | % 149.18/21.96 | | | | End of split % 149.18/21.96 | | | | % 149.18/21.96 | | | End of split % 149.18/21.96 | | | % 149.18/21.96 | | End of split % 149.18/21.96 | | % 149.18/21.96 | End of split % 149.18/21.96 | % 149.18/21.96 End of proof % 149.18/21.96 % 149.18/21.96 Sub-proof #10 shows that the following formulas are inconsistent: % 149.18/21.96 ---------------------------------------------------------------- % 149.18/21.96 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 149.18/21.96 (2) all_58_31 = all_4_2 % 149.18/21.96 (3) ~ (all_52_8 = all_52_9) % 149.18/21.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/21.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/21.96 (5) ~ (all_52_2 = all_52_3) % 149.18/21.96 (6) all_58_11 = all_52_9 % 149.18/21.96 (7) all_56_15 = all_4_2 % 149.18/21.97 (8) all_56_7 = all_52_6 % 149.18/21.97 (9) ~ (all_52_6 = all_6_2) % 149.18/21.97 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 149.18/21.97 (11) all_54_2 = all_52_8 % 149.18/21.97 (12) op(e1, all_6_2) = all_58_18 % 149.18/21.97 (13) op(e3, all_52_4) = all_58_1 % 149.18/21.97 (14) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 149.18/21.97 (15) ~ (all_52_8 = all_10_2) % 149.18/21.97 (16) all_58_15 = all_52_2 % 149.18/21.97 (17) all_58_26 = all_52_11 % 149.18/21.97 (18) op(e1, all_52_14) = all_58_19 % 149.18/21.97 (19) ~ (all_52_8 = all_52_11) % 149.18/21.97 (20) ~ (all_52_11 = all_4_2) % 149.18/21.97 (21) all_54_7 = all_52_13 % 149.18/21.97 (22) all_58_6 = all_52_12 % 149.18/21.97 (23) ~ (all_52_6 = all_8_2) % 149.18/21.97 (24) all_56_4 = all_52_8 % 149.18/21.97 (25) ~ (all_52_4 = all_8_2) % 149.18/21.97 (26) all_54_3 = all_52_12 % 149.18/21.97 (27) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/21.97 (28) all_54_1 = all_52_4 % 149.18/21.97 (29) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 149.18/21.97 (30) all_6_2 = e0 % 149.18/21.97 (31) ~ (all_52_4 = all_52_6) % 149.18/21.97 (32) all_58_13 = all_52_13 % 149.18/21.97 (33) op(e2, e2) = all_8_2 % 149.18/21.97 (34) op(e0, e1) = all_52_11 % 149.18/21.97 (35) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 149.18/21.97 (36) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.18/21.97 (37) ~ (all_52_6 = all_52_7) % 149.18/21.97 (38) op(e3, e2) = all_52_4 % 149.18/21.97 (39) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 149.18/21.97 (40) all_58_20 = all_52_14 % 149.18/21.97 (41) ~ (all_52_8 = all_6_2) % 149.18/21.97 (42) ~ (all_52_12 = all_52_13) % 149.18/21.97 (43) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.18/21.97 (44) op(e0, all_52_3) = all_58_21 % 149.18/21.97 (45) all_54_5 = all_8_2 % 149.18/21.97 (46) ~ (all_52_6 = all_52_14) % 149.18/21.97 (47) all_54_6 = all_52_9 % 149.18/21.97 (48) ~ (all_52_4 = all_52_7) % 149.18/21.97 (49) ~ (all_52_2 = all_6_2) % 149.18/21.97 (50) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 149.18/21.97 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 149.18/21.97 (51) ~ (all_52_8 = all_52_12) % 149.18/21.97 (52) all_54_9 = all_52_6 % 149.18/21.97 (53) ~ (all_52_13 = all_4_2) % 149.18/21.97 (54) op(e1, e2) = all_52_6 % 149.18/21.97 (55) ~ (all_52_13 = all_8_2) % 149.18/21.97 (56) op(e1, all_52_6) = all_58_16 % 149.18/21.97 (57) ~ (e3 = e1) % 149.18/21.97 (58) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.18/21.97 (59) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.18/21.97 (60) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.18/21.97 (61) ~ (all_52_1 = all_52_13) % 149.18/21.97 (62) all_56_5 = all_52_9 % 149.18/21.97 (63) all_54_14 = all_52_11 % 149.18/21.97 (64) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 149.18/21.97 (65) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.18/21.97 (66) all_56_12 = all_52_3 % 149.18/21.97 (67) ~ (all_52_3 = all_52_7) % 149.18/21.97 (68) all_58_2 = all_52_4 % 149.18/21.97 (69) all_20_2 = all_4_2 % 149.18/21.97 (70) all_56_11 = all_52_14 % 149.18/21.97 (71) all_56_1 = all_52_4 % 149.18/21.97 (72) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.18/21.97 (73) ~ (all_52_3 = all_4_2) % 149.18/21.97 (74) op(e1, e3) = all_52_2 % 149.18/21.97 (75) op(e1, e0) = all_52_14 % 149.18/21.97 (76) ~ (all_52_9 = all_52_11) % 149.18/21.97 (77) ~ (all_52_1 = all_8_2) % 149.18/21.97 (78) all_56_3 = all_8_2 % 149.18/21.97 (79) all_58_24 = all_52_7 % 149.18/21.97 (80) ~ (all_52_13 = all_52_14) % 149.18/21.97 (81) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/21.97 (82) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.18/21.97 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.18/21.97 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.18/21.97 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.18/21.97 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.18/21.97 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.18/21.97 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.18/21.97 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.18/21.97 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.18/21.97 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.18/21.97 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.18/21.97 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.18/21.97 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.18/21.97 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.18/21.97 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.97 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.97 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.18/21.97 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.18/21.97 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.18/21.97 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.18/21.97 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.18/21.97 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.18/21.97 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.18/21.97 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.18/21.97 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.18/21.97 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.18/21.97 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.18/21.97 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.18/21.97 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.18/21.97 e0) % 149.18/21.97 (83) ~ (all_52_4 = all_52_8) % 149.18/21.97 (84) all_56_9 = all_52_12 % 149.18/21.97 (85) all_58_29 = all_8_2 % 149.18/21.97 (86) ~ (all_52_12 = all_52_14) % 149.18/21.97 (87) all_58_8 = all_52_1 % 149.18/21.97 (88) ~ (e2 = e1) % 149.18/21.97 (89) op(e3, e0) = all_52_12 % 149.18/21.97 (90) all_56_6 = all_52_2 % 149.18/21.97 (91) ~ (all_52_2 = all_52_6) % 149.18/21.97 (92) op(all_8_2, e2) = e0 % 149.18/21.97 (93) all_56_13 = all_52_7 % 149.18/21.97 (94) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 149.18/21.97 (95) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.18/21.97 (96) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.18/21.97 (97) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.18/21.97 (98) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 149.18/21.97 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 149.18/21.97 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 149.18/21.97 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 149.18/21.97 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 149.18/21.97 (all_58_27 = e0)) % 149.18/21.97 (99) ~ (all_52_9 = all_52_13) % 149.18/21.97 (100) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 149.18/21.97 (101) op(all_6_2, e1) = all_6_1 % 149.18/21.97 (102) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.18/21.97 (103) ~ (all_52_11 = all_6_2) % 149.18/21.97 (104) ~ (e3 = e0) % 149.18/21.97 (105) all_56_2 = all_52_1 % 149.18/21.97 (106) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.18/21.97 (107) all_56_10 = all_52_13 % 149.18/21.97 (108) ~ (all_52_12 = all_10_2) % 149.18/21.97 (109) ~ (all_52_1 = all_52_3) % 149.18/21.97 (110) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.18/21.97 (111) ~ (all_52_9 = all_8_2) % 149.18/21.97 (112) all_56_14 = all_52_11 % 149.18/21.97 (113) all_58_28 = all_10_2 % 149.18/21.98 (114) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 149.18/21.98 (115) op(all_8_2, e0) = all_8_0 % 149.18/21.98 (116) all_58_17 = all_52_6 % 149.18/21.98 (117) ~ (all_52_1 = all_52_9) % 149.18/21.98 (118) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.18/21.98 (119) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/21.98 (120) ~ (all_52_7 = all_52_11) % 149.18/21.98 (121) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/21.98 (122) ~ (e2 = e0) % 149.18/21.98 (123) ~ (all_52_9 = all_6_2) % 149.18/21.98 (124) ~ (all_52_2 = all_10_2) % 149.18/21.98 (125) all_56_0 = all_10_2 % 149.18/21.98 (126) op(e0, e0) = all_4_2 % 149.18/21.98 (127) ~ (all_52_3 = all_52_11) % 149.18/21.98 (128) all_58_22 = all_52_3 % 149.18/21.98 (129) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 149.18/21.98 (130) ~ (all_52_12 = all_4_2) % 149.18/21.98 (131) ~ (all_52_3 = all_10_2) % 149.18/21.98 (132) all_56_8 = all_6_2 % 149.18/21.98 (133) op(e1, e1) = all_6_2 % 149.18/21.98 (134) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.18/21.98 (135) ~ (all_52_1 = all_52_2) % 149.18/21.98 (136) ~ (all_52_7 = all_8_2) % 149.18/21.98 (137) op(e2, e0) = all_52_13 % 149.18/21.98 (138) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.18/21.98 (139) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 149.18/21.98 (140) op(e2, all_52_13) = all_58_12 % 149.18/21.98 (141) all_58_4 = all_52_8 % 149.18/21.98 (142) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/21.98 (143) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.18/21.98 (144) all_54_0 = all_10_2 % 149.18/21.98 (145) ~ (all_52_2 = all_52_14) % 149.18/21.98 (146) ~ (all_52_14 = all_4_2) % 149.18/21.98 (147) ~ (e1 = e0) % 149.18/21.98 (148) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 149.18/21.98 (149) ~ (all_52_7 = all_4_2) % 149.18/21.98 (150) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.18/21.98 (151) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.18/21.98 (152) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.18/21.98 (153) op(e0, e2) = all_52_7 % 149.18/21.98 (154) ~ (all_52_4 = all_10_2) % 149.18/21.98 (155) all_58_30 = all_6_2 % 149.18/21.98 (156) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/21.98 (157) ~ (e3 = e2) % 149.18/21.98 (158) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.18/21.98 (159) ~ (all_52_14 = all_6_2) % 149.18/21.98 (160) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 149.18/21.98 (161) op(all_4_2, e0) = all_4_1 % 149.18/21.98 (162) op(all_10_2, e3) = all_10_1 % 149.18/21.98 (163) ~ (all_52_4 = all_52_12) % 149.18/21.98 (164) all_54_12 = all_52_3 % 149.18/21.98 (165) op(e2, all_8_2) = all_58_9 % 149.18/21.98 (166) all_54_4 = all_52_1 % 149.18/21.98 (167) ~ (all_52_1 = all_10_2) % 149.18/21.98 % 149.18/21.98 Begin of proof % 149.18/21.98 | % 149.18/21.98 | COMBINE_EQS: (30), (132) imply: % 149.18/21.98 | (168) all_56_8 = e0 % 149.18/21.98 | % 149.18/21.98 | COMBINE_EQS: (30), (155) imply: % 149.18/21.98 | (169) all_58_30 = e0 % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (49) imply: % 149.18/21.98 | (170) ~ (all_52_2 = e0) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (9), (30) imply: % 149.18/21.98 | (171) ~ (all_52_6 = e0) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (41) imply: % 149.18/21.98 | (172) ~ (all_52_8 = e0) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (123) imply: % 149.18/21.98 | (173) ~ (all_52_9 = e0) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (103) imply: % 149.18/21.98 | (174) ~ (all_52_11 = e0) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (159) imply: % 149.18/21.98 | (175) ~ (all_52_14 = e0) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (101) imply: % 149.18/21.98 | (176) op(e0, e1) = all_6_1 % 149.18/21.98 | % 149.18/21.98 | REDUCE: (12), (30) imply: % 149.18/21.98 | (177) op(e1, e0) = all_58_18 % 149.18/21.98 | % 149.18/21.98 | REDUCE: (30), (133) imply: % 149.18/21.98 | (178) op(e1, e1) = e0 % 149.18/21.98 | % 149.18/21.98 | GROUND_INST: instantiating (4) with all_52_11, all_6_1, e1, e0, simplifying % 149.18/21.98 | with (34), (176) gives: % 149.18/21.98 | (179) all_52_11 = all_6_1 % 149.18/21.98 | % 149.18/21.98 | GROUND_INST: instantiating (4) with all_52_14, all_58_18, e0, e1, simplifying % 149.18/21.98 | with (75), (177) gives: % 149.18/21.98 | (180) all_58_18 = all_52_14 % 149.18/21.98 | % 149.18/21.98 | COMBINE_EQS: (63), (179) imply: % 149.18/21.98 | (181) all_54_14 = all_6_1 % 149.18/21.98 | % 149.18/21.98 | COMBINE_EQS: (112), (179) imply: % 149.18/21.98 | (182) all_56_14 = all_6_1 % 149.18/21.98 | % 149.18/21.98 | COMBINE_EQS: (17), (179) imply: % 149.18/21.98 | (183) all_58_26 = all_6_1 % 149.18/21.98 | % 149.18/21.98 | REDUCE: (127), (179) imply: % 149.18/21.98 | (184) ~ (all_52_3 = all_6_1) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (120), (179) imply: % 149.18/21.98 | (185) ~ (all_52_7 = all_6_1) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (19), (179) imply: % 149.18/21.98 | (186) ~ (all_52_8 = all_6_1) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (76), (179) imply: % 149.18/21.98 | (187) ~ (all_52_9 = all_6_1) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (20), (179) imply: % 149.18/21.98 | (188) ~ (all_6_1 = all_4_2) % 149.18/21.98 | % 149.18/21.98 | REDUCE: (174), (179) imply: % 149.18/21.98 | (189) ~ (all_6_1 = e0) % 149.18/21.98 | % 149.18/21.98 | BETA: splitting (129) gives: % 149.18/21.98 | % 149.18/21.98 | Case 1: % 149.18/21.98 | | % 149.18/21.98 | | (190) all_56_0 = e0 % 149.18/21.98 | | % 149.18/21.98 | | COMBINE_EQS: (125), (190) imply: % 149.18/21.98 | | (191) all_10_2 = e0 % 149.18/21.98 | | % 149.18/21.98 | | COMBINE_EQS: (113), (191) imply: % 149.18/21.98 | | (192) all_58_28 = e0 % 149.18/21.98 | | % 149.18/21.98 | | REF_CLOSE: (2), (4), (27), (54), (57), (69), (85), (88), (92), (104), (118), % 149.18/21.98 | | (122), (142), (147), (156), (157), (169), (171), (192) are % 149.18/21.98 | | inconsistent by sub-proof #85. % 149.18/21.98 | | % 149.18/21.98 | Case 2: % 149.18/21.98 | | % 149.18/21.98 | | (193) ~ (all_56_0 = e0) % 149.18/21.98 | | % 149.18/21.98 | | REDUCE: (125), (193) imply: % 149.18/21.98 | | (194) ~ (all_10_2 = e0) % 149.18/21.98 | | % 149.18/21.98 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 149.18/21.98 | | (14), (15), (16), (18), (21), (22), (23), (24), (25), (26), (27), % 149.18/21.98 | | (28), (29), (31), (32), (33), (35), (36), (37), (38), (39), (40), % 149.18/21.98 | | (41), (42), (43), (44), (45), (46), (47), (48), (50), (51), (52), % 149.18/21.98 | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (64), % 149.18/21.98 | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), % 149.18/21.98 | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86), (87), % 149.18/21.98 | | (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98), % 149.18/21.98 | | (99), (100), (102), (104), (105), (106), (107), (108), (109), % 149.18/21.98 | | (110), (111), (113), (114), (115), (116), (117), (118), (119), % 149.18/21.98 | | (121), (122), (124), (125), (126), (128), (129), (130), (131), % 149.18/21.98 | | (134), (135), (136), (137), (138), (139), (140), (141), (142), % 149.18/21.98 | | (143), (144), (145), (146), (147), (148), (149), (150), (151), % 149.18/21.98 | | (152), (153), (154), (155), (156), (157), (158), (160), (161), % 149.18/21.98 | | (162), (163), (164), (165), (166), (167), (168), (169), (170), % 149.18/21.98 | | (171), (172), (173), (175), (178), (181), (182), (183), (184), % 149.18/21.98 | | (185), (186), (187), (188), (189), (194) are inconsistent by % 149.18/21.98 | | sub-proof #102. % 149.18/21.98 | | % 149.18/21.98 | End of split % 149.18/21.98 | % 149.18/21.98 End of proof % 149.18/21.98 % 149.18/21.98 Sub-proof #11 shows that the following formulas are inconsistent: % 149.18/21.98 ---------------------------------------------------------------- % 149.18/21.98 (1) all_58_31 = all_4_2 % 149.18/21.98 (2) ~ (all_52_8 = all_52_9) % 149.18/21.98 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/21.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/21.98 (4) all_58_28 = e0 % 149.18/21.98 (5) ~ (all_52_2 = all_52_3) % 149.18/21.98 (6) all_58_11 = all_52_9 % 149.18/21.98 (7) all_56_15 = all_4_2 % 149.18/21.98 (8) all_56_7 = all_52_6 % 149.18/21.98 (9) ~ (all_52_6 = all_6_2) % 149.18/21.98 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 149.18/21.98 (11) all_54_2 = all_52_8 % 149.18/21.98 (12) ~ (all_52_2 = e0) % 149.18/21.98 (13) all_54_8 = all_52_2 % 149.18/21.98 (14) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 149.18/21.98 (15) op(e3, e0) = all_58_0 % 149.18/21.98 (16) all_12_2 = all_4_2 % 149.18/21.98 (17) all_58_15 = all_52_2 % 149.18/21.98 (18) all_58_26 = all_52_11 % 149.18/21.98 (19) op(e0, all_10_1) = e0 % 149.18/21.98 (20) ~ (all_52_8 = all_52_11) % 149.18/21.98 (21) ~ (all_52_11 = all_4_2) % 149.18/21.98 (22) all_58_6 = all_52_12 % 149.18/21.99 (23) ~ (all_52_6 = all_8_2) % 149.18/21.99 (24) all_56_4 = all_52_8 % 149.18/21.99 (25) ~ (all_52_4 = all_8_2) % 149.18/21.99 (26) all_54_3 = all_52_12 % 149.18/21.99 (27) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/21.99 (28) all_54_1 = all_52_4 % 149.18/21.99 (29) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 149.18/21.99 (30) ~ (all_6_2 = e0) % 149.18/21.99 (31) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.18/21.99 (32) ~ (all_52_4 = all_52_6) % 149.18/21.99 (33) all_58_13 = all_52_13 % 149.18/21.99 (34) op(e0, e1) = all_52_11 % 149.18/21.99 (35) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 149.18/21.99 (36) ~ (all_52_6 = all_52_7) % 149.18/21.99 (37) all_54_11 = all_52_14 % 149.18/21.99 (38) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 149.18/21.99 (39) all_58_20 = all_52_14 % 149.18/21.99 (40) ~ (all_52_8 = all_6_2) % 149.18/21.99 (41) ~ (all_52_12 = all_52_13) % 149.18/21.99 (42) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.18/21.99 (43) op(e0, all_52_3) = all_58_21 % 149.18/21.99 (44) all_56_0 = e0 % 149.18/21.99 (45) all_54_5 = all_8_2 % 149.18/21.99 (46) ~ (all_52_6 = all_52_14) % 149.18/21.99 (47) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 149.18/21.99 (48) ~ (all_52_4 = all_52_7) % 149.18/21.99 (49) ~ (all_52_2 = all_6_2) % 149.18/21.99 (50) ~ (all_52_8 = all_52_12) % 149.18/21.99 (51) all_54_9 = all_52_6 % 149.18/21.99 (52) ~ (all_52_13 = all_4_2) % 149.18/21.99 (53) ~ (all_52_3 = e0) % 149.18/21.99 (54) ~ (all_52_13 = all_8_2) % 149.18/21.99 (55) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 149.18/21.99 (56) ~ (e3 = e1) % 149.18/21.99 (57) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.18/21.99 (58) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.18/21.99 (59) all_12_1 = all_4_1 % 149.18/21.99 (60) all_56_5 = all_52_9 % 149.18/21.99 (61) all_54_14 = all_52_11 % 149.18/21.99 (62) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 149.18/21.99 (63) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.18/21.99 (64) all_56_12 = all_52_3 % 149.18/21.99 (65) ~ (all_52_12 = e0) % 149.18/21.99 (66) ~ (all_52_3 = all_52_7) % 149.18/21.99 (67) all_58_2 = all_52_4 % 149.18/21.99 (68) all_56_11 = all_52_14 % 149.18/21.99 (69) all_56_1 = all_52_4 % 149.18/21.99 (70) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 149.18/21.99 (71) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.18/21.99 (72) ~ (all_52_3 = all_4_2) % 149.18/21.99 (73) op(e0, e3) = all_10_1 % 149.18/21.99 (74) ~ (all_52_9 = all_52_11) % 149.18/21.99 (75) ~ (all_52_1 = all_8_2) % 149.18/21.99 (76) all_56_3 = all_8_2 % 149.18/21.99 (77) all_58_24 = all_52_7 % 149.18/21.99 (78) ~ (all_52_13 = all_52_14) % 149.18/21.99 (79) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/21.99 (80) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.18/21.99 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.18/21.99 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.18/21.99 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.18/21.99 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.18/21.99 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.18/21.99 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.18/21.99 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.18/21.99 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.18/21.99 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.18/21.99 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.18/21.99 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.18/21.99 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.18/21.99 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.18/21.99 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.99 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/21.99 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.18/21.99 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.18/21.99 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.18/21.99 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.18/21.99 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.18/21.99 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.18/21.99 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.18/21.99 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.18/21.99 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.18/21.99 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.18/21.99 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.18/21.99 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.18/21.99 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.18/21.99 e0) % 149.18/21.99 (81) ~ (all_52_4 = all_52_8) % 149.18/21.99 (82) op(e2, e1) = all_52_9 % 149.18/21.99 (83) all_56_9 = all_52_12 % 149.18/21.99 (84) all_58_29 = all_8_2 % 149.18/21.99 (85) ~ (all_52_12 = all_52_14) % 149.18/21.99 (86) all_58_8 = all_52_1 % 149.18/21.99 (87) ~ (e2 = e1) % 149.18/21.99 (88) op(e3, e0) = all_52_12 % 149.18/21.99 (89) all_56_6 = all_52_2 % 149.18/21.99 (90) ~ (all_52_2 = all_52_6) % 149.18/21.99 (91) all_56_13 = all_52_7 % 149.18/21.99 (92) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 149.18/21.99 (93) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.18/21.99 (94) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.18/21.99 (95) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.18/21.99 (96) ~ (all_52_9 = all_52_13) % 149.18/21.99 (97) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 149.18/21.99 (98) op(all_6_2, e1) = all_6_1 % 149.18/21.99 (99) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.18/21.99 (100) ~ (all_52_4 = e0) % 149.18/21.99 (101) ~ (all_52_11 = all_6_2) % 149.18/21.99 (102) ~ (e3 = e0) % 149.18/21.99 (103) all_56_2 = all_52_1 % 149.18/21.99 (104) op(e0, e3) = all_52_3 % 149.18/21.99 (105) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.18/21.99 (106) all_56_10 = all_52_13 % 149.18/21.99 (107) ~ (all_52_1 = all_52_3) % 149.18/21.99 (108) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.18/21.99 (109) ~ (all_52_9 = all_8_2) % 149.18/21.99 (110) all_56_14 = all_52_11 % 149.18/21.99 (111) all_58_28 = all_10_2 % 149.18/21.99 (112) ~ (all_6_1 = e0) % 149.18/21.99 (113) ~ (all_12_1 = e2) | ~ (all_12_2 = e3) % 149.18/21.99 (114) all_58_17 = all_52_6 % 149.18/21.99 (115) ~ (all_52_1 = all_52_9) % 149.18/21.99 (116) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/21.99 (117) ~ (all_52_7 = all_52_11) % 149.18/21.99 (118) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/21.99 (119) ~ (e2 = e0) % 149.18/21.99 (120) ~ (all_52_9 = all_6_2) % 149.18/21.99 (121) all_56_0 = all_10_2 % 149.18/21.99 (122) ~ (all_52_1 = e0) % 149.18/21.99 (123) ~ (all_52_3 = all_52_11) % 149.18/21.99 (124) all_58_22 = all_52_3 % 149.18/21.99 (125) all_56_8 = all_6_2 % 149.18/21.99 (126) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.18/21.99 (127) ~ (all_52_1 = all_52_2) % 149.18/21.99 (128) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.18/21.99 (129) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 149.18/21.99 (130) all_58_4 = all_52_8 % 149.18/21.99 (131) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/21.99 (132) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.18/22.00 (133) ~ (all_52_2 = all_52_14) % 149.18/22.00 (134) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.18/22.00 (135) ~ (all_52_14 = all_4_2) % 149.18/22.00 (136) ~ (e1 = e0) % 149.18/22.00 (137) ~ (all_52_7 = all_4_2) % 149.18/22.00 (138) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.18/22.00 (139) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.18/22.00 (140) op(e0, e2) = all_52_7 % 149.18/22.00 (141) ~ (all_52_8 = e0) % 149.18/22.00 (142) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 149.18/22.00 (143) all_58_30 = all_6_2 % 149.18/22.00 (144) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/22.00 (145) ~ (e3 = e2) % 149.18/22.00 (146) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.18/22.00 (147) ~ (all_52_14 = all_6_2) % 149.18/22.00 (148) op(all_4_2, e0) = all_4_1 % 149.18/22.00 (149) ~ (all_52_4 = all_52_12) % 149.18/22.00 (150) all_54_12 = all_52_3 % 149.18/22.00 (151) all_54_4 = all_52_1 % 149.18/22.00 % 149.18/22.00 Begin of proof % 149.18/22.00 | % 149.18/22.00 | GROUND_INST: instantiating (3) with all_52_3, all_10_1, e3, e0, simplifying % 149.18/22.00 | with (73), (104) gives: % 149.18/22.00 | (152) all_52_3 = all_10_1 % 149.18/22.00 | % 149.18/22.00 | GROUND_INST: instantiating (3) with all_52_12, all_58_0, e0, e3, simplifying % 149.18/22.00 | with (15), (88) gives: % 149.18/22.00 | (153) all_58_0 = all_52_12 % 149.18/22.00 | % 149.18/22.00 | COMBINE_EQS: (150), (152) imply: % 149.18/22.00 | (154) all_54_12 = all_10_1 % 149.18/22.00 | % 149.18/22.00 | COMBINE_EQS: (64), (152) imply: % 149.18/22.00 | (155) all_56_12 = all_10_1 % 149.18/22.00 | % 149.18/22.00 | COMBINE_EQS: (124), (152) imply: % 149.18/22.00 | (156) all_58_22 = all_10_1 % 149.18/22.00 | % 149.18/22.00 | REDUCE: (107), (152) imply: % 149.18/22.00 | (157) ~ (all_52_1 = all_10_1) % 149.18/22.00 | % 149.18/22.00 | REDUCE: (5), (152) imply: % 149.18/22.00 | (158) ~ (all_52_2 = all_10_1) % 149.18/22.00 | % 149.18/22.00 | REDUCE: (66), (152) imply: % 149.18/22.00 | (159) ~ (all_52_7 = all_10_1) % 149.18/22.00 | % 149.18/22.00 | SIMP: (159) implies: % 149.18/22.00 | (160) ~ (all_52_7 = all_10_1) % 149.18/22.00 | % 149.18/22.00 | REDUCE: (123), (152) imply: % 149.18/22.00 | (161) ~ (all_52_11 = all_10_1) % 149.18/22.00 | % 149.18/22.00 | SIMP: (161) implies: % 149.18/22.00 | (162) ~ (all_52_11 = all_10_1) % 149.18/22.00 | % 149.18/22.00 | REDUCE: (72), (152) imply: % 149.18/22.00 | (163) ~ (all_10_1 = all_4_2) % 149.18/22.00 | % 149.18/22.00 | REDUCE: (53), (152) imply: % 149.18/22.00 | (164) ~ (all_10_1 = e0) % 149.18/22.00 | % 149.18/22.00 | REDUCE: (43), (152) imply: % 149.18/22.00 | (165) op(e0, all_10_1) = all_58_21 % 149.18/22.00 | % 149.18/22.00 | GROUND_INST: instantiating (3) with e0, all_58_21, all_10_1, e0, simplifying % 149.18/22.00 | with (19), (165) gives: % 149.18/22.00 | (166) all_58_21 = e0 % 149.18/22.00 | % 149.18/22.00 | BETA: splitting (97) gives: % 149.18/22.00 | % 149.18/22.00 | Case 1: % 149.18/22.00 | | % 149.18/22.00 | | (167) all_56_1 = e0 % 149.18/22.00 | | % 149.18/22.00 | | COMBINE_EQS: (69), (167) imply: % 149.18/22.00 | | (168) all_52_4 = e0 % 149.18/22.00 | | % 149.18/22.00 | | REDUCE: (100), (168) imply: % 149.18/22.00 | | (169) $false % 149.18/22.00 | | % 149.18/22.00 | | CLOSE: (169) is inconsistent. % 149.18/22.00 | | % 149.18/22.00 | Case 2: % 149.18/22.00 | | % 149.18/22.00 | | (170) ~ (all_56_1 = e0) % 149.18/22.00 | | (171) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 149.18/22.00 | | % 149.18/22.00 | | BETA: splitting (29) gives: % 149.18/22.00 | | % 149.18/22.00 | | Case 1: % 149.18/22.00 | | | % 149.18/22.00 | | | (172) all_56_2 = e0 % 149.18/22.00 | | | % 149.18/22.00 | | | COMBINE_EQS: (103), (172) imply: % 149.18/22.00 | | | (173) all_52_1 = e0 % 149.18/22.00 | | | % 149.18/22.00 | | | REDUCE: (122), (173) imply: % 149.18/22.00 | | | (174) $false % 149.18/22.00 | | | % 149.18/22.00 | | | CLOSE: (174) is inconsistent. % 149.18/22.00 | | | % 149.18/22.00 | | Case 2: % 149.18/22.00 | | | % 149.18/22.00 | | | (175) ~ (all_56_2 = e0) % 149.18/22.00 | | | (176) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 149.18/22.00 | | | % 149.18/22.00 | | | BETA: splitting (134) gives: % 149.18/22.00 | | | % 149.18/22.00 | | | Case 1: % 149.18/22.00 | | | | % 149.18/22.00 | | | | (177) all_56_6 = e0 % 149.18/22.00 | | | | % 149.18/22.00 | | | | COMBINE_EQS: (89), (177) imply: % 149.18/22.00 | | | | (178) all_52_2 = e0 % 149.18/22.00 | | | | % 149.18/22.00 | | | | REDUCE: (12), (178) imply: % 149.18/22.00 | | | | (179) $false % 149.18/22.00 | | | | % 149.18/22.00 | | | | CLOSE: (179) is inconsistent. % 149.18/22.00 | | | | % 149.18/22.00 | | | Case 2: % 149.18/22.00 | | | | % 149.18/22.00 | | | | (180) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.18/22.00 | | | | % 149.18/22.00 | | | | BETA: splitting (70) gives: % 149.18/22.00 | | | | % 149.18/22.00 | | | | Case 1: % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | (181) all_56_4 = e0 % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | COMBINE_EQS: (24), (181) imply: % 149.18/22.00 | | | | | (182) all_52_8 = e0 % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | REDUCE: (141), (182) imply: % 149.18/22.00 | | | | | (183) $false % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | CLOSE: (183) is inconsistent. % 149.18/22.00 | | | | | % 149.18/22.00 | | | | Case 2: % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | (184) ~ (all_56_4 = e0) % 149.18/22.00 | | | | | (185) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | BETA: splitting (93) gives: % 149.18/22.00 | | | | | % 149.18/22.00 | | | | | Case 1: % 149.18/22.00 | | | | | | % 149.18/22.00 | | | | | | (186) all_54_4 = e0 % 149.18/22.00 | | | | | | % 149.18/22.00 | | | | | | REF_CLOSE: (122), (151), (186) are inconsistent by sub-proof #859. % 149.18/22.00 | | | | | | % 149.18/22.00 | | | | | Case 2: % 149.18/22.00 | | | | | | % 149.18/22.00 | | | | | | (187) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 149.18/22.00 | | | | | | % 149.18/22.00 | | | | | | BETA: splitting (10) gives: % 149.18/22.00 | | | | | | % 149.18/22.00 | | | | | | Case 1: % 149.18/22.00 | | | | | | | % 149.18/22.00 | | | | | | | (188) all_54_3 = e0 % 149.18/22.00 | | | | | | | % 149.18/22.00 | | | | | | | REF_CLOSE: (26), (65), (188) are inconsistent by sub-proof #733. % 149.18/22.00 | | | | | | | % 149.18/22.00 | | | | | | Case 2: % 149.18/22.00 | | | | | | | % 149.18/22.00 | | | | | | | (189) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 149.18/22.00 | | | | | | | % 149.18/22.00 | | | | | | | BETA: splitting (128) gives: % 149.18/22.00 | | | | | | | % 149.18/22.00 | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | % 149.18/22.00 | | | | | | | | (190) all_54_1 = e0 % 149.18/22.00 | | | | | | | | % 149.18/22.00 | | | | | | | | REF_CLOSE: (28), (100), (190) are inconsistent by sub-proof % 149.18/22.00 | | | | | | | | #798. % 149.18/22.00 | | | | | | | | % 149.18/22.00 | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | % 149.18/22.00 | | | | | | | | (191) ~ (all_54_1 = e0) % 149.18/22.00 | | | | | | | | (192) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 149.18/22.00 | | | | | | | | % 149.18/22.00 | | | | | | | | BETA: splitting (105) gives: % 149.18/22.00 | | | | | | | | % 149.18/22.00 | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | % 149.18/22.00 | | | | | | | | | (193) all_54_12 = e0 % 149.18/22.00 | | | | | | | | | % 149.18/22.00 | | | | | | | | | REF_CLOSE: (154), (164), (193) are inconsistent by sub-proof % 149.18/22.00 | | | | | | | | | #459. % 149.18/22.00 | | | | | | | | | % 149.18/22.00 | | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | | % 149.18/22.00 | | | | | | | | | (194) ~ (all_54_12 = e0) % 149.18/22.00 | | | | | | | | | (195) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.18/22.00 | | | | | | | | | % 149.18/22.00 | | | | | | | | | BETA: splitting (138) gives: % 149.18/22.00 | | | | | | | | | % 149.18/22.00 | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | (196) all_54_2 = e0 % 149.18/22.00 | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | REF_CLOSE: (11), (141), (196) are inconsistent by sub-proof % 149.18/22.00 | | | | | | | | | | #860. % 149.18/22.00 | | | | | | | | | | % 149.18/22.00 | | | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | (197) ~ (all_54_2 = e0) % 149.18/22.00 | | | | | | | | | | (198) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 149.18/22.00 | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | BETA: splitting (47) gives: % 149.18/22.00 | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | (199) all_54_11 = e0 % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | COMBINE_EQS: (37), (199) imply: % 149.18/22.00 | | | | | | | | | | | (200) all_52_14 = e0 % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | SIMP: (200) implies: % 149.18/22.00 | | | | | | | | | | | (201) all_52_14 = e0 % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | COMBINE_EQS: (68), (201) imply: % 149.18/22.00 | | | | | | | | | | | (202) all_56_11 = e0 % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | COMBINE_EQS: (39), (201) imply: % 149.18/22.00 | | | | | | | | | | | (203) all_58_20 = e0 % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | REDUCE: (46), (201) imply: % 149.18/22.00 | | | | | | | | | | | (204) ~ (all_52_6 = e0) % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | REDUCE: (147), (201) imply: % 149.18/22.00 | | | | | | | | | | | (205) ~ (all_6_2 = e0) % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | BETA: splitting (171) gives: % 149.18/22.00 | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | (206) all_56_3 = e0 % 149.18/22.00 | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | REF_CLOSE: (8), (24), (27), (30), (56), (62), (68), (69), % 149.18/22.00 | | | | | | | | | | | | (76), (83), (84), (85), (87), (100), (102), (111), % 149.18/22.00 | | | | | | | | | | | | (119), (121), (125), (131), (136), (141), (143), % 149.18/22.00 | | | | | | | | | | | | (144), (145), (180), (204), (206) are inconsistent % 149.18/22.00 | | | | | | | | | | | | by sub-proof #480. % 149.18/22.00 | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | (207) all_56_7 = e0 | all_56_13 = e0 % 149.18/22.00 | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | BETA: splitting (207) gives: % 149.18/22.00 | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | (208) all_56_7 = e0 % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | COMBINE_EQS: (8), (208) imply: % 149.18/22.00 | | | | | | | | | | | | | (209) all_52_6 = e0 % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | REDUCE: (204), (209) imply: % 149.18/22.00 | | | | | | | | | | | | | (210) $false % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | (211) all_56_13 = e0 % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | COMBINE_EQS: (91), (211) imply: % 149.18/22.00 | | | | | | | | | | | | | (212) all_52_7 = e0 % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | SIMP: (212) implies: % 149.18/22.00 | | | | | | | | | | | | | (213) all_52_7 = e0 % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | COMBINE_EQS: (77), (213) imply: % 149.18/22.00 | | | | | | | | | | | | | (214) all_58_24 = e0 % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | REDUCE: (117), (213) imply: % 149.18/22.00 | | | | | | | | | | | | | (215) ~ (all_52_11 = e0) % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | SIMP: (215) implies: % 149.18/22.00 | | | | | | | | | | | | | (216) ~ (all_52_11 = e0) % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | REDUCE: (160), (213) imply: % 149.18/22.00 | | | | | | | | | | | | | (217) ~ (all_10_1 = e0) % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | REDUCE: (137), (213) imply: % 149.18/22.00 | | | | | | | | | | | | | (218) ~ (all_4_2 = e0) % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | SIMP: (218) implies: % 149.18/22.00 | | | | | | | | | | | | | (219) ~ (all_4_2 = e0) % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | BETA: splitting (185) gives: % 149.18/22.00 | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | (220) all_56_5 = e0 % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | COMBINE_EQS: (60), (220) imply: % 149.18/22.00 | | | | | | | | | | | | | | (221) all_52_9 = e0 % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | COMBINE_EQS: (6), (221) imply: % 149.18/22.00 | | | | | | | | | | | | | | (222) all_58_11 = e0 % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | REDUCE: (96), (221) imply: % 149.18/22.00 | | | | | | | | | | | | | | (223) ~ (all_52_13 = e0) % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | SIMP: (223) implies: % 149.18/22.00 | | | | | | | | | | | | | | (224) ~ (all_52_13 = e0) % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | REDUCE: (109), (221) imply: % 149.18/22.00 | | | | | | | | | | | | | | (225) ~ (all_8_2 = e0) % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | SIMP: (225) implies: % 149.18/22.00 | | | | | | | | | | | | | | (226) ~ (all_8_2 = e0) % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | REDUCE: (82), (221) imply: % 149.18/22.00 | | | | | | | | | | | | | | (227) op(e2, e1) = e0 % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | BETA: splitting (57) gives: % 149.18/22.00 | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | (228) all_54_9 = e0 % 149.18/22.00 | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | REF_CLOSE: (51), (204), (228) are inconsistent by sub-proof % 149.18/22.00 | | | | | | | | | | | | | | | #572. % 149.18/22.00 | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | (229) ~ (all_54_9 = e0) % 149.18/22.00 | | | | | | | | | | | | | | | (230) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 149.18/22.00 | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 149.18/22.00 | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | | (231) all_54_14 = e0 % 149.18/22.00 | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | | REF_CLOSE: (61), (216), (231) are inconsistent by sub-proof % 149.18/22.00 | | | | | | | | | | | | | | | | #517. % 149.18/22.00 | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | Case 2: % 149.18/22.00 | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | | (232) ~ (all_54_14 = e0) % 149.18/22.00 | | | | | | | | | | | | | | | | (233) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 149.18/22.00 | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 149.18/22.00 | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | | Case 1: % 149.18/22.00 | | | | | | | | | | | | | | | | | % 149.18/22.00 | | | | | | | | | | | | | | | | | (234) all_56_4 = e1 % 149.18/22.00 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (12), (13), (14), % 149.18/22.01 | | | | | | | | | | | | | | | | | (17), (18), (19), (20), (21), (22), (23), (24), % 149.18/22.01 | | | | | | | | | | | | | | | | | (25), (26), (27), (28), (30), (31), (32), (33), % 149.18/22.01 | | | | | | | | | | | | | | | | | (34), (41), (42), (44), (45), (49), (50), (51), % 149.18/22.01 | | | | | | | | | | | | | | | | | (52), (54), (55), (56), (58), (61), (62), (63), % 149.18/22.01 | | | | | | | | | | | | | | | | | (65), (67), (68), (69), (71), (73), (75), (76), % 149.18/22.01 | | | | | | | | | | | | | | | | | (79), (80), (81), (83), (84), (85), (86), (87), % 149.18/22.01 | | | | | | | | | | | | | | | | | (89), (90), (94), (95), (99), (100), (101), (102), % 149.18/22.01 | | | | | | | | | | | | | | | | | (103), (106), (110), (111), (114), (116), (118), % 149.18/22.01 | | | | | | | | | | | | | | | | | (119), (121), (122), (125), (126), (127), (129), % 149.18/22.01 | | | | | | | | | | | | | | | | | (130), (131), (132), (139), (141), (143), (144), % 149.18/22.01 | | | | | | | | | | | | | | | | | (145), (146), (149), (151), (154), (155), (156), % 149.18/22.01 | | | | | | | | | | | | | | | | | (157), (158), (162), (163), (164), (180), (187), % 149.18/22.01 | | | | | | | | | | | | | | | | | (189), (192), (195), (202), (203), (204), (211), % 149.18/22.01 | | | | | | | | | | | | | | | | | (214), (216), (219), (220), (222), (224), (226), % 149.18/22.01 | | | | | | | | | | | | | | | | | (230), (233), (234) are inconsistent by sub-proof % 149.18/22.01 | | | | | | | | | | | | | | | | | #14. % 149.18/22.01 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | (235) ~ (all_56_4 = e1) % 149.18/22.01 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | REDUCE: (24), (235) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | (236) ~ (all_52_8 = e1) % 149.18/22.01 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | (237) all_56_0 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (237) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | (238) e2 = e0 % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | SIMP: (238) implies: % 149.18/22.01 | | | | | | | | | | | | | | | | | | (239) e2 = e0 % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | REDUCE: (119), (239) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | (240) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | (241) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | (242) all_56_4 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (8), (9), (19), (23), (24), (27), % 149.18/22.01 | | | | | | | | | | | | | | | | | | | (34), (40), (73), (84), (89), (118), (125), (141), % 149.18/22.01 | | | | | | | | | | | | | | | | | | | (143), (146), (154), (155), (158), (163), (164), % 149.18/22.01 | | | | | | | | | | | | | | | | | | | (195), (202), (204), (216), (242) are inconsistent % 149.18/22.01 | | | | | | | | | | | | | | | | | | | by sub-proof #13. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | (243) ~ (all_56_4 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | REDUCE: (24), (243) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | (244) ~ (all_52_8 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | (245) all_54_2 = e1 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (236), (245) are inconsistent by sub-proof % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | #819. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | (246) all_54_2 = e3 | all_54_2 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (247) all_54_2 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (244), (247) are inconsistent by sub-proof % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | #556. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (248) all_54_2 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (248) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (249) all_52_8 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (250) all_52_8 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (250) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (251) all_56_4 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (250) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_52_4 = e3) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (250) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_52_11 = e3) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | SIMP: (253) implies: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_52_11 = e3) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | (255) all_56_12 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (19), (73), (155), (164), (255) are % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #196. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | (256) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | (257) all_56_13 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (257) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | (258) e3 = e0 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (258) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | (259) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | (260) all_56_14 = e3 | all_56_15 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (261) all_56_14 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (254), (261) are inconsistent by sub-proof % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | #759. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_56_15 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (262) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (263) all_4_2 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (263) implies: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (264) all_4_2 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (264) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (265) all_12_2 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (264) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (266) all_58_31 = e3 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (264) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | (267) op(e3, e0) = all_4_1 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | (268) ~ (all_12_1 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (268) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | (269) ~ (all_4_1 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_12, all_4_1, e0, e3, % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (88), (267) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_52_12 = all_4_1 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (270) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_56_9 = all_4_1 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_56_1 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (272) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_52_4 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (273) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (274) ~ (all_8_2 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (274) implies: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (275) ~ (all_8_2 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (273) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (276) ~ (e3 = e2) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_28 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (119), (277) are inconsistent by sub-proof % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | #688. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_29 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (279) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_8_2 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (280) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_30 = e2 | all_58_31 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_30 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (283) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_6_2 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (98), (112), (227), (284) are inconsistent by % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #842. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_31 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (285) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) e3 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (286) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_56_4 = e2 | all_56_9 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_56_4 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (289) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) e3 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (290) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_56_9 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (292) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_4_1 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_4_1 = e2 % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (294) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_12_2 = e3) % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (265), (296) imply: % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | (297) $false % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent. % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | (298) all_56_8 = e0 | all_56_14 = e0 % 149.18/22.01 | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | | REF_CLOSE: (30), (110), (125), (216), (298) are inconsistent % 149.18/22.01 | | | | | | | | | | | | | | by sub-proof #805. % 149.18/22.01 | | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | Case 2: % 149.18/22.01 | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | (299) ~ (all_54_11 = e0) % 149.18/22.01 | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | REDUCE: (37), (299) imply: % 149.18/22.01 | | | | | | | | | | | (300) ~ (all_52_14 = e0) % 149.18/22.01 | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (17), (18), (19), (23), % 149.18/22.01 | | | | | | | | | | | (24), (25), (27), (30), (33), (36), (39), (41), % 149.18/22.01 | | | | | | | | | | | (44), (52), (54), (56), (60), (68), (69), (73), % 149.18/22.01 | | | | | | | | | | | (74), (76), (77), (78), (80), (83), (84), (85), % 149.18/22.01 | | | | | | | | | | | (87), (89), (91), (92), (94), (99), (102), (106), % 149.18/22.01 | | | | | | | | | | | (110), (114), (116), (117), (118), (119), (125), % 149.18/22.01 | | | | | | | | | | | (129), (130), (131), (133), (135), (140), (142), % 149.18/22.01 | | | | | | | | | | | (143), (144), (145), (147), (149), (154), (155), % 149.18/22.01 | | | | | | | | | | | (156), (158), (160), (162), (163), (164), (176), % 149.18/22.01 | | | | | | | | | | | (180), (195), (300) are inconsistent by sub-proof % 149.18/22.01 | | | | | | | | | | | #12. % 149.18/22.01 | | | | | | | | | | | % 149.18/22.01 | | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | | % 149.18/22.01 | | | | | | | | | End of split % 149.18/22.01 | | | | | | | | | % 149.18/22.01 | | | | | | | | End of split % 149.18/22.01 | | | | | | | | % 149.18/22.01 | | | | | | | End of split % 149.18/22.01 | | | | | | | % 149.18/22.01 | | | | | | End of split % 149.18/22.01 | | | | | | % 149.18/22.01 | | | | | End of split % 149.18/22.01 | | | | | % 149.18/22.01 | | | | End of split % 149.18/22.01 | | | | % 149.18/22.01 | | | End of split % 149.18/22.01 | | | % 149.18/22.01 | | End of split % 149.18/22.01 | | % 149.18/22.01 | End of split % 149.18/22.01 | % 149.18/22.01 End of proof % 149.18/22.01 % 149.18/22.01 Sub-proof #12 shows that the following formulas are inconsistent: % 149.18/22.01 ---------------------------------------------------------------- % 149.18/22.01 (1) all_58_31 = all_4_2 % 149.18/22.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/22.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/22.01 (3) all_58_28 = e0 % 149.18/22.01 (4) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 149.18/22.01 (5) all_56_15 = all_4_2 % 149.18/22.01 (6) all_56_7 = all_52_6 % 149.18/22.01 (7) ~ (all_10_1 = e0) % 149.18/22.01 (8) ~ (all_52_7 = all_10_1) % 149.18/22.01 (9) ~ (all_52_11 = all_10_1) % 149.18/22.01 (10) all_58_15 = all_52_2 % 149.18/22.01 (11) all_58_26 = all_52_11 % 149.18/22.01 (12) op(e0, all_10_1) = e0 % 149.18/22.01 (13) ~ (all_52_6 = all_8_2) % 149.18/22.01 (14) all_56_4 = all_52_8 % 149.18/22.01 (15) ~ (all_52_4 = all_8_2) % 149.18/22.01 (16) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/22.01 (17) ~ (all_6_2 = e0) % 149.18/22.01 (18) ~ (all_10_1 = all_4_2) % 149.18/22.01 (19) all_58_13 = all_52_13 % 149.18/22.01 (20) all_56_12 = all_10_1 % 149.18/22.01 (21) ~ (all_52_6 = all_52_7) % 149.18/22.01 (22) all_58_20 = all_52_14 % 149.18/22.01 (23) ~ (all_52_12 = all_52_13) % 149.18/22.01 (24) all_56_0 = e0 % 149.18/22.01 (25) ~ (all_52_13 = all_4_2) % 149.18/22.01 (26) ~ (all_52_13 = all_8_2) % 149.18/22.01 (27) ~ (e3 = e1) % 149.18/22.02 (28) all_54_12 = all_10_1 % 149.18/22.02 (29) all_56_5 = all_52_9 % 149.18/22.02 (30) all_56_11 = all_52_14 % 149.18/22.02 (31) all_56_1 = all_52_4 % 149.18/22.02 (32) op(e0, e3) = all_10_1 % 149.18/22.02 (33) ~ (all_52_9 = all_52_11) % 149.18/22.02 (34) all_56_3 = all_8_2 % 149.18/22.02 (35) all_58_24 = all_52_7 % 149.18/22.02 (36) ~ (all_52_13 = all_52_14) % 149.18/22.02 (37) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.18/22.02 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.18/22.02 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.18/22.02 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.18/22.02 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.18/22.02 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.18/22.02 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.18/22.02 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.18/22.02 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.18/22.02 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.18/22.02 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.18/22.02 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.18/22.02 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.18/22.02 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.18/22.02 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/22.02 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/22.02 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.18/22.02 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.18/22.02 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.18/22.02 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.18/22.02 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.18/22.02 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.18/22.02 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.18/22.02 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.18/22.02 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.18/22.02 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.18/22.02 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.18/22.02 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.18/22.02 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.18/22.02 e0) % 149.18/22.02 (38) all_56_9 = all_52_12 % 149.18/22.02 (39) all_58_29 = all_8_2 % 149.18/22.02 (40) ~ (all_52_12 = all_52_14) % 149.18/22.02 (41) ~ (e2 = e1) % 149.18/22.02 (42) all_56_6 = all_52_2 % 149.18/22.02 (43) all_56_13 = all_52_7 % 149.18/22.02 (44) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 149.18/22.02 (45) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.18/22.02 (46) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.18/22.02 (47) ~ (e3 = e0) % 149.18/22.02 (48) all_58_22 = all_10_1 % 149.18/22.02 (49) all_56_10 = all_52_13 % 149.18/22.02 (50) all_56_14 = all_52_11 % 149.18/22.02 (51) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.18/22.02 (52) all_58_17 = all_52_6 % 149.18/22.02 (53) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/22.02 (54) ~ (all_52_7 = all_52_11) % 149.18/22.02 (55) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/22.02 (56) ~ (e2 = e0) % 149.18/22.02 (57) all_56_8 = all_6_2 % 149.18/22.02 (58) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 149.18/22.02 (59) all_58_4 = all_52_8 % 149.18/22.02 (60) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/22.02 (61) ~ (all_52_2 = all_52_14) % 149.18/22.02 (62) ~ (all_52_14 = all_4_2) % 149.18/22.02 (63) ~ (all_52_14 = e0) % 149.18/22.02 (64) op(e0, e2) = all_52_7 % 149.18/22.02 (65) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 149.18/22.02 (66) all_58_30 = all_6_2 % 149.18/22.02 (67) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/22.02 (68) ~ (e3 = e2) % 149.18/22.02 (69) ~ (all_52_14 = all_6_2) % 149.18/22.02 (70) ~ (all_52_4 = all_52_12) % 149.18/22.02 (71) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.18/22.02 (72) ~ (all_52_2 = all_10_1) % 149.18/22.02 % 149.18/22.02 Begin of proof % 149.18/22.02 | % 149.18/22.02 | BETA: splitting (51) gives: % 149.18/22.02 | % 149.18/22.02 | Case 1: % 149.18/22.02 | | % 149.18/22.02 | | (73) all_56_7 = e0 % 149.18/22.02 | | % 149.18/22.02 | | COMBINE_EQS: (6), (73) imply: % 149.18/22.02 | | (74) all_52_6 = e0 % 149.18/22.02 | | % 149.18/22.02 | | COMBINE_EQS: (52), (74) imply: % 149.18/22.02 | | (75) all_58_17 = e0 % 149.18/22.02 | | % 149.18/22.02 | | REDUCE: (21), (74) imply: % 149.18/22.02 | | (76) ~ (all_52_7 = e0) % 149.18/22.02 | | % 149.18/22.02 | | SIMP: (76) implies: % 149.18/22.02 | | (77) ~ (all_52_7 = e0) % 149.18/22.02 | | % 149.18/22.02 | | REDUCE: (13), (74) imply: % 149.18/22.02 | | (78) ~ (all_8_2 = e0) % 149.18/22.02 | | % 149.18/22.02 | | SIMP: (78) implies: % 149.18/22.02 | | (79) ~ (all_8_2 = e0) % 149.18/22.02 | | % 149.18/22.02 | | BETA: splitting (65) gives: % 149.18/22.02 | | % 149.18/22.02 | | Case 1: % 149.18/22.02 | | | % 149.18/22.02 | | | (80) all_56_12 = e0 % 149.18/22.02 | | | % 149.18/22.02 | | | REF_CLOSE: (7), (20), (80) are inconsistent by sub-proof #230. % 149.18/22.02 | | | % 149.18/22.02 | | Case 2: % 149.18/22.02 | | | % 149.18/22.02 | | | (81) all_56_13 = e0 | all_56_14 = e0 % 149.18/22.02 | | | % 149.18/22.02 | | | BETA: splitting (81) gives: % 149.18/22.02 | | | % 149.18/22.02 | | | Case 1: % 149.18/22.02 | | | | % 149.18/22.02 | | | | (82) all_56_13 = e0 % 149.18/22.02 | | | | % 149.18/22.02 | | | | REF_CLOSE: (43), (77), (82) are inconsistent by sub-proof #802. % 149.18/22.02 | | | | % 149.18/22.02 | | | Case 2: % 149.18/22.02 | | | | % 149.18/22.02 | | | | (83) all_56_14 = e0 % 149.18/22.02 | | | | % 149.18/22.02 | | | | COMBINE_EQS: (50), (83) imply: % 149.18/22.02 | | | | (84) all_52_11 = e0 % 149.18/22.02 | | | | % 149.18/22.02 | | | | SIMP: (84) implies: % 149.18/22.02 | | | | (85) all_52_11 = e0 % 149.18/22.02 | | | | % 149.18/22.02 | | | | COMBINE_EQS: (11), (85) imply: % 149.18/22.02 | | | | (86) all_58_26 = e0 % 149.18/22.02 | | | | % 149.18/22.02 | | | | REDUCE: (33), (85) imply: % 149.18/22.02 | | | | (87) ~ (all_52_9 = e0) % 149.18/22.02 | | | | % 149.18/22.02 | | | | REDUCE: (9), (85) imply: % 149.18/22.02 | | | | (88) ~ (all_10_1 = e0) % 149.18/22.02 | | | | % 149.18/22.02 | | | | BETA: splitting (55) gives: % 149.18/22.02 | | | | % 149.18/22.02 | | | | Case 1: % 149.18/22.02 | | | | | % 149.18/22.02 | | | | | (89) all_56_12 = e1 % 149.18/22.02 | | | | | % 149.18/22.02 | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (14), (15), (16), (18), % 149.18/22.02 | | | | | (19), (20), (22), (23), (24), (25), (26), (27), (29), (30), % 149.18/22.02 | | | | | (31), (34), (35), (36), (37), (38), (39), (40), (41), (42), % 149.18/22.02 | | | | | (43), (44), (45), (46), (47), (48), (49), (53), (56), (57), % 149.18/22.02 | | | | | (59), (60), (61), (62), (66), (67), (68), (69), (70), (72), % 149.18/22.02 | | | | | (73), (75), (77), (79), (86), (87), (89) are inconsistent % 149.18/22.02 | | | | | by sub-proof #222. % 149.18/22.02 | | | | | % 149.18/22.02 | | | | Case 2: % 149.18/22.02 | | | | | % 149.18/22.02 | | | | | (90) ~ (all_56_12 = e1) % 149.18/22.02 | | | | | % 149.18/22.02 | | | | | REDUCE: (20), (90) imply: % 149.18/22.02 | | | | | (91) ~ (all_10_1 = e1) % 149.18/22.02 | | | | | % 149.18/22.02 | | | | | REF_CLOSE: (2), (7), (12), (20), (28), (32), (58), (64), (71), (77), % 149.18/22.02 | | | | | (91) are inconsistent by sub-proof #212. % 149.18/22.02 | | | | | % 149.18/22.02 | | | | End of split % 149.18/22.02 | | | | % 149.18/22.02 | | | End of split % 149.18/22.02 | | | % 149.18/22.02 | | End of split % 149.18/22.02 | | % 149.18/22.02 | Case 2: % 149.18/22.02 | | % 149.18/22.02 | | (92) all_56_8 = e0 | all_56_11 = e0 % 149.18/22.02 | | % 149.18/22.02 | | REF_CLOSE: (17), (30), (57), (63), (92) are inconsistent by sub-proof #763. % 149.18/22.02 | | % 149.18/22.02 | End of split % 149.18/22.02 | % 149.18/22.02 End of proof % 149.18/22.02 % 149.18/22.02 Sub-proof #13 shows that the following formulas are inconsistent: % 149.18/22.02 ---------------------------------------------------------------- % 149.18/22.02 (1) all_58_31 = all_4_2 % 149.18/22.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/22.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/22.02 (3) all_58_28 = e0 % 149.18/22.02 (4) all_56_7 = all_52_6 % 149.18/22.02 (5) ~ (all_52_6 = all_6_2) % 149.18/22.02 (6) ~ (all_10_1 = e0) % 149.18/22.02 (7) op(e0, all_10_1) = e0 % 149.18/22.02 (8) ~ (all_52_6 = all_8_2) % 149.18/22.02 (9) all_56_4 = all_52_8 % 149.18/22.02 (10) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/22.02 (11) ~ (all_10_1 = all_4_2) % 149.18/22.02 (12) op(e0, e1) = all_52_11 % 149.18/22.02 (13) all_56_12 = all_10_1 % 149.18/22.02 (14) ~ (all_52_8 = all_6_2) % 149.18/22.02 (15) all_54_12 = all_10_1 % 149.18/22.02 (16) ~ (all_52_6 = e0) % 149.18/22.02 (17) all_56_4 = e2 % 149.18/22.02 (18) op(e0, e3) = all_10_1 % 149.18/22.02 (19) all_58_29 = all_8_2 % 149.18/22.02 (20) all_56_6 = all_52_2 % 149.18/22.02 (21) ~ (all_52_11 = e0) % 149.18/22.02 (22) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/22.02 (23) all_56_8 = all_6_2 % 149.18/22.02 (24) ~ (all_52_8 = e0) % 149.18/22.02 (25) all_58_30 = all_6_2 % 149.18/22.02 (26) all_56_11 = e0 % 149.18/22.02 (27) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.18/22.02 (28) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.18/22.02 (29) ~ (all_52_2 = all_10_1) % 149.18/22.02 % 149.18/22.02 Begin of proof % 149.18/22.02 | % 149.18/22.02 | COMBINE_EQS: (9), (17) imply: % 149.18/22.02 | (30) all_52_8 = e2 % 149.18/22.02 | % 149.18/22.02 | REDUCE: (14), (30) imply: % 149.18/22.02 | (31) ~ (all_6_2 = e2) % 149.18/22.02 | % 149.18/22.02 | SIMP: (31) implies: % 149.18/22.02 | (32) ~ (all_6_2 = e2) % 149.18/22.02 | % 149.18/22.02 | REDUCE: (24), (30) imply: % 149.18/22.02 | (33) ~ (e2 = e0) % 149.18/22.02 | % 149.18/22.02 | BETA: splitting (27) gives: % 149.18/22.02 | % 149.18/22.02 | Case 1: % 149.18/22.02 | | % 149.18/22.03 | | (34) all_56_6 = e2 % 149.18/22.03 | | % 149.18/22.03 | | REF_CLOSE: (2), (6), (7), (12), (13), (15), (18), (20), (21), (22), (28), % 149.18/22.03 | | (29), (34) are inconsistent by sub-proof #210. % 149.18/22.03 | | % 149.18/22.03 | Case 2: % 149.18/22.03 | | % 149.18/22.03 | | (35) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.18/22.03 | | % 149.18/22.03 | | BETA: splitting (35) gives: % 149.18/22.03 | | % 149.18/22.03 | | Case 1: % 149.18/22.03 | | | % 149.18/22.03 | | | (36) all_56_7 = e2 % 149.18/22.03 | | | % 149.18/22.03 | | | COMBINE_EQS: (4), (36) imply: % 149.18/22.03 | | | (37) all_52_6 = e2 % 149.18/22.03 | | | % 149.18/22.03 | | | SIMP: (37) implies: % 149.18/22.03 | | | (38) all_52_6 = e2 % 149.18/22.03 | | | % 149.18/22.03 | | | REDUCE: (8), (38) imply: % 149.18/22.03 | | | (39) ~ (all_8_2 = e2) % 149.18/22.03 | | | % 149.18/22.03 | | | SIMP: (39) implies: % 149.18/22.03 | | | (40) ~ (all_8_2 = e2) % 149.18/22.03 | | | % 149.18/22.03 | | | BETA: splitting (10) gives: % 149.18/22.03 | | | % 149.18/22.03 | | | Case 1: % 149.18/22.03 | | | | % 149.18/22.03 | | | | (41) all_58_28 = e2 % 149.18/22.03 | | | | % 149.18/22.03 | | | | REF_CLOSE: (3), (33), (41) are inconsistent by sub-proof #688. % 149.18/22.03 | | | | % 149.18/22.03 | | | Case 2: % 149.18/22.03 | | | | % 149.18/22.03 | | | | (42) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/22.03 | | | | % 149.18/22.03 | | | | BETA: splitting (42) gives: % 149.18/22.03 | | | | % 149.18/22.03 | | | | Case 1: % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | (43) all_58_29 = e2 % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | COMBINE_EQS: (19), (43) imply: % 149.18/22.03 | | | | | (44) all_8_2 = e2 % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | REDUCE: (40), (44) imply: % 149.18/22.03 | | | | | (45) $false % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | CLOSE: (45) is inconsistent. % 149.18/22.03 | | | | | % 149.18/22.03 | | | | Case 2: % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | (46) all_58_30 = e2 | all_58_31 = e2 % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | BETA: splitting (46) gives: % 149.18/22.03 | | | | | % 149.18/22.03 | | | | | Case 1: % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | (47) all_58_30 = e2 % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | COMBINE_EQS: (25), (47) imply: % 149.18/22.03 | | | | | | (48) all_6_2 = e2 % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | REDUCE: (32), (48) imply: % 149.18/22.03 | | | | | | (49) $false % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | CLOSE: (49) is inconsistent. % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | Case 2: % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | (50) all_58_31 = e2 % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | COMBINE_EQS: (1), (50) imply: % 149.18/22.03 | | | | | | (51) all_4_2 = e2 % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | REDUCE: (11), (51) imply: % 149.18/22.03 | | | | | | (52) ~ (all_10_1 = e2) % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | | REF_CLOSE: (2), (6), (7), (12), (13), (15), (18), (21), (22), (28), % 149.18/22.03 | | | | | | (52) are inconsistent by sub-proof #235. % 149.18/22.03 | | | | | | % 149.18/22.03 | | | | | End of split % 149.18/22.03 | | | | | % 149.18/22.03 | | | | End of split % 149.18/22.03 | | | | % 149.18/22.03 | | | End of split % 149.18/22.03 | | | % 149.18/22.03 | | Case 2: % 149.18/22.03 | | | % 149.18/22.03 | | | (53) all_56_8 = e2 | all_56_11 = e2 % 149.18/22.03 | | | % 149.18/22.03 | | | BETA: splitting (53) gives: % 149.18/22.03 | | | % 149.18/22.03 | | | Case 1: % 149.18/22.03 | | | | % 149.18/22.03 | | | | (54) all_56_8 = e2 % 149.18/22.03 | | | | % 149.18/22.03 | | | | REF_CLOSE: (23), (32), (54) are inconsistent by sub-proof #337. % 149.18/22.03 | | | | % 149.18/22.03 | | | Case 2: % 149.18/22.03 | | | | % 149.18/22.03 | | | | (55) all_56_11 = e2 % 149.18/22.03 | | | | % 149.18/22.03 | | | | COMBINE_EQS: (26), (55) imply: % 149.18/22.03 | | | | (56) e2 = e0 % 149.18/22.03 | | | | % 149.18/22.03 | | | | REDUCE: (33), (56) imply: % 149.18/22.03 | | | | (57) $false % 149.18/22.03 | | | | % 149.18/22.03 | | | | CLOSE: (57) is inconsistent. % 149.18/22.03 | | | | % 149.18/22.03 | | | End of split % 149.18/22.03 | | | % 149.18/22.03 | | End of split % 149.18/22.03 | | % 149.18/22.03 | End of split % 149.18/22.03 | % 149.18/22.03 End of proof % 149.18/22.03 % 149.18/22.03 Sub-proof #14 shows that the following formulas are inconsistent: % 149.18/22.03 ---------------------------------------------------------------- % 149.18/22.03 (1) all_58_31 = all_4_2 % 149.18/22.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/22.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/22.03 (3) all_58_28 = e0 % 149.18/22.03 (4) all_56_15 = all_4_2 % 149.18/22.03 (5) all_56_7 = all_52_6 % 149.18/22.03 (6) ~ (all_52_6 = all_6_2) % 149.18/22.03 (7) ~ (all_52_2 = e0) % 149.18/22.03 (8) ~ (all_10_1 = e0) % 149.18/22.03 (9) all_54_8 = all_52_2 % 149.18/22.03 (10) ~ (all_52_11 = all_10_1) % 149.18/22.03 (11) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 149.18/22.03 (12) all_58_15 = all_52_2 % 149.18/22.03 (13) all_58_26 = all_52_11 % 149.18/22.03 (14) op(e0, all_10_1) = e0 % 149.18/22.03 (15) ~ (all_52_8 = all_52_11) % 149.18/22.03 (16) ~ (all_52_11 = all_4_2) % 149.18/22.03 (17) all_58_6 = all_52_12 % 149.18/22.03 (18) ~ (all_52_6 = all_8_2) % 149.18/22.03 (19) all_56_4 = all_52_8 % 149.18/22.03 (20) ~ (all_52_4 = all_8_2) % 149.18/22.03 (21) all_54_3 = all_52_12 % 149.18/22.03 (22) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/22.03 (23) all_54_1 = all_52_4 % 149.18/22.03 (24) ~ (all_6_2 = e0) % 149.18/22.03 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.18/22.03 (26) ~ (all_52_4 = all_52_6) % 149.18/22.03 (27) ~ (all_10_1 = all_4_2) % 149.18/22.03 (28) all_58_13 = all_52_13 % 149.18/22.03 (29) op(e0, e1) = all_52_11 % 149.18/22.03 (30) all_56_12 = all_10_1 % 149.18/22.03 (31) all_58_11 = e0 % 149.18/22.03 (32) all_58_20 = e0 % 149.18/22.03 (33) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 149.18/22.03 (34) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 149.18/22.03 (35) ~ (all_52_12 = all_52_13) % 149.18/22.03 (36) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.18/22.03 (37) all_56_13 = e0 % 149.18/22.03 (38) all_56_0 = e0 % 149.18/22.03 (39) all_54_5 = all_8_2 % 149.18/22.03 (40) ~ (all_52_2 = all_6_2) % 149.18/22.03 (41) ~ (all_52_8 = all_52_12) % 149.18/22.03 (42) all_54_9 = all_52_6 % 149.18/22.03 (43) ~ (all_52_13 = all_4_2) % 149.18/22.03 (44) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 149.18/22.03 (45) ~ (all_52_13 = all_8_2) % 149.18/22.03 (46) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 149.18/22.03 (47) ~ (e3 = e1) % 149.18/22.03 (48) all_54_12 = all_10_1 % 149.18/22.03 (49) ~ (all_52_6 = e0) % 149.18/22.03 (50) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.18/22.03 (51) all_54_14 = all_52_11 % 149.18/22.03 (52) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 149.18/22.03 (53) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.18/22.03 (54) ~ (all_52_12 = e0) % 149.18/22.03 (55) all_58_2 = all_52_4 % 149.18/22.03 (56) all_56_11 = all_52_14 % 149.18/22.03 (57) all_56_1 = all_52_4 % 149.18/22.03 (58) ~ (all_52_13 = e0) % 149.18/22.03 (59) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.18/22.03 (60) all_58_24 = e0 % 149.18/22.03 (61) ~ (all_52_1 = all_10_1) % 149.18/22.03 (62) op(e0, e3) = all_10_1 % 149.18/22.03 (63) ~ (all_52_1 = all_8_2) % 149.18/22.03 (64) all_56_3 = all_8_2 % 149.18/22.03 (65) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 149.18/22.03 (66) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.18/22.03 (67) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.18/22.03 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.18/22.03 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.18/22.03 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.18/22.03 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.18/22.03 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.18/22.03 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.18/22.03 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.18/22.03 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.18/22.03 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.18/22.03 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.18/22.03 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.18/22.03 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.18/22.03 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.18/22.03 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/22.03 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.18/22.03 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.18/22.03 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.18/22.03 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.18/22.03 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.18/22.03 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.18/22.03 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.18/22.03 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.18/22.03 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.18/22.03 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.18/22.03 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.18/22.03 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.18/22.03 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.18/22.03 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.18/22.03 e0) % 149.18/22.03 (68) ~ (all_52_4 = all_52_8) % 149.18/22.03 (69) all_56_9 = all_52_12 % 149.18/22.03 (70) all_58_29 = all_8_2 % 149.18/22.03 (71) ~ (all_52_12 = all_52_14) % 149.18/22.03 (72) all_58_8 = all_52_1 % 149.18/22.03 (73) ~ (e2 = e1) % 149.18/22.03 (74) all_56_6 = all_52_2 % 149.18/22.03 (75) ~ (all_52_2 = all_52_6) % 149.18/22.03 (76) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 149.18/22.03 (77) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.18/22.03 (78) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.18/22.03 (79) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.18/22.03 (80) ~ (all_52_4 = e0) % 149.18/22.03 (81) ~ (all_52_11 = all_6_2) % 149.18/22.03 (82) ~ (e3 = e0) % 149.18/22.03 (83) all_56_2 = all_52_1 % 149.18/22.03 (84) ~ (all_52_11 = e0) % 149.18/22.03 (85) all_58_22 = all_10_1 % 149.18/22.03 (86) all_56_10 = all_52_13 % 149.18/22.03 (87) all_56_5 = e0 % 149.18/22.03 (88) all_56_14 = all_52_11 % 149.18/22.03 (89) all_58_28 = all_10_2 % 149.18/22.04 (90) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.18/22.04 (91) all_58_17 = all_52_6 % 149.18/22.04 (92) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.18/22.04 (93) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.18/22.04 (94) ~ (e2 = e0) % 149.18/22.04 (95) ~ (all_4_2 = e0) % 149.18/22.04 (96) all_56_0 = all_10_2 % 149.18/22.04 (97) ~ (all_52_1 = e0) % 149.18/22.04 (98) all_56_8 = all_6_2 % 149.18/22.04 (99) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.18/22.04 (100) ~ (all_52_1 = all_52_2) % 149.18/22.04 (101) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 149.18/22.04 (102) all_58_4 = all_52_8 % 149.18/22.04 (103) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.18/22.04 (104) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.18/22.04 (105) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.18/22.04 (106) ~ (all_52_8 = e0) % 149.18/22.04 (107) all_58_30 = all_6_2 % 149.18/22.04 (108) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.18/22.04 (109) all_56_11 = e0 % 149.18/22.04 (110) ~ (e3 = e2) % 149.18/22.04 (111) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.18/22.04 (112) all_56_4 = e1 % 149.18/22.04 (113) ~ (all_8_2 = e0) % 149.18/22.04 (114) ~ (all_52_4 = all_52_12) % 149.18/22.04 (115) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.18/22.04 (116) ~ (all_52_2 = all_10_1) % 149.18/22.04 (117) all_54_4 = all_52_1 % 149.18/22.04 % 149.18/22.04 Begin of proof % 149.18/22.04 | % 149.18/22.04 | COMBINE_EQS: (19), (112) imply: % 149.18/22.04 | (118) all_52_8 = e1 % 149.18/22.04 | % 149.18/22.04 | REDUCE: (68), (118) imply: % 149.18/22.04 | (119) ~ (all_52_4 = e1) % 149.18/22.04 | % 149.18/22.04 | REDUCE: (15), (118) imply: % 149.18/22.04 | (120) ~ (all_52_11 = e1) % 149.18/22.04 | % 149.18/22.04 | SIMP: (120) implies: % 149.18/22.04 | (121) ~ (all_52_11 = e1) % 149.18/22.04 | % 149.18/22.04 | REDUCE: (41), (118) imply: % 149.18/22.04 | (122) ~ (all_52_12 = e1) % 149.18/22.04 | % 149.18/22.04 | SIMP: (122) implies: % 149.18/22.04 | (123) ~ (all_52_12 = e1) % 149.18/22.04 | % 149.18/22.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 149.18/22.04 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 149.18/22.04 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 149.18/22.04 | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 149.18/22.04 | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 149.18/22.04 | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 149.18/22.04 | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), % 149.18/22.04 | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), % 149.18/22.04 | (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), % 149.18/22.04 | (101), (102), (103), (104), (105), (106), (107), (108), (109), % 149.18/22.04 | (110), (111), (113), (114), (115), (116), (117), (118), (119), % 149.18/22.04 | (121), (123) are inconsistent by sub-proof #15. % 149.18/22.04 | % 149.18/22.04 End of proof % 149.18/22.04 % 149.18/22.04 Sub-proof #15 shows that the following formulas are inconsistent: % 149.18/22.04 ---------------------------------------------------------------- % 149.18/22.04 (1) all_58_31 = all_4_2 % 149.18/22.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.18/22.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.18/22.04 (3) all_58_28 = e0 % 149.18/22.04 (4) all_56_15 = all_4_2 % 149.18/22.04 (5) all_56_7 = all_52_6 % 149.18/22.04 (6) ~ (all_52_6 = all_6_2) % 149.18/22.04 (7) ~ (all_52_2 = e0) % 149.18/22.04 (8) ~ (all_10_1 = e0) % 149.18/22.04 (9) all_54_8 = all_52_2 % 149.18/22.04 (10) ~ (all_52_11 = all_10_1) % 149.18/22.04 (11) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 149.18/22.04 (12) all_58_15 = all_52_2 % 149.18/22.04 (13) all_58_26 = all_52_11 % 149.18/22.04 (14) op(e0, all_10_1) = e0 % 149.18/22.04 (15) ~ (all_52_8 = all_52_11) % 149.18/22.04 (16) ~ (all_52_11 = all_4_2) % 149.18/22.04 (17) all_58_6 = all_52_12 % 149.18/22.04 (18) ~ (all_52_6 = all_8_2) % 149.18/22.04 (19) all_56_4 = all_52_8 % 149.18/22.04 (20) ~ (all_52_4 = all_8_2) % 149.18/22.04 (21) all_54_3 = all_52_12 % 149.18/22.04 (22) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.18/22.04 (23) all_54_1 = all_52_4 % 149.18/22.04 (24) ~ (all_6_2 = e0) % 149.18/22.04 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.18/22.04 (26) ~ (all_52_4 = all_52_6) % 149.18/22.04 (27) ~ (all_10_1 = all_4_2) % 149.18/22.04 (28) all_58_13 = all_52_13 % 149.18/22.04 (29) op(e0, e1) = all_52_11 % 149.18/22.04 (30) all_56_12 = all_10_1 % 149.18/22.04 (31) all_58_11 = e0 % 149.18/22.04 (32) all_58_20 = e0 % 149.18/22.04 (33) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 149.18/22.04 (34) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 149.18/22.04 (35) ~ (all_52_12 = all_52_13) % 149.18/22.04 (36) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.18/22.04 (37) all_56_13 = e0 % 149.18/22.04 (38) all_56_0 = e0 % 149.18/22.04 (39) all_54_5 = all_8_2 % 149.18/22.04 (40) ~ (all_52_2 = all_6_2) % 149.18/22.04 (41) ~ (all_52_8 = all_52_12) % 149.18/22.04 (42) all_54_9 = all_52_6 % 149.18/22.04 (43) ~ (all_52_13 = all_4_2) % 149.18/22.04 (44) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 149.18/22.04 (45) ~ (all_52_13 = all_8_2) % 149.18/22.04 (46) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 149.18/22.04 (47) ~ (e3 = e1) % 149.18/22.04 (48) all_54_12 = all_10_1 % 149.18/22.04 (49) ~ (all_52_6 = e0) % 149.73/22.04 (50) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.73/22.04 (51) all_54_14 = all_52_11 % 149.73/22.04 (52) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 149.73/22.04 (53) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 149.73/22.04 (54) ~ (all_52_12 = e0) % 149.73/22.04 (55) all_58_2 = all_52_4 % 149.73/22.04 (56) all_56_11 = all_52_14 % 149.73/22.04 (57) all_56_1 = all_52_4 % 149.73/22.04 (58) ~ (all_52_13 = e0) % 149.73/22.04 (59) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.73/22.04 (60) all_58_24 = e0 % 149.73/22.04 (61) ~ (all_52_1 = all_10_1) % 149.73/22.04 (62) op(e0, e3) = all_10_1 % 149.73/22.04 (63) ~ (all_52_1 = all_8_2) % 149.73/22.04 (64) all_56_3 = all_8_2 % 149.73/22.04 (65) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 149.73/22.04 (66) ~ (all_52_11 = e1) % 149.73/22.04 (67) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.73/22.04 (68) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.73/22.04 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.73/22.04 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.73/22.04 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.73/22.04 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.73/22.04 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.73/22.04 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.73/22.04 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.73/22.04 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.73/22.04 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.73/22.04 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.04 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.73/22.04 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.04 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.04 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.04 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.04 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.04 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.73/22.04 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.04 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.73/22.04 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.04 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.73/22.04 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.04 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.04 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.73/22.04 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.73/22.04 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.73/22.04 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.73/22.04 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.04 e0) % 149.73/22.04 (69) ~ (all_52_4 = all_52_8) % 149.73/22.04 (70) all_56_9 = all_52_12 % 149.73/22.04 (71) all_58_29 = all_8_2 % 149.73/22.04 (72) ~ (all_52_12 = all_52_14) % 149.73/22.04 (73) ~ (all_52_4 = e1) % 149.73/22.05 (74) all_58_8 = all_52_1 % 149.73/22.05 (75) ~ (e2 = e1) % 149.73/22.05 (76) all_56_6 = all_52_2 % 149.73/22.05 (77) ~ (all_52_2 = all_52_6) % 149.73/22.05 (78) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 149.73/22.05 (79) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.73/22.05 (80) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.73/22.05 (81) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.73/22.05 (82) ~ (all_52_4 = e0) % 149.73/22.05 (83) ~ (all_52_11 = all_6_2) % 149.73/22.05 (84) ~ (e3 = e0) % 149.73/22.05 (85) all_56_2 = all_52_1 % 149.73/22.05 (86) ~ (all_52_11 = e0) % 149.73/22.05 (87) all_58_22 = all_10_1 % 149.73/22.05 (88) all_56_10 = all_52_13 % 149.73/22.05 (89) all_56_5 = e0 % 149.73/22.05 (90) ~ (all_52_12 = e1) % 149.73/22.05 (91) all_56_14 = all_52_11 % 149.73/22.05 (92) all_58_28 = all_10_2 % 149.73/22.05 (93) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 149.73/22.05 (94) all_52_8 = e1 % 149.73/22.05 (95) all_58_17 = all_52_6 % 149.73/22.05 (96) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.73/22.05 (97) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.73/22.05 (98) ~ (e2 = e0) % 149.73/22.05 (99) ~ (all_4_2 = e0) % 149.73/22.05 (100) all_56_0 = all_10_2 % 149.73/22.05 (101) ~ (all_52_1 = e0) % 149.73/22.05 (102) all_56_8 = all_6_2 % 149.73/22.05 (103) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.73/22.05 (104) ~ (all_52_1 = all_52_2) % 149.73/22.05 (105) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 149.73/22.05 (106) all_58_4 = all_52_8 % 149.73/22.05 (107) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.05 (108) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.73/22.05 (109) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.73/22.05 (110) ~ (all_52_8 = e0) % 149.73/22.05 (111) all_58_30 = all_6_2 % 149.73/22.05 (112) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.73/22.05 (113) all_56_11 = e0 % 149.73/22.05 (114) ~ (e3 = e2) % 149.73/22.05 (115) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 149.73/22.05 (116) ~ (all_8_2 = e0) % 149.73/22.05 (117) ~ (all_52_4 = all_52_12) % 149.73/22.05 (118) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.73/22.05 (119) ~ (all_52_2 = all_10_1) % 149.73/22.05 (120) all_54_4 = all_52_1 % 149.73/22.05 % 149.73/22.05 Begin of proof % 149.73/22.05 | % 149.73/22.05 | REDUCE: (94), (110) imply: % 149.73/22.05 | (121) ~ (e1 = e0) % 149.73/22.05 | % 149.73/22.05 | BETA: splitting (96) gives: % 149.73/22.05 | % 149.73/22.05 | Case 1: % 149.73/22.05 | | % 149.73/22.05 | | (122) all_56_6 = e1 % 149.73/22.05 | | % 149.73/22.05 | | COMBINE_EQS: (76), (122) imply: % 149.73/22.05 | | (123) all_52_2 = e1 % 149.73/22.05 | | % 149.73/22.05 | | SIMP: (123) implies: % 149.73/22.05 | | (124) all_52_2 = e1 % 149.73/22.05 | | % 149.73/22.05 | | COMBINE_EQS: (12), (124) imply: % 149.73/22.05 | | (125) all_58_15 = e1 % 149.73/22.05 | | % 149.73/22.05 | | REDUCE: (77), (124) imply: % 149.73/22.05 | | (126) ~ (all_52_6 = e1) % 149.73/22.05 | | % 149.73/22.05 | | SIMP: (126) implies: % 149.73/22.05 | | (127) ~ (all_52_6 = e1) % 149.73/22.05 | | % 149.73/22.05 | | REDUCE: (119), (124) imply: % 149.73/22.05 | | (128) ~ (all_10_1 = e1) % 149.73/22.05 | | % 149.73/22.05 | | SIMP: (128) implies: % 149.73/22.05 | | (129) ~ (all_10_1 = e1) % 149.73/22.05 | | % 149.73/22.05 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (13), (17), (18), (19), % 149.73/22.05 | | (20), (21), (22), (23), (24), (26), (28), (30), (31), (32), (33), % 149.73/22.05 | | (34), (35), (37), (38), (42), (44), (45), (46), (47), (49), (51), % 149.73/22.05 | | (52), (54), (55), (56), (57), (58), (59), (60), (61), (63), (64), % 149.73/22.05 | | (65), (66), (67), (68), (70), (71), (72), (73), (74), (75), (78), % 149.73/22.05 | | (79), (80), (82), (83), (84), (85), (86), (87), (88), (90), (91), % 149.73/22.05 | | (92), (93), (95), (97), (98), (100), (102), (103), (105), (107), % 149.73/22.05 | | (110), (111), (112), (113), (114), (116), (117), (120), (121), % 149.73/22.05 | | (125), (127), (129) are inconsistent by sub-proof #66. % 149.73/22.05 | | % 149.73/22.05 | Case 2: % 149.73/22.05 | | % 149.73/22.05 | | (130) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.73/22.05 | | % 149.73/22.05 | | BETA: splitting (130) gives: % 149.73/22.05 | | % 149.73/22.05 | | Case 1: % 149.73/22.05 | | | % 149.73/22.05 | | | (131) all_56_7 = e1 % 149.73/22.05 | | | % 149.73/22.05 | | | COMBINE_EQS: (5), (131) imply: % 149.73/22.05 | | | (132) all_52_6 = e1 % 149.73/22.05 | | | % 149.73/22.05 | | | SIMP: (132) implies: % 149.73/22.05 | | | (133) all_52_6 = e1 % 149.73/22.05 | | | % 149.73/22.05 | | | REDUCE: (18), (133) imply: % 149.73/22.05 | | | (134) ~ (all_8_2 = e1) % 149.73/22.05 | | | % 149.73/22.05 | | | SIMP: (134) implies: % 149.73/22.05 | | | (135) ~ (all_8_2 = e1) % 149.73/22.05 | | | % 149.73/22.05 | | | REDUCE: (6), (133) imply: % 149.73/22.05 | | | (136) ~ (all_6_2 = e1) % 149.73/22.05 | | | % 149.73/22.05 | | | SIMP: (136) implies: % 149.73/22.05 | | | (137) ~ (all_6_2 = e1) % 149.73/22.05 | | | % 149.73/22.05 | | | BETA: splitting (112) gives: % 149.73/22.05 | | | % 149.73/22.05 | | | Case 1: % 149.73/22.05 | | | | % 149.73/22.05 | | | | (138) all_58_28 = e1 % 149.73/22.05 | | | | % 149.73/22.05 | | | | REF_CLOSE: (3), (121), (138) are inconsistent by sub-proof #690. % 149.73/22.05 | | | | % 149.73/22.05 | | | Case 2: % 149.73/22.05 | | | | % 149.73/22.05 | | | | (139) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.73/22.05 | | | | % 149.73/22.05 | | | | BETA: splitting (139) gives: % 149.73/22.05 | | | | % 149.73/22.05 | | | | Case 1: % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | (140) all_58_29 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | COMBINE_EQS: (71), (140) imply: % 149.73/22.05 | | | | | (141) all_8_2 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | REDUCE: (135), (141) imply: % 149.73/22.05 | | | | | (142) $false % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | CLOSE: (142) is inconsistent. % 149.73/22.05 | | | | | % 149.73/22.05 | | | | Case 2: % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | (143) all_58_30 = e1 | all_58_31 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | BETA: splitting (143) gives: % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | Case 1: % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | (144) all_58_30 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | COMBINE_EQS: (111), (144) imply: % 149.73/22.05 | | | | | | (145) all_6_2 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | REDUCE: (137), (145) imply: % 149.73/22.05 | | | | | | (146) $false % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | CLOSE: (146) is inconsistent. % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | Case 2: % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | (147) all_58_31 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | COMBINE_EQS: (1), (147) imply: % 149.73/22.05 | | | | | | (148) all_4_2 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | COMBINE_EQS: (4), (148) imply: % 149.73/22.05 | | | | | | (149) all_56_15 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | REDUCE: (43), (148) imply: % 149.73/22.05 | | | | | | (150) ~ (all_52_13 = e1) % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | REDUCE: (27), (148) imply: % 149.73/22.05 | | | | | | (151) ~ (all_10_1 = e1) % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), % 149.73/22.05 | | | | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), % 149.73/22.05 | | | | | | (24), (25), (26), (28), (29), (30), (31), (32), (33), % 149.73/22.05 | | | | | | (35), (36), (37), (39), (40), (41), (45), (47), (48), % 149.73/22.05 | | | | | | (49), (50), (51), (52), (53), (55), (56), (57), (60), % 149.73/22.05 | | | | | | (61), (62), (63), (64), (65), (66), (67), (68), (69), % 149.73/22.05 | | | | | | (70), (71), (72), (74), (75), (76), (77), (78), (79), % 149.73/22.05 | | | | | | (80), (82), (83), (84), (85), (86), (87), (88), (89), % 149.73/22.05 | | | | | | (91), (92), (93), (95), (96), (97), (98), (100), (101), % 149.73/22.05 | | | | | | (102), (103), (104), (105), (106), (107), (108), (109), % 149.73/22.05 | | | | | | (110), (111), (112), (113), (114), (115), (117), (118), % 149.73/22.05 | | | | | | (119), (121), (147), (149), (150), (151) are inconsistent % 149.73/22.05 | | | | | | by sub-proof #193. % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | End of split % 149.73/22.05 | | | | | % 149.73/22.05 | | | | End of split % 149.73/22.05 | | | | % 149.73/22.05 | | | End of split % 149.73/22.05 | | | % 149.73/22.05 | | Case 2: % 149.73/22.05 | | | % 149.73/22.05 | | | (152) ~ (all_56_7 = e1) % 149.73/22.05 | | | (153) all_56_8 = e1 | all_56_11 = e1 % 149.73/22.05 | | | % 149.73/22.05 | | | REDUCE: (5), (152) imply: % 149.73/22.05 | | | (154) ~ (all_52_6 = e1) % 149.73/22.05 | | | % 149.73/22.05 | | | BETA: splitting (79) gives: % 149.73/22.05 | | | % 149.73/22.05 | | | Case 1: % 149.73/22.05 | | | | % 149.73/22.05 | | | | (155) all_56_1 = e1 % 149.73/22.05 | | | | % 149.73/22.05 | | | | COMBINE_EQS: (57), (155) imply: % 149.73/22.05 | | | | (156) all_52_4 = e1 % 149.73/22.05 | | | | % 149.73/22.05 | | | | REDUCE: (73), (156) imply: % 149.73/22.05 | | | | (157) $false % 149.73/22.05 | | | | % 149.73/22.05 | | | | CLOSE: (157) is inconsistent. % 149.73/22.05 | | | | % 149.73/22.05 | | | Case 2: % 149.73/22.05 | | | | % 149.73/22.05 | | | | (158) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.73/22.05 | | | | % 149.73/22.05 | | | | BETA: splitting (158) gives: % 149.73/22.05 | | | | % 149.73/22.05 | | | | Case 1: % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | (159) all_56_3 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | COMBINE_EQS: (64), (159) imply: % 149.73/22.05 | | | | | (160) all_8_2 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | COMBINE_EQS: (71), (160) imply: % 149.73/22.05 | | | | | (161) all_58_29 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | REDUCE: (45), (160) imply: % 149.73/22.05 | | | | | (162) ~ (all_52_13 = e1) % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | BETA: splitting (81) gives: % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | Case 1: % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | (163) all_56_9 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | REF_CLOSE: (70), (90), (163) are inconsistent by sub-proof #486. % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | Case 2: % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | (164) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | BETA: splitting (164) gives: % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | | Case 1: % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | | (165) all_56_10 = e1 % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | | REF_CLOSE: (88), (162), (165) are inconsistent by sub-proof #606. % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | Case 2: % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | | (166) all_56_11 = e1 | all_56_15 = e1 % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | | BETA: splitting (166) gives: % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | | Case 1: % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | | (167) all_56_11 = e1 % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | | COMBINE_EQS: (113), (167) imply: % 149.73/22.05 | | | | | | | | (168) e1 = e0 % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | | COMBINE_EQS: (161), (168) imply: % 149.73/22.05 | | | | | | | | (169) all_58_29 = e0 % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | | REF_CLOSE: (5), (19), (22), (24), (47), (49), (52), (56), (57), % 149.73/22.05 | | | | | | | | (70), (72), (75), (82), (84), (92), (93), (98), % 149.73/22.05 | | | | | | | | (100), (102), (107), (110), (111), (112), (114), % 149.73/22.05 | | | | | | | | (121), (169) are inconsistent by sub-proof #481. % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | Case 2: % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | | (170) all_56_15 = e1 % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | | REF_CLOSE: (1), (3), (4), (22), (47), (71), (75), (84), (98), % 149.73/22.05 | | | | | | | | (102), (107), (111), (113), (114), (121), (153), % 149.73/22.05 | | | | | | | | (170) are inconsistent by sub-proof #65. % 149.73/22.05 | | | | | | | | % 149.73/22.05 | | | | | | | End of split % 149.73/22.05 | | | | | | | % 149.73/22.05 | | | | | | End of split % 149.73/22.05 | | | | | | % 149.73/22.05 | | | | | End of split % 149.73/22.05 | | | | | % 149.73/22.05 | | | | Case 2: % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | (171) all_56_7 = e1 | all_56_13 = e1 % 149.73/22.05 | | | | | % 149.73/22.05 | | | | | REF_CLOSE: (5), (37), (121), (154), (171) are inconsistent by % 149.73/22.05 | | | | | sub-proof #529. % 149.73/22.05 | | | | | % 149.73/22.05 | | | | End of split % 149.73/22.05 | | | | % 149.73/22.05 | | | End of split % 149.73/22.05 | | | % 149.73/22.05 | | End of split % 149.73/22.05 | | % 149.73/22.05 | End of split % 149.73/22.05 | % 149.73/22.05 End of proof % 149.73/22.05 % 149.73/22.05 Sub-proof #16 shows that the following formulas are inconsistent: % 149.73/22.05 ---------------------------------------------------------------- % 149.73/22.05 (1) all_58_31 = all_4_2 % 149.73/22.05 (2) ~ (all_52_8 = all_52_9) % 149.73/22.05 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.73/22.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.73/22.06 (4) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 149.73/22.06 (5) all_58_11 = all_52_9 % 149.73/22.06 (6) all_54_2 = all_52_8 % 149.73/22.06 (7) ~ (all_52_8 = all_10_2) % 149.73/22.06 (8) all_58_26 = all_52_11 % 149.73/22.06 (9) all_56_3 = e0 % 149.73/22.06 (10) all_58_24 = all_8_1 % 149.73/22.06 (11) all_58_6 = all_52_12 % 149.73/22.06 (12) all_56_4 = all_52_8 % 149.73/22.06 (13) all_56_6 = e0 % 149.73/22.06 (14) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.06 (15) all_58_13 = all_52_13 % 149.73/22.06 (16) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 149.73/22.06 (17) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.73/22.06 (18) all_56_13 = all_8_1 % 149.73/22.06 (19) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 149.73/22.06 (20) all_58_20 = all_52_14 % 149.73/22.06 (21) ~ (all_52_8 = all_6_2) % 149.73/22.06 (22) op(e2, e3) = all_52_1 % 149.73/22.06 (23) ~ (all_52_12 = all_52_13) % 149.73/22.06 (24) all_54_6 = all_52_9 % 149.73/22.06 (25) op(e3, e3) = all_10_2 % 149.73/22.06 (26) ~ (all_52_8 = all_52_12) % 149.73/22.06 (27) ~ (all_52_13 = all_4_2) % 149.73/22.06 (28) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 149.73/22.06 (29) ~ (all_52_3 = e0) % 149.73/22.06 (30) ~ (e3 = e1) % 149.73/22.06 (31) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.73/22.06 (32) ~ (all_52_1 = all_52_13) % 149.73/22.06 (33) all_56_5 = all_52_9 % 149.73/22.06 (34) all_56_12 = all_52_3 % 149.73/22.06 (35) all_58_2 = all_52_4 % 149.73/22.06 (36) all_20_2 = all_4_2 % 149.73/22.06 (37) all_56_11 = all_52_14 % 149.73/22.06 (38) all_56_1 = all_52_4 % 149.73/22.06 (39) ~ (all_52_13 = e0) % 149.73/22.06 (40) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.73/22.06 (41) ~ (all_52_3 = all_4_2) % 149.73/22.06 (42) ~ (all_52_4 = all_8_1) % 149.73/22.06 (43) ~ (all_52_9 = all_52_11) % 149.73/22.06 (44) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.73/22.06 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.73/22.06 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.73/22.06 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.73/22.06 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.73/22.06 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.73/22.06 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.73/22.06 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.73/22.06 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.73/22.06 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.73/22.06 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.06 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.73/22.06 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.06 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.06 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.06 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.06 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.06 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.73/22.06 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.06 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.73/22.06 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.06 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.73/22.06 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.06 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.06 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.73/22.06 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.73/22.06 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.73/22.06 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.73/22.06 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.06 e0) % 149.73/22.06 (45) ~ (all_52_4 = all_52_8) % 149.73/22.06 (46) all_58_29 = e0 % 149.73/22.06 (47) all_56_9 = all_52_12 % 149.73/22.06 (48) ~ (all_52_12 = all_52_14) % 149.73/22.06 (49) all_58_8 = all_52_1 % 149.73/22.06 (50) ~ (e2 = e1) % 149.73/22.06 (51) all_58_15 = e0 % 149.73/22.06 (52) ~ (all_52_9 = all_52_13) % 149.73/22.06 (53) op(all_10_2, e3) = e0 % 149.73/22.06 (54) ~ (all_52_11 = all_6_2) % 149.73/22.06 (55) op(e3, all_10_2) = all_58_0 % 149.73/22.06 (56) ~ (e3 = e0) % 149.73/22.06 (57) all_56_2 = all_52_1 % 149.73/22.06 (58) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 149.73/22.06 (59) all_56_10 = all_52_13 % 149.73/22.06 (60) ~ (all_52_1 = all_52_3) % 149.73/22.06 (61) all_56_14 = all_52_11 % 149.73/22.06 (62) all_58_28 = all_10_2 % 149.73/22.06 (63) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 149.73/22.06 (64) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.73/22.06 (65) ~ (e2 = e0) % 149.73/22.06 (66) ~ (all_52_9 = all_6_2) % 149.73/22.06 (67) all_56_0 = all_10_2 % 149.73/22.06 (68) ~ (all_52_1 = e0) % 149.73/22.06 (69) ~ (all_52_3 = all_52_11) % 149.73/22.06 (70) all_58_22 = all_52_3 % 149.73/22.06 (71) ~ (all_52_3 = all_10_2) % 149.73/22.06 (72) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.73/22.06 (73) all_58_4 = all_52_8 % 149.73/22.06 (74) ~ (all_8_1 = e0) % 149.73/22.06 (75) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.06 (76) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.73/22.06 (77) all_54_0 = all_10_2 % 149.73/22.06 (78) ~ (e1 = e0) % 149.73/22.06 (79) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 149.73/22.06 (80) ~ (all_52_14 = e0) % 149.73/22.06 (81) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 149.73/22.06 (82) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.73/22.06 (83) ~ (all_52_4 = all_10_2) % 149.73/22.06 (84) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 149.73/22.06 (85) all_58_30 = all_6_2 % 149.73/22.06 (86) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.73/22.06 (87) ~ (e3 = e2) % 149.73/22.06 (88) ~ (all_52_4 = all_52_12) % 149.73/22.06 (89) all_54_12 = all_52_3 % 149.73/22.06 (90) ~ (all_52_1 = all_10_2) % 149.73/22.06 % 149.73/22.06 Begin of proof % 149.73/22.06 | % 149.73/22.06 | BETA: splitting (84) gives: % 149.73/22.06 | % 149.73/22.06 | Case 1: % 149.73/22.06 | | % 149.73/22.06 | | (91) all_56_12 = e0 % 149.73/22.06 | | % 149.73/22.06 | | REF_CLOSE: (29), (34), (91) are inconsistent by sub-proof #607. % 149.73/22.06 | | % 149.73/22.06 | Case 2: % 149.73/22.06 | | % 149.73/22.06 | | (92) all_56_13 = e0 | all_56_14 = e0 % 149.73/22.06 | | % 149.73/22.06 | | BETA: splitting (92) gives: % 149.73/22.06 | | % 149.73/22.06 | | Case 1: % 149.73/22.06 | | | % 149.73/22.06 | | | (93) all_56_13 = e0 % 149.73/22.06 | | | % 149.73/22.06 | | | REF_CLOSE: (18), (74), (93) are inconsistent by sub-proof #269. % 149.73/22.06 | | | % 149.73/22.06 | | Case 2: % 149.73/22.06 | | | % 149.73/22.06 | | | (94) all_56_14 = e0 % 149.73/22.06 | | | % 149.73/22.06 | | | COMBINE_EQS: (61), (94) imply: % 149.73/22.06 | | | (95) all_52_11 = e0 % 149.73/22.06 | | | % 149.73/22.06 | | | SIMP: (95) implies: % 149.73/22.06 | | | (96) all_52_11 = e0 % 149.73/22.06 | | | % 149.73/22.06 | | | COMBINE_EQS: (8), (96) imply: % 149.73/22.06 | | | (97) all_58_26 = e0 % 149.73/22.06 | | | % 149.73/22.06 | | | REDUCE: (43), (96) imply: % 149.73/22.06 | | | (98) ~ (all_52_9 = e0) % 149.73/22.06 | | | % 149.73/22.06 | | | REDUCE: (54), (96) imply: % 149.73/22.06 | | | (99) ~ (all_6_2 = e0) % 149.73/22.06 | | | % 149.73/22.06 | | | SIMP: (99) implies: % 149.73/22.06 | | | (100) ~ (all_6_2 = e0) % 149.73/22.06 | | | % 149.73/22.06 | | | BETA: splitting (4) gives: % 149.73/22.06 | | | % 149.73/22.06 | | | Case 1: % 149.73/22.06 | | | | % 149.73/22.06 | | | | (101) all_56_9 = e0 % 149.73/22.06 | | | | % 149.73/22.06 | | | | COMBINE_EQS: (47), (101) imply: % 149.73/22.06 | | | | (102) all_52_12 = e0 % 149.73/22.06 | | | | % 149.73/22.06 | | | | COMBINE_EQS: (11), (102) imply: % 149.73/22.06 | | | | (103) all_58_6 = e0 % 149.73/22.06 | | | | % 149.73/22.06 | | | | REDUCE: (88), (102) imply: % 149.73/22.06 | | | | (104) ~ (all_52_4 = e0) % 149.73/22.06 | | | | % 149.73/22.06 | | | | REDUCE: (26), (102) imply: % 149.73/22.06 | | | | (105) ~ (all_52_8 = e0) % 149.73/22.06 | | | | % 149.73/22.06 | | | | REDUCE: (23), (102) imply: % 149.73/22.06 | | | | (106) ~ (all_52_13 = e0) % 149.73/22.06 | | | | % 149.73/22.06 | | | | REDUCE: (48), (102) imply: % 149.73/22.06 | | | | (107) ~ (all_52_14 = e0) % 149.73/22.06 | | | | % 149.73/22.06 | | | | BETA: splitting (82) gives: % 149.73/22.06 | | | | % 149.73/22.06 | | | | Case 1: % 149.73/22.06 | | | | | % 149.73/22.06 | | | | | (108) all_54_6 = e0 % 149.73/22.06 | | | | | % 149.73/22.06 | | | | | REF_CLOSE: (24), (98), (108) are inconsistent by sub-proof #797. % 149.73/22.06 | | | | | % 149.73/22.06 | | | | Case 2: % 149.73/22.06 | | | | | % 149.73/22.06 | | | | | (109) ~ (all_54_6 = e0) % 149.73/22.06 | | | | | (110) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 149.73/22.06 | | | | | % 149.73/22.06 | | | | | BETA: splitting (31) gives: % 149.73/22.06 | | | | | % 149.73/22.06 | | | | | Case 1: % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | | (111) all_54_0 = e0 % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (62), (65), (75), (77), % 149.73/22.06 | | | | | | (78), (85), (86), (87), (111) are inconsistent by % 149.73/22.06 | | | | | | sub-proof #395. % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | Case 2: % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | | (112) ~ (all_54_0 = e0) % 149.73/22.06 | | | | | | (113) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | | REDUCE: (77), (112) imply: % 149.73/22.06 | | | | | | (114) ~ (all_10_2 = e0) % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | | BETA: splitting (81) gives: % 149.73/22.06 | | | | | | % 149.73/22.06 | | | | | | Case 1: % 149.73/22.06 | | | | | | | % 149.73/22.06 | | | | | | | (115) all_54_2 = e0 % 149.73/22.06 | | | | | | | % 149.73/22.06 | | | | | | | REF_CLOSE: (6), (105), (115) are inconsistent by sub-proof #860. % 149.73/22.06 | | | | | | | % 149.73/22.06 | | | | | | Case 2: % 149.73/22.06 | | | | | | | % 149.73/22.06 | | | | | | | (116) ~ (all_54_2 = e0) % 149.73/22.06 | | | | | | | (117) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 149.73/22.06 | | | | | | | % 149.73/22.06 | | | | | | | BETA: splitting (58) gives: % 149.73/22.06 | | | | | | | % 149.73/22.06 | | | | | | | Case 1: % 149.73/22.06 | | | | | | | | % 149.73/22.06 | | | | | | | | (118) all_54_12 = e0 % 149.73/22.06 | | | | | | | | % 149.73/22.06 | | | | | | | | REF_CLOSE: (29), (89), (118) are inconsistent by sub-proof #762. % 149.73/22.06 | | | | | | | | % 149.73/22.07 | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | % 149.73/22.07 | | | | | | | | (119) ~ (all_54_12 = e0) % 149.73/22.07 | | | | | | | | (120) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 149.73/22.07 | | | | | | | | % 149.73/22.07 | | | | | | | | BETA: splitting (28) gives: % 149.73/22.07 | | | | | | | | % 149.73/22.07 | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | (121) all_56_2 = e2 % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | COMBINE_EQS: (57), (121) imply: % 149.73/22.07 | | | | | | | | | (122) all_52_1 = e2 % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | COMBINE_EQS: (49), (122) imply: % 149.73/22.07 | | | | | | | | | (123) all_58_8 = e2 % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | REDUCE: (60), (122) imply: % 149.73/22.07 | | | | | | | | | (124) ~ (all_52_3 = e2) % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | SIMP: (124) implies: % 149.73/22.07 | | | | | | | | | (125) ~ (all_52_3 = e2) % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | REDUCE: (32), (122) imply: % 149.73/22.07 | | | | | | | | | (126) ~ (all_52_13 = e2) % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | SIMP: (126) implies: % 149.73/22.07 | | | | | | | | | (127) ~ (all_52_13 = e2) % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | REDUCE: (90), (122) imply: % 149.73/22.07 | | | | | | | | | (128) ~ (all_10_2 = e2) % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | SIMP: (128) implies: % 149.73/22.07 | | | | | | | | | (129) ~ (all_10_2 = e2) % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | BETA: splitting (17) gives: % 149.73/22.07 | | | | | | | | | % 149.73/22.07 | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | (130) all_56_0 = e1 % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | COMBINE_EQS: (67), (130) imply: % 149.73/22.07 | | | | | | | | | | (131) all_10_2 = e1 % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | COMBINE_EQS: (62), (131) imply: % 149.73/22.07 | | | | | | | | | | (132) all_58_28 = e1 % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | REDUCE: (83), (131) imply: % 149.73/22.07 | | | | | | | | | | (133) ~ (all_52_4 = e1) % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | REDUCE: (7), (131) imply: % 149.73/22.07 | | | | | | | | | | (134) ~ (all_52_8 = e1) % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | BETA: splitting (40) gives: % 149.73/22.07 | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | (135) all_56_0 = e3 % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | REF_CLOSE: (30), (130), (135) are inconsistent by sub-proof % 149.73/22.07 | | | | | | | | | | | #569. % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | (136) ~ (all_56_0 = e3) % 149.73/22.07 | | | | | | | | | | | (137) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | REDUCE: (130), (136) imply: % 149.73/22.07 | | | | | | | | | | | (138) ~ (e3 = e1) % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | BETA: splitting (120) gives: % 149.73/22.07 | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | (139) all_54_12 = e1 % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | COMBINE_EQS: (89), (139) imply: % 149.73/22.07 | | | | | | | | | | | | (140) all_52_3 = e1 % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | SIMP: (140) implies: % 149.73/22.07 | | | | | | | | | | | | (141) all_52_3 = e1 % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | COMBINE_EQS: (34), (141) imply: % 149.73/22.07 | | | | | | | | | | | | (142) all_56_12 = e1 % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | REF_CLOSE: (13), (30), (56), (87), (121), (137), (142) are % 149.73/22.07 | | | | | | | | | | | | inconsistent by sub-proof #837. % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | (143) ~ (all_54_12 = e1) % 149.73/22.07 | | | | | | | | | | | | (144) all_54_12 = e3 | all_54_12 = e2 % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | REDUCE: (89), (143) imply: % 149.73/22.07 | | | | | | | | | | | | (145) ~ (all_52_3 = e1) % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | BETA: splitting (144) gives: % 149.73/22.07 | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | (146) all_54_12 = e2 % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | REF_CLOSE: (89), (125), (146) are inconsistent by sub-proof % 149.73/22.07 | | | | | | | | | | | | | #749. % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | (147) all_54_12 = e3 % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | COMBINE_EQS: (89), (147) imply: % 149.73/22.07 | | | | | | | | | | | | | (148) all_52_3 = e3 % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | SIMP: (148) implies: % 149.73/22.07 | | | | | | | | | | | | | (149) all_52_3 = e3 % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | COMBINE_EQS: (34), (149) imply: % 149.73/22.07 | | | | | | | | | | | | | (150) all_56_12 = e3 % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | COMBINE_EQS: (70), (149) imply: % 149.73/22.07 | | | | | | | | | | | | | (151) all_58_22 = e3 % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | REDUCE: (41), (149) imply: % 149.73/22.07 | | | | | | | | | | | | | (152) ~ (all_4_2 = e3) % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | SIMP: (152) implies: % 149.73/22.07 | | | | | | | | | | | | | (153) ~ (all_4_2 = e3) % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | BETA: splitting (75) gives: % 149.73/22.07 | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | (154) all_58_28 = e3 % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | COMBINE_EQS: (132), (154) imply: % 149.73/22.07 | | | | | | | | | | | | | | (155) e3 = e1 % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (56), (87), (121), (137), (150), (155) % 149.73/22.07 | | | | | | | | | | | | | | are inconsistent by sub-proof #29. % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | (156) ~ (all_58_28 = e3) % 149.73/22.07 | | | | | | | | | | | | | | (157) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | BETA: splitting (157) gives: % 149.73/22.07 | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | (158) all_58_29 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (158) are inconsistent by sub-proof % 149.73/22.07 | | | | | | | | | | | | | | | #707. % 149.73/22.07 | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | (159) all_58_30 = e3 | all_58_31 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 149.73/22.07 | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | (160) all_58_30 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (160) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | (161) all_6_2 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | REDUCE: (21), (161) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | (162) ~ (all_52_8 = e3) % 149.73/22.07 | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | REDUCE: (66), (161) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | (163) ~ (all_52_9 = e3) % 149.73/22.07 | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | BETA: splitting (16) gives: % 149.73/22.07 | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | (164) all_56_4 = e2 % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (164) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | (165) all_52_8 = e2 % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (165) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | (166) all_58_4 = e2 % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | REDUCE: (45), (165) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | (167) ~ (all_52_4 = e2) % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | REDUCE: (2), (165) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | (168) ~ (all_52_9 = e2) % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | SIMP: (168) implies: % 149.73/22.07 | | | | | | | | | | | | | | | | | (169) ~ (all_52_9 = e2) % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | REDUCE: (162), (165) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | (170) ~ (e3 = e2) % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 149.73/22.07 | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | (171) all_56_0 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (171) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | | (172) e3 = e1 % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (56), (87), (121), (137), (150), (172) % 149.73/22.07 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #29. % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | (173) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 149.73/22.07 | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | (174) all_56_1 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (174) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | (175) all_52_4 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (175) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | (176) all_58_2 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | (177) all_58_31 = e0 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (87), % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | (132), (177) are inconsistent by sub-proof #850. % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | (178) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | e0) % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | (179) all_58_30 = e1 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (179) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | (180) e3 = e1 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (180) imply: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | (181) all_56_12 = e1 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (56), (87), (121), (137), (181) are % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #837. % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | (182) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 149.73/22.07 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | (183) all_56_2 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (121), (183) are inconsistent by sub-proof % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | #840. % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | (184) ~ (all_56_2 = e3) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | (185) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | (186) all_56_3 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (46), (50), (56), (65), (87), (132), % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | (157), (160), (186) are inconsistent by sub-proof % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | #28. % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | (187) ~ (all_56_3 = e3) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | (188) all_56_5 = e3 | all_56_10 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (187) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | (189) ~ (e3 = e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (190) all_54_6 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (190) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (191) all_52_9 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (191) implies: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (192) all_52_9 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (192) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (193) all_56_5 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (192) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (194) all_58_11 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (192) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (195) ~ (all_52_13 = e1) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (195) implies: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (196) ~ (all_52_13 = e1) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (192) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | (197) ~ (e2 = e1) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_28 = e2 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (198) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | (199) e2 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (199) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | (200) $false % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | (201) ~ (all_58_28 = e2) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_56_5 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (203) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) e3 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (204) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_58_30 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (46), (50), (56), (65), (87), (157), (202), % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) are inconsistent by sub-proof #661. % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_56_10 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (206) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_52_13 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (207) implies: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_52_13 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (208) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_58_13 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_29 = e2 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (210) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) e2 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (211) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) $false % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent. % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) ~ (all_58_29 = e2) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (213) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) ~ (e2 = e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_28 = e3 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (216) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) e3 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (217) imply: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_30 = e1 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (46), (50), (56), (65), (87), (157), (202), % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) are inconsistent by sub-proof #661. % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (85), (86), (87), (132), (223) are % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_22 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_58_8 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (227) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) e3 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (226) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) e3 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (229) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) e3 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230) are inconsistent by sub-proof #27. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_11 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_8 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (233) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) e3 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (232) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) e2 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) e2 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (234), (236) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) e3 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (237) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_30 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (46), (50), (56), (65), (87), (157), (202), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) are inconsistent by sub-proof #661. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_13 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (209), (242) are inconsistent by sub-proof % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_15 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_4 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (51), (56), (65), (87), (159), (160), (166), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (244), (245) are inconsistent by sub-proof % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #25. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_6 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_58_2 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (176), (249) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) e3 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (248) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) e3 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (251) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) e3 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (252) are inconsistent by sub-proof #27. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_2 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (176), (254) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) e3 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (255) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) $false % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_13 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (261) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) e3 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (262) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (176), (263) are inconsistent by sub-proof % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_58_22 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (266) imply: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) e3 = e0 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (267) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_15 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_4 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (51), (56), (65), (87), (159), (160), (166), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202), (269), (270) are inconsistent by sub-proof % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #25. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (85), (86), (87), (97), (132), (271) are % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #23. % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (85), (86), (87), (132), (275) are % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #312. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_13 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (278) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (279) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_6 = e3 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (281) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (282) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_58_22 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (286) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (287) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (97), (132), (288) are % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #310. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_22 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (291) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (292) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_13 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (294) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (295) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_26 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (300) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) e1 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (301) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_28 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (302) are inconsistent by % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_13 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (209), (304) are inconsistent by sub-proof % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (50), (80), (305) are inconsistent by % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_13 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (209), (309) are inconsistent by sub-proof % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #26. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_26 = e1 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (311) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) e1 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (312) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_28 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (313) are inconsistent by % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_13 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (316) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) e3 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (56), (65), (87), (159), (160), (202), (317) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #24. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) e1 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (319) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_28 = e0 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (320) are inconsistent by % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | (321) all_54_6 = e3 | all_54_6 = e2 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (24), (117), (134), (162), (163), (321) % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #122. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | (322) all_56_4 = e3 | all_56_9 = e3 % 149.73/22.10 | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (56), (101), (162), (322) are inconsistent % 149.73/22.10 | | | | | | | | | | | | | | | | | | | by sub-proof #751. % 149.73/22.10 | | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | (323) ~ (all_56_4 = e2) % 149.73/22.10 | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | REDUCE: (12), (323) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | | (324) ~ (all_52_8 = e2) % 149.73/22.10 | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (117), (134), (162), (324) are inconsistent % 149.73/22.10 | | | | | | | | | | | | | | | | | by sub-proof #554. % 149.73/22.10 | | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | (325) all_58_31 = e3 % 149.73/22.10 | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (325) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | (326) all_4_2 = e3 % 149.73/22.10 | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | REDUCE: (153), (326) imply: % 149.73/22.10 | | | | | | | | | | | | | | | | (327) $false % 149.73/22.10 | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent. % 149.73/22.10 | | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | (328) ~ (all_56_0 = e1) % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | REDUCE: (67), (328) imply: % 149.73/22.10 | | | | | | | | | | (329) ~ (all_10_2 = e1) % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | REF_CLOSE: (3), (25), (53), (55), (77), (113), (114), (129), % 149.73/22.10 | | | | | | | | | | (329) are inconsistent by sub-proof #736. % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | End of split % 149.73/22.10 | | | | | | | | | % 149.73/22.10 | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | % 149.73/22.10 | | | | | | | | | (330) ~ (all_56_2 = e2) % 149.73/22.10 | | | | | | | | | (331) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 149.73/22.10 | | | | | | | | | % 149.73/22.10 | | | | | | | | | REDUCE: (57), (330) imply: % 149.73/22.10 | | | | | | | | | (332) ~ (all_52_1 = e2) % 149.73/22.10 | | | | | | | | | % 149.73/22.10 | | | | | | | | | BETA: splitting (63) gives: % 149.73/22.10 | | | | | | | | | % 149.73/22.10 | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | (333) all_56_0 = e2 % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | COMBINE_EQS: (67), (333) imply: % 149.73/22.10 | | | | | | | | | | (334) all_10_2 = e2 % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | REDUCE: (53), (334) imply: % 149.73/22.10 | | | | | | | | | | (335) op(e2, e3) = e0 % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_1, e0, e3, e2, % 149.73/22.10 | | | | | | | | | | simplifying with (22), (335) gives: % 149.73/22.10 | | | | | | | | | | (336) all_52_1 = e0 % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | REDUCE: (68), (336) imply: % 149.73/22.10 | | | | | | | | | | (337) $false % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | CLOSE: (337) is inconsistent. % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | (338) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | BETA: splitting (338) gives: % 149.73/22.10 | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | (339) all_56_2 = e2 % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | COMBINE_EQS: (57), (339) imply: % 149.73/22.10 | | | | | | | | | | | (340) all_52_1 = e2 % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | REDUCE: (332), (340) imply: % 149.73/22.10 | | | | | | | | | | | (341) $false % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | CLOSE: (341) is inconsistent. % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | (342) all_56_6 = e2 | all_56_12 = e2 % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | BETA: splitting (342) gives: % 149.73/22.10 | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | (343) all_56_6 = e2 % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | REF_CLOSE: (13), (65), (343) are inconsistent by sub-proof % 149.73/22.10 | | | | | | | | | | | | #328. % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | (344) all_56_12 = e2 % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | COMBINE_EQS: (34), (344) imply: % 149.73/22.10 | | | | | | | | | | | | (345) all_52_3 = e2 % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | SIMP: (345) implies: % 149.73/22.10 | | | | | | | | | | | | (346) all_52_3 = e2 % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | COMBINE_EQS: (70), (346) imply: % 149.73/22.10 | | | | | | | | | | | | (347) all_58_22 = e2 % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | REDUCE: (71), (346) imply: % 149.73/22.10 | | | | | | | | | | | | (348) ~ (all_10_2 = e2) % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | SIMP: (348) implies: % 149.73/22.10 | | | | | | | | | | | | (349) ~ (all_10_2 = e2) % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | REDUCE: (41), (346) imply: % 149.73/22.10 | | | | | | | | | | | | (350) ~ (all_4_2 = e2) % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | SIMP: (350) implies: % 149.73/22.10 | | | | | | | | | | | | (351) ~ (all_4_2 = e2) % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | BETA: splitting (14) gives: % 149.73/22.10 | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | Case 1: % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | (352) all_58_28 = e2 % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | COMBINE_EQS: (62), (352) imply: % 149.73/22.10 | | | | | | | | | | | | | (353) all_10_2 = e2 % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | REDUCE: (349), (353) imply: % 149.73/22.10 | | | | | | | | | | | | | (354) $false % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | | CLOSE: (354) is inconsistent. % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.10 | | | | | | | | | | | | Case 2: % 149.73/22.10 | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | (355) ~ (all_58_28 = e2) % 149.73/22.11 | | | | | | | | | | | | | (356) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.11 | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | BETA: splitting (356) gives: % 149.73/22.11 | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | (357) all_58_29 = e2 % 149.73/22.11 | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | REF_CLOSE: (46), (65), (357) are inconsistent by sub-proof % 149.73/22.11 | | | | | | | | | | | | | | #706. % 149.73/22.11 | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | (358) all_58_30 = e2 | all_58_31 = e2 % 149.73/22.11 | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | BETA: splitting (358) gives: % 149.73/22.11 | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | (359) all_58_30 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (359) imply: % 149.73/22.11 | | | | | | | | | | | | | | | (360) all_6_2 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | REDUCE: (21), (360) imply: % 149.73/22.11 | | | | | | | | | | | | | | | (361) ~ (all_52_8 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | REDUCE: (66), (360) imply: % 149.73/22.11 | | | | | | | | | | | | | | | (362) ~ (all_52_9 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 149.73/22.11 | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | (363) all_58_31 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.11 | | | | | | | | | | | | | | | | (85), (86), (87), (363) are inconsistent by % 149.73/22.11 | | | | | | | | | | | | | | | | sub-proof #844. % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | (364) ~ (all_58_31 = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | (365) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 149.73/22.11 | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.11 | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.11 | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 149.73/22.11 | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.11 | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 149.73/22.11 | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 149.73/22.11 | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 149.73/22.11 | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 149.73/22.11 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 149.73/22.11 | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.11 | | | | | | | | | | | | | | | | e0) % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | REDUCE: (1), (364) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | (366) ~ (all_4_2 = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | (367) all_56_1 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (367) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | (368) all_52_4 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (368) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | (369) all_58_2 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | REDUCE: (42), (368) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | (370) ~ (all_8_1 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | SIMP: (370) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | (371) ~ (all_8_1 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | (372) all_56_3 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (14), (30), (36), (46), (50), (56), % 149.73/22.11 | | | | | | | | | | | | | | | | | | (62), (64), (65), (75), (78), (86), (87), (359), % 149.73/22.11 | | | | | | | | | | | | | | | | | | (372) are inconsistent by sub-proof #22. % 149.73/22.11 | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | (373) all_56_5 = e2 | all_56_10 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (374) all_56_5 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (374) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (375) all_52_9 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | REDUCE: (362), (375) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (376) $false % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | CLOSE: (376) is inconsistent. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (377) all_56_10 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (377) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (378) all_52_13 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | SIMP: (378) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (379) all_52_13 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (379) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | (380) all_58_13 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (381) all_58_30 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (381) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (382) e2 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | SIMP: (382) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (383) e2 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (383) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (384) all_56_12 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (65), (342), (384) are inconsistent by % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | sub-proof #327. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (385) ~ (all_58_30 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (386) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (387) all_58_29 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (387) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (388) e2 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (388) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (389) all_58_30 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (14), (30), (36), (46), (50), (56), (62), % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (64), (65), (75), (78), (86), (87), (389) are % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #691. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (390) ~ (all_58_29 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (391) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (390) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | (392) ~ (e2 = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (391) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (393) all_58_28 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (393) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (394) all_10_2 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | SIMP: (394) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (395) all_10_2 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (25), (53), (55), (114), (395) are % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #737. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_58_28 = e3) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (397) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (396) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | (398) ~ (all_10_2 = e3) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | (399) all_58_28 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (398), (399) are inconsistent by sub-proof % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | #783. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | (400) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (400) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | (401) all_58_29 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (401) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | (402) e3 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (402) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | (403) $false % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (403) is inconsistent. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | (404) all_58_30 = e3 | all_58_31 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_54_0 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (405) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_10_2 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (406) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_10_2 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (407) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_58_28 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (407) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | (409) ~ (e3 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (407) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | (410) ~ (e2 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_58_30 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (411) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (412) e3 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (412) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (413) $false % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (413) is inconsistent. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_58_31 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (414) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_4_2 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (415) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_4_2 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (397) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (417) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (419) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (85), (86), (87), (408), (420) are % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_58_22 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (423) imply: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) e2 = e0 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (414), (424) are % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_58_2 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (359), (369), (404), (414), (426) are % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21. % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (427) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (428) gives: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (429) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_58_2 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (359), (369), (404), (414), (430) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_58_15 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (87), (408), (414), (432) are inconsistent by % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #20. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (103), (347), (358), (359), (414), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) are inconsistent by sub-proof #162. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (435) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_58_8 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (436) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_52_1 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (437) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_52_1 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (332), (438) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) $false % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (439) is inconsistent. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (442) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_58_13 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (380), (414), (444) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) e3 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (414), (446) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_58_31 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (359), (404), (447) are inconsistent by % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #476. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (449) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_58_22 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (450) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) e2 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (414), (451) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (452) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_58_15 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (87), (408), (414), (453) are inconsistent by % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #20. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (85), (86), (87), (97), (408), (454) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #23. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (456) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (51), (56), (65), (75), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (85), (86), (87), (408), (458) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #312. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_58_22 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_58_6 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (103), (347), (358), (359), (414), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461), (462) are inconsistent by sub-proof #18. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_58_22 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_58_6 = e3 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (103), (347), (358), (359), (414), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464), (465) are inconsistent by sub-proof #18. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (468) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_58_22 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (469) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) e2 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (414), (470) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (97), (408), (471) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #310. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_58_22 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (474) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) e2 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (414), (475) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (476) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_58_13 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (380), (414), (477) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_58_26 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (97), (408), (482) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #309. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (371), (484) are inconsistent by sub-proof % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #17. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (485) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (486) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_58_20 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (80), (487) are inconsistent by sub-proof % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #39. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) e2 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (489) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_58_30 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (30), (46), (50), (56), (57), (65), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (87), (332), (338), (344), (400), (408), (490) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (492) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (493) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_24 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (371), (494) are inconsistent by sub-proof % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #17. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (495) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_26 = e1 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (97), (408), (496) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #309. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (497) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (498) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_13 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (87), (358), (359), (380), (414), (499) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #19. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) e1 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (408), (501) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_58_28 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (46), (50), (56), (65), (75), (78), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (502) are inconsistent by % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_54_0 = e3 | all_54_0 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (349), (398), (503) are inconsistent by % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #814. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | (504) ~ (all_56_1 = e2) % 149.73/22.12 | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | REDUCE: (38), (504) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | (505) ~ (all_52_4 = e2) % 149.73/22.12 | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | (506) all_56_0 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (506) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | (507) all_10_2 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | REDUCE: (349), (507) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | (508) $false % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | CLOSE: (508) is inconsistent. % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | (509) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | BETA: splitting (509) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | (510) all_56_1 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (510) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | (511) all_52_4 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | REDUCE: (505), (511) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | (512) $false % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | CLOSE: (512) is inconsistent. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | (513) all_56_4 = e2 | all_56_9 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (513) gives: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | Case 1: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (514) all_56_4 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (514) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (515) all_52_8 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (515) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (516) $false % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | CLOSE: (516) is inconsistent. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (517) all_56_9 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (517) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (518) e2 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (518) imply: % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (519) all_58_30 = e0 % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (14), (30), (36), (46), (50), (56), (62), % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | (64), (65), (75), (78), (86), (87), (519) are % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #691. % 149.73/22.12 | | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | Case 2: % 149.73/22.12 | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | (520) all_58_31 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | COMBINE_EQS: (1), (520) imply: % 149.73/22.12 | | | | | | | | | | | | | | | (521) all_4_2 = e2 % 149.73/22.12 | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | REDUCE: (351), (521) imply: % 149.73/22.12 | | | | | | | | | | | | | | | (522) $false % 149.73/22.12 | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | | CLOSE: (522) is inconsistent. % 149.73/22.12 | | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | | % 149.73/22.12 | | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | | % 149.73/22.12 | | | | | | | | | End of split % 149.73/22.12 | | | | | | | | | % 149.73/22.13 | | | | | | | | End of split % 149.73/22.13 | | | | | | | | % 149.73/22.13 | | | | | | | End of split % 149.73/22.13 | | | | | | | % 149.73/22.13 | | | | | | End of split % 149.73/22.13 | | | | | | % 149.73/22.13 | | | | | End of split % 149.73/22.13 | | | | | % 149.73/22.13 | | | | End of split % 149.73/22.13 | | | | % 149.73/22.13 | | | Case 2: % 149.73/22.13 | | | | % 149.73/22.13 | | | | (523) all_56_10 = e0 | all_56_11 = e0 % 149.73/22.13 | | | | % 149.73/22.13 | | | | REF_CLOSE: (37), (39), (59), (80), (523) are inconsistent by sub-proof % 149.73/22.13 | | | | #294. % 149.73/22.13 | | | | % 149.73/22.13 | | | End of split % 149.73/22.13 | | | % 149.73/22.13 | | End of split % 149.73/22.13 | | % 149.73/22.13 | End of split % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #17 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_24 = all_8_1 % 149.73/22.13 (2) all_58_24 = e2 % 149.73/22.13 (3) ~ (all_8_1 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (2) imply: % 149.73/22.13 | (4) all_8_1 = e2 % 149.73/22.13 | % 149.73/22.13 | SIMP: (4) implies: % 149.73/22.13 | (5) all_8_1 = e2 % 149.73/22.13 | % 149.73/22.13 | REDUCE: (3), (5) imply: % 149.73/22.13 | (6) $false % 149.73/22.13 | % 149.73/22.13 | CLOSE: (6) is inconsistent. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #18 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_30 = e2 % 149.73/22.13 (2) all_58_6 = e0 % 149.73/22.13 (3) all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (4) all_58_31 = e3 % 149.73/22.13 (5) all_58_6 = e3 % 149.73/22.13 (6) ~ (e2 = e0) % 149.73/22.13 (7) all_58_22 = e2 % 149.73/22.13 (8) ~ (e3 = e2) % 149.73/22.13 (9) all_58_22 = e3 % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (2), (5) imply: % 149.73/22.13 | (10) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | SIMP: (10) implies: % 149.73/22.13 | (11) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (7), (9) imply: % 149.73/22.13 | (12) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (11), (12) imply: % 149.73/22.13 | (13) e2 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (1), (3), (4), (6), (8), (13) are inconsistent by sub-proof #170. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #19 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_13 = e0 % 149.73/22.13 (2) all_58_30 = e2 % 149.73/22.13 (3) all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (4) all_58_31 = e3 % 149.73/22.13 (5) all_58_13 = e2 % 149.73/22.13 (6) ~ (e2 = e0) % 149.73/22.13 (7) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (5) imply: % 149.73/22.13 | (8) e2 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (2), (8) imply: % 149.73/22.13 | (9) all_58_30 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (3), (4), (6), (7), (9) are inconsistent by sub-proof #705. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #20 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (2) ~ (e3 = e1) % 149.73/22.13 (3) all_58_28 = e1 % 149.73/22.13 (4) all_58_29 = e0 % 149.73/22.13 (5) ~ (e2 = e1) % 149.73/22.13 (6) all_58_15 = e0 % 149.73/22.13 (7) ~ (e3 = e0) % 149.73/22.13 (8) all_58_31 = e3 % 149.73/22.13 (9) ~ (e2 = e0) % 149.73/22.13 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (11) all_58_15 = e3 % 149.73/22.13 (12) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (6), (11) imply: % 149.73/22.13 | (13) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (8), (13) imply: % 149.73/22.13 | (14) all_58_31 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (12), (14) are % 149.73/22.13 | inconsistent by sub-proof #850. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #21 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_2 = e2 % 149.73/22.13 (2) all_58_30 = e2 % 149.73/22.13 (3) all_58_31 = e3 % 149.73/22.13 (4) all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (5) all_58_2 = e3 % 149.73/22.13 (6) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (5) imply: % 149.73/22.13 | (7) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | SIMP: (7) implies: % 149.73/22.13 | (8) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (3), (8) imply: % 149.73/22.13 | (9) all_58_31 = e2 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #476. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #22 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_31 = all_4_2 % 149.73/22.13 (2) all_56_3 = e0 % 149.73/22.13 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (4) all_58_30 = e2 % 149.73/22.13 (5) ~ (e3 = e1) % 149.73/22.13 (6) all_20_2 = all_4_2 % 149.73/22.13 (7) all_58_29 = e0 % 149.73/22.13 (8) ~ (e2 = e1) % 149.73/22.13 (9) ~ (e3 = e0) % 149.73/22.13 (10) all_58_28 = all_10_2 % 149.73/22.13 (11) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.73/22.13 (12) ~ (e2 = e0) % 149.73/22.13 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (14) ~ (e1 = e0) % 149.73/22.13 (15) all_56_3 = e2 % 149.73/22.13 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.73/22.13 (17) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (2), (15) imply: % 149.73/22.13 | (18) e2 = e0 % 149.73/22.13 | % 149.73/22.13 | SIMP: (18) implies: % 149.73/22.13 | (19) e2 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (4), (19) imply: % 149.73/22.13 | (20) all_58_30 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 149.73/22.13 | (16), (17), (20) are inconsistent by sub-proof #691. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #23 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (2) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.13 (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 149.73/22.13 (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 149.73/22.13 (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 149.73/22.13 (3) ~ (e3 = e1) % 149.73/22.13 (4) all_58_28 = e1 % 149.73/22.13 (5) all_58_29 = e0 % 149.73/22.13 (6) ~ (e2 = e1) % 149.73/22.13 (7) all_58_26 = e0 % 149.73/22.13 (8) all_58_15 = e0 % 149.73/22.13 (9) ~ (e3 = e0) % 149.73/22.13 (10) ~ (e2 = e0) % 149.73/22.13 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (12) ~ (e1 = e0) % 149.73/22.13 (13) all_58_30 = all_6_2 % 149.73/22.13 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.73/22.13 (15) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | BETA: splitting (2) gives: % 149.73/22.13 | % 149.73/22.13 | Case 1: % 149.73/22.13 | | % 149.73/22.13 | | (16) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.13 | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) % 149.73/22.13 | | % 149.73/22.13 | | BETA: splitting (16) gives: % 149.73/22.13 | | % 149.73/22.13 | | Case 1: % 149.73/22.13 | | | % 149.73/22.13 | | | (17) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1 % 149.73/22.13 | | | % 149.73/22.13 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 149.73/22.13 | | | (14), (15), (17) are inconsistent by sub-proof #315. % 149.73/22.13 | | | % 149.73/22.13 | | Case 2: % 149.73/22.13 | | | % 149.73/22.13 | | | (18) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3 % 149.73/22.13 | | | % 149.73/22.13 | | | ALPHA: (18) implies: % 149.73/22.13 | | | (19) all_58_15 = e1 % 149.73/22.13 | | | % 149.73/22.13 | | | COMBINE_EQS: (8), (19) imply: % 149.73/22.13 | | | (20) e1 = e0 % 149.73/22.13 | | | % 149.73/22.13 | | | COMBINE_EQS: (4), (20) imply: % 149.73/22.13 | | | (21) all_58_28 = e0 % 149.73/22.13 | | | % 149.73/22.13 | | | REF_CLOSE: (1), (3), (5), (6), (9), (10), (11), (12), (13), (14), (15), % 149.73/22.13 | | | (21) are inconsistent by sub-proof #483. % 149.73/22.13 | | | % 149.73/22.13 | | End of split % 149.73/22.13 | | % 149.73/22.13 | Case 2: % 149.73/22.13 | | % 149.73/22.13 | | (22) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 149.73/22.13 | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 149.73/22.13 | | % 149.73/22.13 | | BETA: splitting (22) gives: % 149.73/22.13 | | % 149.73/22.13 | | Case 1: % 149.73/22.13 | | | % 149.73/22.13 | | | (23) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2 % 149.73/22.13 | | | % 149.73/22.13 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), % 149.73/22.13 | | | (14), (15), (23) are inconsistent by sub-proof #314. % 149.73/22.13 | | | % 149.73/22.13 | | Case 2: % 149.73/22.13 | | | % 149.73/22.13 | | | (24) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0 % 149.73/22.13 | | | % 149.73/22.13 | | | ALPHA: (24) implies: % 149.73/22.13 | | | (25) all_58_15 = e1 % 149.73/22.13 | | | % 149.73/22.13 | | | COMBINE_EQS: (8), (25) imply: % 149.73/22.13 | | | (26) e1 = e0 % 149.73/22.13 | | | % 149.73/22.13 | | | COMBINE_EQS: (4), (26) imply: % 149.73/22.13 | | | (27) all_58_28 = e0 % 149.73/22.13 | | | % 149.73/22.13 | | | REF_CLOSE: (1), (3), (5), (6), (9), (10), (11), (12), (13), (14), (15), % 149.73/22.13 | | | (27) are inconsistent by sub-proof #483. % 149.73/22.13 | | | % 149.73/22.13 | | End of split % 149.73/22.13 | | % 149.73/22.13 | End of split % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #24 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_30 = e3 % 149.73/22.13 (2) all_58_29 = e0 % 149.73/22.13 (3) ~ (e3 = e0) % 149.73/22.13 (4) e3 = e0 % 149.73/22.13 (5) all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (6) ~ (e2 = e0) % 149.73/22.13 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (8) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | SIMP: (4) implies: % 149.73/22.13 | (9) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (9) imply: % 149.73/22.13 | (10) all_58_30 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10) are inconsistent by sub-proof % 149.73/22.13 | #703. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #25 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_4 = e3 % 149.73/22.13 (2) all_58_30 = e3 % 149.73/22.13 (3) all_58_29 = e0 % 149.73/22.13 (4) all_58_15 = e0 % 149.73/22.13 (5) ~ (e3 = e0) % 149.73/22.13 (6) all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (7) ~ (e2 = e0) % 149.73/22.13 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (9) all_58_15 = e3 % 149.73/22.13 (10) all_58_4 = e2 % 149.73/22.13 (11) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (10) imply: % 149.73/22.13 | (12) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | SIMP: (12) implies: % 149.73/22.13 | (13) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (4), (9) imply: % 149.73/22.13 | (14) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (11), (13), (14) are inconsistent by % 149.73/22.13 | sub-proof #27. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #26 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_13 = e3 % 149.73/22.13 (2) all_58_13 = e2 % 149.73/22.13 (3) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (2) imply: % 149.73/22.13 | (4) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | SIMP: (4) implies: % 149.73/22.13 | (5) e3 = e2 % 149.73/22.13 | % 149.73/22.13 | REDUCE: (3), (5) imply: % 149.73/22.13 | (6) $false % 149.73/22.13 | % 149.73/22.13 | CLOSE: (6) is inconsistent. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #27 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_58_30 = e3 % 149.73/22.13 (2) all_58_29 = e0 % 149.73/22.13 (3) ~ (e3 = e0) % 149.73/22.13 (4) e3 = e0 % 149.73/22.13 (5) all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (6) ~ (e2 = e0) % 149.73/22.13 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (8) ~ (e3 = e2) % 149.73/22.13 (9) e3 = e2 % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (4), (9) imply: % 149.73/22.13 | (10) e2 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (4) imply: % 149.73/22.13 | (11) all_58_30 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (11) are inconsistent by sub-proof % 149.73/22.13 | #703. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #28 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_56_3 = e0 % 149.73/22.13 (2) all_58_30 = e3 % 149.73/22.13 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.13 (4) all_56_3 = e3 % 149.73/22.13 (5) all_58_28 = e1 % 149.73/22.13 (6) all_58_29 = e0 % 149.73/22.13 (7) ~ (e2 = e1) % 149.73/22.13 (8) ~ (e3 = e0) % 149.73/22.13 (9) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.13 (10) ~ (e2 = e0) % 149.73/22.13 (11) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (1), (4) imply: % 149.73/22.13 | (12) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | SIMP: (12) implies: % 149.73/22.13 | (13) e3 = e0 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (2), (13) imply: % 149.73/22.13 | (14) all_58_30 = e0 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (14) are inconsistent by % 149.73/22.13 | sub-proof #702. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #29 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_56_6 = e0 % 149.73/22.13 (2) ~ (e3 = e1) % 149.73/22.13 (3) all_56_2 = e2 % 149.73/22.13 (4) ~ (e3 = e0) % 149.73/22.13 (5) all_56_12 = e3 % 149.73/22.13 (6) e3 = e1 % 149.73/22.13 (7) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 149.73/22.13 (8) ~ (e3 = e2) % 149.73/22.13 % 149.73/22.13 Begin of proof % 149.73/22.13 | % 149.73/22.13 | SIMP: (6) implies: % 149.73/22.13 | (9) e3 = e1 % 149.73/22.13 | % 149.73/22.13 | COMBINE_EQS: (5), (9) imply: % 149.73/22.13 | (10) all_56_12 = e1 % 149.73/22.13 | % 149.73/22.13 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10) are inconsistent by sub-proof % 149.73/22.13 | #837. % 149.73/22.13 | % 149.73/22.13 End of proof % 149.73/22.13 % 149.73/22.13 Sub-proof #30 shows that the following formulas are inconsistent: % 149.73/22.13 ---------------------------------------------------------------- % 149.73/22.13 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 149.73/22.13 (2) all_58_23 = all_8_0 % 149.73/22.13 (3) all_58_31 = all_4_2 % 149.73/22.13 (4) ~ (all_52_8 = all_52_9) % 149.73/22.13 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 149.73/22.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 149.73/22.13 (6) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 149.73/22.13 (7) all_58_11 = all_52_9 % 149.73/22.13 (8) all_56_15 = all_4_2 % 149.73/22.13 (9) all_56_7 = all_52_6 % 149.73/22.13 (10) ~ (all_52_6 = all_6_2) % 149.73/22.13 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 149.73/22.13 (12) ~ (all_52_2 = e0) % 149.73/22.13 (13) all_54_8 = all_52_2 % 149.73/22.13 (14) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 149.73/22.14 (15) all_58_15 = all_52_2 % 149.73/22.14 (16) all_58_26 = all_52_11 % 149.73/22.14 (17) op(e1, all_52_14) = all_58_19 % 149.73/22.14 (18) all_56_3 = e0 % 149.73/22.14 (19) ~ (all_52_8 = all_52_11) % 149.73/22.14 (20) all_58_24 = all_8_1 % 149.73/22.14 (21) ~ (all_52_11 = all_4_2) % 149.73/22.14 (22) all_54_7 = all_52_13 % 149.73/22.14 (23) all_58_6 = all_52_12 % 149.73/22.14 (24) all_56_4 = all_52_8 % 149.73/22.14 (25) ~ (all_52_6 = all_8_1) % 149.73/22.14 (26) ~ (all_52_4 = all_8_2) % 149.73/22.14 (27) all_54_3 = all_52_12 % 149.73/22.14 (28) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 149.73/22.14 (29) all_54_1 = all_52_4 % 149.73/22.14 (30) op(e0, e2) = all_8_1 % 149.73/22.14 (31) ~ (all_6_2 = e0) % 149.73/22.14 (32) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 149.73/22.14 (33) ~ (all_52_4 = all_52_6) % 149.73/22.14 (34) all_58_13 = all_52_13 % 149.73/22.14 (35) op(e0, e1) = all_52_11 % 149.73/22.14 (36) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 149.73/22.14 (37) all_56_13 = all_8_1 % 149.73/22.14 (38) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 149.73/22.14 (39) all_58_20 = all_52_14 % 149.73/22.14 (40) ~ (all_52_12 = all_52_13) % 149.73/22.14 (41) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 149.73/22.14 (42) all_54_10 = all_6_2 % 149.73/22.14 (43) op(e0, all_52_3) = all_58_21 % 149.73/22.14 (44) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 149.73/22.14 (45) ~ (all_52_6 = all_52_14) % 149.73/22.14 (46) all_54_6 = all_52_9 % 149.73/22.14 (47) ~ (all_52_2 = all_6_2) % 149.73/22.14 (48) op(e3, e3) = all_10_2 % 149.73/22.14 (49) op(e3, all_52_8) = all_58_3 % 149.73/22.14 (50) ~ (all_52_8 = all_52_12) % 149.73/22.14 (51) all_54_9 = all_52_6 % 149.73/22.14 (52) ~ (all_52_13 = all_4_2) % 149.73/22.14 (53) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 149.73/22.14 (54) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 149.73/22.14 (55) ~ (e3 = e1) % 149.73/22.14 (56) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 149.73/22.14 (57) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 149.73/22.14 (58) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 149.73/22.14 (59) ~ (all_52_1 = all_52_13) % 149.73/22.14 (60) all_56_5 = all_52_9 % 149.73/22.14 (61) all_54_14 = all_52_11 % 149.73/22.14 (62) op(e0, all_8_1) = all_8_0 % 149.73/22.14 (63) all_56_12 = all_52_3 % 149.73/22.14 (64) all_58_2 = all_52_4 % 149.73/22.14 (65) all_20_2 = all_4_2 % 149.73/22.14 (66) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 149.73/22.14 (67) all_56_11 = all_52_14 % 149.73/22.14 (68) all_56_1 = all_52_4 % 149.73/22.14 (69) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 149.73/22.14 (70) ~ (all_52_13 = e0) % 149.73/22.14 (71) op(e1, e3) = all_52_2 % 149.73/22.14 (72) all_58_9 = all_52_13 % 149.73/22.14 (73) ~ (all_52_4 = all_8_1) % 149.73/22.14 (74) op(e1, e0) = all_52_14 % 149.73/22.14 (75) ~ (all_52_9 = all_52_11) % 149.73/22.14 (76) ~ (all_52_9 = e0) % 149.73/22.14 (77) ~ (all_52_13 = all_52_14) % 149.73/22.14 (78) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 149.73/22.14 (79) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 149.73/22.14 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 149.73/22.14 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 149.73/22.14 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 149.73/22.14 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 149.73/22.14 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 149.73/22.14 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 149.73/22.14 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 149.73/22.14 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 149.73/22.14 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 149.73/22.14 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 149.73/22.14 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 149.73/22.14 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 149.73/22.14 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 149.73/22.14 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.14 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 149.73/22.14 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 149.73/22.14 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 149.73/22.14 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 149.73/22.14 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 149.73/22.14 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 149.73/22.14 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 149.73/22.14 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 149.73/22.14 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 149.73/22.14 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 149.73/22.14 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 149.73/22.14 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 149.73/22.14 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 149.73/22.14 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 149.73/22.14 e0) % 149.73/22.14 (80) ~ (all_52_4 = all_52_8) % 149.73/22.14 (81) all_58_29 = e0 % 149.73/22.14 (82) op(e2, e1) = all_52_9 % 149.73/22.14 (83) all_56_9 = all_52_12 % 149.73/22.14 (84) all_58_29 = all_8_2 % 149.73/22.14 (85) ~ (all_52_12 = all_52_14) % 149.73/22.14 (86) all_58_8 = all_52_1 % 149.73/22.14 (87) ~ (e2 = e1) % 149.73/22.14 (88) op(e3, e0) = all_52_12 % 149.73/22.14 (89) all_56_6 = all_52_2 % 149.73/22.14 (90) ~ (all_52_2 = all_52_6) % 149.73/22.14 (91) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 149.73/22.14 (92) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 149.73/22.14 (93) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 149.73/22.14 (94) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 149.73/22.14 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 149.73/22.14 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 149.73/22.14 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 149.73/22.14 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 149.73/22.14 (all_58_27 = e0)) % 149.73/22.14 (95) ~ (all_52_9 = all_52_13) % 149.73/22.14 (96) ~ (all_52_11 = all_8_1) % 149.73/22.14 (97) op(all_6_2, e1) = all_6_1 % 149.73/22.14 (98) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 149.73/22.14 (99) all_54_13 = all_8_1 % 149.73/22.14 (100) op(e2, all_52_9) = all_58_10 % 149.73/22.14 (101) ~ (all_52_11 = all_6_2) % 149.73/22.14 (102) op(e3, all_10_2) = all_58_0 % 149.73/22.14 (103) ~ (e3 = e0) % 149.73/22.14 (104) all_56_2 = all_52_1 % 149.73/22.14 (105) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 149.73/22.14 (106) op(e3, all_52_12) = all_58_5 % 149.73/22.14 (107) all_56_10 = all_52_13 % 149.73/22.14 (108) ~ (all_52_3 = all_8_1) % 149.73/22.14 (109) ~ (all_52_12 = all_10_2) % 149.73/22.14 (110) ~ (all_52_1 = all_52_3) % 149.73/22.14 (111) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 149.73/22.14 (112) all_56_14 = all_52_11 % 149.73/22.14 (113) all_58_28 = all_10_2 % 149.73/22.14 (114) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 149.73/22.14 (115) ~ (all_6_1 = e0) % 149.73/22.14 (116) all_58_17 = all_52_6 % 149.73/22.14 (117) ~ (all_52_1 = all_52_9) % 149.73/22.14 (118) op(e3, e1) = all_52_8 % 149.73/22.14 (119) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 149.73/22.14 (120) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 149.73/22.14 (121) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 149.73/22.14 (122) all_14_0 = all_8_0 % 149.73/22.14 (123) ~ (e2 = e0) % 149.73/22.14 (124) ~ (all_52_9 = all_6_2) % 149.73/22.14 (125) ~ (all_8_1 = all_4_2) % 149.73/22.14 (126) ~ (all_52_2 = all_10_2) % 149.73/22.14 (127) all_56_0 = all_10_2 % 149.73/22.14 (128) op(e0, e0) = all_4_2 % 149.73/22.14 (129) ~ (all_52_1 = e0) % 149.73/22.14 (130) ~ (all_52_3 = all_52_11) % 149.73/22.14 (131) all_58_22 = all_52_3 % 149.73/22.14 (132) ~ (all_52_12 = all_4_2) % 149.73/22.14 (133) all_56_8 = all_6_2 % 149.73/22.14 (134) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 149.73/22.14 (135) ~ (all_52_1 = all_52_2) % 149.73/22.14 (136) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 149.73/22.14 (137) all_58_4 = all_52_8 % 149.73/22.14 (138) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 149.73/22.14 (139) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 149.73/22.14 (140) all_54_0 = all_10_2 % 149.73/22.14 (141) ~ (all_52_2 = all_52_14) % 149.73/22.14 (142) all_14_1 = all_8_1 % 149.73/22.14 (143) ~ (all_52_14 = all_4_2) % 149.73/22.14 (144) ~ (e1 = e0) % 149.73/22.14 (145) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 149.73/22.14 (146) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 149.73/22.14 (147) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 149.73/22.14 (148) ~ (all_52_4 = all_10_2) % 149.73/22.14 (149) all_58_30 = all_6_2 % 149.73/22.14 (150) op(e2, all_52_1) = all_58_7 % 149.73/22.14 (151) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 149.73/22.14 (152) ~ (e3 = e2) % 149.73/22.14 (153) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 149.73/22.14 (154) op(all_10_2, e3) = all_10_1 % 149.73/22.14 (155) ~ (all_52_4 = all_52_12) % 149.73/22.14 (156) all_54_4 = all_52_1 % 149.73/22.14 (157) ~ (all_52_1 = all_10_2) % 149.73/22.14 % 149.73/22.14 Begin of proof % 149.73/22.14 | % 149.73/22.14 | BETA: splitting (44) gives: % 149.73/22.14 | % 149.73/22.14 | Case 1: % 149.73/22.14 | | % 149.73/22.14 | | (158) all_56_2 = e0 % 149.73/22.14 | | % 149.73/22.14 | | COMBINE_EQS: (104), (158) imply: % 149.73/22.14 | | (159) all_52_1 = e0 % 149.73/22.14 | | % 149.73/22.14 | | REDUCE: (129), (159) imply: % 149.73/22.14 | | (160) $false % 149.73/22.14 | | % 149.73/22.14 | | CLOSE: (160) is inconsistent. % 149.73/22.14 | | % 149.73/22.14 | Case 2: % 149.73/22.14 | | % 149.73/22.14 | | (161) all_56_6 = e0 | all_56_12 = e0 % 149.73/22.14 | | % 149.73/22.14 | | BETA: splitting (161) gives: % 149.73/22.14 | | % 149.73/22.14 | | Case 1: % 149.73/22.14 | | | % 149.73/22.14 | | | (162) all_56_6 = e0 % 149.73/22.14 | | | % 149.73/22.14 | | | COMBINE_EQS: (89), (162) imply: % 149.73/22.14 | | | (163) all_52_2 = e0 % 149.73/22.14 | | | % 149.73/22.14 | | | REDUCE: (12), (163) imply: % 149.73/22.14 | | | (164) $false % 149.73/22.14 | | | % 149.73/22.14 | | | CLOSE: (164) is inconsistent. % 149.73/22.14 | | | % 149.73/22.14 | | Case 2: % 149.73/22.14 | | | % 149.73/22.14 | | | (165) all_56_12 = e0 % 149.73/22.14 | | | % 149.73/22.14 | | | COMBINE_EQS: (63), (165) imply: % 149.73/22.14 | | | (166) all_52_3 = e0 % 149.73/22.14 | | | % 149.73/22.14 | | | SIMP: (166) implies: % 149.73/22.14 | | | (167) all_52_3 = e0 % 149.73/22.14 | | | % 150.16/22.14 | | | COMBINE_EQS: (131), (167) imply: % 150.16/22.14 | | | (168) all_58_22 = e0 % 150.16/22.14 | | | % 150.16/22.14 | | | REDUCE: (130), (167) imply: % 150.16/22.14 | | | (169) ~ (all_52_11 = e0) % 150.16/22.14 | | | % 150.16/22.14 | | | SIMP: (169) implies: % 150.16/22.14 | | | (170) ~ (all_52_11 = e0) % 150.16/22.14 | | | % 150.16/22.14 | | | REDUCE: (108), (167) imply: % 150.16/22.14 | | | (171) ~ (all_8_1 = e0) % 150.16/22.14 | | | % 150.16/22.14 | | | SIMP: (171) implies: % 150.16/22.14 | | | (172) ~ (all_8_1 = e0) % 150.16/22.14 | | | % 150.16/22.14 | | | REDUCE: (43), (167) imply: % 150.16/22.14 | | | (173) op(e0, e0) = all_58_21 % 150.16/22.14 | | | % 150.16/22.14 | | | BETA: splitting (69) gives: % 150.16/22.14 | | | % 150.16/22.14 | | | Case 1: % 150.16/22.14 | | | | % 150.16/22.14 | | | | (174) all_56_4 = e0 % 150.16/22.14 | | | | % 150.16/22.14 | | | | COMBINE_EQS: (24), (174) imply: % 150.16/22.14 | | | | (175) all_52_8 = e0 % 150.16/22.14 | | | | % 150.16/22.14 | | | | COMBINE_EQS: (137), (175) imply: % 150.16/22.14 | | | | (176) all_58_4 = e0 % 150.16/22.14 | | | | % 150.16/22.14 | | | | REDUCE: (80), (175) imply: % 150.16/22.14 | | | | (177) ~ (all_52_4 = e0) % 150.16/22.14 | | | | % 150.16/22.14 | | | | REDUCE: (4), (175) imply: % 150.16/22.14 | | | | (178) ~ (all_52_9 = e0) % 150.16/22.14 | | | | % 150.16/22.14 | | | | REDUCE: (50), (175) imply: % 150.16/22.14 | | | | (179) ~ (all_52_12 = e0) % 150.16/22.14 | | | | % 150.16/22.14 | | | | SIMP: (179) implies: % 150.16/22.14 | | | | (180) ~ (all_52_12 = e0) % 150.16/22.14 | | | | % 150.16/22.14 | | | | REDUCE: (49), (175) imply: % 150.16/22.14 | | | | (181) op(e3, e0) = all_58_3 % 150.16/22.14 | | | | % 150.16/22.14 | | | | REDUCE: (118), (175) imply: % 150.16/22.14 | | | | (182) op(e3, e1) = e0 % 150.16/22.14 | | | | % 150.16/22.14 | | | | BETA: splitting (6) gives: % 150.16/22.14 | | | | % 150.16/22.14 | | | | Case 1: % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | (183) all_56_9 = e0 % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | COMBINE_EQS: (83), (183) imply: % 150.16/22.14 | | | | | (184) all_52_12 = e0 % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | REDUCE: (180), (184) imply: % 150.16/22.14 | | | | | (185) $false % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | CLOSE: (185) is inconsistent. % 150.16/22.14 | | | | | % 150.16/22.14 | | | | Case 2: % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | (186) all_56_10 = e0 | all_56_11 = e0 % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | BETA: splitting (186) gives: % 150.16/22.14 | | | | | % 150.16/22.14 | | | | | Case 1: % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | (187) all_56_10 = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | COMBINE_EQS: (107), (187) imply: % 150.16/22.14 | | | | | | (188) all_52_13 = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | REDUCE: (70), (188) imply: % 150.16/22.14 | | | | | | (189) $false % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | CLOSE: (189) is inconsistent. % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | Case 2: % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | (190) all_56_11 = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | COMBINE_EQS: (67), (190) imply: % 150.16/22.14 | | | | | | (191) all_52_14 = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | COMBINE_EQS: (39), (191) imply: % 150.16/22.14 | | | | | | (192) all_58_20 = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | REDUCE: (45), (191) imply: % 150.16/22.14 | | | | | | (193) ~ (all_52_6 = e0) % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | REDUCE: (143), (191) imply: % 150.16/22.14 | | | | | | (194) ~ (all_4_2 = e0) % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | SIMP: (194) implies: % 150.16/22.14 | | | | | | (195) ~ (all_4_2 = e0) % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | REDUCE: (17), (191) imply: % 150.16/22.14 | | | | | | (196) op(e1, e0) = all_58_19 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | REDUCE: (74), (191) imply: % 150.16/22.14 | | | | | | (197) op(e1, e0) = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | GROUND_INST: instantiating (5) with all_4_2, all_58_21, e0, e0, % 150.16/22.14 | | | | | | simplifying with (128), (173) gives: % 150.16/22.14 | | | | | | (198) all_58_21 = all_4_2 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | GROUND_INST: instantiating (5) with e0, all_58_19, e0, e1, % 150.16/22.14 | | | | | | simplifying with (196), (197) gives: % 150.16/22.14 | | | | | | (199) all_58_19 = e0 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | GROUND_INST: instantiating (5) with all_52_12, all_58_3, e0, e3, % 150.16/22.14 | | | | | | simplifying with (88), (181) gives: % 150.16/22.14 | | | | | | (200) all_58_3 = all_52_12 % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | BETA: splitting (136) gives: % 150.16/22.14 | | | | | | % 150.16/22.14 | | | | | | Case 1: % 150.16/22.14 | | | | | | | % 150.16/22.14 | | | | | | | (201) all_54_1 = e0 % 150.16/22.14 | | | | | | | % 150.16/22.14 | | | | | | | REF_CLOSE: (29), (177), (201) are inconsistent by sub-proof #798. % 150.16/22.14 | | | | | | | % 150.16/22.14 | | | | | | Case 2: % 150.16/22.14 | | | | | | | % 150.16/22.14 | | | | | | | (202) ~ (all_54_1 = e0) % 150.16/22.14 | | | | | | | (203) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 150.16/22.14 | | | | | | | % 150.16/22.14 | | | | | | | BETA: splitting (38) gives: % 150.16/22.14 | | | | | | | % 150.16/22.14 | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | % 150.16/22.14 | | | | | | | | (204) all_54_13 = e0 % 150.16/22.14 | | | | | | | | % 150.16/22.14 | | | | | | | | REF_CLOSE: (99), (172), (204) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | #397. % 150.16/22.14 | | | | | | | | % 150.16/22.14 | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | % 150.16/22.14 | | | | | | | | (205) ~ (all_54_13 = e0) % 150.16/22.14 | | | | | | | | (206) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 150.16/22.14 | | | | | | | | % 150.16/22.14 | | | | | | | | BETA: splitting (147) gives: % 150.16/22.14 | | | | | | | | % 150.16/22.14 | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | % 150.16/22.14 | | | | | | | | | (207) all_54_6 = e0 % 150.16/22.14 | | | | | | | | | % 150.16/22.14 | | | | | | | | | REF_CLOSE: (46), (76), (207) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | | #797. % 150.16/22.14 | | | | | | | | | % 150.16/22.14 | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | % 150.16/22.14 | | | | | | | | | (208) ~ (all_54_6 = e0) % 150.16/22.14 | | | | | | | | | (209) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 150.16/22.14 | | | | | | | | | % 150.16/22.14 | | | | | | | | | BETA: splitting (153) gives: % 150.16/22.14 | | | | | | | | | % 150.16/22.14 | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | (210) all_54_7 = e0 % 150.16/22.14 | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | REF_CLOSE: (22), (70), (210) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | | | #742. % 150.16/22.14 | | | | | | | | | | % 150.16/22.14 | | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | (211) ~ (all_54_7 = e0) % 150.16/22.14 | | | | | | | | | | (212) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 150.16/22.14 | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | BETA: splitting (91) gives: % 150.16/22.14 | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | (213) all_54_4 = e0 % 150.16/22.14 | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | REF_CLOSE: (129), (156), (213) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | | | | #859. % 150.16/22.14 | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | (214) ~ (all_54_4 = e0) % 150.16/22.14 | | | | | | | | | | | (215) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 150.16/22.14 | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | BETA: splitting (56) gives: % 150.16/22.14 | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | (216) all_54_9 = e0 % 150.16/22.14 | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | REF_CLOSE: (51), (193), (216) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | | | | | #572. % 150.16/22.14 | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | (217) ~ (all_54_9 = e0) % 150.16/22.14 | | | | | | | | | | | | (218) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 150.16/22.14 | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | BETA: splitting (58) gives: % 150.16/22.14 | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | (219) all_54_0 = e0 % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | REF_CLOSE: (28), (55), (81), (87), (103), (113), (123), % 150.16/22.14 | | | | | | | | | | | | | (138), (140), (144), (149), (151), (152), (219) % 150.16/22.14 | | | | | | | | | | | | | are inconsistent by sub-proof #395. % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | (220) ~ (all_54_0 = e0) % 150.16/22.14 | | | | | | | | | | | | | (221) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | REDUCE: (140), (220) imply: % 150.16/22.14 | | | | | | | | | | | | | (222) ~ (all_10_2 = e0) % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | BETA: splitting (105) gives: % 150.16/22.14 | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | (223) all_54_10 = e0 % 150.16/22.14 | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | REF_CLOSE: (3), (28), (42), (55), (65), (81), (87), (103), % 150.16/22.14 | | | | | | | | | | | | | | (113), (119), (123), (138), (144), (149), (151), % 150.16/22.14 | | | | | | | | | | | | | | (152), (223) are inconsistent by sub-proof #36. % 150.16/22.14 | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | (224) ~ (all_54_10 = e0) % 150.16/22.14 | | | | | | | | | | | | | | (225) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 150.16/22.14 | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | BETA: splitting (32) gives: % 150.16/22.14 | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | (226) all_54_8 = e0 % 150.16/22.14 | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (226) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | | | | | | | | #731. % 150.16/22.14 | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | Case 2: % 150.16/22.14 | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | (227) ~ (all_54_8 = e0) % 150.16/22.14 | | | | | | | | | | | | | | | (228) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 150.16/22.14 | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | BETA: splitting (11) gives: % 150.16/22.14 | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | Case 1: % 150.16/22.14 | | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | | (229) all_54_3 = e0 % 150.16/22.14 | | | | | | | | | | | | | | | | % 150.16/22.14 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (180), (229) are inconsistent by sub-proof % 150.16/22.14 | | | | | | | | | | | | | | | | #733. % 150.16/22.15 | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | (230) ~ (all_54_3 = e0) % 150.16/22.15 | | | | | | | | | | | | | | | | (231) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | (232) all_56_6 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (232) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | (233) all_52_2 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | REDUCE: (126), (233) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | (234) ~ (all_10_2 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | SIMP: (234) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | (235) ~ (all_10_2 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | REDUCE: (47), (233) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | (236) ~ (all_6_2 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | SIMP: (236) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | (237) ~ (all_6_2 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (9), (10), (12), (15), (16), % 150.16/22.15 | | | | | | | | | | | | | | | | | (18), (21), (23), (28), (30), (31), (36), (37), % 150.16/22.15 | | | | | | | | | | | | | | | | | (41), (48), (52), (55), (57), (60), (62), (64), % 150.16/22.15 | | | | | | | | | | | | | | | | | (68), (76), (79), (81), (82), (87), (89), (90), % 150.16/22.15 | | | | | | | | | | | | | | | | | (92), (94), (95), (100), (102), (103), (104), % 150.16/22.15 | | | | | | | | | | | | | | | | | (107), (112), (113), (116), (117), (123), (125), % 150.16/22.15 | | | | | | | | | | | | | | | | | (127), (133), (134), (138), (144), (149), (151), % 150.16/22.15 | | | | | | | | | | | | | | | | | (152), (165), (168), (170), (174), (176), (177), % 150.16/22.15 | | | | | | | | | | | | | | | | | (180), (192), (193), (195), (199), (235), (237) % 150.16/22.15 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #34. % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | (238) ~ (all_56_6 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | REDUCE: (89), (238) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | (239) ~ (all_52_2 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | (240) all_56_0 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (240) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (241) all_10_2 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (241) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (242) all_58_28 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (157), (241) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (243) ~ (all_52_1 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (148), (241) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (244) ~ (all_52_4 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (109), (241) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (245) ~ (all_52_12 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (154), (241) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (246) op(e1, e3) = all_10_1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (102), (241) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (247) op(e3, e1) = all_58_0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_2, all_10_1, e3, e1, % 150.16/22.15 | | | | | | | | | | | | | | | | | | simplifying with (71), (246) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (248) all_52_2 = all_10_1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_58_0, e1, e3, % 150.16/22.15 | | | | | | | | | | | | | | | | | | simplifying with (182), (247) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (249) all_58_0 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (250) all_54_8 = all_10_1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (251) all_56_6 = all_10_1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (252) all_58_15 = all_10_1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (135), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (253) ~ (all_52_1 = all_10_1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (47), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (254) ~ (all_10_1 = all_6_2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (239), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (255) ~ (all_10_1 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | REDUCE: (12), (248) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | (256) ~ (all_10_1 = e0) % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | (257) all_56_0 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (240), (257) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | #796. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | (258) ~ (all_56_0 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | (259) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | REDUCE: (240), (258) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | (260) ~ (e2 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | (261) all_56_0 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (240), (261) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | #569. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | (262) ~ (all_56_0 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | (263) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (240), (262) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | (264) ~ (e3 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | (265) all_56_9 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (245), (265) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | #486. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | (266) ~ (all_56_9 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | (267) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | (268) all_58_28 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (242), (268) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | #857. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | (269) ~ (all_58_28 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | (270) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_28 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (242), (271) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | #856. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | (272) ~ (all_58_28 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (274) all_56_4 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (274) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (275) e1 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (276) e1 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (276) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_28 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (55), (81), (87), (103), (123), (138), % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (144), (149), (151), (152), (277) are inconsistent % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #483. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (278) ~ (all_56_4 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (279) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (278) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | (280) ~ (e1 = e0) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_56_4 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (174), (281) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_56_2 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (283) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_52_1 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (284) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_8 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (284) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_52_9 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (287) ~ (all_52_9 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (284) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_10_1 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (289) ~ (all_10_1 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_54_8 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (255), (290) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | #728. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_54_8 = e3 | all_54_8 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_54_8 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (289), (292) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #727. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_54_8 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (293) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_10_1 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (294) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_10_1 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (295) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_15 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (295) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) ~ (all_6_2 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (297) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) ~ (all_6_2 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_29 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (103), (299) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #707. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_30 = e3 | all_58_31 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_30 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (301) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_6_2 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (302) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) $false % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_31 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (304) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_4_2 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (305) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_56_15 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (305) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) ~ (all_52_12 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_56_1 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (308) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_52_4 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (309) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_2 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (309) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) ~ (all_52_6 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (311) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) ~ (all_52_6 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (309) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) ~ (all_52_12 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (309) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) ~ (all_8_1 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_8_1 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_56_9 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (316) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_52_12 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (317) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_52_12 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (318) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_6 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (318) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_52_13 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (320) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) ~ (all_52_13 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_56_10 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (322) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_52_13 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (323) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_52_13 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (324) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_13 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (324) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_52_9 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_31 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (26), (27), (29), (68), (84), (97), (115), % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (155), (177), (182), (203), (231), (244), % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245), (247), (263), (270), (307), (327) are % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_29 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (329) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) e2 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (330) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) $false % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_30 = e2 | all_58_31 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_56_5 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (333) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_52_9 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_52_9 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (335) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_58_11 = e3 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (335) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_52_11 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (337) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) ~ (all_52_11 = e3) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_58_30 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (339) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_6_2 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (340) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_6_2 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (341) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_56_8 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (341) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_52_6 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (341) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (e3 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_56_1 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (345) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) e3 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (346) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) e3 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (347) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_58_31 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (152), (300), (339), (348) are inconsistent by % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #476. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_56_1 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (350) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_56_3 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (351) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) e2 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (352) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_30 = e0 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (152), (304), (332), (353) are inconsistent % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #705. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_56_3 = e2) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_56_7 = e2 | all_56_13 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (354) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) ~ (e2 = e0) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_56_5 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (357) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) e3 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (358) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) e3 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (359) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_58_31 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (81), (87), (123), (149), (152), (273), % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300), (360) are inconsistent by sub-proof #655. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_56_5 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_56_8 = e1 | all_56_14 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_56_8 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (363) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) e2 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (364) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) e2 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (365) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_30 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (81), (87), (103), (152), (270), (332), % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) are inconsistent by sub-proof #662. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_56_14 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (367) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_52_11 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (368) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_52_11 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (369) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_58_26 = e1 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (369) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) ~ (all_8_1 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (371) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) ~ (all_8_1 = e1) % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_56_7 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (343), (373) are inconsistent by sub-proof % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #279. % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_56_13 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (374) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_8_1 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (375) implies: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_8_1 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (376) imply: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_58_24 = e2 % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_54_9 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (378) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_52_6 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (379) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_52_6 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (380) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_58_17 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (55), (81), (87), (103), (123), (138), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (149), (151), (152), (168), (176), (192), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (273), (285), (296), (304), (310), (319), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (328), (336), (339), (370), (377), (381) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #361. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_54_9 = e3 | all_54_9 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (312), (343), (382) are inconsistent by % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #559. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_58_31 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (55), (149), (152), (225), (298), (300), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) are inconsistent by sub-proof #475. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) ~ (all_56_5 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (384) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) ~ (all_52_9 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (209), (287), (326), (385) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #771. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_56_11 = e1 | all_56_15 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_56_11 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (387) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) e1 = e0 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (388) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) $false % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (389) is inconsistent. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_56_15 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (390) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) e3 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (391) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) e3 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (392) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) $false % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (393) is inconsistent. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_56_9 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (394) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_52_12 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (245), (307), (395) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_56_1 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (396) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) ~ (all_52_4 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_56_9 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (398) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_52_12 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (399) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_52_12 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (400) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) ~ (all_52_4 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (203), (244), (397), (401) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_56_9 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (402) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) ~ (all_52_12 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (245), (307), (403) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (404) ~ (all_56_2 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (404) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (405) ~ (all_52_1 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_56_2 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (406) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_52_1 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (407) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) $false % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (408) is inconsistent. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_56_6 = e2 | all_56_12 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_56_6 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (410) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_10_1 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (411) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_58_15 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (411) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_6_2 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (413) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_6_2 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_54_4 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (243), (415) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #832. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_54_4 = e3 | all_54_4 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_58_29 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (123), (417) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #706. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_58_30 = e2 | all_58_31 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_58_30 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (419) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_6_2 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (414), (420) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) $false % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_58_31 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) ~ (all_58_30 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (422) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_4_2 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (424) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) ~ (all_52_11 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (424) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) ~ (all_52_12 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (424) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) ~ (all_52_13 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_56_1 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (428) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_52_4 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (429) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_58_2 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (429) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_52_6 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (431) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) ~ (all_52_6 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (429) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) ~ (all_52_12 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (429) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) ~ (all_8_1 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (434) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) ~ (all_8_1 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_54_3 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (245), (436) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #723. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_54_3 = e1) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_54_3 = e3 | all_54_3 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_58_31 = e0 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (149), (414), (418), (439) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #817. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) ~ (all_58_31 = e0) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_54_4 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (405), (442) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #831. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_54_4 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (443) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_52_1 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (444) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_52_1 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (445) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_58_8 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (445) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) ~ (all_52_9 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (447) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) ~ (all_52_9 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_56_9 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (449) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_52_12 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (450) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_52_12 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (451) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_58_6 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (451) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) ~ (all_52_13 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (453) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) ~ (all_52_13 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_56_10 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (455) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_52_13 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (456) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_52_13 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (457) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_58_13 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (457) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) ~ (all_52_9 = e1) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_54_6 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (459), (460) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_54_6 = e3 | all_54_6 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_54_6 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (462) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_52_9 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (463) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_52_9 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (464) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_56_5 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (464) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_58_11 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (16), (18), (20), (28), (31), (37), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (41), (42), (55), (78), (81), (87), (92), (96), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (101), (103), (112), (116), (123), (133), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (144), (149), (152), (165), (168), (170), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172), (174), (176), (192), (193), (206), (225), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (273), (412), (414), (418), (422), (425), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428), (430), (432), (435), (441), (446), (452), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458), (465), (466) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #338. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_54_6 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (448), (467) are inconsistent by sub-proof % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #772. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) ~ (all_56_10 = e1) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (468) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) ~ (all_52_13 = e1) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (27), (40), (212), (231), (245), (426), % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427), (469) are inconsistent by sub-proof #510. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) ~ (all_56_9 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (83), (426), (438), (470) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #523. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) ~ (all_56_1 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (471) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_52_4 = e2) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_56_9 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (473) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_52_12 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (474) implies: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_52_12 = e3 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (475) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) ~ (all_52_4 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (203), (244), (472), (476) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) ~ (all_56_9 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (477) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) ~ (all_52_12 = e3) % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (231), (245), (426), (478) are inconsistent % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_56_12 = e2 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (479) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) e2 = e0 % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (480) imply: % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) $false % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (481) is inconsistent. % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.16 | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | (482) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.16/22.16 | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (12), (13), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (15), (16), (18), (21), (22), (23), (25), (27), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (28), (30), (31), (35), (36), (37), (40), (41), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (47), (48), (51), (52), (55), (57), (59), (60), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (61), (62), (64), (65), (66), (68), (72), (76), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (78), (79), (81), (82), (83), (89), (90), (92), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (94), (95), (96), (98), (99), (100), (102), (103), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (104), (106), (107), (109), (111), (112), (113), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (114), (116), (117), (119), (121), (122), (125), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (126), (127), (129), (132), (133), (134), (135), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (138), (139), (140), (142), (144), (146), (149), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (150), (151), (152), (157), (165), (168), (170), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (174), (176), (177), (180), (182), (192), (193), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (195), (198), (199), (200), (206), (212), (218), % 150.16/22.16 | | | | | | | | | | | | | | | | | | (221), (222), (228), (231), (239), (482) are % 150.16/22.16 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #31. % 150.16/22.16 | | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | | % 150.16/22.16 | | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | | % 150.16/22.16 | | | | | | | | | End of split % 150.16/22.16 | | | | | | | | | % 150.16/22.16 | | | | | | | | End of split % 150.16/22.16 | | | | | | | | % 150.16/22.16 | | | | | | | End of split % 150.16/22.16 | | | | | | | % 150.16/22.16 | | | | | | End of split % 150.16/22.16 | | | | | | % 150.16/22.16 | | | | | End of split % 150.16/22.16 | | | | | % 150.16/22.16 | | | | End of split % 150.16/22.16 | | | | % 150.16/22.16 | | | Case 2: % 150.16/22.16 | | | | % 150.16/22.16 | | | | (483) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 150.16/22.16 | | | | % 150.16/22.16 | | | | REF_CLOSE: (31), (60), (76), (112), (133), (170), (483) are inconsistent % 150.16/22.16 | | | | by sub-proof #766. % 150.16/22.16 | | | | % 150.16/22.16 | | | End of split % 150.16/22.16 | | | % 150.16/22.16 | | End of split % 150.16/22.16 | | % 150.16/22.16 | End of split % 150.16/22.16 | % 150.16/22.16 End of proof % 150.16/22.16 % 150.16/22.16 Sub-proof #31 shows that the following formulas are inconsistent: % 150.16/22.16 ---------------------------------------------------------------- % 150.16/22.16 (1) all_58_23 = all_8_0 % 150.16/22.16 (2) all_58_31 = all_4_2 % 150.16/22.16 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.16/22.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.16/22.16 (4) all_58_11 = all_52_9 % 150.16/22.16 (5) all_56_15 = all_4_2 % 150.16/22.16 (6) all_56_7 = all_52_6 % 150.16/22.16 (7) ~ (all_52_6 = all_6_2) % 150.16/22.16 (8) all_58_22 = e0 % 150.16/22.16 (9) ~ (all_52_2 = e0) % 150.16/22.16 (10) all_54_8 = all_52_2 % 150.16/22.16 (11) all_58_15 = all_52_2 % 150.16/22.16 (12) all_58_26 = all_52_11 % 150.16/22.16 (13) all_56_3 = e0 % 150.16/22.16 (14) ~ (all_52_11 = all_4_2) % 150.16/22.16 (15) all_54_7 = all_52_13 % 150.16/22.16 (16) all_58_6 = all_52_12 % 150.16/22.16 (17) all_58_4 = e0 % 150.16/22.16 (18) ~ (all_52_6 = all_8_1) % 150.16/22.16 (19) all_54_3 = all_52_12 % 150.16/22.16 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.16 (21) op(e0, e2) = all_8_1 % 150.16/22.16 (22) ~ (all_6_2 = e0) % 150.16/22.16 (23) op(e0, e1) = all_52_11 % 150.16/22.16 (24) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.16/22.17 (25) all_56_13 = all_8_1 % 150.16/22.17 (26) all_58_20 = e0 % 150.16/22.17 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 150.16/22.17 (28) ~ (all_52_12 = all_52_13) % 150.16/22.17 (29) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.16/22.17 (30) ~ (all_10_2 = e0) % 150.16/22.17 (31) ~ (all_52_2 = all_6_2) % 150.16/22.17 (32) op(e3, e3) = all_10_2 % 150.16/22.17 (33) all_54_9 = all_52_6 % 150.16/22.17 (34) ~ (all_52_13 = all_4_2) % 150.16/22.17 (35) all_58_19 = e0 % 150.16/22.17 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 150.16/22.17 (37) ~ (e3 = e1) % 150.16/22.17 (38) ~ (all_52_6 = e0) % 150.16/22.17 (39) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.16/22.17 (40) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 150.16/22.17 (41) ~ (all_52_1 = all_52_13) % 150.16/22.17 (42) all_56_5 = all_52_9 % 150.16/22.17 (43) all_54_14 = all_52_11 % 150.16/22.17 (44) op(e0, all_8_1) = all_8_0 % 150.16/22.17 (45) ~ (all_52_2 = e1) % 150.16/22.17 (46) ~ (all_52_12 = e0) % 150.16/22.17 (47) all_58_2 = all_52_4 % 150.16/22.17 (48) all_20_2 = all_4_2 % 150.16/22.17 (49) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 150.16/22.17 (50) all_56_1 = all_52_4 % 150.16/22.17 (51) all_58_9 = all_52_13 % 150.16/22.17 (52) ~ (all_52_9 = e0) % 150.16/22.17 (53) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.16/22.17 (54) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 150.16/22.17 (55) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 150.16/22.17 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.16/22.17 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.16/22.17 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 150.16/22.17 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.16/22.17 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.16/22.17 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 150.16/22.17 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.16/22.17 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.16/22.17 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 150.16/22.17 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.16/22.17 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.16/22.17 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.17 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.17 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.17 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.17 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.17 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.16/22.17 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.17 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.16/22.17 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.17 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.16/22.17 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.16/22.17 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.16/22.17 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.16/22.17 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 150.16/22.17 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.16/22.17 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.16/22.17 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.17 e0) % 150.16/22.17 (56) all_58_29 = e0 % 150.16/22.17 (57) op(e2, e1) = all_52_9 % 150.16/22.17 (58) all_56_9 = all_52_12 % 150.16/22.17 (59) all_56_6 = all_52_2 % 150.16/22.17 (60) ~ (all_52_2 = all_52_6) % 150.16/22.17 (61) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.16/22.17 (62) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.16/22.17 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.16/22.17 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.16/22.17 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.16/22.17 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.16/22.17 (all_58_27 = e0)) % 150.16/22.17 (63) ~ (all_52_9 = all_52_13) % 150.16/22.17 (64) ~ (all_52_11 = all_8_1) % 150.16/22.17 (65) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.16/22.17 (66) all_54_13 = all_8_1 % 150.16/22.17 (67) ~ (all_52_4 = e0) % 150.16/22.17 (68) op(e2, all_52_9) = all_58_10 % 150.16/22.17 (69) op(e3, all_10_2) = all_58_0 % 150.16/22.17 (70) ~ (e3 = e0) % 150.16/22.17 (71) all_56_2 = all_52_1 % 150.16/22.17 (72) all_56_4 = e0 % 150.16/22.17 (73) ~ (all_52_11 = e0) % 150.16/22.17 (74) op(e3, all_52_12) = all_58_5 % 150.16/22.17 (75) all_56_10 = all_52_13 % 150.16/22.17 (76) ~ (all_52_12 = all_10_2) % 150.16/22.17 (77) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.16/22.17 (78) all_56_14 = all_52_11 % 150.16/22.17 (79) all_58_28 = all_10_2 % 150.16/22.17 (80) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 150.16/22.17 (81) all_58_21 = all_4_2 % 150.16/22.17 (82) all_58_17 = all_52_6 % 150.16/22.17 (83) ~ (all_52_1 = all_52_9) % 150.16/22.17 (84) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 150.16/22.17 (85) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 150.16/22.17 (86) all_14_0 = all_8_0 % 150.16/22.17 (87) ~ (all_4_2 = e0) % 150.16/22.17 (88) ~ (all_8_1 = all_4_2) % 150.16/22.17 (89) all_56_12 = e0 % 150.16/22.17 (90) ~ (all_52_2 = all_10_2) % 150.16/22.17 (91) all_56_0 = all_10_2 % 150.16/22.17 (92) ~ (all_52_1 = e0) % 150.16/22.17 (93) ~ (all_52_12 = all_4_2) % 150.16/22.17 (94) all_56_8 = all_6_2 % 150.16/22.17 (95) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.16/22.17 (96) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.16/22.17 (97) ~ (all_52_1 = all_52_2) % 150.16/22.17 (98) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 150.16/22.17 (99) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.17 (100) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 150.16/22.17 (101) all_54_0 = all_10_2 % 150.16/22.17 (102) all_14_1 = all_8_1 % 150.16/22.17 (103) ~ (e1 = e0) % 150.16/22.17 (104) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 150.16/22.17 (105) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 150.16/22.17 (106) all_58_3 = all_52_12 % 150.16/22.17 (107) all_58_30 = all_6_2 % 150.16/22.17 (108) op(e2, all_52_1) = all_58_7 % 150.16/22.17 (109) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.17 (110) ~ (e3 = e2) % 150.16/22.17 (111) ~ (all_52_1 = all_10_2) % 150.16/22.17 (112) op(e3, e1) = e0 % 150.16/22.17 % 150.16/22.17 Begin of proof % 150.16/22.17 | % 150.16/22.17 | BETA: splitting (95) gives: % 150.16/22.17 | % 150.16/22.17 | Case 1: % 150.16/22.17 | | % 150.16/22.17 | | (113) all_56_2 = e1 % 150.16/22.17 | | % 150.16/22.17 | | COMBINE_EQS: (71), (113) imply: % 150.16/22.17 | | (114) all_52_1 = e1 % 150.16/22.17 | | % 150.16/22.17 | | REDUCE: (97), (114) imply: % 150.16/22.17 | | (115) ~ (all_52_2 = e1) % 150.16/22.17 | | % 150.16/22.17 | | REDUCE: (41), (114) imply: % 150.16/22.17 | | (116) ~ (all_52_13 = e1) % 150.16/22.17 | | % 150.16/22.17 | | SIMP: (116) implies: % 150.16/22.17 | | (117) ~ (all_52_13 = e1) % 150.16/22.17 | | % 150.16/22.17 | | REDUCE: (111), (114) imply: % 150.16/22.17 | | (118) ~ (all_10_2 = e1) % 150.16/22.17 | | % 150.16/22.17 | | SIMP: (118) implies: % 150.16/22.17 | | (119) ~ (all_10_2 = e1) % 150.16/22.17 | | % 150.16/22.17 | | REDUCE: (108), (114) imply: % 150.16/22.17 | | (120) op(e2, e1) = all_58_7 % 150.16/22.17 | | % 150.16/22.17 | | GROUND_INST: instantiating (3) with all_52_9, all_58_7, e1, e2, simplifying % 150.16/22.17 | | with (57), (120) gives: % 150.16/22.17 | | (121) all_58_7 = all_52_9 % 150.16/22.17 | | % 150.16/22.17 | | BETA: splitting (80) gives: % 150.16/22.17 | | % 150.16/22.17 | | Case 1: % 150.16/22.17 | | | % 150.16/22.17 | | | (122) all_56_0 = e2 % 150.16/22.17 | | | % 150.16/22.17 | | | COMBINE_EQS: (91), (122) imply: % 150.16/22.17 | | | (123) all_10_2 = e2 % 150.16/22.17 | | | % 150.16/22.17 | | | COMBINE_EQS: (79), (123) imply: % 150.16/22.17 | | | (124) all_58_28 = e2 % 150.16/22.17 | | | % 150.16/22.17 | | | REDUCE: (90), (123) imply: % 150.16/22.17 | | | (125) ~ (all_52_2 = e2) % 150.16/22.17 | | | % 150.16/22.17 | | | REDUCE: (76), (123) imply: % 150.16/22.17 | | | (126) ~ (all_52_12 = e2) % 150.16/22.17 | | | % 150.16/22.17 | | | REDUCE: (119), (123) imply: % 150.16/22.17 | | | (127) ~ (e2 = e1) % 150.16/22.17 | | | % 150.16/22.17 | | | REDUCE: (30), (123) imply: % 150.16/22.17 | | | (128) ~ (e2 = e0) % 150.16/22.17 | | | % 150.16/22.17 | | | BETA: splitting (55) gives: % 150.16/22.17 | | | % 150.16/22.17 | | | Case 1: % 150.16/22.17 | | | | % 150.16/22.17 | | | | (129) all_58_31 = e0 % 150.16/22.17 | | | | % 150.16/22.17 | | | | REF_CLOSE: (20), (37), (56), (70), (99), (103), (107), (109), (110), % 150.16/22.17 | | | | (127), (128), (129) are inconsistent by sub-proof #844. % 150.16/22.17 | | | | % 150.16/22.17 | | | Case 2: % 150.16/22.17 | | | | % 150.16/22.17 | | | | (130) ~ (all_58_31 = e0) % 150.16/22.17 | | | | (131) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = % 150.16/22.17 | | | | e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.16/22.17 | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 150.16/22.17 | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 150.16/22.17 | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 % 150.16/22.17 | | | | = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 150.16/22.17 | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 150.16/22.17 | | | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.17 | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 % 150.16/22.17 | | | | = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.16/22.17 | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 150.16/22.17 | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 % 150.16/22.17 | | | | = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 150.16/22.17 | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 150.16/22.17 | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.16/22.17 | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 % 150.16/22.17 | | | | = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.17 | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 % 150.16/22.17 | | | | = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 % 150.16/22.17 | | | | = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 150.16/22.17 | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 % 150.16/22.17 | | | | = e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 150.16/22.17 | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 % 150.16/22.17 | | | | = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & % 150.16/22.17 | | | | all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.16/22.17 | | | | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = % 150.16/22.17 | | | | e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 150.16/22.17 | | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 150.16/22.17 | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 150.16/22.17 | | | | all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 % 150.16/22.17 | | | | & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.16/22.17 | | | | all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.16/22.17 | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 150.16/22.17 | | | | all_58_26 = e0 & e1 = e0) % 150.16/22.17 | | | | % 150.16/22.17 | | | | BETA: splitting (98) gives: % 150.16/22.17 | | | | % 150.16/22.17 | | | | Case 1: % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | (132) all_54_8 = e1 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | REF_CLOSE: (10), (45), (132) are inconsistent by sub-proof #618. % 150.16/22.17 | | | | | % 150.16/22.17 | | | | Case 2: % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | (133) ~ (all_54_8 = e1) % 150.16/22.17 | | | | | (134) all_54_8 = e3 | all_54_8 = e2 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | BETA: splitting (134) gives: % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | Case 1: % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | (135) all_54_8 = e2 % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | REF_CLOSE: (10), (125), (135) are inconsistent by sub-proof #787. % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | Case 2: % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | (136) all_54_8 = e3 % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | COMBINE_EQS: (10), (136) imply: % 150.16/22.17 | | | | | | (137) all_52_2 = e3 % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | SIMP: (137) implies: % 150.16/22.17 | | | | | | (138) all_52_2 = e3 % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | REDUCE: (31), (138) imply: % 150.16/22.17 | | | | | | (139) ~ (all_6_2 = e3) % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | SIMP: (139) implies: % 150.16/22.17 | | | | | | (140) ~ (all_6_2 = e3) % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | BETA: splitting (131) gives: % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | Case 1: % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | (141) all_58_30 = e1 % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | COMBINE_EQS: (107), (141) imply: % 150.16/22.17 | | | | | | | (142) all_6_2 = e1 % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REDUCE: (140), (142) imply: % 150.16/22.17 | | | | | | | (143) ~ (e3 = e1) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REF_CLOSE: (2), (15), (19), (28), (34), (35), (37), (40), (51), % 150.16/22.17 | | | | | | | (53), (56), (58), (62), (65), (70), (81), (93), (99), % 150.16/22.17 | | | | | | | (106), (110), (124), (126), (141) are inconsistent by % 150.16/22.17 | | | | | | | sub-proof #32. % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | Case 2: % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | (144) ~ (all_58_30 = e1) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REDUCE: (107), (144) imply: % 150.16/22.17 | | | | | | | (145) ~ (all_6_2 = e1) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), % 150.16/22.17 | | | | | | | (13), (14), (16), (17), (20), (21), (22), (24), (25), % 150.16/22.17 | | | | | | | (26), (29), (32), (34), (35), (37), (38), (39), (42), % 150.16/22.17 | | | | | | | (44), (46), (47), (50), (52), (55), (56), (57), (59), % 150.16/22.17 | | | | | | | (60), (61), (62), (63), (67), (68), (69), (70), (71), % 150.16/22.17 | | | | | | | (72), (73), (75), (78), (79), (82), (83), (87), (88), % 150.16/22.17 | | | | | | | (89), (91), (94), (96), (99), (103), (107), (109), % 150.16/22.17 | | | | | | | (110), (119), (127), (128), (145) are inconsistent by % 150.16/22.17 | | | | | | | sub-proof #34. % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | End of split % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | End of split % 150.16/22.17 | | | | | % 150.16/22.17 | | | | End of split % 150.16/22.17 | | | | % 150.16/22.17 | | | End of split % 150.16/22.17 | | | % 150.16/22.17 | | Case 2: % 150.16/22.17 | | | % 150.16/22.17 | | | (146) ~ (all_56_0 = e2) % 150.16/22.17 | | | % 150.16/22.17 | | | REDUCE: (91), (146) imply: % 150.16/22.17 | | | (147) ~ (all_10_2 = e2) % 150.16/22.17 | | | % 150.16/22.17 | | | BETA: splitting (27) gives: % 150.16/22.17 | | | % 150.16/22.17 | | | Case 1: % 150.16/22.17 | | | | % 150.16/22.17 | | | | (148) all_54_0 = e1 % 150.16/22.17 | | | | % 150.16/22.17 | | | | REF_CLOSE: (101), (119), (148) are inconsistent by sub-proof #841. % 150.16/22.17 | | | | % 150.16/22.17 | | | Case 2: % 150.16/22.17 | | | | % 150.16/22.17 | | | | (149) all_54_0 = e3 | all_54_0 = e2 % 150.16/22.17 | | | | % 150.16/22.17 | | | | BETA: splitting (149) gives: % 150.16/22.17 | | | | % 150.16/22.17 | | | | Case 1: % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | (150) all_54_0 = e2 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | REF_CLOSE: (101), (147), (150) are inconsistent by sub-proof #822. % 150.16/22.17 | | | | | % 150.16/22.17 | | | | Case 2: % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | (151) all_54_0 = e3 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | COMBINE_EQS: (101), (151) imply: % 150.16/22.17 | | | | | (152) all_10_2 = e3 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | SIMP: (152) implies: % 150.16/22.17 | | | | | (153) all_10_2 = e3 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | COMBINE_EQS: (79), (153) imply: % 150.16/22.17 | | | | | (154) all_58_28 = e3 % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | REDUCE: (90), (153) imply: % 150.16/22.17 | | | | | (155) ~ (all_52_2 = e3) % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | REDUCE: (76), (153) imply: % 150.16/22.17 | | | | | (156) ~ (all_52_12 = e3) % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | BETA: splitting (98) gives: % 150.16/22.17 | | | | | % 150.16/22.17 | | | | | Case 1: % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | (157) all_54_8 = e1 % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | REF_CLOSE: (10), (45), (157) are inconsistent by sub-proof #618. % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | Case 2: % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | (158) all_54_8 = e3 | all_54_8 = e2 % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | BETA: splitting (158) gives: % 150.16/22.17 | | | | | | % 150.16/22.17 | | | | | | Case 1: % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | (159) all_54_8 = e2 % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | COMBINE_EQS: (10), (159) imply: % 150.16/22.17 | | | | | | | (160) all_52_2 = e2 % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | SIMP: (160) implies: % 150.16/22.17 | | | | | | | (161) all_52_2 = e2 % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | COMBINE_EQS: (59), (161) imply: % 150.16/22.17 | | | | | | | (162) all_56_6 = e2 % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REDUCE: (60), (161) imply: % 150.16/22.17 | | | | | | | (163) ~ (all_52_6 = e2) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | SIMP: (163) implies: % 150.16/22.17 | | | | | | | (164) ~ (all_52_6 = e2) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REDUCE: (31), (161) imply: % 150.16/22.17 | | | | | | | (165) ~ (all_6_2 = e2) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | SIMP: (165) implies: % 150.16/22.17 | | | | | | | (166) ~ (all_6_2 = e2) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REDUCE: (155), (161) imply: % 150.16/22.17 | | | | | | | (167) ~ (e3 = e2) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | REDUCE: (9), (161) imply: % 150.16/22.17 | | | | | | | (168) ~ (e2 = e0) % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | BETA: splitting (20) gives: % 150.16/22.17 | | | | | | | % 150.16/22.17 | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | (169) all_58_28 = e2 % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | COMBINE_EQS: (154), (169) imply: % 150.16/22.17 | | | | | | | | (170) e3 = e2 % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | REDUCE: (110), (170) imply: % 150.16/22.17 | | | | | | | | (171) $false % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | CLOSE: (171) is inconsistent. % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | Case 2: % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | (172) ~ (all_58_28 = e2) % 150.16/22.17 | | | | | | | | (173) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | BETA: splitting (173) gives: % 150.16/22.17 | | | | | | | | % 150.16/22.17 | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | % 150.16/22.17 | | | | | | | | | (174) all_58_29 = e2 % 150.16/22.17 | | | | | | | | | % 150.16/22.17 | | | | | | | | | REF_CLOSE: (56), (168), (174) are inconsistent by sub-proof % 150.16/22.17 | | | | | | | | | #706. % 150.16/22.17 | | | | | | | | | % 150.16/22.17 | | | | | | | | Case 2: % 150.16/22.17 | | | | | | | | | % 150.16/22.17 | | | | | | | | | (175) all_58_30 = e2 | all_58_31 = e2 % 150.16/22.17 | | | | | | | | | % 150.16/22.17 | | | | | | | | | BETA: splitting (175) gives: % 150.16/22.17 | | | | | | | | | % 150.16/22.17 | | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | (176) all_58_30 = e2 % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | COMBINE_EQS: (107), (176) imply: % 150.16/22.17 | | | | | | | | | | (177) all_6_2 = e2 % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | REDUCE: (166), (177) imply: % 150.16/22.17 | | | | | | | | | | (178) $false % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | CLOSE: (178) is inconsistent. % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | Case 2: % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | (179) all_58_31 = e2 % 150.16/22.17 | | | | | | | | | | (180) ~ (all_58_30 = e2) % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | COMBINE_EQS: (2), (179) imply: % 150.16/22.17 | | | | | | | | | | (181) all_4_2 = e2 % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | REDUCE: (93), (181) imply: % 150.16/22.17 | | | | | | | | | | (182) ~ (all_52_12 = e2) % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | REDUCE: (34), (181) imply: % 150.16/22.17 | | | | | | | | | | (183) ~ (all_52_13 = e2) % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | REDUCE: (88), (181) imply: % 150.16/22.17 | | | | | | | | | | (184) ~ (all_8_1 = e2) % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | BETA: splitting (65) gives: % 150.16/22.17 | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | (185) all_56_9 = e1 % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | COMBINE_EQS: (58), (185) imply: % 150.16/22.17 | | | | | | | | | | | (186) all_52_12 = e1 % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | SIMP: (186) implies: % 150.16/22.17 | | | | | | | | | | | (187) all_52_12 = e1 % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | REDUCE: (156), (187) imply: % 150.16/22.17 | | | | | | | | | | | (188) ~ (e3 = e1) % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | REDUCE: (182), (187) imply: % 150.16/22.17 | | | | | | | | | | | (189) ~ (e2 = e1) % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | SIMP: (189) implies: % 150.16/22.17 | | | | | | | | | | | (190) ~ (e2 = e1) % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | REDUCE: (74), (187) imply: % 150.16/22.17 | | | | | | | | | | | (191) op(e3, e1) = all_58_5 % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | BETA: splitting (109) gives: % 150.16/22.17 | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | (192) all_58_28 = e1 % 150.16/22.17 | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | REF_CLOSE: (37), (154), (192) are inconsistent by sub-proof % 150.16/22.17 | | | | | | | | | | | | #857. % 150.16/22.17 | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | Case 2: % 150.16/22.17 | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | (193) ~ (all_58_28 = e1) % 150.16/22.17 | | | | | | | | | | | | (194) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.17 | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | BETA: splitting (194) gives: % 150.16/22.17 | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | (195) all_58_29 = e1 % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | COMBINE_EQS: (56), (195) imply: % 150.16/22.17 | | | | | | | | | | | | | (196) e1 = e0 % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | REDUCE: (103), (196) imply: % 150.16/22.17 | | | | | | | | | | | | | (197) $false % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | Case 2: % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | (198) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | BETA: splitting (198) gives: % 150.16/22.17 | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | (199) all_58_30 = e1 % 150.16/22.17 | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | COMBINE_EQS: (107), (199) imply: % 150.16/22.17 | | | | | | | | | | | | | | (200) all_6_2 = e1 % 150.16/22.17 | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | SIMP: (200) implies: % 150.16/22.17 | | | | | | | | | | | | | | (201) all_6_2 = e1 % 150.16/22.17 | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | REDUCE: (7), (201) imply: % 150.16/22.17 | | | | | | | | | | | | | | (202) ~ (all_52_6 = e1) % 150.16/22.17 | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | BETA: splitting (104) gives: % 150.16/22.17 | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | Case 1: % 150.16/22.17 | | | | | | | | | | | | | | | % 150.16/22.17 | | | | | | | | | | | | | | | (203) all_56_6 = e3 % 150.16/22.17 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | COMBINE_EQS: (162), (203) imply: % 150.16/22.18 | | | | | | | | | | | | | | | (204) e3 = e2 % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | COMBINE_EQS: (154), (204) imply: % 150.16/22.18 | | | | | | | | | | | | | | | (205) all_58_28 = e2 % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (19), (28), (34), (35), (37), (40), % 150.16/22.18 | | | | | | | | | | | | | | | (51), (53), (56), (58), (62), (65), (70), (81), % 150.16/22.18 | | | | | | | | | | | | | | | (93), (99), (106), (110), (182), (199), (205) are % 150.16/22.18 | | | | | | | | | | | | | | | inconsistent by sub-proof #32. % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | (206) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | Case 1: % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | (207) all_56_7 = e3 % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (207) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | (208) all_52_6 = e3 % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | SIMP: (208) implies: % 150.16/22.18 | | | | | | | | | | | | | | | | (209) all_52_6 = e3 % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | REDUCE: (18), (209) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | (210) ~ (all_8_1 = e3) % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | SIMP: (210) implies: % 150.16/22.18 | | | | | | | | | | | | | | | | (211) ~ (all_8_1 = e3) % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | Case 1: % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | (212) all_56_12 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (212) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | (213) e1 = e0 % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (213) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | (214) all_58_30 = e0 % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (20), (37), (48), (56), (70), (79), (84), % 150.16/22.18 | | | | | | | | | | | | | | | | | (99), (103), (109), (110), (168), (190), (214) are % 150.16/22.18 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #691. % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | (215) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | (216) all_56_13 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (216) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | (217) all_8_1 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | SIMP: (217) implies: % 150.16/22.18 | | | | | | | | | | | | | | | | | | (218) all_8_1 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (218) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | (219) all_14_1 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | REDUCE: (64), (218) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | (220) ~ (all_52_11 = e1) % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | REDUCE: (44), (218) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | (221) op(e0, e1) = all_8_0 % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (13), (23), (34), (35), (37), (42), % 150.16/22.18 | | | | | | | | | | | | | | | | | | (43), (49), (54), (57), (62), (70), (73), (75), % 150.16/22.18 | | | | | | | | | | | | | | | | | | (77), (78), (86), (89), (100), (112), (113), % 150.16/22.18 | | | | | | | | | | | | | | | | | | (120), (191), (216), (219), (220), (221) are % 150.16/22.18 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391. % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | (222) ~ (all_56_13 = e1) % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | REDUCE: (25), (222) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | (223) ~ (all_8_1 = e1) % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives: % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | | (224) all_54_13 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (224) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | | (225) all_8_1 = e1 % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | | REDUCE: (223), (225) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | | | | (226) $false % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | | (227) all_54_13 = e3 | all_54_13 = e2 % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (184), (211), (227) are inconsistent by % 150.16/22.18 | | | | | | | | | | | | | | | | | | | sub-proof #339. % 150.16/22.18 | | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | (228) ~ (all_56_7 = e3) % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | REDUCE: (6), (228) imply: % 150.16/22.18 | | | | | | | | | | | | | | | | (229) ~ (all_52_6 = e3) % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (36), (164), (202), (229) are inconsistent % 150.16/22.18 | | | | | | | | | | | | | | | | by sub-proof #619. % 150.16/22.18 | | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | (230) all_58_31 = e1 % 150.16/22.18 | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | | REF_CLOSE: (107), (166), (175), (190), (230) are inconsistent % 150.16/22.18 | | | | | | | | | | | | | | by sub-proof #435. % 150.16/22.18 | | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | (231) ~ (all_56_9 = e1) % 150.16/22.18 | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | REDUCE: (58), (231) imply: % 150.16/22.18 | | | | | | | | | | | (232) ~ (all_52_12 = e1) % 150.16/22.18 | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | | REF_CLOSE: (15), (19), (28), (40), (53), (117), (182), (183), % 150.16/22.18 | | | | | | | | | | | (232) are inconsistent by sub-proof #510. % 150.16/22.18 | | | | | | | | | | | % 150.16/22.18 | | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | | % 150.16/22.18 | | | | | | | | | End of split % 150.16/22.18 | | | | | | | | | % 150.16/22.18 | | | | | | | | End of split % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | End of split % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | Case 2: % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | (233) all_54_8 = e3 % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | REF_CLOSE: (10), (155), (233) are inconsistent by sub-proof #786. % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | End of split % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | End of split % 150.16/22.18 | | | | | % 150.16/22.18 | | | | End of split % 150.16/22.18 | | | | % 150.16/22.18 | | | End of split % 150.16/22.18 | | | % 150.16/22.18 | | End of split % 150.16/22.18 | | % 150.16/22.18 | Case 2: % 150.16/22.18 | | % 150.16/22.18 | | (234) all_56_6 = e1 | all_56_12 = e1 % 150.16/22.18 | | % 150.16/22.18 | | REF_CLOSE: (45), (59), (89), (103), (234) are inconsistent by sub-proof % 150.16/22.18 | | #638. % 150.16/22.18 | | % 150.16/22.18 | End of split % 150.16/22.18 | % 150.16/22.18 End of proof % 150.16/22.18 % 150.16/22.18 Sub-proof #32 shows that the following formulas are inconsistent: % 150.16/22.18 ---------------------------------------------------------------- % 150.16/22.18 (1) all_58_31 = all_4_2 % 150.16/22.18 (2) all_54_7 = all_52_13 % 150.16/22.18 (3) all_54_3 = all_52_12 % 150.16/22.18 (4) ~ (all_52_12 = all_52_13) % 150.16/22.18 (5) ~ (all_52_13 = all_4_2) % 150.16/22.18 (6) all_58_19 = e0 % 150.16/22.18 (7) ~ (e3 = e1) % 150.16/22.18 (8) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 150.16/22.18 (9) all_58_9 = all_52_13 % 150.16/22.18 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.16/22.18 (11) all_58_29 = e0 % 150.16/22.18 (12) all_56_9 = all_52_12 % 150.16/22.18 (13) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.16/22.18 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.16/22.18 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.16/22.18 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.16/22.18 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.16/22.18 (all_58_27 = e0)) % 150.16/22.18 (14) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.16/22.18 (15) ~ (e3 = e0) % 150.16/22.18 (16) all_58_30 = e1 % 150.16/22.18 (17) all_58_21 = all_4_2 % 150.16/22.18 (18) ~ (all_52_12 = all_4_2) % 150.16/22.18 (19) all_58_28 = e2 % 150.16/22.18 (20) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.18 (21) all_58_3 = all_52_12 % 150.16/22.18 (22) ~ (e3 = e2) % 150.16/22.18 (23) ~ (all_52_12 = e2) % 150.16/22.18 % 150.16/22.18 Begin of proof % 150.16/22.18 | % 150.16/22.18 | BETA: splitting (20) gives: % 150.16/22.18 | % 150.16/22.18 | Case 1: % 150.16/22.18 | | % 150.16/22.18 | | (24) all_58_28 = e3 % 150.16/22.18 | | % 150.16/22.18 | | REF_CLOSE: (19), (22), (24) are inconsistent by sub-proof #849. % 150.16/22.18 | | % 150.16/22.18 | Case 2: % 150.16/22.18 | | % 150.16/22.18 | | (25) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.18 | | % 150.16/22.18 | | BETA: splitting (25) gives: % 150.16/22.18 | | % 150.16/22.18 | | Case 1: % 150.16/22.18 | | | % 150.16/22.18 | | | (26) all_58_29 = e3 % 150.16/22.18 | | | % 150.16/22.18 | | | COMBINE_EQS: (11), (26) imply: % 150.16/22.18 | | | (27) e3 = e0 % 150.16/22.18 | | | % 150.16/22.18 | | | REDUCE: (15), (27) imply: % 150.16/22.18 | | | (28) $false % 150.16/22.18 | | | % 150.16/22.18 | | | CLOSE: (28) is inconsistent. % 150.16/22.18 | | | % 150.16/22.18 | | Case 2: % 150.16/22.18 | | | % 150.16/22.18 | | | (29) all_58_30 = e3 | all_58_31 = e3 % 150.16/22.18 | | | % 150.16/22.18 | | | BETA: splitting (29) gives: % 150.16/22.18 | | | % 150.16/22.18 | | | Case 1: % 150.16/22.18 | | | | % 150.16/22.18 | | | | (30) all_58_30 = e3 % 150.16/22.18 | | | | % 150.16/22.18 | | | | COMBINE_EQS: (16), (30) imply: % 150.16/22.18 | | | | (31) e3 = e1 % 150.16/22.18 | | | | % 150.16/22.18 | | | | REDUCE: (7), (31) imply: % 150.16/22.18 | | | | (32) $false % 150.16/22.18 | | | | % 150.16/22.18 | | | | CLOSE: (32) is inconsistent. % 150.16/22.18 | | | | % 150.16/22.18 | | | Case 2: % 150.16/22.18 | | | | % 150.16/22.18 | | | | (33) all_58_31 = e3 % 150.16/22.18 | | | | % 150.16/22.18 | | | | COMBINE_EQS: (1), (33) imply: % 150.16/22.18 | | | | (34) all_4_2 = e3 % 150.16/22.18 | | | | % 150.16/22.18 | | | | SIMP: (34) implies: % 150.16/22.18 | | | | (35) all_4_2 = e3 % 150.16/22.18 | | | | % 150.16/22.18 | | | | COMBINE_EQS: (17), (35) imply: % 150.16/22.18 | | | | (36) all_58_21 = e3 % 150.16/22.18 | | | | % 150.16/22.18 | | | | REDUCE: (18), (35) imply: % 150.16/22.18 | | | | (37) ~ (all_52_12 = e3) % 150.16/22.18 | | | | % 150.16/22.18 | | | | REDUCE: (5), (35) imply: % 150.16/22.18 | | | | (38) ~ (all_52_13 = e3) % 150.16/22.18 | | | | % 150.16/22.18 | | | | BETA: splitting (14) gives: % 150.16/22.18 | | | | % 150.16/22.18 | | | | Case 1: % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | (39) all_56_9 = e1 % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | COMBINE_EQS: (12), (39) imply: % 150.16/22.18 | | | | | (40) all_52_12 = e1 % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | SIMP: (40) implies: % 150.16/22.18 | | | | | (41) all_52_12 = e1 % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | COMBINE_EQS: (21), (41) imply: % 150.16/22.18 | | | | | (42) all_58_3 = e1 % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | REDUCE: (4), (41) imply: % 150.16/22.18 | | | | | (43) ~ (all_52_13 = e1) % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | SIMP: (43) implies: % 150.16/22.18 | | | | | (44) ~ (all_52_13 = e1) % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | BETA: splitting (8) gives: % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | Case 1: % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | | (45) all_54_7 = e1 % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | | REF_CLOSE: (2), (44), (45) are inconsistent by sub-proof #605. % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | Case 2: % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | | (46) all_54_7 = e3 | all_54_7 = e2 % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | | BETA: splitting (13) gives: % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | | Case 1: % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | (47) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = % 150.16/22.18 | | | | | | | e1) & ~ (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ % 150.16/22.18 | | | | | | | (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ (all_58_12 = % 150.16/22.18 | | | | | | | e0)) % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | BETA: splitting (47) gives: % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | Case 1: % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | (48) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = % 150.16/22.18 | | | | | | | | e1) & ~ (all_58_5 = e0) % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | ALPHA: (48) implies: % 150.16/22.18 | | | | | | | | (49) ~ (all_58_3 = e1) % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | REDUCE: (42), (49) imply: % 150.16/22.18 | | | | | | | | (50) $false % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | CLOSE: (50) is inconsistent. % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | Case 2: % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | (51) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 % 150.16/22.18 | | | | | | | | = e1) & ~ (all_58_12 = e0) % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | ALPHA: (51) implies: % 150.16/22.18 | | | | | | | | (52) ~ (all_58_9 = e2) % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | REDUCE: (9), (52) imply: % 150.16/22.18 | | | | | | | | (53) ~ (all_52_13 = e2) % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | | REF_CLOSE: (2), (38), (46), (53) are inconsistent by sub-proof % 150.16/22.18 | | | | | | | | #511. % 150.16/22.18 | | | | | | | | % 150.16/22.18 | | | | | | | End of split % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | Case 2: % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | (54) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 % 150.16/22.18 | | | | | | | = e1) & ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & % 150.16/22.18 | | | | | | | ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ (all_58_27 % 150.16/22.18 | | | | | | | = e0)) % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | | REF_CLOSE: (6), (36), (54) are inconsistent by sub-proof #616. % 150.16/22.18 | | | | | | | % 150.16/22.18 | | | | | | End of split % 150.16/22.18 | | | | | | % 150.16/22.18 | | | | | End of split % 150.16/22.18 | | | | | % 150.16/22.18 | | | | Case 2: % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | (55) ~ (all_56_9 = e1) % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | REDUCE: (12), (55) imply: % 150.16/22.18 | | | | | (56) ~ (all_52_12 = e1) % 150.16/22.18 | | | | | % 150.16/22.18 | | | | | REF_CLOSE: (3), (10), (23), (37), (56) are inconsistent by sub-proof % 150.16/22.18 | | | | | #612. % 150.16/22.18 | | | | | % 150.16/22.18 | | | | End of split % 150.16/22.18 | | | | % 150.16/22.18 | | | End of split % 150.16/22.18 | | | % 150.16/22.18 | | End of split % 150.16/22.18 | | % 150.16/22.18 | End of split % 150.16/22.18 | % 150.16/22.18 End of proof % 150.16/22.18 % 150.16/22.18 Sub-proof #33 shows that the following formulas are inconsistent: % 150.16/22.18 ---------------------------------------------------------------- % 150.16/22.18 (1) all_56_4 = e3 % 150.16/22.18 (2) all_56_4 = e0 % 150.16/22.18 (3) ~ (e3 = e0) % 150.16/22.18 % 150.16/22.18 Begin of proof % 150.16/22.18 | % 150.16/22.18 | COMBINE_EQS: (1), (2) imply: % 150.16/22.18 | (4) e3 = e0 % 150.16/22.18 | % 150.16/22.18 | SIMP: (4) implies: % 150.16/22.18 | (5) e3 = e0 % 150.16/22.18 | % 150.16/22.18 | REDUCE: (3), (5) imply: % 150.16/22.18 | (6) $false % 150.16/22.18 | % 150.16/22.18 | CLOSE: (6) is inconsistent. % 150.16/22.18 | % 150.16/22.18 End of proof % 150.16/22.18 % 150.16/22.18 Sub-proof #34 shows that the following formulas are inconsistent: % 150.16/22.18 ---------------------------------------------------------------- % 150.16/22.18 (1) all_58_23 = all_8_0 % 150.16/22.18 (2) all_58_31 = all_4_2 % 150.16/22.18 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.16/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.16/22.18 (4) all_58_11 = all_52_9 % 150.16/22.18 (5) all_56_7 = all_52_6 % 150.16/22.18 (6) ~ (all_52_6 = all_6_2) % 150.16/22.18 (7) all_58_22 = e0 % 150.16/22.18 (8) ~ (all_52_2 = e0) % 150.16/22.18 (9) all_58_15 = all_52_2 % 150.16/22.18 (10) all_58_26 = all_52_11 % 150.16/22.18 (11) all_56_3 = e0 % 150.16/22.18 (12) ~ (all_52_11 = all_4_2) % 150.16/22.18 (13) all_58_6 = all_52_12 % 150.16/22.18 (14) all_58_4 = e0 % 150.16/22.18 (15) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.18 (16) op(e0, e2) = all_8_1 % 150.16/22.18 (17) ~ (all_6_2 = e0) % 150.16/22.18 (18) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.16/22.18 (19) all_56_13 = all_8_1 % 150.16/22.18 (20) all_58_20 = e0 % 150.16/22.18 (21) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.16/22.18 (22) op(e3, e3) = all_10_2 % 150.16/22.18 (23) ~ (all_52_13 = all_4_2) % 150.16/22.18 (24) all_58_19 = e0 % 150.16/22.18 (25) ~ (e3 = e1) % 150.16/22.18 (26) ~ (all_52_6 = e0) % 150.16/22.18 (27) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.16/22.18 (28) all_56_5 = all_52_9 % 150.16/22.18 (29) op(e0, all_8_1) = all_8_0 % 150.16/22.18 (30) ~ (all_52_12 = e0) % 150.16/22.18 (31) all_58_2 = all_52_4 % 150.16/22.18 (32) all_56_1 = all_52_4 % 150.16/22.18 (33) ~ (all_10_2 = e1) % 150.16/22.18 (34) ~ (all_52_9 = e0) % 150.16/22.18 (35) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 150.16/22.18 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.16/22.18 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.16/22.18 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 150.16/22.18 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.16/22.18 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.16/22.18 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 150.16/22.18 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.16/22.18 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.16/22.18 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 150.16/22.18 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.16/22.18 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.16/22.18 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.18 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.18 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.18 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.18 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.18 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.16/22.18 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.18 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.16/22.18 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.18 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.16/22.18 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.16/22.18 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.16/22.18 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.16/22.18 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 150.16/22.18 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.16/22.18 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.16/22.18 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.18 e0) % 150.16/22.18 (36) all_58_29 = e0 % 150.16/22.18 (37) op(e2, e1) = all_52_9 % 150.16/22.18 (38) ~ (e2 = e1) % 150.16/22.18 (39) all_56_6 = all_52_2 % 150.16/22.18 (40) ~ (all_52_2 = all_52_6) % 150.16/22.18 (41) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.16/22.18 (42) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.16/22.18 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.16/22.18 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.16/22.18 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.16/22.18 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.16/22.18 (all_58_27 = e0)) % 150.16/22.18 (43) ~ (all_52_9 = all_52_13) % 150.16/22.18 (44) ~ (all_52_4 = e0) % 150.16/22.18 (45) op(e2, all_52_9) = all_58_10 % 150.16/22.18 (46) op(e3, all_10_2) = all_58_0 % 150.16/22.18 (47) ~ (e3 = e0) % 150.16/22.18 (48) all_56_2 = all_52_1 % 150.16/22.18 (49) all_56_4 = e0 % 150.16/22.18 (50) ~ (all_52_11 = e0) % 150.16/22.18 (51) all_56_10 = all_52_13 % 150.16/22.18 (52) all_56_14 = all_52_11 % 150.16/22.18 (53) all_58_28 = all_10_2 % 150.16/22.18 (54) all_58_17 = all_52_6 % 150.16/22.18 (55) ~ (all_52_1 = all_52_9) % 150.16/22.18 (56) ~ (e2 = e0) % 150.16/22.18 (57) ~ (all_4_2 = e0) % 150.16/22.18 (58) ~ (all_8_1 = all_4_2) % 150.16/22.18 (59) all_56_12 = e0 % 150.16/22.18 (60) all_56_0 = all_10_2 % 150.16/22.18 (61) all_56_8 = all_6_2 % 150.16/22.18 (62) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.16/22.18 (63) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.18 (64) ~ (e1 = e0) % 150.16/22.18 (65) ~ (all_6_2 = e1) % 150.16/22.18 (66) all_58_30 = all_6_2 % 150.16/22.18 (67) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.18 (68) ~ (e3 = e2) % 150.16/22.18 % 150.16/22.18 Begin of proof % 150.16/22.18 | % 150.16/22.18 | BETA: splitting (67) gives: % 150.16/22.18 | % 150.16/22.18 | Case 1: % 150.16/22.18 | | % 150.16/22.18 | | (69) all_58_28 = e1 % 150.16/22.18 | | % 150.16/22.18 | | COMBINE_EQS: (53), (69) imply: % 150.16/22.18 | | (70) all_10_2 = e1 % 150.16/22.18 | | % 150.16/22.18 | | REDUCE: (33), (70) imply: % 150.16/22.18 | | (71) $false % 150.16/22.18 | | % 150.16/22.18 | | CLOSE: (71) is inconsistent. % 150.16/22.18 | | % 150.16/22.18 | Case 2: % 150.16/22.18 | | % 150.16/22.18 | | (72) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.18 | | % 150.16/22.18 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 150.16/22.18 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 150.16/22.18 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), % 150.16/22.18 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 150.16/22.18 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 150.16/22.18 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 150.16/22.18 | | (72) are inconsistent by sub-proof #35. % 150.16/22.18 | | % 150.16/22.18 | End of split % 150.16/22.18 | % 150.16/22.18 End of proof % 150.16/22.18 % 150.16/22.18 Sub-proof #35 shows that the following formulas are inconsistent: % 150.16/22.18 ---------------------------------------------------------------- % 150.16/22.18 (1) all_58_23 = all_8_0 % 150.16/22.18 (2) all_58_31 = all_4_2 % 150.16/22.18 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.16/22.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.16/22.18 (4) all_58_11 = all_52_9 % 150.16/22.18 (5) all_56_7 = all_52_6 % 150.16/22.18 (6) ~ (all_52_6 = all_6_2) % 150.16/22.18 (7) all_58_22 = e0 % 150.16/22.18 (8) ~ (all_52_2 = e0) % 150.16/22.18 (9) all_58_15 = all_52_2 % 150.16/22.18 (10) all_58_26 = all_52_11 % 150.16/22.18 (11) all_56_3 = e0 % 150.16/22.18 (12) ~ (all_52_11 = all_4_2) % 150.16/22.18 (13) all_58_6 = all_52_12 % 150.16/22.18 (14) all_58_4 = e0 % 150.16/22.18 (15) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.18 (16) op(e0, e2) = all_8_1 % 150.16/22.18 (17) ~ (all_6_2 = e0) % 150.16/22.18 (18) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.16/22.18 (19) all_56_13 = all_8_1 % 150.16/22.18 (20) all_58_20 = e0 % 150.16/22.18 (21) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.16/22.18 (22) op(e3, e3) = all_10_2 % 150.16/22.18 (23) ~ (all_52_13 = all_4_2) % 150.16/22.18 (24) all_58_19 = e0 % 150.16/22.18 (25) ~ (e3 = e1) % 150.16/22.18 (26) ~ (all_52_6 = e0) % 150.16/22.19 (27) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.16/22.19 (28) all_56_5 = all_52_9 % 150.16/22.19 (29) op(e0, all_8_1) = all_8_0 % 150.16/22.19 (30) ~ (all_52_12 = e0) % 150.16/22.19 (31) all_58_2 = all_52_4 % 150.16/22.19 (32) all_56_1 = all_52_4 % 150.16/22.19 (33) ~ (all_52_9 = e0) % 150.16/22.19 (34) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 150.16/22.19 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.16/22.19 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.16/22.19 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 150.16/22.19 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.16/22.19 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.16/22.19 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 150.16/22.19 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.16/22.19 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.16/22.19 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 150.16/22.19 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.16/22.19 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.16/22.19 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.19 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.19 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.19 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.19 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.19 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.16/22.19 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.19 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.16/22.19 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.19 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.16/22.19 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.16/22.19 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.16/22.19 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.16/22.19 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 150.16/22.19 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.16/22.19 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.16/22.19 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.19 e0) % 150.16/22.19 (35) all_58_29 = e0 % 150.16/22.19 (36) op(e2, e1) = all_52_9 % 150.16/22.19 (37) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.19 (38) ~ (e2 = e1) % 150.16/22.19 (39) all_56_6 = all_52_2 % 150.16/22.19 (40) ~ (all_52_2 = all_52_6) % 150.16/22.19 (41) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.16/22.19 (42) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.16/22.19 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.16/22.19 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.16/22.19 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.16/22.19 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.16/22.19 (all_58_27 = e0)) % 150.16/22.19 (43) ~ (all_52_9 = all_52_13) % 150.16/22.19 (44) ~ (all_52_4 = e0) % 150.16/22.19 (45) op(e2, all_52_9) = all_58_10 % 150.16/22.19 (46) op(e3, all_10_2) = all_58_0 % 150.16/22.19 (47) ~ (e3 = e0) % 150.16/22.19 (48) all_56_2 = all_52_1 % 150.16/22.19 (49) all_56_4 = e0 % 150.16/22.19 (50) ~ (all_52_11 = e0) % 150.16/22.19 (51) all_56_10 = all_52_13 % 150.16/22.19 (52) all_56_14 = all_52_11 % 150.16/22.19 (53) all_58_28 = all_10_2 % 150.16/22.19 (54) all_58_17 = all_52_6 % 150.16/22.19 (55) ~ (all_52_1 = all_52_9) % 150.16/22.19 (56) ~ (e2 = e0) % 150.16/22.19 (57) ~ (all_4_2 = e0) % 150.16/22.19 (58) ~ (all_8_1 = all_4_2) % 150.16/22.19 (59) all_56_12 = e0 % 150.16/22.19 (60) all_56_0 = all_10_2 % 150.16/22.19 (61) all_56_8 = all_6_2 % 150.16/22.19 (62) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.16/22.19 (63) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.19 (64) ~ (e1 = e0) % 150.16/22.19 (65) ~ (all_6_2 = e1) % 150.16/22.19 (66) all_58_30 = all_6_2 % 150.16/22.19 (67) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.19 (68) ~ (e3 = e2) % 150.16/22.19 % 150.16/22.19 Begin of proof % 150.16/22.19 | % 150.16/22.19 | BETA: splitting (37) gives: % 150.16/22.19 | % 150.16/22.19 | Case 1: % 150.16/22.19 | | % 150.16/22.19 | | (69) all_58_29 = e1 % 150.16/22.19 | | % 150.16/22.19 | | REF_CLOSE: (35), (64), (69) are inconsistent by sub-proof #700. % 150.16/22.19 | | % 150.16/22.19 | Case 2: % 150.16/22.19 | | % 150.16/22.19 | | (70) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.19 | | % 150.16/22.19 | | BETA: splitting (70) gives: % 150.16/22.19 | | % 150.16/22.19 | | Case 1: % 150.16/22.19 | | | % 150.16/22.19 | | | (71) all_58_30 = e1 % 150.16/22.19 | | | % 150.16/22.19 | | | COMBINE_EQS: (66), (71) imply: % 150.16/22.19 | | | (72) all_6_2 = e1 % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (65), (72) imply: % 150.16/22.19 | | | (73) $false % 150.16/22.19 | | | % 150.16/22.19 | | | CLOSE: (73) is inconsistent. % 150.16/22.19 | | | % 150.16/22.19 | | Case 2: % 150.16/22.19 | | | % 150.16/22.19 | | | (74) all_58_31 = e1 % 150.16/22.19 | | | % 150.16/22.19 | | | COMBINE_EQS: (2), (74) imply: % 150.16/22.19 | | | (75) all_4_2 = e1 % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (12), (75) imply: % 150.16/22.19 | | | (76) ~ (all_52_11 = e1) % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (23), (75) imply: % 150.16/22.19 | | | (77) ~ (all_52_13 = e1) % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (58), (75) imply: % 150.16/22.19 | | | (78) ~ (all_8_1 = e1) % 150.16/22.19 | | | % 150.16/22.19 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), % 150.16/22.19 | | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), % 150.16/22.19 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 150.16/22.19 | | | (36), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 150.16/22.19 | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 150.16/22.19 | | | (59), (60), (61), (62), (63), (64), (66), (67), (68), (74), % 150.16/22.19 | | | (76), (77), (78) are inconsistent by sub-proof #270. % 150.16/22.19 | | | % 150.16/22.19 | | End of split % 150.16/22.19 | | % 150.16/22.19 | End of split % 150.16/22.19 | % 150.16/22.19 End of proof % 150.16/22.19 % 150.16/22.19 Sub-proof #36 shows that the following formulas are inconsistent: % 150.16/22.19 ---------------------------------------------------------------- % 150.16/22.19 (1) all_58_31 = all_4_2 % 150.16/22.19 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.19 (3) all_54_10 = all_6_2 % 150.16/22.19 (4) ~ (e3 = e1) % 150.16/22.19 (5) all_20_2 = all_4_2 % 150.16/22.19 (6) all_58_29 = e0 % 150.16/22.19 (7) ~ (e2 = e1) % 150.16/22.19 (8) ~ (e3 = e0) % 150.16/22.19 (9) all_58_28 = all_10_2 % 150.16/22.19 (10) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 150.16/22.19 (11) ~ (e2 = e0) % 150.16/22.19 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.19 (13) ~ (e1 = e0) % 150.16/22.19 (14) all_54_10 = e0 % 150.16/22.19 (15) all_58_30 = all_6_2 % 150.16/22.19 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.19 (17) ~ (e3 = e2) % 150.16/22.19 % 150.16/22.19 Begin of proof % 150.16/22.19 | % 150.16/22.19 | COMBINE_EQS: (3), (14) imply: % 150.16/22.19 | (18) all_6_2 = e0 % 150.16/22.19 | % 150.16/22.19 | SIMP: (18) implies: % 150.16/22.19 | (19) all_6_2 = e0 % 150.16/22.19 | % 150.16/22.19 | COMBINE_EQS: (15), (19) imply: % 150.16/22.19 | (20) all_58_30 = e0 % 150.16/22.19 | % 150.16/22.19 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.16/22.19 | (16), (17), (20) are inconsistent by sub-proof #691. % 150.16/22.19 | % 150.16/22.19 End of proof % 150.16/22.19 % 150.16/22.19 Sub-proof #37 shows that the following formulas are inconsistent: % 150.16/22.19 ---------------------------------------------------------------- % 150.16/22.19 (1) all_58_23 = all_8_0 % 150.16/22.19 (2) all_58_31 = all_4_2 % 150.16/22.19 (3) ~ (all_52_8 = all_52_9) % 150.16/22.19 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.16/22.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.16/22.19 (5) all_58_11 = all_52_9 % 150.16/22.19 (6) all_56_7 = all_52_6 % 150.16/22.19 (7) all_54_2 = all_52_8 % 150.16/22.19 (8) ~ (all_48_0 = e1) | ~ (all_48_1 = e3) % 150.16/22.19 (9) ~ (all_10_1 = e0) % 150.16/22.19 (10) op(e1, all_6_2) = all_58_18 % 150.16/22.19 (11) ~ (all_52_8 = all_10_2) % 150.16/22.19 (12) all_58_26 = all_52_11 % 150.16/22.19 (13) all_56_3 = e0 % 150.16/22.19 (14) ~ (all_52_8 = all_52_11) % 150.16/22.19 (15) all_58_6 = all_52_12 % 150.16/22.19 (16) all_56_4 = all_52_8 % 150.16/22.19 (17) all_56_6 = e0 % 150.16/22.19 (18) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.19 (19) op(e0, e2) = all_8_1 % 150.16/22.19 (20) all_56_13 = all_8_1 % 150.16/22.19 (21) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.16/22.19 (22) all_54_11 = all_52_14 % 150.16/22.19 (23) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 150.16/22.19 (24) all_58_20 = all_52_14 % 150.16/22.19 (25) ~ (all_52_8 = all_6_2) % 150.16/22.19 (26) op(e2, e3) = all_52_1 % 150.16/22.19 (27) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.16/22.19 (28) ~ (all_52_6 = all_52_14) % 150.16/22.19 (29) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.16/22.19 (30) ~ (all_52_8 = all_52_12) % 150.16/22.19 (31) ~ (all_52_13 = all_4_2) % 150.16/22.19 (32) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 150.16/22.19 (33) ~ (all_52_3 = e0) % 150.16/22.19 (34) ~ (e3 = e1) % 150.16/22.19 (35) ~ (all_52_6 = e0) % 150.16/22.19 (36) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.16/22.19 (37) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.16/22.19 (38) all_56_5 = all_52_9 % 150.16/22.19 (39) op(e0, all_8_1) = all_8_0 % 150.16/22.19 (40) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 150.16/22.19 (41) all_56_12 = all_52_3 % 150.16/22.19 (42) all_56_1 = all_52_4 % 150.16/22.19 (43) ~ (all_52_3 = all_4_2) % 150.16/22.19 (44) all_58_9 = all_52_13 % 150.16/22.19 (45) op(e0, all_52_11) = all_58_25 % 150.16/22.19 (46) op(e1, e0) = all_52_14 % 150.16/22.19 (47) ~ (all_52_13 = all_52_14) % 150.16/22.19 (48) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 150.16/22.19 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.16/22.19 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.16/22.19 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 150.16/22.19 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.16/22.19 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.16/22.19 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 150.16/22.19 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.16/22.19 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.16/22.19 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 150.16/22.19 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.16/22.19 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.16/22.19 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.19 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.19 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.19 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.19 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.19 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.16/22.19 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.19 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.16/22.19 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.19 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.16/22.19 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.16/22.19 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.16/22.19 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.16/22.19 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 150.16/22.19 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.16/22.19 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.16/22.19 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.19 e0) % 150.16/22.19 (49) ~ (all_52_4 = all_52_8) % 150.16/22.19 (50) all_58_29 = e0 % 150.16/22.19 (51) all_56_9 = all_52_12 % 150.16/22.19 (52) ~ (all_52_12 = all_52_14) % 150.16/22.19 (53) all_58_8 = all_52_1 % 150.16/22.19 (54) op(e1, e3) = e0 % 150.16/22.19 (55) ~ (e2 = e1) % 150.16/22.19 (56) op(e3, e0) = all_52_12 % 150.16/22.19 (57) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 150.16/22.19 (58) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.16/22.19 (59) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.16/22.19 (60) all_58_15 = e0 % 150.16/22.19 (61) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.16/22.19 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.16/22.19 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.16/22.19 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.16/22.19 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.16/22.19 (all_58_27 = e0)) % 150.16/22.19 (62) ~ (all_52_11 = all_8_1) % 150.16/22.19 (63) all_54_13 = all_8_1 % 150.16/22.19 (64) ~ (all_52_4 = e0) % 150.16/22.19 (65) ~ (all_52_11 = all_6_2) % 150.16/22.19 (66) ~ (e3 = e0) % 150.16/22.19 (67) all_56_2 = all_52_1 % 150.16/22.19 (68) op(e0, e3) = all_52_3 % 150.16/22.19 (69) op(e3, all_52_12) = all_58_5 % 150.16/22.19 (70) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.16/22.19 (71) all_56_10 = all_52_13 % 150.16/22.19 (72) ~ (all_52_3 = all_8_1) % 150.16/22.19 (73) ~ (all_52_1 = all_52_3) % 150.16/22.19 (74) all_56_14 = all_52_11 % 150.16/22.19 (75) all_58_28 = all_10_2 % 150.16/22.19 (76) all_58_17 = all_52_6 % 150.16/22.19 (77) ~ (all_52_1 = all_52_9) % 150.16/22.19 (78) all_48_1 = all_8_1 % 150.16/22.19 (79) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.16/22.19 (80) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 150.16/22.19 (81) ~ (e2 = e0) % 150.16/22.19 (82) ~ (all_52_9 = all_6_2) % 150.16/22.19 (83) ~ (all_8_1 = all_4_2) % 150.16/22.19 (84) all_56_0 = all_10_2 % 150.16/22.19 (85) op(e0, e0) = all_4_2 % 150.16/22.19 (86) ~ (all_52_1 = e0) % 150.16/22.19 (87) ~ (all_52_3 = all_52_11) % 150.16/22.19 (88) all_58_22 = all_52_3 % 150.16/22.19 (89) ~ (all_52_12 = all_4_2) % 150.16/22.19 (90) ~ (all_52_3 = all_10_2) % 150.16/22.19 (91) op(e1, e1) = all_6_2 % 150.16/22.19 (92) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 150.16/22.19 (93) all_58_4 = all_52_8 % 150.16/22.19 (94) ~ (all_8_1 = e0) % 150.16/22.19 (95) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.19 (96) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 150.16/22.19 (97) all_54_0 = all_10_2 % 150.16/22.19 (98) ~ (all_52_14 = all_4_2) % 150.16/22.19 (99) ~ (e1 = e0) % 150.16/22.19 (100) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.16/22.19 (101) op(e1, e0) = all_58_14 % 150.16/22.19 (102) ~ (all_52_4 = all_10_2) % 150.16/22.19 (103) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 150.16/22.19 (104) all_58_30 = all_6_2 % 150.16/22.19 (105) op(e2, all_52_1) = all_58_7 % 150.16/22.19 (106) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.19 (107) ~ (e3 = e2) % 150.16/22.19 (108) ~ (all_52_14 = all_6_2) % 150.16/22.19 (109) op(all_10_2, e3) = all_10_1 % 150.16/22.19 (110) all_48_0 = all_8_0 % 150.16/22.19 (111) all_54_12 = all_52_3 % 150.16/22.19 (112) all_54_4 = all_52_1 % 150.16/22.19 (113) ~ (all_52_1 = all_10_2) % 150.16/22.19 % 150.16/22.19 Begin of proof % 150.16/22.19 | % 150.16/22.19 | BETA: splitting (103) gives: % 150.16/22.19 | % 150.16/22.19 | Case 1: % 150.16/22.19 | | % 150.16/22.19 | | (114) all_56_12 = e0 % 150.16/22.19 | | % 150.16/22.19 | | REF_CLOSE: (33), (41), (114) are inconsistent by sub-proof #607. % 150.16/22.19 | | % 150.16/22.19 | Case 2: % 150.16/22.19 | | % 150.16/22.19 | | (115) all_56_13 = e0 | all_56_14 = e0 % 150.16/22.19 | | % 150.16/22.19 | | BETA: splitting (115) gives: % 150.16/22.19 | | % 150.16/22.19 | | Case 1: % 150.16/22.19 | | | % 150.16/22.19 | | | (116) all_56_13 = e0 % 150.16/22.19 | | | % 150.16/22.19 | | | REF_CLOSE: (20), (94), (116) are inconsistent by sub-proof #269. % 150.16/22.19 | | | % 150.16/22.19 | | Case 2: % 150.16/22.19 | | | % 150.16/22.19 | | | (117) all_56_14 = e0 % 150.16/22.19 | | | % 150.16/22.19 | | | COMBINE_EQS: (74), (117) imply: % 150.16/22.19 | | | (118) all_52_11 = e0 % 150.16/22.19 | | | % 150.16/22.19 | | | SIMP: (118) implies: % 150.16/22.19 | | | (119) all_52_11 = e0 % 150.16/22.19 | | | % 150.16/22.19 | | | COMBINE_EQS: (12), (119) imply: % 150.16/22.19 | | | (120) all_58_26 = e0 % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (14), (119) imply: % 150.16/22.19 | | | (121) ~ (all_52_8 = e0) % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (62), (119) imply: % 150.16/22.19 | | | (122) ~ (all_8_1 = e0) % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (65), (119) imply: % 150.16/22.19 | | | (123) ~ (all_6_2 = e0) % 150.16/22.19 | | | % 150.16/22.19 | | | SIMP: (123) implies: % 150.16/22.19 | | | (124) ~ (all_6_2 = e0) % 150.16/22.19 | | | % 150.16/22.19 | | | REDUCE: (45), (119) imply: % 150.16/22.19 | | | (125) op(e0, e0) = all_58_25 % 150.16/22.19 | | | % 150.16/22.19 | | | BETA: splitting (40) gives: % 150.16/22.19 | | | % 150.16/22.19 | | | Case 1: % 150.16/22.19 | | | | % 150.16/22.19 | | | | (126) all_56_0 = e0 % 150.16/22.19 | | | | % 150.16/22.19 | | | | COMBINE_EQS: (84), (126) imply: % 150.16/22.19 | | | | (127) all_10_2 = e0 % 150.16/22.19 | | | | % 150.16/22.19 | | | | COMBINE_EQS: (75), (127) imply: % 150.16/22.19 | | | | (128) all_58_28 = e0 % 150.16/22.19 | | | | % 150.16/22.19 | | | | REF_CLOSE: (18), (34), (50), (55), (66), (81), (95), (99), (104), (106), % 150.16/22.19 | | | | (107), (128) are inconsistent by sub-proof #483. % 150.16/22.19 | | | | % 150.16/22.19 | | | Case 2: % 150.16/22.19 | | | | % 150.16/22.19 | | | | (129) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 150.16/22.19 | | | | % 150.16/22.19 | | | | BETA: splitting (129) gives: % 150.16/22.19 | | | | % 150.16/22.19 | | | | Case 1: % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | (130) all_56_1 = e0 % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | COMBINE_EQS: (42), (130) imply: % 150.16/22.19 | | | | | (131) all_52_4 = e0 % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | REDUCE: (64), (131) imply: % 150.16/22.19 | | | | | (132) $false % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | CLOSE: (132) is inconsistent. % 150.16/22.19 | | | | | % 150.16/22.19 | | | | Case 2: % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | (133) all_56_4 = e0 | all_56_9 = e0 % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | BETA: splitting (133) gives: % 150.16/22.19 | | | | | % 150.16/22.19 | | | | | Case 1: % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | (134) all_56_4 = e0 % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | COMBINE_EQS: (16), (134) imply: % 150.16/22.19 | | | | | | (135) all_52_8 = e0 % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | REDUCE: (121), (135) imply: % 150.16/22.19 | | | | | | (136) $false % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | CLOSE: (136) is inconsistent. % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | Case 2: % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | (137) all_56_9 = e0 % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | COMBINE_EQS: (51), (137) imply: % 150.16/22.19 | | | | | | (138) all_52_12 = e0 % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | COMBINE_EQS: (15), (138) imply: % 150.16/22.19 | | | | | | (139) all_58_6 = e0 % 150.16/22.19 | | | | | | % 150.16/22.19 | | | | | | REDUCE: (52), (138) imply: % 150.16/22.19 | | | | | | (140) ~ (all_52_14 = e0) % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | SIMP: (140) implies: % 150.16/22.20 | | | | | | (141) ~ (all_52_14 = e0) % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | REDUCE: (89), (138) imply: % 150.16/22.20 | | | | | | (142) ~ (all_4_2 = e0) % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | SIMP: (142) implies: % 150.16/22.20 | | | | | | (143) ~ (all_4_2 = e0) % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | REDUCE: (69), (138) imply: % 150.16/22.20 | | | | | | (144) op(e3, e0) = all_58_5 % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | REDUCE: (56), (138) imply: % 150.16/22.20 | | | | | | (145) op(e3, e0) = e0 % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_25, e0, e0, % 150.16/22.20 | | | | | | simplifying with (85), (125) gives: % 150.16/22.20 | | | | | | (146) all_58_25 = all_4_2 % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | GROUND_INST: instantiating (4) with all_52_14, all_58_14, e0, e1, % 150.16/22.20 | | | | | | simplifying with (46), (101) gives: % 150.16/22.20 | | | | | | (147) all_58_14 = all_52_14 % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | GROUND_INST: instantiating (4) with e0, all_58_5, e0, e3, % 150.16/22.20 | | | | | | simplifying with (144), (145) gives: % 150.16/22.20 | | | | | | (148) all_58_5 = e0 % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | BETA: splitting (21) gives: % 150.16/22.20 | | | | | | % 150.16/22.20 | | | | | | Case 1: % 150.16/22.20 | | | | | | | % 150.16/22.20 | | | | | | | (149) all_54_13 = e0 % 150.16/22.20 | | | | | | | % 150.16/22.20 | | | | | | | REF_CLOSE: (63), (94), (149) are inconsistent by sub-proof #397. % 150.16/22.20 | | | | | | | % 150.16/22.20 | | | | | | Case 2: % 150.16/22.20 | | | | | | | % 150.16/22.20 | | | | | | | (150) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 150.16/22.20 | | | | | | | % 150.16/22.20 | | | | | | | BETA: splitting (58) gives: % 150.16/22.20 | | | | | | | % 150.16/22.20 | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | % 150.16/22.20 | | | | | | | | (151) all_54_4 = e0 % 150.16/22.20 | | | | | | | | % 150.16/22.20 | | | | | | | | REF_CLOSE: (86), (112), (151) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | #859. % 150.16/22.20 | | | | | | | | % 150.16/22.20 | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | % 150.16/22.20 | | | | | | | | (152) ~ (all_54_4 = e0) % 150.16/22.20 | | | | | | | | (153) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 150.16/22.20 | | | | | | | | % 150.16/22.20 | | | | | | | | BETA: splitting (37) gives: % 150.16/22.20 | | | | | | | | % 150.16/22.20 | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | % 150.16/22.20 | | | | | | | | | (154) all_54_0 = e0 % 150.16/22.20 | | | | | | | | | % 150.16/22.20 | | | | | | | | | REF_CLOSE: (18), (34), (50), (55), (66), (75), (81), (95), % 150.16/22.20 | | | | | | | | | (97), (99), (104), (106), (107), (154) are % 150.16/22.20 | | | | | | | | | inconsistent by sub-proof #395. % 150.16/22.20 | | | | | | | | | % 150.16/22.20 | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | % 150.16/22.20 | | | | | | | | | (155) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 150.16/22.20 | | | | | | | | | % 150.16/22.20 | | | | | | | | | BETA: splitting (29) gives: % 150.16/22.20 | | | | | | | | | % 150.16/22.20 | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | (156) all_54_11 = e0 % 150.16/22.20 | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | REF_CLOSE: (22), (141), (156) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | #743. % 150.16/22.20 | | | | | | | | | | % 150.16/22.20 | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | (157) ~ (all_54_11 = e0) % 150.16/22.20 | | | | | | | | | | (158) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 150.16/22.20 | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | BETA: splitting (100) gives: % 150.16/22.20 | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | (159) all_54_2 = e0 % 150.16/22.20 | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | REF_CLOSE: (7), (121), (159) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | #860. % 150.16/22.20 | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | (160) ~ (all_54_2 = e0) % 150.16/22.20 | | | | | | | | | | | (161) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 150.16/22.20 | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | BETA: splitting (70) gives: % 150.16/22.20 | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | (162) all_54_12 = e0 % 150.16/22.20 | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | REF_CLOSE: (33), (111), (162) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | #762. % 150.16/22.20 | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | (163) ~ (all_54_12 = e0) % 150.16/22.20 | | | | | | | | | | | | (164) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 150.16/22.20 | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | BETA: splitting (79) gives: % 150.16/22.20 | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | (165) all_56_6 = e1 % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | REF_CLOSE: (17), (99), (165) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | | #253. % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | (166) ~ (all_56_6 = e1) % 150.16/22.20 | | | | | | | | | | | | | (167) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | REDUCE: (17), (166) imply: % 150.16/22.20 | | | | | | | | | | | | | (168) ~ (e1 = e0) % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | BETA: splitting (27) gives: % 150.16/22.20 | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | (169) all_56_4 = e1 % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | COMBINE_EQS: (16), (169) imply: % 150.16/22.20 | | | | | | | | | | | | | | (170) all_52_8 = e1 % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | COMBINE_EQS: (93), (170) imply: % 150.16/22.20 | | | | | | | | | | | | | | (171) all_58_4 = e1 % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | REDUCE: (49), (170) imply: % 150.16/22.20 | | | | | | | | | | | | | | (172) ~ (all_52_4 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | REDUCE: (3), (170) imply: % 150.16/22.20 | | | | | | | | | | | | | | (173) ~ (all_52_9 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | SIMP: (173) implies: % 150.16/22.20 | | | | | | | | | | | | | | (174) ~ (all_52_9 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | REDUCE: (11), (170) imply: % 150.16/22.20 | | | | | | | | | | | | | | (175) ~ (all_10_2 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | SIMP: (175) implies: % 150.16/22.20 | | | | | | | | | | | | | | (176) ~ (all_10_2 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | REDUCE: (25), (170) imply: % 150.16/22.20 | | | | | | | | | | | | | | (177) ~ (all_6_2 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | SIMP: (177) implies: % 150.16/22.20 | | | | | | | | | | | | | | (178) ~ (all_6_2 = e1) % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | BETA: splitting (106) gives: % 150.16/22.20 | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | (179) all_58_28 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | COMBINE_EQS: (75), (179) imply: % 150.16/22.20 | | | | | | | | | | | | | | | (180) all_10_2 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | REDUCE: (176), (180) imply: % 150.16/22.20 | | | | | | | | | | | | | | | (181) $false % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | (182) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 150.16/22.20 | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | (183) all_58_29 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | REF_CLOSE: (50), (99), (183) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | | | | | #700. % 150.16/22.20 | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | (184) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | (185) all_58_30 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (185) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | (186) all_6_2 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | REDUCE: (178), (186) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | (187) $false % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | (188) all_58_31 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | (189) ~ (all_58_30 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (188) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | (190) all_4_2 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (190) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | (191) all_58_25 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | REDUCE: (31), (190) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | (192) ~ (all_52_13 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | REDUCE: (83), (190) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | (193) ~ (all_8_1 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | (194) all_56_2 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (194) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | (195) all_52_1 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (195) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | (196) all_58_8 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | (197) all_58_31 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (197) are inconsistent % 150.16/22.20 | | | | | | | | | | | | | | | | | | | by sub-proof #824. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | (198) ~ (all_58_31 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | (199) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | (200) all_56_1 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (200) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | (201) all_52_4 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (201) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | (202) $false % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | (203) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | (204) all_56_3 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (99), (104), (178), (184), (188), (204) are % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #43. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | (205) all_56_7 = e1 | all_56_13 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | (206) all_56_7 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (206) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | (207) all_52_6 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (207) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | (208) all_58_17 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (207) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | (209) ~ (all_52_14 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | SIMP: (209) implies: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | (210) ~ (all_52_14 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_30 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (34), (50), (55), (66), (75), (81), (95), % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | (107), (188), (211) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | #283. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_29 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (213) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (214) e2 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (214) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (215) $false % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (216) ~ (all_58_29 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (216) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | (218) ~ (e2 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_28 = e3 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_28 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (219), (220) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | #849. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_58_28 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_29 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (223) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) e2 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (224) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) $false % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_30 = e2 | all_58_31 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_58_30 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (227) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_6_2 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_6_2 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (229) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_52_9 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_56_2 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (231) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) e2 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (232) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_30 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (188), (226), (233) are inconsistent by % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_56_2 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (234) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (e2 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_56_3 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (237) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) e2 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (238) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_30 = e0 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (50), (55), (81), (107), (188), (219), (239) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #695. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_56_5 = e2 | all_56_10 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_56_5 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (230), (241) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #90. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_56_10 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (242) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_52_13 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (243) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_9 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (243) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_52_14 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (245) implies: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) ~ (all_52_14 = e2) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (244), (247) are inconsistent by sub-proof % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #584. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_58_14 = e3) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (250) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_52_14 = e3) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (158), (210), (246), (251) are inconsistent % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #46. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_58_25 = e1) % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (253) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) $false % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (254) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_31 = e2 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (255) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) e2 = e1 % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (256) imply: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) $false % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent. % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | (258) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (259) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_15 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (263) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) e1 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (264) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_31 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (265) are inconsistent % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_8 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (268) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) e3 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (269) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (208), (271) are inconsistent by sub-proof % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #264. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_8 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (275) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) e3 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (276) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_15 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_4 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (99), (104), (171), (178), (184), (188), % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279), (280) are inconsistent by sub-proof #42. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (196), (282) are inconsistent by sub-proof % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_8 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (284) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) e2 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (285) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_8 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (291) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) e2 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (292) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (196), (294) are inconsistent by sub-proof % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #261. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_15 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_58_4 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (99), (104), (171), (178), (184), (188), % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297), (298) are inconsistent by sub-proof #41. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_15 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_4 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (99), (104), (171), (178), (184), (188), % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300), (301) are inconsistent by sub-proof #42. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_15 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_4 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (99), (104), (171), (178), (184), (188), % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305), (306) are inconsistent by sub-proof #41. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_15 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (308) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) e1 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (309) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_31 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (310) are inconsistent % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_15 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (313) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) e1 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (314) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_31 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (315) are inconsistent % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_15 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (317) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) e1 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (318) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_58_31 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (319) are inconsistent % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (320) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_15 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (324) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) e1 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (325) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_31 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (326) are inconsistent % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_6 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (139), (329) are inconsistent by sub-proof % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #107. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_58_6 = e3 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (139), (331) are inconsistent by sub-proof % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #107. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_58_22 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (335) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_52_3 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_52_3 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (337) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (338) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_58_26 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (340) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) e1 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (341) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_58_31 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (342) are inconsistent % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) e3 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (345) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (346) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_58_17 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (348) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) e2 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (349) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) $false % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_26 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (120), (178), (184), (188), (355) are % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40. % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_58_11 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (357) imply: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_52_9 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (358) implies: % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_52_9 = e1 % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (359) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (55), (141), (361) are inconsistent by % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (364) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_58_20 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (141), (365) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #39. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_26 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (120), (178), (184), (188), (367) are % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (369) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) e2 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (370) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (371) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) e1 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (373) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_31 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (104), (178), (184), (374) are inconsistent % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_56_7 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (375) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (376) ~ (all_52_6 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (377) all_56_7 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (376), (377) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | #547. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (378) all_56_13 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (193), (378) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | #271. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | (379) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (380) all_56_3 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (99), (104), (178), (184), (188), (380) are % 150.16/22.22 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #43. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (381) all_56_5 = e1 | all_56_10 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (71), (174), (192), (381) are inconsistent % 150.16/22.22 | | | | | | | | | | | | | | | | | | | by sub-proof #176. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | (382) ~ (all_56_4 = e1) % 150.16/22.22 | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | REDUCE: (16), (382) imply: % 150.16/22.22 | | | | | | | | | | | | | | (383) ~ (all_52_8 = e1) % 150.16/22.22 | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | BETA: splitting (57) gives: % 150.16/22.22 | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | (384) all_56_0 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | COMBINE_EQS: (84), (384) imply: % 150.16/22.22 | | | | | | | | | | | | | | | (385) all_10_2 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | REDUCE: (109), (385) imply: % 150.16/22.22 | | | | | | | | | | | | | | | (386) op(e1, e3) = all_10_1 % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (54), (386) are inconsistent by % 150.16/22.22 | | | | | | | | | | | | | | | sub-proof #810. % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | (387) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 150.16/22.22 | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | (388) all_56_1 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (388) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | (389) all_52_4 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | REDUCE: (49), (389) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | (390) ~ (all_52_8 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | REDUCE: (102), (389) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | (391) ~ (all_10_2 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | SIMP: (391) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | (392) ~ (all_10_2 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | BETA: splitting (23) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | (393) all_56_0 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (393) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | (394) all_10_2 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (394) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | (395) all_58_28 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | REDUCE: (113), (394) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | (396) ~ (all_52_1 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | REDUCE: (90), (394) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | (397) ~ (all_52_3 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | REDUCE: (11), (394) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | (398) ~ (all_52_8 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | (399) all_54_2 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (383), (399) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | #819. % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | (400) all_54_2 = e3 | all_54_2 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | BETA: splitting (400) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (401) all_54_2 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (398), (401) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | #556. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (402) all_54_2 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (402) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (403) all_52_8 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | SIMP: (403) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (404) all_52_8 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | REDUCE: (25), (404) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (405) ~ (all_6_2 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | SIMP: (405) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (406) ~ (all_6_2 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (407) all_58_28 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (395), (407) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | #849. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (408) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (408) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (409) all_58_29 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (66), (409) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | #707. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (410) all_58_30 = e3 | all_58_31 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (411) all_58_30 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (411) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (412) all_6_2 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (406), (412) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (413) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (413) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (414) all_58_31 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (415) ~ (all_58_30 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (414) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (416) all_4_2 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (416) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (417) ~ (all_52_3 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (416) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (418) ~ (all_52_14 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (419) all_56_12 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (419) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (420) all_52_3 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (420) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (421) all_52_3 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (421) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (422) ~ (all_52_1 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (421) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (423) ~ (all_8_1 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (423) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (424) ~ (all_8_1 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (421) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (425) ~ (e2 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (426) all_58_28 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (395), (426) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (427) e2 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (427) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (428) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (428) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (429) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_56_2 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (430) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_52_1 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (431) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (432) op(e2, e3) = all_58_7 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (431) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (433) op(e2, e3) = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (429) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_58_29 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (434) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (435) e1 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (435) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (436) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (436) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_58_30 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (438) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_6_2 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (439) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_6_2 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (440) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_52_14 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (406), (440) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) ~ (e3 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (440) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) op(e1, e1) = all_58_18 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (440) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) op(e1, e1) = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_54_11 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (441), (445) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) ~ (all_54_11 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_54_11 = e3 | all_54_11 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (447) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_54_11 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (448) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_52_14 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (449) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_52_14 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (418), (450) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) ~ (e3 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_58_18, e1, e1, % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (443), (444) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_58_18 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (19), (20), (34), (39), (50), (55), % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (63), (66), (83), (92), (95), (107), (148), % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (395), (419), (424), (432), (433), (438), % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) are inconsistent by sub-proof #330. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_54_11 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (418), (453) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #776. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_58_31 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (104), (406), (410), (454) are inconsistent % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #432. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (455) ~ (all_56_2 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (455) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (456) ~ (all_52_1 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (153), (396), (422), (456) are inconsistent % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #828. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (457) ~ (all_56_12 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (457) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (458) ~ (all_52_3 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (164), (397), (417), (458) are inconsistent % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #557. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | (459) ~ (all_56_0 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | (460) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | REDUCE: (84), (459) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | (461) ~ (all_10_2 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | (462) all_56_1 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (388), (462) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | #452. % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | (463) all_56_4 = e2 | all_56_9 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (464) all_54_0 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (392), (464) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | #841. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | (465) all_54_0 = e3 | all_54_0 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (465) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (466) all_54_0 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (461), (466) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | #822. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (467) all_54_0 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (467) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (468) all_10_2 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | SIMP: (468) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (469) all_10_2 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (469) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (470) all_58_28 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (469) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (471) ~ (all_52_3 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (469) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | (472) ~ (all_52_8 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (473) all_56_4 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (473) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (474) all_52_8 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (474) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (475) ~ (all_6_2 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | SIMP: (475) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (476) ~ (all_6_2 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | REDUCE: (472), (474) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (477) ~ (e3 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (478) all_58_28 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (470), (478) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (479) e3 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (479) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (480) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (480) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | (481) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (482) all_58_29 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (81), (482) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | #706. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | (483) all_58_30 = e2 | all_58_31 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (484) all_58_30 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (484) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (485) all_6_2 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (476), (485) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (486) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (486) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (487) all_58_31 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (487) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (488) all_4_2 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (488) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_52_3 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (488) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | (490) ~ (all_8_1 = e2) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_56_12 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (491) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_52_3 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (492) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_52_3 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (493) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (494) ~ (all_8_1 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (494) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (495) ~ (all_8_1 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (493) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (496) op(e0, e3) = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_54_13 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (495), (497) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | #352. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_54_13 = e3 | all_54_13 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_54_13 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (490), (499) are inconsistent by sub-proof % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | #340. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_54_13 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (500) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_8_1 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (501) implies: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_8_1 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (502) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_48_1 = e3 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (502) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) op(e0, e3) = all_8_0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) ~ (all_48_0 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (505) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) ~ (all_8_0 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_8_0, e3, e0, % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (496), (504) gives: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_8_0 = e1 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (506), (507) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (508) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) ~ (all_48_1 = e3) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (503), (509) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) $false % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (510) is inconsistent. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (511) ~ (all_56_12 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (511) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | (512) ~ (all_52_3 = e1) % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (164), (471), (489), (512) are inconsistent % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #557. % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (513) all_56_9 = e2 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (513) imply: % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | (514) e2 = e0 % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.22 | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (514) imply: % 150.16/22.23 | | | | | | | | | | | | | | | | | | | | | (515) $false % 150.16/22.23 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | | | | | CLOSE: (515) is inconsistent. % 150.16/22.23 | | | | | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | Case 2: % 150.16/22.23 | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | (516) all_56_4 = e1 | all_56_9 = e1 % 150.16/22.23 | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | BETA: splitting (516) gives: % 150.16/22.23 | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | Case 1: % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | (517) all_56_4 = e1 % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (517) imply: % 150.16/22.23 | | | | | | | | | | | | | | | | | (518) all_52_8 = e1 % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | REDUCE: (383), (518) imply: % 150.16/22.23 | | | | | | | | | | | | | | | | | (519) $false % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent. % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | Case 2: % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | (520) all_56_9 = e1 % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (520) imply: % 150.16/22.23 | | | | | | | | | | | | | | | | | (521) e1 = e0 % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | REDUCE: (99), (521) imply: % 150.16/22.23 | | | | | | | | | | | | | | | | | (522) $false % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | | CLOSE: (522) is inconsistent. % 150.16/22.23 | | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | | % 150.16/22.23 | | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | | % 150.16/22.23 | | | | | | | | | End of split % 150.16/22.23 | | | | | | | | | % 150.16/22.23 | | | | | | | | End of split % 150.16/22.23 | | | | | | | | % 150.16/22.23 | | | | | | | End of split % 150.16/22.23 | | | | | | | % 150.16/22.23 | | | | | | End of split % 150.16/22.23 | | | | | | % 150.16/22.23 | | | | | End of split % 150.16/22.23 | | | | | % 150.16/22.23 | | | | End of split % 150.16/22.23 | | | | % 150.16/22.23 | | | End of split % 150.16/22.23 | | | % 150.16/22.23 | | End of split % 150.16/22.23 | | % 150.16/22.23 | End of split % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #38 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.16/22.23 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) % 150.16/22.23 (2) all_58_20 = all_52_14 % 150.16/22.23 (3) ~ (all_52_14 = e0) % 150.16/22.23 (4) ~ (e2 = e1) % 150.16/22.23 % 150.16/22.23 Begin of proof % 150.16/22.23 | % 150.16/22.23 | BETA: splitting (1) gives: % 150.16/22.23 | % 150.16/22.23 | Case 1: % 150.16/22.23 | | % 150.16/22.23 | | (5) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0 % 150.16/22.23 | | % 150.16/22.23 | | ALPHA: (5) implies: % 150.16/22.23 | | (6) all_58_20 = e0 % 150.16/22.23 | | % 150.16/22.23 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #39. % 150.16/22.23 | | % 150.16/22.23 | Case 2: % 150.16/22.23 | | % 150.16/22.23 | | (7) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 150.16/22.23 | | % 150.16/22.23 | | ALPHA: (7) implies: % 150.16/22.23 | | (8) e2 = e1 % 150.16/22.23 | | % 150.16/22.23 | | REDUCE: (4), (8) imply: % 150.16/22.23 | | (9) $false % 150.16/22.23 | | % 150.16/22.23 | | CLOSE: (9) is inconsistent. % 150.16/22.23 | | % 150.16/22.23 | End of split % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #39 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) all_58_20 = all_52_14 % 150.16/22.23 (2) all_58_20 = e0 % 150.16/22.23 (3) ~ (all_52_14 = e0) % 150.16/22.23 % 150.16/22.23 Begin of proof % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (1), (2) imply: % 150.16/22.23 | (4) all_52_14 = e0 % 150.16/22.23 | % 150.16/22.23 | SIMP: (4) implies: % 150.16/22.23 | (5) all_52_14 = e0 % 150.16/22.23 | % 150.16/22.23 | REDUCE: (3), (5) imply: % 150.16/22.23 | (6) $false % 150.16/22.23 | % 150.16/22.23 | CLOSE: (6) is inconsistent. % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #40 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) all_58_31 = e1 % 150.16/22.23 (2) all_58_26 = e1 % 150.16/22.23 (3) all_58_26 = e0 % 150.16/22.23 (4) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.23 (5) ~ (e1 = e0) % 150.16/22.23 (6) ~ (all_6_2 = e1) % 150.16/22.23 (7) all_58_30 = all_6_2 % 150.16/22.23 % 150.16/22.23 Begin of proof % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (2), (3) imply: % 150.16/22.23 | (8) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | SIMP: (8) implies: % 150.16/22.23 | (9) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (1), (9) imply: % 150.16/22.23 | (10) all_58_31 = e0 % 150.16/22.23 | % 150.16/22.23 | REF_CLOSE: (4), (5), (6), (7), (10) are inconsistent by sub-proof #512. % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #41 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) all_58_4 = e3 % 150.16/22.23 (2) all_58_31 = e1 % 150.16/22.23 (3) all_58_4 = e1 % 150.16/22.23 (4) all_58_15 = e0 % 150.16/22.23 (5) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.23 (6) all_58_15 = e3 % 150.16/22.23 (7) ~ (e1 = e0) % 150.16/22.23 (8) ~ (all_6_2 = e1) % 150.16/22.23 (9) all_58_30 = all_6_2 % 150.16/22.23 % 150.16/22.23 Begin of proof % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (1), (3) imply: % 150.16/22.23 | (10) e3 = e1 % 150.16/22.23 | % 150.16/22.23 | SIMP: (10) implies: % 150.16/22.23 | (11) e3 = e1 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (4), (6) imply: % 150.16/22.23 | (12) e3 = e0 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (11), (12) imply: % 150.16/22.23 | (13) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | SIMP: (13) implies: % 150.16/22.23 | (14) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (2), (14) imply: % 150.16/22.23 | (15) all_58_31 = e0 % 150.16/22.23 | % 150.16/22.23 | REF_CLOSE: (5), (7), (8), (9), (15) are inconsistent by sub-proof #512. % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #42 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) all_58_4 = e3 % 150.16/22.23 (2) all_58_31 = e1 % 150.16/22.23 (3) all_58_4 = e1 % 150.16/22.23 (4) all_58_15 = e0 % 150.16/22.23 (5) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.23 (6) all_58_15 = e3 % 150.16/22.23 (7) ~ (e1 = e0) % 150.16/22.23 (8) ~ (all_6_2 = e1) % 150.16/22.23 (9) all_58_30 = all_6_2 % 150.16/22.23 % 150.16/22.23 Begin of proof % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (1), (3) imply: % 150.16/22.23 | (10) e3 = e1 % 150.16/22.23 | % 150.16/22.23 | SIMP: (10) implies: % 150.16/22.23 | (11) e3 = e1 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (4), (6) imply: % 150.16/22.23 | (12) e3 = e0 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (11), (12) imply: % 150.16/22.23 | (13) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (2), (13) imply: % 150.16/22.23 | (14) all_58_31 = e0 % 150.16/22.23 | % 150.16/22.23 | REF_CLOSE: (5), (7), (8), (9), (14) are inconsistent by sub-proof #512. % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #43 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) all_58_31 = e1 % 150.16/22.23 (2) all_56_3 = e0 % 150.16/22.23 (3) all_56_3 = e1 % 150.16/22.23 (4) all_58_30 = e1 | all_58_31 = e1 % 150.16/22.23 (5) ~ (e1 = e0) % 150.16/22.23 (6) ~ (all_6_2 = e1) % 150.16/22.23 (7) all_58_30 = all_6_2 % 150.16/22.23 % 150.16/22.23 Begin of proof % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (2), (3) imply: % 150.16/22.23 | (8) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | SIMP: (8) implies: % 150.16/22.23 | (9) e1 = e0 % 150.16/22.23 | % 150.16/22.23 | COMBINE_EQS: (1), (9) imply: % 150.16/22.23 | (10) all_58_31 = e0 % 150.16/22.23 | % 150.16/22.23 | REF_CLOSE: (4), (5), (6), (7), (10) are inconsistent by sub-proof #512. % 150.16/22.23 | % 150.16/22.23 End of proof % 150.16/22.23 % 150.16/22.23 Sub-proof #44 shows that the following formulas are inconsistent: % 150.16/22.23 ---------------------------------------------------------------- % 150.16/22.23 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 150.16/22.23 (2) all_58_31 = all_4_2 % 150.16/22.23 (3) ~ (all_52_8 = all_52_9) % 150.16/22.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.16/22.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.16/22.23 (5) all_26_0 = all_4_0 % 150.16/22.23 (6) all_54_13 = all_52_7 % 150.16/22.23 (7) ~ (all_52_2 = all_52_3) % 150.16/22.23 (8) all_58_11 = all_52_9 % 150.16/22.23 (9) all_56_15 = all_4_2 % 150.16/22.23 (10) all_56_7 = all_52_6 % 150.16/22.23 (11) ~ (all_52_6 = all_6_2) % 150.16/22.23 (12) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 150.16/22.23 (13) all_54_2 = all_52_8 % 150.16/22.23 (14) all_54_8 = all_52_2 % 150.16/22.23 (15) op(e1, all_6_2) = all_58_18 % 150.16/22.23 (16) op(e3, all_52_4) = all_58_1 % 150.16/22.23 (17) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 150.16/22.23 (18) ~ (all_52_8 = all_10_2) % 150.16/22.23 (19) all_58_15 = all_52_2 % 150.16/22.23 (20) all_58_26 = all_52_11 % 150.16/22.23 (21) all_44_1 = all_4_1 % 150.16/22.23 (22) op(e1, all_52_14) = all_58_19 % 150.16/22.23 (23) ~ (all_52_8 = all_52_11) % 150.16/22.23 (24) ~ (all_52_11 = all_4_2) % 150.16/22.23 (25) all_54_7 = all_52_13 % 150.16/22.23 (26) all_58_6 = all_52_12 % 150.16/22.23 (27) ~ (all_52_6 = all_8_2) % 150.16/22.23 (28) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 150.16/22.23 (29) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) | ~ (all_16_2 = e0) % 150.16/22.23 (30) all_56_4 = all_52_8 % 150.16/22.23 (31) ~ (all_52_4 = all_8_2) % 150.16/22.23 (32) ~ (all_34_0 = e3) | ~ (all_34_1 = e2) | ~ (all_34_2 = e1) % 150.16/22.23 (33) all_54_3 = all_52_12 % 150.16/22.23 (34) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.16/22.23 (35) all_54_1 = all_52_4 % 150.16/22.23 (36) op(e0, all_4_2) = all_58_27 % 150.16/22.23 (37) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 150.53/22.23 (38) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 150.53/22.23 (39) ~ (all_52_4 = all_52_6) % 150.53/22.23 (40) ~ (all_44_0 = e3) | ~ (all_44_1 = e1) | ~ (all_44_2 = e2) % 150.53/22.23 (41) all_58_13 = all_52_13 % 150.53/22.23 (42) op(e2, e2) = all_8_2 % 150.53/22.23 (43) all_20_1 = all_4_1 % 150.53/22.23 (44) op(e0, e1) = all_52_11 % 150.53/22.23 (45) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 150.53/22.23 (46) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.53/22.23 (47) all_34_0 = all_4_0 % 150.53/22.23 (48) ~ (all_52_6 = all_52_7) % 150.53/22.23 (49) all_50_2 = all_10_2 % 150.53/22.23 (50) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 150.53/22.23 (51) op(all_10_2, all_10_1) = all_10_0 % 150.53/22.23 (52) all_54_11 = all_52_14 % 150.53/22.23 (53) op(e3, e2) = all_52_4 % 150.53/22.23 (54) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 150.53/22.23 (55) all_58_20 = all_52_14 % 150.53/22.23 (56) ~ (all_52_8 = all_6_2) % 150.53/22.23 (57) ~ (all_52_12 = all_52_13) % 150.53/22.23 (58) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.53/22.23 (59) all_54_10 = all_6_2 % 150.53/22.23 (60) op(e0, all_52_3) = all_58_21 % 150.53/22.23 (61) all_16_2 = all_10_2 % 150.53/22.23 (62) op(e0, all_52_7) = all_58_23 % 150.53/22.23 (63) all_54_5 = all_8_2 % 150.53/22.23 (64) ~ (all_52_6 = all_52_14) % 150.53/22.23 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 150.53/22.23 (66) all_54_6 = all_52_9 % 150.53/22.23 (67) all_54_15 = all_4_2 % 150.53/22.23 (68) all_26_2 = all_4_2 % 150.53/22.23 (69) ~ (all_52_4 = all_52_7) % 150.53/22.23 (70) ~ (all_52_2 = all_6_2) % 150.53/22.23 (71) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 150.53/22.23 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 150.53/22.23 (72) ~ (all_26_0 = e2) | ~ (all_26_1 = e1) | ~ (all_26_2 = e3) % 150.53/22.23 (73) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 150.53/22.23 (74) op(e3, e3) = all_10_2 % 150.53/22.23 (75) op(e3, all_52_8) = all_58_3 % 150.53/22.23 (76) ~ (all_52_8 = all_52_12) % 150.53/22.23 (77) all_54_9 = all_52_6 % 150.53/22.23 (78) ~ (all_52_13 = all_4_2) % 150.53/22.23 (79) op(e1, e2) = all_52_6 % 150.53/22.23 (80) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 150.53/22.23 (81) ~ (all_52_13 = all_8_2) % 150.53/22.23 (82) op(e1, all_52_6) = all_58_16 % 150.53/22.23 (83) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 150.53/22.23 (84) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 150.53/22.23 (85) ~ (e3 = e1) % 150.53/22.23 (86) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 150.53/22.23 (87) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.53/22.23 (88) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 150.53/22.23 (89) ~ (all_52_1 = all_52_13) % 150.53/22.23 (90) all_56_5 = all_52_9 % 150.53/22.23 (91) all_54_14 = all_52_11 % 150.53/22.23 (92) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 150.53/22.23 (93) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 150.53/22.23 (94) all_56_12 = all_52_3 % 150.53/22.23 (95) ~ (all_52_3 = all_52_7) % 150.53/22.23 (96) all_58_2 = all_52_4 % 150.53/22.23 (97) all_20_2 = all_4_2 % 150.53/22.23 (98) all_56_11 = all_52_14 % 150.53/22.23 (99) all_56_1 = all_52_4 % 150.53/22.23 (100) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 150.53/22.23 (101) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 150.53/22.23 (102) ~ (all_52_3 = all_4_2) % 150.53/22.23 (103) op(e1, e3) = all_52_2 % 150.53/22.23 (104) op(e0, all_52_11) = all_58_25 % 150.53/22.23 (105) op(e1, e0) = all_52_14 % 150.53/22.23 (106) ~ (all_52_9 = all_52_11) % 150.53/22.23 (107) ~ (all_52_1 = all_8_2) % 150.53/22.23 (108) all_56_3 = all_8_2 % 150.53/22.23 (109) all_58_24 = all_52_7 % 150.53/22.23 (110) ~ (all_52_13 = all_52_14) % 150.53/22.23 (111) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 150.53/22.23 (112) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 150.53/22.23 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.53/22.23 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.53/22.23 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 150.53/22.23 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.53/22.23 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.53/22.23 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 150.53/22.23 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.53/22.23 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.53/22.23 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 150.53/22.23 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.53/22.23 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.53/22.23 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = % 150.53/22.23 e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 150.53/22.23 e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 150.53/22.23 e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 150.53/22.23 e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.53/22.23 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.53/22.23 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.53/22.23 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.53/22.23 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.53/22.23 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.53/22.23 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.53/22.23 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.53/22.23 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.53/22.23 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 150.53/22.23 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.53/22.23 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.53/22.23 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.53/22.23 e0) % 150.53/22.23 (113) ~ (all_52_4 = all_52_8) % 150.53/22.23 (114) all_50_0 = all_10_0 % 150.53/22.23 (115) ~ (all_50_0 = e1) | ~ (all_50_1 = e2) | ~ (all_50_2 = e0) % 150.53/22.23 (116) op(e1, all_52_2) = all_58_14 % 150.53/22.23 (117) ~ (all_10_0 = e0) % 150.53/22.23 (118) op(e2, e1) = all_52_9 % 150.53/22.23 (119) all_56_9 = all_52_12 % 150.53/22.23 (120) all_58_29 = all_8_2 % 150.53/22.23 (121) ~ (all_52_12 = all_52_14) % 150.53/22.23 (122) all_58_8 = all_52_1 % 150.53/22.23 (123) ~ (e2 = e1) % 150.53/22.23 (124) op(e3, e0) = all_52_12 % 150.53/22.23 (125) all_20_0 = all_4_0 % 150.53/22.23 (126) all_56_6 = all_52_2 % 150.53/22.23 (127) all_34_1 = all_4_1 % 150.53/22.23 (128) ~ (all_52_2 = all_52_6) % 150.53/22.23 (129) all_18_2 = all_6_2 % 150.53/22.23 (130) all_56_13 = all_52_7 % 150.53/22.23 (131) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 150.53/22.23 (132) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 150.53/22.23 (133) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.53/22.23 (134) op(all_6_2, all_6_1) = all_6_0 % 150.53/22.23 (135) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 150.53/22.23 (136) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.53/22.23 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.53/22.23 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.53/22.23 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.53/22.23 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.53/22.23 (all_58_27 = e0)) % 150.53/22.23 (137) ~ (all_52_9 = all_52_13) % 150.53/22.23 (138) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 150.53/22.23 (139) op(all_6_2, e1) = all_6_1 % 150.53/22.23 (140) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.53/22.23 (141) all_34_2 = all_4_2 % 150.53/22.23 (142) op(e2, all_52_9) = all_58_10 % 150.53/22.23 (143) ~ (all_52_11 = all_6_2) % 150.53/22.23 (144) op(e3, all_10_2) = all_58_0 % 150.53/22.23 (145) all_44_2 = all_4_2 % 150.53/22.23 (146) ~ (e3 = e0) % 150.53/22.23 (147) all_56_2 = all_52_1 % 150.53/22.23 (148) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 150.53/22.23 (149) op(e0, e3) = all_52_3 % 150.53/22.23 (150) op(e3, all_52_12) = all_58_5 % 150.53/22.23 (151) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 150.53/22.23 (152) all_56_10 = all_52_13 % 150.53/22.23 (153) ~ (all_52_12 = all_10_2) % 150.53/22.23 (154) ~ (all_52_1 = all_52_3) % 150.53/22.23 (155) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 150.53/22.23 (156) ~ (all_52_9 = all_8_2) % 150.53/22.23 (157) all_56_14 = all_52_11 % 150.53/22.23 (158) all_58_28 = all_10_2 % 150.53/22.23 (159) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 150.53/22.23 (160) all_58_17 = all_52_6 % 150.53/22.23 (161) ~ (all_52_1 = all_52_9) % 150.53/22.23 (162) op(e3, e1) = all_52_8 % 150.53/22.23 (163) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 150.53/22.23 (164) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.53/22.23 (165) ~ (all_52_7 = all_52_11) % 150.53/22.23 (166) op(all_8_2, e2) = all_8_1 % 150.53/22.24 (167) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 150.53/22.24 (168) ~ (e2 = e0) % 150.53/22.24 (169) ~ (all_52_9 = all_6_2) % 150.53/22.24 (170) ~ (all_52_2 = all_10_2) % 150.53/22.24 (171) all_56_0 = all_10_2 % 150.53/22.24 (172) op(e0, e0) = all_4_2 % 150.53/22.24 (173) ~ (all_52_3 = all_52_11) % 150.53/22.24 (174) all_58_22 = all_52_3 % 150.53/22.24 (175) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 150.53/22.24 (176) ~ (all_52_12 = all_4_2) % 150.53/22.24 (177) all_50_1 = all_10_1 % 150.53/22.24 (178) ~ (all_52_3 = all_10_2) % 150.53/22.24 (179) all_56_8 = all_6_2 % 150.53/22.24 (180) op(e1, e1) = all_6_2 % 150.53/22.24 (181) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.53/22.24 (182) ~ (all_52_1 = all_52_2) % 150.53/22.24 (183) ~ (all_52_7 = all_8_2) % 150.53/22.24 (184) op(all_4_2, all_4_1) = all_4_0 % 150.53/22.24 (185) op(e2, e0) = all_52_13 % 150.53/22.24 (186) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 150.53/22.24 (187) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 150.53/22.24 (188) op(e2, all_52_13) = all_58_12 % 150.53/22.24 (189) all_58_4 = all_52_8 % 150.53/22.24 (190) ~ (all_8_1 = e0) % 150.53/22.24 (191) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.53/22.24 (192) all_16_1 = all_10_1 % 150.53/22.24 (193) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 150.53/22.24 (194) all_16_0 = all_10_0 % 150.53/22.24 (195) all_54_0 = all_10_2 % 150.53/22.24 (196) ~ (all_52_2 = all_52_14) % 150.53/22.24 (197) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 150.53/22.24 (198) ~ (all_52_14 = all_4_2) % 150.53/22.24 (199) ~ (e1 = e0) % 150.53/22.24 (200) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 150.53/22.24 (201) all_26_1 = all_4_1 % 150.53/22.24 (202) ~ (all_52_7 = all_4_2) % 150.53/22.24 (203) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 150.53/22.24 (204) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 150.53/22.24 (205) op(all_4_2, all_4_1) = e1 % 150.53/22.24 (206) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 150.53/22.24 (207) op(e0, e2) = all_52_7 % 150.53/22.24 (208) ~ (all_52_4 = all_10_2) % 150.53/22.24 (209) all_44_0 = all_4_0 % 150.53/22.24 (210) all_58_30 = all_6_2 % 150.53/22.24 (211) op(e2, all_52_1) = all_58_7 % 150.53/22.24 (212) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.53/22.24 (213) ~ (e3 = e2) % 150.53/22.24 (214) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 150.53/22.24 (215) ~ (all_52_14 = all_6_2) % 150.53/22.24 (216) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 150.53/22.24 (217) op(all_4_2, e0) = all_4_1 % 150.53/22.24 (218) op(all_10_2, e3) = all_10_1 % 150.53/22.24 (219) ~ (all_8_2 = e0) % 150.53/22.24 (220) ~ (all_52_4 = all_52_12) % 150.53/22.24 (221) all_54_12 = all_52_3 % 150.53/22.24 (222) op(e2, all_8_2) = all_58_9 % 150.53/22.24 (223) all_54_4 = all_52_1 % 150.53/22.24 (224) ~ (all_52_1 = all_10_2) % 150.53/22.24 % 150.53/22.24 Begin of proof % 150.53/22.24 | % 150.53/22.24 | BETA: splitting (29) gives: % 150.53/22.24 | % 150.53/22.24 | Case 1: % 150.53/22.24 | | % 150.53/22.24 | | (225) ~ (all_16_2 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (61), (225) imply: % 150.53/22.24 | | (226) ~ (all_10_2 = e0) % 150.53/22.24 | | % 150.53/22.24 | | BETA: splitting (84) gives: % 150.53/22.24 | | % 150.53/22.24 | | Case 1: % 150.53/22.24 | | | % 150.53/22.24 | | | (227) ~ (all_18_2 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (129), (227) imply: % 150.53/22.24 | | | (228) ~ (all_6_2 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | BETA: splitting (73) gives: % 150.53/22.24 | | | % 150.53/22.24 | | | Case 1: % 150.53/22.24 | | | | % 150.53/22.24 | | | | (229) all_58_28 = e0 % 150.53/22.24 | | | | % 150.53/22.24 | | | | REF_CLOSE: (158), (226), (229) are inconsistent by sub-proof #865. % 150.53/22.24 | | | | % 150.53/22.24 | | | Case 2: % 150.53/22.24 | | | | % 150.53/22.24 | | | | (230) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 150.53/22.24 | | | | % 150.53/22.24 | | | | BETA: splitting (230) gives: % 150.53/22.24 | | | | % 150.53/22.24 | | | | Case 1: % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | (231) all_58_29 = e0 % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | REF_CLOSE: (120), (219), (231) are inconsistent by sub-proof #864. % 150.53/22.24 | | | | | % 150.53/22.24 | | | | Case 2: % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | (232) all_58_30 = e0 | all_58_31 = e0 % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | BETA: splitting (232) gives: % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | Case 1: % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | (233) all_58_30 = e0 % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | REF_CLOSE: (210), (228), (233) are inconsistent by sub-proof #863. % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | Case 2: % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | (234) all_58_31 = e0 % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | COMBINE_EQS: (2), (234) imply: % 150.53/22.24 | | | | | | (235) all_4_2 = e0 % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | REF_CLOSE: (4), (36), (172), (199), (205), (217), (235) are % 150.53/22.24 | | | | | | inconsistent by sub-proof #70. % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | End of split % 150.53/22.24 | | | | | % 150.53/22.24 | | | | End of split % 150.53/22.24 | | | | % 150.53/22.24 | | | End of split % 150.53/22.24 | | | % 150.53/22.24 | | Case 2: % 150.53/22.24 | | | % 150.53/22.24 | | | (236) all_18_2 = e0 % 150.53/22.24 | | | % 150.53/22.24 | | | COMBINE_EQS: (129), (236) imply: % 150.53/22.24 | | | (237) all_6_2 = e0 % 150.53/22.24 | | | % 150.53/22.24 | | | COMBINE_EQS: (179), (237) imply: % 150.53/22.24 | | | (238) all_56_8 = e0 % 150.53/22.24 | | | % 150.53/22.24 | | | COMBINE_EQS: (210), (237) imply: % 150.53/22.24 | | | (239) all_58_30 = e0 % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (70), (237) imply: % 150.53/22.24 | | | (240) ~ (all_52_2 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (11), (237) imply: % 150.53/22.24 | | | (241) ~ (all_52_6 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (56), (237) imply: % 150.53/22.24 | | | (242) ~ (all_52_8 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (169), (237) imply: % 150.53/22.24 | | | (243) ~ (all_52_9 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (143), (237) imply: % 150.53/22.24 | | | (244) ~ (all_52_11 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (215), (237) imply: % 150.53/22.24 | | | (245) ~ (all_52_14 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (134), (237) imply: % 150.53/22.24 | | | (246) op(e0, all_6_1) = all_6_0 % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (139), (237) imply: % 150.53/22.24 | | | (247) op(e0, e1) = all_6_1 % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (15), (237) imply: % 150.53/22.24 | | | (248) op(e1, e0) = all_58_18 % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (180), (237) imply: % 150.53/22.24 | | | (249) op(e1, e1) = e0 % 150.53/22.24 | | | % 150.53/22.24 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), % 150.53/22.24 | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 150.53/22.24 | | | (26), (27), (28), (30), (31), (32), (33), (34), (35), (37), % 150.53/22.24 | | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), % 150.53/22.24 | | | (48), (51), (52), (53), (54), (55), (57), (58), (60), (62), % 150.53/22.24 | | | (63), (64), (65), (66), (67), (68), (69), (71), (72), (74), % 150.53/22.24 | | | (76), (77), (78), (79), (80), (81), (82), (83), (85), (86), % 150.53/22.24 | | | (87), (88), (89), (90), (92), (93), (94), (95), (96), (97), % 150.53/22.24 | | | (98), (99), (101), (102), (103), (104), (105), (106), (107), % 150.53/22.24 | | | (108), (109), (110), (111), (112), (113), (116), (118), (119), % 150.53/22.24 | | | (120), (121), (122), (123), (124), (125), (126), (127), (128), % 150.53/22.24 | | | (130), (131), (132), (133), (135), (136), (137), (138), (140), % 150.53/22.24 | | | (141), (143), (144), (145), (146), (147), (150), (151), (152), % 150.53/22.24 | | | (153), (154), (156), (157), (158), (159), (160), (161), (162), % 150.53/22.24 | | | (163), (164), (165), (166), (167), (168), (170), (171), (172), % 150.53/22.24 | | | (173), (174), (175), (176), (178), (181), (182), (183), (184), % 150.53/22.24 | | | (185), (186), (187), (188), (189), (190), (191), (193), (195), % 150.53/22.24 | | | (196), (198), (199), (200), (201), (202), (203), (204), (206), % 150.53/22.24 | | | (208), (209), (210), (211), (212), (213), (214), (216), (217), % 150.53/22.24 | | | (218), (219), (220), (221), (222), (223), (224), (238), (239), % 150.53/22.24 | | | (240), (241), (242), (243), (244), (245), (246), (247), (248), % 150.53/22.24 | | | (249) are inconsistent by sub-proof #518. % 150.53/22.24 | | | % 150.53/22.24 | | End of split % 150.53/22.24 | | % 150.53/22.24 | Case 2: % 150.53/22.24 | | % 150.53/22.24 | | (250) all_16_2 = e0 % 150.53/22.24 | | (251) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (61), (250) imply: % 150.53/22.24 | | (252) all_10_2 = e0 % 150.53/22.24 | | % 150.53/22.24 | | SIMP: (252) implies: % 150.53/22.24 | | (253) all_10_2 = e0 % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (49), (253) imply: % 150.53/22.24 | | (254) all_50_2 = e0 % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (171), (253) imply: % 150.53/22.24 | | (255) all_56_0 = e0 % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (158), (253) imply: % 150.53/22.24 | | (256) all_58_28 = e0 % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (224), (253) imply: % 150.53/22.24 | | (257) ~ (all_52_1 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (170), (253) imply: % 150.53/22.24 | | (258) ~ (all_52_2 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (178), (253) imply: % 150.53/22.24 | | (259) ~ (all_52_3 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (208), (253) imply: % 150.53/22.24 | | (260) ~ (all_52_4 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (18), (253) imply: % 150.53/22.24 | | (261) ~ (all_52_8 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (153), (253) imply: % 150.53/22.24 | | (262) ~ (all_52_12 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (51), (253) imply: % 150.53/22.24 | | (263) op(e0, all_10_1) = all_10_0 % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (218), (253) imply: % 150.53/22.24 | | (264) op(e0, e3) = all_10_1 % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (144), (253) imply: % 150.53/22.24 | | (265) op(e3, e0) = all_58_0 % 150.53/22.24 | | % 150.53/22.24 | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, simplifying % 150.53/22.24 | | with (149), (264) gives: % 150.53/22.24 | | (266) all_52_3 = all_10_1 % 150.53/22.24 | | % 150.53/22.24 | | GROUND_INST: instantiating (4) with all_52_12, all_58_0, e0, e3, simplifying % 150.53/22.24 | | with (124), (265) gives: % 150.53/22.24 | | (267) all_58_0 = all_52_12 % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (221), (266) imply: % 150.53/22.24 | | (268) all_54_12 = all_10_1 % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (94), (266) imply: % 150.53/22.24 | | (269) all_56_12 = all_10_1 % 150.53/22.24 | | % 150.53/22.24 | | COMBINE_EQS: (174), (266) imply: % 150.53/22.24 | | (270) all_58_22 = all_10_1 % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (154), (266) imply: % 150.53/22.24 | | (271) ~ (all_52_1 = all_10_1) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (7), (266) imply: % 150.53/22.24 | | (272) ~ (all_52_2 = all_10_1) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (95), (266) imply: % 150.53/22.24 | | (273) ~ (all_52_7 = all_10_1) % 150.53/22.24 | | % 150.53/22.24 | | SIMP: (273) implies: % 150.53/22.24 | | (274) ~ (all_52_7 = all_10_1) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (173), (266) imply: % 150.53/22.24 | | (275) ~ (all_52_11 = all_10_1) % 150.53/22.24 | | % 150.53/22.24 | | SIMP: (275) implies: % 150.53/22.24 | | (276) ~ (all_52_11 = all_10_1) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (102), (266) imply: % 150.53/22.24 | | (277) ~ (all_10_1 = all_4_2) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (259), (266) imply: % 150.53/22.24 | | (278) ~ (all_10_1 = e0) % 150.53/22.24 | | % 150.53/22.24 | | REDUCE: (60), (266) imply: % 150.53/22.24 | | (279) op(e0, all_10_1) = all_58_21 % 150.53/22.24 | | % 150.53/22.24 | | GROUND_INST: instantiating (4) with all_10_0, all_58_21, all_10_1, e0, % 150.53/22.24 | | simplifying with (263), (279) gives: % 150.53/22.24 | | (280) all_58_21 = all_10_0 % 150.53/22.24 | | % 150.53/22.24 | | BETA: splitting (115) gives: % 150.53/22.24 | | % 150.53/22.24 | | Case 1: % 150.53/22.24 | | | % 150.53/22.24 | | | (281) ~ (all_50_2 = e0) % 150.53/22.24 | | | % 150.53/22.24 | | | REDUCE: (254), (281) imply: % 150.53/22.24 | | | (282) $false % 150.53/22.24 | | | % 150.53/22.24 | | | CLOSE: (282) is inconsistent. % 150.53/22.24 | | | % 150.53/22.24 | | Case 2: % 150.53/22.24 | | | % 150.53/22.24 | | | (283) ~ (all_50_0 = e1) | ~ (all_50_1 = e2) % 150.53/22.24 | | | % 150.53/22.24 | | | BETA: splitting (71) gives: % 150.53/22.24 | | | % 150.53/22.24 | | | Case 1: % 150.53/22.24 | | | | % 150.53/22.24 | | | | (284) all_56_15 = e0 % 150.53/22.24 | | | | % 150.53/22.24 | | | | REF_CLOSE: (2), (4), (9), (34), (36), (85), (99), (108), (120), (123), % 150.53/22.24 | | | | (130), (138), (146), (168), (172), (191), (199), (202), % 150.53/22.24 | | | | (205), (210), (212), (213), (217), (260), (284) are % 150.53/22.24 | | | | inconsistent by sub-proof #69. % 150.53/22.24 | | | | % 150.53/22.24 | | | Case 2: % 150.53/22.24 | | | | % 150.53/22.24 | | | | (285) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 % 150.53/22.24 | | | | = e0 | all_56_13 = e0 | all_56_14 = e0) % 150.53/22.24 | | | | % 150.53/22.24 | | | | ALPHA: (285) implies: % 150.53/22.24 | | | | (286) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 150.53/22.24 | | | | (287) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 150.53/22.24 | | | | % 150.53/22.24 | | | | BETA: splitting (197) gives: % 150.53/22.24 | | | | % 150.53/22.24 | | | | Case 1: % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | (288) all_56_6 = e0 % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | COMBINE_EQS: (126), (288) imply: % 150.53/22.24 | | | | | (289) all_52_2 = e0 % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | REDUCE: (258), (289) imply: % 150.53/22.24 | | | | | (290) $false % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | CLOSE: (290) is inconsistent. % 150.53/22.24 | | | | | % 150.53/22.24 | | | | Case 2: % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | (291) ~ (all_56_6 = e0) % 150.53/22.24 | | | | | (292) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | BETA: splitting (100) gives: % 150.53/22.24 | | | | | % 150.53/22.24 | | | | | Case 1: % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | (293) all_56_4 = e0 % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | COMBINE_EQS: (30), (293) imply: % 150.53/22.24 | | | | | | (294) all_52_8 = e0 % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | REDUCE: (261), (294) imply: % 150.53/22.24 | | | | | | (295) $false % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | CLOSE: (295) is inconsistent. % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | Case 2: % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | (296) ~ (all_56_4 = e0) % 150.53/22.24 | | | | | | (297) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | BETA: splitting (37) gives: % 150.53/22.24 | | | | | | % 150.53/22.24 | | | | | | Case 1: % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | (298) all_56_2 = e0 % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | COMBINE_EQS: (147), (298) imply: % 150.53/22.24 | | | | | | | (299) all_52_1 = e0 % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | REDUCE: (257), (299) imply: % 150.53/22.24 | | | | | | | (300) $false % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | CLOSE: (300) is inconsistent. % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | Case 2: % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | (301) ~ (all_56_2 = e0) % 150.53/22.24 | | | | | | | (302) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | BETA: splitting (138) gives: % 150.53/22.24 | | | | | | | % 150.53/22.24 | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | (303) all_56_1 = e0 % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | COMBINE_EQS: (99), (303) imply: % 150.53/22.24 | | | | | | | | (304) all_52_4 = e0 % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | REDUCE: (260), (304) imply: % 150.53/22.24 | | | | | | | | (305) $false % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | CLOSE: (305) is inconsistent. % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | (306) ~ (all_56_1 = e0) % 150.53/22.24 | | | | | | | | (307) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | BETA: splitting (93) gives: % 150.53/22.24 | | | | | | | | % 150.53/22.24 | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | % 150.53/22.24 | | | | | | | | | (308) all_54_5 = e0 % 150.53/22.24 | | | | | | | | | % 150.53/22.24 | | | | | | | | | REF_CLOSE: (34), (63), (85), (120), (123), (146), (168), % 150.53/22.24 | | | | | | | | | (191), (199), (210), (212), (213), (256), (308) are % 150.53/22.24 | | | | | | | | | inconsistent by sub-proof #231. % 150.53/22.24 | | | | | | | | | % 150.53/22.24 | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | % 150.53/22.24 | | | | | | | | | (309) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 150.53/22.24 | | | | | | | | | % 150.53/22.24 | | | | | | | | | BETA: splitting (12) gives: % 150.53/22.24 | | | | | | | | | % 150.53/22.24 | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | (310) all_54_3 = e0 % 150.53/22.24 | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | REF_CLOSE: (33), (262), (310) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | #733. % 150.53/22.24 | | | | | | | | | | % 150.53/22.24 | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | (311) ~ (all_54_3 = e0) % 150.53/22.24 | | | | | | | | | | (312) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.53/22.24 | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | BETA: splitting (38) gives: % 150.53/22.24 | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | (313) all_54_8 = e0 % 150.53/22.24 | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | REF_CLOSE: (14), (258), (313) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | | #731. % 150.53/22.24 | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | (314) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 150.53/22.24 | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | BETA: splitting (132) gives: % 150.53/22.24 | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | (315) all_54_4 = e0 % 150.53/22.24 | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | REF_CLOSE: (223), (257), (315) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | | | #859. % 150.53/22.24 | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | (316) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 150.53/22.24 | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | BETA: splitting (186) gives: % 150.53/22.24 | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | (317) all_54_1 = e0 % 150.53/22.24 | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | REF_CLOSE: (35), (260), (317) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | | | | #798. % 150.53/22.24 | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | (318) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 150.53/22.24 | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | BETA: splitting (151) gives: % 150.53/22.24 | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | (319) all_54_12 = e0 % 150.53/22.24 | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | REF_CLOSE: (268), (278), (319) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | | | | | #459. % 150.53/22.24 | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | (320) ~ (all_54_12 = e0) % 150.53/22.24 | | | | | | | | | | | | | | (321) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 150.53/22.24 | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | BETA: splitting (203) gives: % 150.53/22.24 | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | (322) all_54_2 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | REF_CLOSE: (13), (261), (322) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | | | | | | #860. % 150.53/22.24 | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | (323) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 150.53/22.24 | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 150.53/22.24 | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | (324) all_54_10 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (34), (59), (85), (97), (120), (123), (146), % 150.53/22.24 | | | | | | | | | | | | | | | | (163), (168), (191), (199), (210), (212), (213), % 150.53/22.24 | | | | | | | | | | | | | | | | (256), (324) are inconsistent by sub-proof #68. % 150.53/22.24 | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | (325) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 150.53/22.24 | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 150.53/22.24 | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | (326) all_54_6 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (326) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | (327) all_52_9 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | SIMP: (327) implies: % 150.53/22.24 | | | | | | | | | | | | | | | | | (328) all_52_9 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (328) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | (329) all_56_5 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (328) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | (330) all_58_11 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | REDUCE: (106), (328) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | (331) ~ (all_52_11 = e0) % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | SIMP: (331) implies: % 150.53/22.24 | | | | | | | | | | | | | | | | | (332) ~ (all_52_11 = e0) % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | REDUCE: (142), (328) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | (333) op(e2, e0) = all_58_10 % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 150.53/22.24 | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | (334) all_56_12 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (278), (334) are inconsistent by sub-proof % 150.53/22.24 | | | | | | | | | | | | | | | | | | #230. % 150.53/22.24 | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.24 | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | (335) all_56_13 = e0 | all_56_14 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 150.53/22.24 | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (336) all_56_13 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (336) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (337) all_52_7 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | SIMP: (337) implies: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (338) all_52_7 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (338) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (339) all_58_24 = e0 % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | REDUCE: (48), (338) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (340) ~ (all_52_6 = e0) % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | REDUCE: (274), (338) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (341) ~ (all_10_1 = e0) % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | REDUCE: (183), (338) imply: % 150.53/22.24 | | | | | | | | | | | | | | | | | | | (342) ~ (all_8_2 = e0) % 150.53/22.24 | | | | | | | | | | | | | | | | | | | % 150.53/22.24 | | | | | | | | | | | | | | | | | | | REDUCE: (62), (338) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (343) op(e0, e0) = all_58_23 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (344) all_56_7 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (340), (344) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | #803. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (345) all_56_8 = e0 | all_56_11 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (346) all_56_8 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (34), (85), (97), (120), (123), (146), (163), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (168), (179), (191), (199), (210), (212), (213), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (256), (346) are inconsistent by sub-proof #75. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (347) all_56_11 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (347) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (348) all_52_14 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (349) all_52_14 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (349) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (350) all_58_20 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (349) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_52_13 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (349) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (352) ~ (all_6_2 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | SIMP: (352) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_6_2 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (349) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_4_2 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | SIMP: (354) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (355) ~ (all_4_2 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (349) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (356) op(e1, e0) = all_58_19 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (349) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (357) op(e1, e0) = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_23, e0, e0, % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | simplifying with (172), (343) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (358) all_58_23 = all_4_2 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_19, e0, e1, % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | simplifying with (356), (357) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (359) all_58_19 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, all_58_10, e0, % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (185), (333) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (360) all_58_10 = all_52_13 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | (361) all_54_14 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (332), (361) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | #517. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | (362) ~ (all_54_14 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | (363) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | (364) all_54_7 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (351), (364) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | #742. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_54_7 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | (366) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | (367) all_54_9 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (340), (367) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | #572. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_54_9 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | (369) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_56_6 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (370) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_52_2 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (371) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_52_2 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (372) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_58_15 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (372) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (374) ~ (all_52_6 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (374) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_52_6 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (372) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (376) ~ (all_10_1 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (376) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (377) ~ (all_10_1 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (372) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (378) ~ (all_6_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (378) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (379) ~ (all_6_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_56_4 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (380) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_52_8 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (381) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (382) ~ (all_52_4 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (381) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (383) ~ (all_52_11 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (383) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (384) ~ (all_52_11 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (381) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (385) ~ (all_52_12 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (385) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ~ (all_52_12 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (10), (11), (17), (20), (26), (27), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (30), (31), (33), (34), (35), (39), (41), (57), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (77), (81), (83), (85), (91), (92), (96), (98), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (101), (107), (108), (111), (112), (119), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (123), (133), (135), (143), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (152), (157), (158), (160), (167), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (171), (179), (181), (187), (191), (199), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (212), (213), (219), (220), (223), (255), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (256), (260), (261), (262), (269), (270), (271), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (276), (278), (292), (312), (316), (318), (330), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (336), (339), (340), (347), (350), (351), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (353), (363), (369), (373), (375), (377), (382), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (384), (386) are inconsistent by sub-proof #66. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_56_5 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (329), (388) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | #305. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_56_8 = e1 | all_56_14 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_56_8 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (379), (390) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_56_14 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (391) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_52_11 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (392) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_52_11 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (393) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_4_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (394) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_4_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (19), (20), (23), (24), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (30), (31), (34), (41), (44), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (57), (59), (62), (69), (78), (81), (85), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (92), (98), (99), (106), (108), (109), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (119), (120), (121), (123), (126), (130), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (135), (136), (137), (142), (143), (146), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (152), (155), (156), (157), (158), (164), (167), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (171), (172), (179), (185), (187), (189), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (194), (199), (202), (210), (212), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (251), (255), (256), (258), (260), (261), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (267), (269), (276), (292), (302), (307), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (340), (347), (350), (351), (353), (356), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357), (366), (395) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #463. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_56_6 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (396) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | (398) ~ (all_52_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_56_0 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (399) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (400) e1 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (400) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (401) $false % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (401) is inconsistent. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_56_2 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (403) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_52_1 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (404) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_52_1 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (10), (11), (19), (20), (23), (24), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (30), (31), (33), (34), (35), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (41), (42), (45), (56), (57), (58), (63), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (75), (76), (78), (80), (81), (83), (85), (89), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (91), (96), (97), (99), (107), (108), (111), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (113), (119), (120), (122), (123), (128), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (133), (135), (136), (140), (143), (146), (152), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (160), (162), (163), (168), (179), (181), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (191), (210), (212), (213), (219), (220), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (256), (257), (260), (261), (262), (263), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (268), (269), (276), (277), (278), (280), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (309), (312), (318), (321), (329), (330), (332), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (336), (339), (340), (347), (350), (351), (353), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (355), (359), (363), (366), (397), (403), (405) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #57. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ~ (all_56_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (406) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) ~ (all_52_1 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (402) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_56_2 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (407), (408) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #450. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_56_6 = e1 | all_56_12 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_56_6 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (398), (410) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #639. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_56_12 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (411) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_10_1 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (412) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_10_1 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (277), (413) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_4_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (414) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) ~ (all_4_2 = e1) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (19), (20), (23), (24), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (30), (31), (34), (41), (44), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (57), (59), (62), (69), (78), (81), (85), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (92), (98), (99), (106), (108), (109), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (119), (120), (121), (123), (126), (130), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (131), (135), (136), (137), (142), (143), (146), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (152), (155), (156), (157), (158), (164), (167), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (171), (172), (179), (185), (187), (189), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (194), (199), (202), (210), (212), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (251), (255), (256), (258), (260), (261), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (267), (269), (276), (292), (302), (307), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (340), (347), (350), (351), (353), (356), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357), (366), (415) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #463. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (416) all_56_14 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (332), (416) are inconsistent by sub-proof % 150.53/22.25 | | | | | | | | | | | | | | | | | | | #806. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | End of split % 150.53/22.25 | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | (417) ~ (all_54_6 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | (418) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 150.53/22.25 | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | REDUCE: (66), (417) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | (419) ~ (all_52_9 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | (420) all_56_5 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (420) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | (421) all_52_9 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | REDUCE: (419), (421) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | (422) $false % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | CLOSE: (422) is inconsistent. % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | (423) all_56_8 = e0 | all_56_14 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | BETA: splitting (423) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (424) all_56_8 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (424) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (425) all_6_2 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (425) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (426) all_58_30 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (34), (85), (97), (120), (123), (146), (163), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (168), (191), (199), (212), (213), (256), (426) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (427) all_56_14 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (427) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (428) all_52_11 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | SIMP: (428) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (429) all_52_11 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (429) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (430) all_58_26 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | REDUCE: (165), (429) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (431) ~ (all_52_7 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | REDUCE: (104), (429) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (432) op(e0, e0) = all_58_25 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (429) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | (433) op(e0, e1) = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (434) all_56_3 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (434) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (435) all_8_2 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (435) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (436) all_58_29 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (199), % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (210), (212), (213), (256), (436) are inconsistent % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | by sub-proof #483. % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | (437) all_56_7 = e0 | all_56_13 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (438) all_56_7 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (438) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (439) all_52_6 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (439) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (440) all_58_17 = e0 % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (439) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_52_7 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (439) imply: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (442) ~ (all_52_14 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | SIMP: (442) implies: % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | (443) ~ (all_52_14 = e0) % 150.53/22.25 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (439) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_6_2 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | SIMP: (444) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | (445) ~ (all_6_2 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (439) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | (446) op(e1, e2) = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | (447) all_56_9 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (447) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | (448) all_52_12 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (262), (448) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | (449) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (449) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | (450) all_56_10 = e0 | all_56_11 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (451) all_56_10 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (451) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (452) all_52_13 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (452) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (453) all_58_13 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (452) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (454) ~ (all_8_2 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (452) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (455) ~ (all_4_2 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (455) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (456) ~ (all_4_2 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (452) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (457) op(e2, e0) = all_58_12 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (452) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (458) op(e2, e0) = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_25, e0, e0, % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (172), (432) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (459) all_58_25 = all_4_2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e0, e2, % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (457), (458) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | (460) all_58_12 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | (461) all_54_13 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (431), (461) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | #732. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | (462) ~ (all_54_13 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | (463) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_54_11 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (443), (464) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | #743. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | (465) ~ (all_54_11 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_56_6 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (467) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_52_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (468) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_58_15 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (468) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (470) ~ (all_52_1 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (468) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (471) ~ (all_52_14 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (471) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_52_14 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (468) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (473) ~ (all_6_2 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (473) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (474) ~ (all_6_2 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (468) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (475) op(e1, e1) = all_58_14 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_2, all_58_14, e1, e1, % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (180), (475) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_58_14 = all_6_2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_56_4 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (477) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_52_8 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (478) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) ~ (all_52_4 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (478) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) ~ (all_52_12 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (480) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) ~ (all_52_12 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_56_9 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (119), (481), (482) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #486. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_56_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (484) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_52_1 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (470), (485) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (486) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_56_10 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (488) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) e1 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (489) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (490) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_56_11 = e1 | all_56_15 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (487) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_56_3 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (492) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_8_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (493) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) op(e1, e2) = all_8_1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (190), (446), (494) are inconsistent by % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #795. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) ~ (all_56_3 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (495) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) ~ (all_8_2 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_56_1 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (497) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_52_4 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (498) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (499) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_56_3 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (501) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_8_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (496), (502) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (503) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_56_7 = e1 | all_56_13 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_56_11 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (98), (472), (505) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #580. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_56_15 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (506) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_4_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (507) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_4_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (508) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) ~ (all_52_7 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (199), (438), (504), (509) are inconsistent % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #419. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (510) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_56_5 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (511) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_52_9 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (512) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_58_11 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (512) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) ~ (all_52_8 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (512) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) ~ (all_8_2 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (515) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) ~ (all_8_2 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_58_28 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (256), (517) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #690. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (518) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_58_29 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (519) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_8_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (516), (520) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (521) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_58_30 = e1 | all_58_31 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_58_30 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (523) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_6_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (474), (524) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) $false % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (525) is inconsistent. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_58_31 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) ~ (all_58_30 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (526) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_4_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (528) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_56_15 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (459), (528) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_25 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (528) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) ~ (all_52_12 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (277), (528) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) ~ (all_10_1 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_56_0 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (533) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) e1 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (534) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) e1 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (535) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_58_31 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (210), (474), (522), (536) are inconsistent % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (537) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_56_1 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (538) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_52_4 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (539) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_58_2 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (539) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) ~ (all_52_7 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (541) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) ~ (all_52_7 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (539) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) ~ (all_52_8 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (539) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ~ (all_52_12 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_58_31 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (210), (474), (522), (545) are inconsistent % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #824. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_58_30 = e1 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (120), (123), (146), (168), (191), % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (547) are inconsistent by % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #497. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (548) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_58_29 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (549) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_8_2 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (33), (45), (56), (76), (85), (119), % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (136), (146), (191), (210), (213), (256), % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267), (312), (323), (460), (476), (514), (526), % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530), (531), (549) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_56_1 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (538), (552) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_58_28 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (256), (554) are inconsistent by sub-proof % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #688. % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) ~ (all_58_28 = e2) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (555) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) ~ (e2 = e0) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_56_2 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (558) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_52_1 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (559) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_58_8 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (559) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) ~ (all_10_1 = e2) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (561) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) ~ (all_10_1 = e2) % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_56_12 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (563) imply: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_10_1 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (564) implies: % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_10_1 = e2 % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (565) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) $false % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (566) is inconsistent. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_56_2 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (213), (558), (568) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #840. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) ~ (all_56_2 = e3) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (569) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) ~ (e3 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_54_5 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (516), (572) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #534. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) ~ (all_54_5 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_54_5 = e3 | all_54_5 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_56_0 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (255), (575) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #430. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_56_2 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (213), (558), (577) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #840. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_56_6 = e3 | all_56_12 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (578) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_56_6 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (467), (579) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #137. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_56_12 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (580) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_10_1 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (581) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) all_10_1 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (582) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_58_22 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (567) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_56_13 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (584) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_52_7 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (585) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_52_7 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (586) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_58_24 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (586) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) ~ (all_8_2 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (588) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) ~ (all_8_2 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (570) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_56_3 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (590) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_8_2 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (591) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_8_2 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (592) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_58_29 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (551) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_58_28 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (594) are inconsistent % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #64. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) ~ (all_58_28 = e3) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (595) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) ~ (e3 = e0) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) all_58_29 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (33), (45), (56), (76), (85), (119), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (136), (146), (191), (210), (213), (256), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267), (312), (323), (460), (476), (514), (526), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530), (531), (598) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) ~ (all_58_29 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_58_30 = e2 | all_58_31 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_58_30 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (601) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_6_2 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (602) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) all_6_2 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (603) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_56_8 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_56_6 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (467), (605) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (606) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) $false % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (607) is inconsistent. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) ~ (all_56_6 = e3) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (467), (608) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) ~ (e3 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (609) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_56_7 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (438), (611) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) e3 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (593), (612) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_58_29 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (613) are inconsistent by % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #653. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) ~ (all_56_7 = e3) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) all_56_8 = e3 | all_56_11 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (615) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_56_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (604), (616) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) e3 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (593), (617) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) all_58_29 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (33), (45), (56), (76), (85), (119), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (136), (146), (191), (210), (213), (256), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267), (312), (323), (460), (476), (514), (526), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530), (531), (618) are inconsistent by sub-proof % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_56_11 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (619) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_52_14 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (620) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_52_14 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (621) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_58_20 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (621) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) ~ (all_52_12 = e3) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_56_9 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (624) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_52_12 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (625) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_58_6 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (625) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) ~ (all_52_8 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_56_4 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (628) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_52_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (629) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_52_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (630) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_58_4 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (596) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (634) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (635) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) all_58_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) all_58_4 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (631), (637) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (638) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (560), (636) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) e3 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (639), (640) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) e2 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (641) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) e2 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (601), (642) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_58_30 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (526), (600), (643) are inconsistent by % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (644) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (645) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_58_22 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_58_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (560), (647) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) e3 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (583), (646) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) e3 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (649) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) e3 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (648), (650) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) e2 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (648), (651) are % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (652) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_58_17 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) all_58_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_58_2 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (655) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (656) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (560), (654) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) e3 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (653) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) e2 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (657), (658) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) e2 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (660) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) e2 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (659), (661) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) e1 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (657), (662) are % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (664) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (665) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_58_13 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_58_8 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_58_2 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (668) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (669) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) e3 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (560), (667) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) e3 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (666) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) e2 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (672) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) e2 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (670), (671) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) e2 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (674) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) e2 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (673), (675) imply: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) e1 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (676) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) e1 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (670), (677) are % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (678) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_58_2 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (526), (540), (600), (601), (679) are % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #55. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (680) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (681) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_58_2 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (526), (540), (600), (601), (682) are % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #55. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (440), (526), (540), (600), (601), % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) are inconsistent by sub-proof #445. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (684) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (685) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (686) gives: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (526), (587), (600), (601), (687) % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #444. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (688) implies: % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_58_2 = e2 % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (526), (540), (600), (601), (689) are % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #55. % 150.53/22.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (690) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (691) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) all_58_22 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_58_15 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (693) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (583), (593), (692), (694) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #54. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (695) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) all_58_17 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_58_15 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (469), (697) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (696) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) e1 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (698), (699) are % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (700) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (701) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (702) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_26 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (430), (526), (593), (622), (703), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) are inconsistent by sub-proof #53. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (705) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) all_58_6 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) all_58_4 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (631), (707) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (708) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (626), (706) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) e3 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (710) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) e3 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (709), (711) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) e2 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (601), (712) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_58_30 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (526), (600), (713) are inconsistent by % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (715) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_58_11 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_58_4 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (631), (718) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (719) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (717) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) e2 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (716) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) e2 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (721), (722) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) e1 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (720), (723) are % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (724) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) all_58_4 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (631), (726) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (727) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (725) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (729) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (728), (730) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) e1 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (728), (731) are % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (732) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (734) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (735) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) all_58_4 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (631), (736) are inconsistent by sub-proof % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #647. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (738) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) all_58_24 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) all_58_6 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (626), (740) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) e3 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (741) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) e3 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (587), (739) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) e2 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (742), (743) are % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (744) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_58_6 = e3 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (626), (746) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) e3 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (747) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) e3 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (745) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (749) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (748), (750) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) e2 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (748), (751) are % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (754) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_58_22 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (583), (755) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (756) are inconsistent % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #52. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (757) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) all_58_22 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (759) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (760) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (583), (593), (758), (761) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #54. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (762) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (763) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_58_22 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (583), (764) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (765) are inconsistent % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #52. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (526), (587), (600), (601), (766) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #438. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (770) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_58_17 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_58_11 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (513), (773) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) e2 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (772) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) e2 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (771) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (776) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) e3 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (774), (775) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) e1 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (778) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) e1 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (777), (779) are % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (780) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_58_13 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (453), (526), (600), (601), (781) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #437. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (782) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (783) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (784) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (785) are inconsistent % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #52. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (786) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) e2 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_58_17 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (440), (526), (600), (601), (787), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) are inconsistent by sub-proof #446. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (789) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (790) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (792) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (793) are inconsistent % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #52. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (794) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_58_26 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_58_20 = e1 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (430), (526), (593), (622), (795), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) are inconsistent by sub-proof #53. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (797) gives: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (526), (587), (600), (601), (798) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #436. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (799) implies: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_58_20 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (800) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) e3 = e0 % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (210), % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (256), (526), (593), (801) are inconsistent % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #52. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) ~ (all_56_4 = e3) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (802) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) ~ (all_52_8 = e3) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (323), (514), (627), (803) are inconsistent % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #554. % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) ~ (all_56_9 = e2) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (804) imply: % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) ~ (all_52_12 = e2) % 150.53/22.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (312), (531), (623), (805) are inconsistent % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_58_31 = e2 % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (806) imply: % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) e2 = e1 % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (807) imply: % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) $false % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (808) is inconsistent. % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) ~ (all_56_3 = e3) % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (809) imply: % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) ~ (all_8_2 = e3) % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (574), (589), (810) are inconsistent by % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #532. % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_56_14 = e2 | all_56_15 = e2 % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (168), (427), (529), (811) are inconsistent % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #256. % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.53/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) ~ (all_56_2 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (812) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) ~ (all_52_1 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_56_3 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (814) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) all_8_2 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (815) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_58_29 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (33), (45), (56), (76), (85), (119), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (136), (146), (191), (210), (213), (256), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267), (312), (323), (460), (476), (514), (526), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530), (531), (816) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_56_7 = e2 | all_56_13 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (817) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_56_7 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (438), (818) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) e2 = e0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (819) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (820) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) all_56_13 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (821) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_52_7 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (822) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_52_7 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (823) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) ~ (all_10_1 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (824) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) ~ (all_10_1 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (223), (268), (271), (316), (321), (470), (532), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813), (825) are inconsistent by sub-proof #504. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_56_4 = e1 | all_56_9 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (119), (514), (531), (826) are inconsistent % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #485. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_56_8 = e1 | all_56_14 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (827) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_56_8 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (474), (828) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_56_14 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (829) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) e1 = e0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (830) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (831) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (832) ~ (all_56_6 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (832) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (834) ~ (all_52_2 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) all_56_0 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (255), (835) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | #516. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) ~ (all_56_0 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (836) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) ~ (e1 = e0) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_56_4 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (839) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_52_8 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (840) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) ~ (all_6_2 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (841) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) ~ (all_6_2 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (98), (120), (166), (179), (190), (198), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (210), (212), (215), (256), (438), (443), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (833), (842) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #51. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) ~ (all_56_4 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (843) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) ~ (all_52_8 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) all_56_0 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (255), (846) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #516. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_56_12 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (848) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_10_1 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (849) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_10_1 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (850) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) ~ (all_52_2 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (850) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) ~ (all_52_7 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (850) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) op(e0, e3) = all_10_0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (850) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) op(e0, e3) = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_54_8 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (834), (855) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) ~ (all_54_8 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_54_8 = e3 | all_54_8 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (857) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) all_54_8 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (858) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) all_52_2 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (859) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) all_52_2 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (860) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) ~ (all_52_14 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (861) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) ~ (all_52_14 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (860) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) ~ (all_6_2 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (863) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) ~ (all_6_2 = e2) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (837) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_56_2 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (865) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_52_1 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (866) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) ~ (all_52_9 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (867) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) ~ (all_52_9 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (844) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_56_5 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (869) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_52_9 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (868), (870) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (871) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_56_8 = e1 | all_56_14 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (872) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_56_8 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (873) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_6_2 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (874) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_58_30 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (874) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) ~ (all_52_14 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (864), (874) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) ~ (e2 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (874) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) op(e1, e1) = all_58_18 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (874) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) op(e1, e1) = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_54_11 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (876), (880) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) ~ (all_54_11 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_54_11 = e3 | all_54_11 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (882) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_54_11 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (862), (883) are inconsistent by sub-proof % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #777. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_54_11 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (884) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_52_14 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (885) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_52_14 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (886) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) ~ (all_52_12 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_58_28 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (888) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) e3 = e0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (889) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (890) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) ~ (all_58_28 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (891) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) ~ (e3 = e0) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (892) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_58_29 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (894) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) all_8_2 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (895) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_8_2 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (896) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_56_3 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (896) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) ~ (all_52_4 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (16), (33), (34), (35), (53), (69), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (119), (123), (133), (136), (140), (168), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (181), (202), (213), (220), (256), (280), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312), (318), (460), (463), (852), (853), (854), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875), (878), (879), (887), (892), (894), (897), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) are inconsistent by sub-proof #50. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) all_58_30 = e3 | all_58_31 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) all_56_1 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (900) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_52_4 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (901) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_52_4 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (902) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) ~ (all_52_12 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (847) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) all_56_1 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (900), (904) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) e3 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (905) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) e3 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (906) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (907) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_56_4 = e1 | all_56_9 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (908) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) all_56_4 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (909) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) all_52_8 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (910) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_52_8 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (845), (911) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (912) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) all_56_9 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (913) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) all_52_12 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (914) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_52_12 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (887), (915) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) ~ (e3 = e1) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) all_56_9 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (913), (917) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) e2 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (918) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (919) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (920) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) all_56_10 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (921) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) e2 = e0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (922) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) e2 = e0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (923) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (924) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_56_11 = e2 | all_56_15 = e2 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (899) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) all_58_30 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (875), (926) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) e3 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (927) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (928) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) all_58_31 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (929) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) all_4_2 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (930) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_4_2 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (931) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_56_15 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (98), (213), (862), (925), (932) are inconsistent % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #161. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) ~ (all_56_1 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (933) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_52_4 = e3) % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (934) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) all_56_3 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (936) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) all_8_2 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (937) implies: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_8_2 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (938) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_58_29 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (16), (33), (34), (35), (53), (69), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (119), (123), (133), (136), (140), (168), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (181), (202), (213), (220), (256), (280), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312), (318), (460), (463), (852), (853), (854), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875), (878), (879), (887), (892), (935), (936), % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) are inconsistent by sub-proof #50. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_56_7 = e3 | all_56_13 = e3 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (146), (438), (852), (940) are inconsistent % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #49. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_56_14 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (941) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) e1 = e0 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (942) imply: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) $false % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (943) is inconsistent. % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_56_6 = e1 | all_56_12 = e1 % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (944) gives: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_56_6 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (834), (945) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #639. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_56_12 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (946) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_10_1 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (947) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_10_1 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (117), (263), (433), (948) are inconsistent % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #491. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_54_8 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (851), (949) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #786. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) ~ (all_56_12 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (950) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) ~ (all_10_1 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_56_4 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (953) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_52_8 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (954) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) ~ (all_52_4 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (954) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) ~ (all_52_9 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (956) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) ~ (all_52_9 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (954) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) ~ (all_6_2 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (958) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) ~ (all_6_2 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_56_1 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (960) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_52_4 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (955), (961) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (962) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_56_2 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (964) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) all_52_1 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (965) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) ~ (all_8_2 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (966) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) ~ (all_8_2 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (963) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_56_3 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (968) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) all_8_2 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (967), (969) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (970) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_56_7 = e3 | all_56_13 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (971) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_56_7 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (438), (972) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) e3 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (973) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (974) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) all_56_13 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (975) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_52_7 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (976) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) all_52_7 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (977) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) ~ (all_10_1 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (977) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) ~ (all_4_2 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (979) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) ~ (all_4_2 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_56_12 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (952), (981) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #48. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_58_28 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (256), (982) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) ~ (all_58_28 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (983) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) ~ (e3 = e0) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (951) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) all_58_29 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (967), (986) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #756. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) all_58_30 = e3 | all_58_31 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (210), (959), (980), (987) are inconsistent % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #47. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) all_56_14 = e3 | all_56_15 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (988) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_56_14 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (989) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) e3 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (990) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (991) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_56_15 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (980), (992) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #392. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (993) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_56_3 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (994) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_8_2 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (995) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) all_58_29 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (995) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) ~ (all_52_7 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (951) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_56_13 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (997), (998) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #760. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_56_14 = e3 | all_56_15 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (999) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_56_14 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (1000) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) e3 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (996), (1001) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) all_58_29 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (123), (146), (168), (191), (199), % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (212), (213), (256), (1002) are % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #483. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_56_15 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (1003) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_4_2 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1004) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_4_2 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (1005) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) all_58_31 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (1005) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) ~ (all_52_12 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (1005) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) ~ (all_52_14 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_58_28 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (256), (1009) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #688. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1010) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) all_58_29 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (996), (1011) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) e3 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (1012) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1013) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) ~ (all_58_29 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) all_58_30 = e2 | all_58_31 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1015) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) all_58_30 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (1016) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) all_6_2 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (1017) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) ~ (all_52_14 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) all_56_9 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (1019) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) all_52_12 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1020) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_52_12 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (1021) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) ~ (all_52_4 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1007), (1021) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) ~ (e3 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) all_54_1 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (1024) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) all_52_4 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1025) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) all_52_4 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (1026) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) ~ (all_52_7 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1027) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) ~ (all_52_7 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (955), (1026) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) ~ (e3 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1022), (1026) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) ~ (e2 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) all_56_12 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1031) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) all_10_1 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1032) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) all_10_1 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (117), (263), (433), (1033) are inconsistent % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #491. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1034) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) all_56_13 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (1028), (1035) are inconsistent by % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_56_14 = e1 | all_56_15 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1036) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_56_14 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (1037) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) e1 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (1038) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1039) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_56_15 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (1040) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) all_4_2 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1041) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) all_4_2 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (1042) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) all_58_31 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (1042) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) ~ (all_52_14 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_56_6 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (1045) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) all_52_2 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (834), (1046) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1047) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (833) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) all_56_7 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (438), (1048) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) all_56_8 = e1 | all_56_11 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_56_8 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (85), (120), (123), (146), (168), (179), % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (210), (213), (256), (1043), (1050) are % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #496. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_56_11 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (98), (1044), (1051) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #580. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_54_1 = e3 | all_54_1 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (955), (1022), (1052) are inconsistent by % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #508. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) ~ (all_56_9 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1053) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) ~ (all_52_12 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) all_54_3 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (1055) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_52_12 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1056) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_52_12 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1057) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) ~ (all_52_14 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1058) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) ~ (all_52_14 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (466), (1008), (1018), (1059) are % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #46. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) all_54_3 = e3 | all_54_3 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (1007), (1054), (1060) are inconsistent by % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #613. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_58_31 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1006), (1061) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) e3 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (1062) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1063) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_56_5 = e3 | all_56_10 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1064) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) all_56_5 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (1065) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_52_9 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (957), (1066) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1067) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_56_10 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (1068) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) e3 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1069) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1070) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) ~ (all_56_4 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (1071) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) ~ (all_52_8 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_54_2 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (845), (1074) are inconsistent by sub-proof % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #819. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_54_2 = e3 | all_54_2 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_54_2 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (1076) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) all_52_8 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1077) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_52_8 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (1078) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) ~ (all_52_9 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1079) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) ~ (all_52_9 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (1078) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) ~ (all_6_2 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1081) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) ~ (all_6_2 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_56_6 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (1083) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_52_2 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (1084) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) ~ (all_10_1 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1085) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) ~ (all_10_1 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_54_12 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1087) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_10_1 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (117), (263), (433), (1088) are inconsistent % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #491. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_54_12 = e3 | all_54_12 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (952), (1086), (1089) are inconsistent by % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1090) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_56_7 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (438), (1091) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) e2 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (1092) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1093) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) all_56_8 = e2 | all_56_11 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1072) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_56_5 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (1095) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_52_9 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (1096) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) ~ (all_52_1 = e3) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1094) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_56_8 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (1082), (1098) are inconsistent by % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_56_11 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (1099) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_52_14 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1100) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_52_14 = e2 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (1101) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) ~ (all_4_2 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1102) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) ~ (all_4_2 = e2) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (844) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_56_5 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1095), (1104) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) e3 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (1105) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1106) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_56_8 = e1 | all_56_14 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1107) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_56_8 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (1108) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_6_2 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1109) implies: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_6_2 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (1110) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_58_30 = e1 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1082), (1110) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) ~ (e2 = e1) % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_58_28 = e3 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1113) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) e3 = e0 % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1114) imply: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) $false % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1115) is inconsistent. % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_58_28 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1117) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) e2 = e0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1099), (1118) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_56_11 = e0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1094) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_56_8 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1108), (1120) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) e2 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (1121) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1122) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (1118) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1123) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) all_58_29 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (1125) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) all_8_2 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1126) implies: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_8_2 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (1127) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) ~ (all_52_1 = e2) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) all_56_2 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (1129) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) all_52_1 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1130) implies: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_52_1 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (1131) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) ~ (all_10_1 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1132) implies: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) ~ (all_10_1 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1097), (1131) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) ~ (e3 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) all_56_12 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1135) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) all_10_1 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1136) implies: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_10_1 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (1137) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_50_1 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (1137) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) ~ (all_52_7 = e2) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (952), (1137) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) ~ (e3 = e2) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (1137) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) op(e0, e2) = all_10_0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1116) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_58_29 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1125), (1142) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) e3 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (1143) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1144) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) all_58_30 = e3 | all_58_31 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1145) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) all_58_30 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1111), (1146) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) e3 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (1147) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1148) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_58_31 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (1149) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_4_2 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1150) implies: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) all_4_2 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (1151) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) ~ (all_52_7 = e3) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_54_13 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (1153) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_52_7 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1154) implies: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) all_52_7 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (1155) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) op(e0, e2) = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) ~ (all_50_0 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1157) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) ~ (all_10_0 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_10_0, e2, e0, % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1141), (1156) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) all_10_0 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1158), (1159) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1160) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) ~ (all_50_1 = e2) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1138), (1161) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1162) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) all_54_13 = e3 | all_54_13 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1139), (1152), (1163) are inconsistent by % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #730. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) ~ (all_56_12 = e2) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (1164) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) ~ (all_10_1 = e2) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (321), (952), (1133), (1165) are % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) ~ (all_56_2 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1166) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) ~ (all_52_1 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (223), (316), (1097), (1128), (1167) are % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #828. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_58_30 = e2 | all_58_31 = e2 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (123), (1103), (1111), (1168) are % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_56_14 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (1169) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) e1 = e0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (1170) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1171) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) ~ (all_56_5 = e3) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (1172) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) ~ (all_52_9 = e3) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) all_54_10 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (1174) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_6_2 = e1 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (1175) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) ~ (all_52_9 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (418), (1080), (1173), (1176) are % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) ~ (all_54_10 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (1177) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) ~ (all_6_2 = e1) % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (98), (120), (166), (179), (190), (198), % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (210), (212), (215), (256), (438), (443), % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446), (833), (1178) are inconsistent by sub-proof % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #51. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) all_54_2 = e3 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1073), (1179) are inconsistent by sub-proof % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #816. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | (1180) all_56_11 = e0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (1180) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | (1181) all_52_14 = e0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (443), (1181) imply: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | (1182) $false % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1182) is inconsistent. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | (1183) all_56_13 = e0 % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (431), (1183) are inconsistent by sub-proof % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | #802. % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | | % 150.75/22.31 | | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | | % 150.75/22.31 | | | | | | | | | End of split % 150.75/22.31 | | | | | | | | | % 150.75/22.31 | | | | | | | | End of split % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | End of split % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | End of split % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | End of split % 150.75/22.31 | | | | | % 150.75/22.31 | | | | End of split % 150.75/22.31 | | | | % 150.75/22.31 | | | End of split % 150.75/22.31 | | | % 150.75/22.31 | | End of split % 150.75/22.31 | | % 150.75/22.31 | End of split % 150.75/22.31 | % 150.75/22.31 End of proof % 150.75/22.31 % 150.75/22.31 Sub-proof #45 shows that the following formulas are inconsistent: % 150.75/22.31 ---------------------------------------------------------------- % 150.75/22.31 (1) all_58_31 = all_4_2 % 150.75/22.31 (2) ~ (e2 = e1) % 150.75/22.31 (3) all_58_30 = e2 | all_58_31 = e2 % 150.75/22.31 (4) all_58_30 = e1 % 150.75/22.31 (5) ~ (all_4_2 = e2) % 150.75/22.31 % 150.75/22.31 Begin of proof % 150.75/22.31 | % 150.75/22.31 | BETA: splitting (3) gives: % 150.75/22.31 | % 150.75/22.31 | Case 1: % 150.75/22.31 | | % 150.75/22.31 | | (6) all_58_30 = e2 % 150.75/22.31 | | % 150.75/22.31 | | COMBINE_EQS: (4), (6) imply: % 150.75/22.31 | | (7) e2 = e1 % 150.75/22.31 | | % 150.75/22.31 | | REDUCE: (2), (7) imply: % 150.75/22.31 | | (8) $false % 150.75/22.31 | | % 150.75/22.31 | | CLOSE: (8) is inconsistent. % 150.75/22.31 | | % 150.75/22.31 | Case 2: % 150.75/22.31 | | % 150.75/22.31 | | (9) all_58_31 = e2 % 150.75/22.31 | | % 150.75/22.31 | | COMBINE_EQS: (1), (9) imply: % 150.75/22.31 | | (10) all_4_2 = e2 % 150.75/22.31 | | % 150.75/22.31 | | SIMP: (10) implies: % 150.75/22.31 | | (11) all_4_2 = e2 % 150.75/22.31 | | % 150.75/22.31 | | REDUCE: (5), (11) imply: % 150.75/22.31 | | (12) $false % 150.75/22.31 | | % 150.75/22.31 | | CLOSE: (12) is inconsistent. % 150.75/22.31 | | % 150.75/22.31 | End of split % 150.75/22.31 | % 150.75/22.31 End of proof % 150.75/22.31 % 150.75/22.31 Sub-proof #46 shows that the following formulas are inconsistent: % 150.75/22.31 ---------------------------------------------------------------- % 150.75/22.31 (1) all_54_11 = all_52_14 % 150.75/22.31 (2) ~ (all_52_14 = e1) % 150.75/22.31 (3) ~ (all_52_14 = e2) % 150.75/22.31 (4) ~ (all_52_14 = e3) % 150.75/22.31 (5) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 150.75/22.31 % 150.75/22.31 Begin of proof % 150.75/22.31 | % 150.75/22.31 | BETA: splitting (5) gives: % 150.75/22.31 | % 150.75/22.31 | Case 1: % 150.75/22.31 | | % 150.75/22.31 | | (6) all_54_11 = e1 % 150.75/22.31 | | % 150.75/22.31 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #567. % 150.75/22.31 | | % 150.75/22.31 | Case 2: % 150.75/22.31 | | % 150.75/22.31 | | (7) all_54_11 = e3 | all_54_11 = e2 % 150.75/22.31 | | % 150.75/22.31 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #775. % 150.75/22.31 | | % 150.75/22.31 | End of split % 150.75/22.31 | % 150.75/22.31 End of proof % 150.75/22.31 % 150.75/22.31 Sub-proof #47 shows that the following formulas are inconsistent: % 150.75/22.31 ---------------------------------------------------------------- % 150.75/22.31 (1) all_58_31 = all_4_2 % 150.75/22.31 (2) ~ (all_4_2 = e3) % 150.75/22.31 (3) all_58_30 = e3 | all_58_31 = e3 % 150.75/22.31 (4) ~ (all_6_2 = e3) % 150.75/22.31 (5) all_58_30 = all_6_2 % 150.75/22.31 % 150.75/22.31 Begin of proof % 150.75/22.31 | % 150.75/22.31 | BETA: splitting (3) gives: % 150.75/22.31 | % 150.75/22.31 | Case 1: % 150.75/22.31 | | % 150.75/22.31 | | (6) all_58_30 = e3 % 150.75/22.31 | | % 150.75/22.31 | | COMBINE_EQS: (5), (6) imply: % 150.75/22.31 | | (7) all_6_2 = e3 % 150.75/22.31 | | % 150.75/22.31 | | SIMP: (7) implies: % 150.75/22.31 | | (8) all_6_2 = e3 % 150.75/22.31 | | % 150.75/22.31 | | REDUCE: (4), (8) imply: % 150.75/22.31 | | (9) $false % 150.75/22.31 | | % 150.75/22.31 | | CLOSE: (9) is inconsistent. % 150.75/22.31 | | % 150.75/22.31 | Case 2: % 150.75/22.31 | | % 150.75/22.31 | | (10) all_58_31 = e3 % 150.75/22.31 | | % 150.75/22.31 | | COMBINE_EQS: (1), (10) imply: % 150.75/22.31 | | (11) all_4_2 = e3 % 150.75/22.31 | | % 150.75/22.31 | | SIMP: (11) implies: % 150.75/22.31 | | (12) all_4_2 = e3 % 150.75/22.31 | | % 150.75/22.31 | | REDUCE: (2), (12) imply: % 150.75/22.31 | | (13) $false % 150.75/22.31 | | % 150.75/22.31 | | CLOSE: (13) is inconsistent. % 150.75/22.31 | | % 150.75/22.31 | End of split % 150.75/22.31 | % 150.75/22.31 End of proof % 150.75/22.31 % 150.75/22.31 Sub-proof #48 shows that the following formulas are inconsistent: % 150.75/22.31 ---------------------------------------------------------------- % 150.75/22.31 (1) all_56_12 = all_10_1 % 150.75/22.31 (2) all_56_12 = e3 % 150.75/22.31 (3) ~ (all_10_1 = e3) % 150.75/22.31 % 150.75/22.31 Begin of proof % 150.75/22.31 | % 150.75/22.31 | COMBINE_EQS: (1), (2) imply: % 150.75/22.31 | (4) all_10_1 = e3 % 150.75/22.31 | % 150.75/22.31 | SIMP: (4) implies: % 150.75/22.31 | (5) all_10_1 = e3 % 150.75/22.31 | % 150.75/22.31 | REDUCE: (3), (5) imply: % 150.75/22.31 | (6) $false % 150.75/22.31 | % 150.75/22.31 | CLOSE: (6) is inconsistent. % 150.75/22.31 | % 150.75/22.31 End of proof % 150.75/22.31 % 150.75/22.31 Sub-proof #49 shows that the following formulas are inconsistent: % 150.75/22.31 ---------------------------------------------------------------- % 150.75/22.31 (1) all_56_7 = e3 | all_56_13 = e3 % 150.75/22.31 (2) all_56_7 = e0 % 150.75/22.31 (3) all_56_13 = all_52_7 % 150.75/22.31 (4) ~ (e3 = e0) % 150.75/22.31 (5) ~ (all_52_7 = e3) % 150.75/22.31 % 150.75/22.31 Begin of proof % 150.75/22.31 | % 150.75/22.31 | BETA: splitting (1) gives: % 150.75/22.31 | % 150.75/22.31 | Case 1: % 150.75/22.31 | | % 150.75/22.31 | | (6) all_56_7 = e3 % 150.75/22.31 | | % 150.75/22.31 | | COMBINE_EQS: (2), (6) imply: % 150.75/22.31 | | (7) e3 = e0 % 150.75/22.31 | | % 150.75/22.31 | | REDUCE: (4), (7) imply: % 150.75/22.31 | | (8) $false % 150.75/22.31 | | % 150.75/22.31 | | CLOSE: (8) is inconsistent. % 150.75/22.31 | | % 150.75/22.31 | Case 2: % 150.75/22.31 | | % 150.75/22.31 | | (9) all_56_13 = e3 % 150.75/22.31 | | % 150.75/22.31 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #760. % 150.75/22.31 | | % 150.75/22.31 | End of split % 150.75/22.31 | % 150.75/22.31 End of proof % 150.75/22.31 % 150.75/22.31 Sub-proof #50 shows that the following formulas are inconsistent: % 150.75/22.31 ---------------------------------------------------------------- % 150.75/22.31 (1) all_58_12 = e0 % 150.75/22.31 (2) all_58_31 = all_4_2 % 150.75/22.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.75/22.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.75/22.31 (4) all_58_28 = e0 % 150.75/22.31 (5) all_54_13 = all_52_7 % 150.75/22.31 (6) op(e3, all_52_4) = all_58_1 % 150.75/22.31 (7) ~ (all_52_12 = e3) % 150.75/22.31 (8) all_54_3 = all_52_12 % 150.75/22.31 (9) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.31 (10) all_54_1 = all_52_4 % 150.75/22.31 (11) ~ (all_52_4 = e3) % 150.75/22.31 (12) op(e3, e2) = all_52_4 % 150.75/22.31 (13) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 150.75/22.31 (14) all_56_3 = e3 % 150.75/22.31 (15) ~ (all_52_4 = all_52_7) % 150.75/22.31 (16) all_56_1 = all_52_4 % 150.75/22.31 (17) op(e1, e1) = all_58_18 % 150.75/22.31 (18) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.75/22.31 (19) all_58_21 = all_10_0 % 150.75/22.31 (20) all_56_9 = all_52_12 % 150.75/22.31 (21) all_58_29 = e3 % 150.75/22.31 (22) ~ (e2 = e1) % 150.75/22.31 (23) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.75/22.31 (24) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.75/22.31 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.75/22.31 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.75/22.31 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.75/22.31 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.75/22.31 (all_58_27 = e0)) % 150.75/22.31 (25) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.75/22.31 (26) op(e0, e3) = e3 % 150.75/22.31 (27) ~ (all_52_7 = e3) % 150.75/22.31 (28) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.31 (29) all_58_30 = e1 % 150.75/22.31 (30) ~ (e2 = e0) % 150.75/22.31 (31) op(e0, e3) = all_10_0 % 150.75/22.31 (32) ~ (all_52_12 = all_4_2) % 150.75/22.31 (33) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.75/22.31 (34) ~ (all_52_7 = all_4_2) % 150.75/22.31 (35) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 150.75/22.31 (36) ~ (e3 = e2) % 150.75/22.31 (37) ~ (all_52_4 = all_52_12) % 150.75/22.31 (38) op(e1, e1) = e1 % 150.75/22.31 % 150.75/22.31 Begin of proof % 150.75/22.31 | % 150.75/22.31 | BETA: splitting (9) gives: % 150.75/22.31 | % 150.75/22.31 | Case 1: % 150.75/22.31 | | % 150.75/22.31 | | (39) all_58_28 = e2 % 150.75/22.31 | | % 150.75/22.31 | | COMBINE_EQS: (4), (39) imply: % 150.75/22.31 | | (40) e2 = e0 % 150.75/22.31 | | % 150.75/22.31 | | REDUCE: (30), (40) imply: % 150.75/22.31 | | (41) $false % 150.75/22.31 | | % 150.75/22.31 | | CLOSE: (41) is inconsistent. % 150.75/22.31 | | % 150.75/22.31 | Case 2: % 150.75/22.31 | | % 150.75/22.31 | | (42) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.31 | | % 150.75/22.31 | | BETA: splitting (42) gives: % 150.75/22.31 | | % 150.75/22.31 | | Case 1: % 150.75/22.31 | | | % 150.75/22.31 | | | (43) all_58_29 = e2 % 150.75/22.31 | | | % 150.75/22.31 | | | REF_CLOSE: (21), (36), (43) are inconsistent by sub-proof #780. % 150.75/22.31 | | | % 150.75/22.31 | | Case 2: % 150.75/22.31 | | | % 150.75/22.31 | | | (44) all_58_30 = e2 | all_58_31 = e2 % 150.75/22.31 | | | % 150.75/22.31 | | | BETA: splitting (44) gives: % 150.75/22.31 | | | % 150.75/22.31 | | | Case 1: % 150.75/22.31 | | | | % 150.75/22.31 | | | | (45) all_58_30 = e2 % 150.75/22.31 | | | | % 150.75/22.31 | | | | COMBINE_EQS: (29), (45) imply: % 150.75/22.31 | | | | (46) e2 = e1 % 150.75/22.31 | | | | % 150.75/22.31 | | | | REDUCE: (22), (46) imply: % 150.75/22.31 | | | | (47) $false % 150.75/22.31 | | | | % 150.75/22.31 | | | | CLOSE: (47) is inconsistent. % 150.75/22.31 | | | | % 150.75/22.31 | | | Case 2: % 150.75/22.31 | | | | % 150.75/22.31 | | | | (48) all_58_31 = e2 % 150.75/22.31 | | | | % 150.75/22.31 | | | | COMBINE_EQS: (2), (48) imply: % 150.75/22.31 | | | | (49) all_4_2 = e2 % 150.75/22.31 | | | | % 150.75/22.31 | | | | SIMP: (49) implies: % 150.75/22.31 | | | | (50) all_4_2 = e2 % 150.75/22.31 | | | | % 150.75/22.31 | | | | REDUCE: (34), (50) imply: % 150.75/22.31 | | | | (51) ~ (all_52_7 = e2) % 150.75/22.31 | | | | % 150.75/22.31 | | | | REDUCE: (32), (50) imply: % 150.75/22.31 | | | | (52) ~ (all_52_12 = e2) % 150.75/22.31 | | | | % 150.75/22.31 | | | | BETA: splitting (25) gives: % 150.75/22.31 | | | | % 150.75/22.31 | | | | Case 1: % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | (53) all_56_9 = e1 % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | COMBINE_EQS: (20), (53) imply: % 150.75/22.31 | | | | | (54) all_52_12 = e1 % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | SIMP: (54) implies: % 150.75/22.31 | | | | | (55) all_52_12 = e1 % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | REDUCE: (37), (55) imply: % 150.75/22.31 | | | | | (56) ~ (all_52_4 = e1) % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | REDUCE: (7), (55) imply: % 150.75/22.31 | | | | | (57) ~ (e3 = e1) % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | SIMP: (57) implies: % 150.75/22.31 | | | | | (58) ~ (e3 = e1) % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | BETA: splitting (23) gives: % 150.75/22.31 | | | | | % 150.75/22.31 | | | | | Case 1: % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | | (59) all_56_1 = e1 % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | | REF_CLOSE: (16), (56), (59) are inconsistent by sub-proof #394. % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | Case 2: % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | | (60) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | | BETA: splitting (33) gives: % 150.75/22.31 | | | | | | % 150.75/22.31 | | | | | | Case 1: % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | (61) all_56_1 = e2 % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | COMBINE_EQS: (16), (61) imply: % 150.75/22.31 | | | | | | | (62) all_52_4 = e2 % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | SIMP: (62) implies: % 150.75/22.31 | | | | | | | (63) all_52_4 = e2 % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | REDUCE: (11), (63) imply: % 150.75/22.31 | | | | | | | (64) ~ (e3 = e2) % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | REDUCE: (6), (63) imply: % 150.75/22.31 | | | | | | | (65) op(e3, e2) = all_58_1 % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | REDUCE: (12), (63) imply: % 150.75/22.31 | | | | | | | (66) op(e3, e2) = e2 % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | BETA: splitting (60) gives: % 150.75/22.31 | | | | | | | % 150.75/22.31 | | | | | | | Case 1: % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | (67) all_56_3 = e1 % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | COMBINE_EQS: (14), (67) imply: % 150.75/22.31 | | | | | | | | (68) e3 = e1 % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | SIMP: (68) implies: % 150.75/22.31 | | | | | | | | (69) e3 = e1 % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | COMBINE_EQS: (21), (69) imply: % 150.75/22.31 | | | | | | | | (70) all_58_29 = e1 % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | REF_CLOSE: (28), (29), (36), (48), (58), (70) are inconsistent % 150.75/22.31 | | | | | | | | by sub-proof #474. % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | Case 2: % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | % 150.75/22.31 | | | | | | | | GROUND_INST: instantiating (3) with e1, all_58_18, e1, e1, % 150.75/22.31 | | | | | | | | simplifying with (17), (38) gives: % 150.75/22.31 | | | | | | | | (71) all_58_18 = e1 % 150.75/22.31 | | | | | | | | % 150.75/22.32 | | | | | | | | REF_CLOSE: (1), (3), (19), (24), (26), (31), (65), (66), (71) % 150.75/22.32 | | | | | | | | are inconsistent by sub-proof #489. % 150.75/22.32 | | | | | | | | % 150.75/22.32 | | | | | | | End of split % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | Case 2: % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | (72) ~ (all_56_1 = e2) % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | REDUCE: (16), (72) imply: % 150.75/22.32 | | | | | | | (73) ~ (all_52_4 = e2) % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | REF_CLOSE: (5), (10), (11), (13), (15), (27), (35), (51), (73) are % 150.75/22.32 | | | | | | | inconsistent by sub-proof #507. % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | End of split % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | End of split % 150.75/22.32 | | | | | % 150.75/22.32 | | | | Case 2: % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | (74) ~ (all_56_9 = e1) % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | REDUCE: (20), (74) imply: % 150.75/22.32 | | | | | (75) ~ (all_52_12 = e1) % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | REF_CLOSE: (7), (8), (18), (52), (75) are inconsistent by sub-proof % 150.75/22.32 | | | | | #612. % 150.75/22.32 | | | | | % 150.75/22.32 | | | | End of split % 150.75/22.32 | | | | % 150.75/22.32 | | | End of split % 150.75/22.32 | | | % 150.75/22.32 | | End of split % 150.75/22.32 | | % 150.75/22.32 | End of split % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #51 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_31 = all_4_2 % 150.75/22.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.75/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.75/22.32 (3) all_58_28 = e0 % 150.75/22.32 (4) all_56_7 = e0 % 150.75/22.32 (5) all_56_11 = all_52_14 % 150.75/22.32 (6) all_58_29 = all_8_2 % 150.75/22.32 (7) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.75/22.32 (8) op(all_8_2, e2) = all_8_1 % 150.75/22.32 (9) all_56_8 = all_6_2 % 150.75/22.32 (10) ~ (all_8_1 = e0) % 150.75/22.32 (11) op(e1, e2) = e0 % 150.75/22.32 (12) ~ (all_52_14 = all_4_2) % 150.75/22.32 (13) ~ (e1 = e0) % 150.75/22.32 (14) ~ (all_6_2 = e1) % 150.75/22.32 (15) ~ (all_52_14 = e0) % 150.75/22.32 (16) all_58_30 = all_6_2 % 150.75/22.32 (17) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.75/22.32 (18) ~ (all_52_14 = all_6_2) % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | BETA: splitting (7) gives: % 150.75/22.32 | % 150.75/22.32 | Case 1: % 150.75/22.32 | | % 150.75/22.32 | | (19) all_56_7 = e1 % 150.75/22.32 | | % 150.75/22.32 | | REF_CLOSE: (4), (13), (19) are inconsistent by sub-proof #501. % 150.75/22.32 | | % 150.75/22.32 | Case 2: % 150.75/22.32 | | % 150.75/22.32 | | (20) all_56_8 = e1 | all_56_11 = e1 % 150.75/22.32 | | % 150.75/22.32 | | BETA: splitting (20) gives: % 150.75/22.32 | | % 150.75/22.32 | | Case 1: % 150.75/22.32 | | | % 150.75/22.32 | | | (21) all_56_8 = e1 % 150.75/22.32 | | | % 150.75/22.32 | | | REF_CLOSE: (9), (14), (21) are inconsistent by sub-proof #353. % 150.75/22.32 | | | % 150.75/22.32 | | Case 2: % 150.75/22.32 | | | % 150.75/22.32 | | | (22) all_56_11 = e1 % 150.75/22.32 | | | % 150.75/22.32 | | | COMBINE_EQS: (5), (22) imply: % 150.75/22.32 | | | (23) all_52_14 = e1 % 150.75/22.32 | | | % 150.75/22.32 | | | SIMP: (23) implies: % 150.75/22.32 | | | (24) all_52_14 = e1 % 150.75/22.32 | | | % 150.75/22.32 | | | REDUCE: (18), (24) imply: % 150.75/22.32 | | | (25) ~ (all_6_2 = e1) % 150.75/22.32 | | | % 150.75/22.32 | | | REDUCE: (12), (24) imply: % 150.75/22.32 | | | (26) ~ (all_4_2 = e1) % 150.75/22.32 | | | % 150.75/22.32 | | | SIMP: (26) implies: % 150.75/22.32 | | | (27) ~ (all_4_2 = e1) % 150.75/22.32 | | | % 150.75/22.32 | | | BETA: splitting (17) gives: % 150.75/22.32 | | | % 150.75/22.32 | | | Case 1: % 150.75/22.32 | | | | % 150.75/22.32 | | | | (28) all_58_28 = e1 % 150.75/22.32 | | | | % 150.75/22.32 | | | | COMBINE_EQS: (3), (28) imply: % 150.75/22.32 | | | | (29) e1 = e0 % 150.75/22.32 | | | | % 150.75/22.32 | | | | REDUCE: (13), (29) imply: % 150.75/22.32 | | | | (30) $false % 150.75/22.32 | | | | % 150.75/22.32 | | | | CLOSE: (30) is inconsistent. % 150.75/22.32 | | | | % 150.75/22.32 | | | Case 2: % 150.75/22.32 | | | | % 150.75/22.32 | | | | (31) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.75/22.32 | | | | % 150.75/22.32 | | | | REF_CLOSE: (1), (2), (6), (8), (10), (11), (14), (16), (27), (31) are % 150.75/22.32 | | | | inconsistent by sub-proof #503. % 150.75/22.32 | | | | % 150.75/22.32 | | | End of split % 150.75/22.32 | | | % 150.75/22.32 | | End of split % 150.75/22.32 | | % 150.75/22.32 | End of split % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #52 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_28 = e0 % 150.75/22.32 (2) all_58_31 = e1 % 150.75/22.32 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.32 (4) ~ (e3 = e1) % 150.75/22.32 (5) all_58_29 = e3 % 150.75/22.32 (6) ~ (e2 = e1) % 150.75/22.32 (7) ~ (e3 = e0) % 150.75/22.32 (8) e3 = e0 % 150.75/22.32 (9) ~ (e2 = e0) % 150.75/22.32 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 (11) all_58_30 = all_6_2 % 150.75/22.32 (12) ~ (e3 = e2) % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | SIMP: (8) implies: % 150.75/22.32 | (13) e3 = e0 % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (5), (13) imply: % 150.75/22.32 | (14) all_58_29 = e0 % 150.75/22.32 | % 150.75/22.32 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (14) are % 150.75/22.32 | inconsistent by sub-proof #653. % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #53 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_28 = e0 % 150.75/22.32 (2) all_58_31 = e1 % 150.75/22.32 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.32 (4) ~ (e3 = e1) % 150.75/22.32 (5) all_58_26 = e1 % 150.75/22.32 (6) all_58_29 = e3 % 150.75/22.32 (7) ~ (e2 = e1) % 150.75/22.32 (8) all_58_26 = e0 % 150.75/22.32 (9) ~ (e3 = e0) % 150.75/22.32 (10) all_58_20 = e3 % 150.75/22.32 (11) ~ (e2 = e0) % 150.75/22.32 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 (13) all_58_20 = e1 % 150.75/22.32 (14) all_58_30 = all_6_2 % 150.75/22.32 (15) ~ (e3 = e2) % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (10), (13) imply: % 150.75/22.32 | (16) e3 = e1 % 150.75/22.32 | % 150.75/22.32 | SIMP: (16) implies: % 150.75/22.32 | (17) e3 = e1 % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (5), (8) imply: % 150.75/22.32 | (18) e1 = e0 % 150.75/22.32 | % 150.75/22.32 | SIMP: (18) implies: % 150.75/22.32 | (19) e1 = e0 % 150.75/22.32 | % 150.75/22.32 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (12), (14), (15), (17), % 150.75/22.32 | (19) are inconsistent by sub-proof #63. % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #54 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_28 = e0 % 150.75/22.32 (2) all_58_22 = e0 % 150.75/22.32 (3) all_58_31 = e1 % 150.75/22.32 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.32 (5) ~ (e3 = e1) % 150.75/22.32 (6) e3 = e1 % 150.75/22.32 (7) all_58_29 = e3 % 150.75/22.32 (8) ~ (e2 = e1) % 150.75/22.32 (9) ~ (e3 = e0) % 150.75/22.32 (10) ~ (e2 = e0) % 150.75/22.32 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 (12) all_58_30 = all_6_2 % 150.75/22.32 (13) ~ (e3 = e2) % 150.75/22.32 (14) all_58_22 = e3 % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (2), (14) imply: % 150.75/22.32 | (15) e3 = e0 % 150.75/22.32 | % 150.75/22.32 | SIMP: (15) implies: % 150.75/22.32 | (16) e3 = e0 % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (6), (16) imply: % 150.75/22.32 | (17) e1 = e0 % 150.75/22.32 | % 150.75/22.32 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 150.75/22.32 | (17) are inconsistent by sub-proof #63. % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #55 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_2 = e2 % 150.75/22.32 (2) all_58_31 = e1 % 150.75/22.32 (3) all_58_30 = e2 % 150.75/22.32 (4) ~ (e2 = e1) % 150.75/22.32 (5) all_58_30 = e2 | all_58_31 = e2 % 150.75/22.32 (6) all_58_2 = e1 % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (1), (6) imply: % 150.75/22.32 | (7) e2 = e1 % 150.75/22.32 | % 150.75/22.32 | SIMP: (7) implies: % 150.75/22.32 | (8) e2 = e1 % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (3), (8) imply: % 150.75/22.32 | (9) all_58_30 = e1 % 150.75/22.32 | % 150.75/22.32 | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #448. % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #56 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_12 = e0 % 150.75/22.32 (2) all_58_28 = e0 % 150.75/22.32 (3) all_54_2 = all_52_8 % 150.75/22.32 (4) all_58_31 = e1 % 150.75/22.32 (5) all_56_4 = all_52_8 % 150.75/22.32 (6) all_54_3 = all_52_12 % 150.75/22.32 (7) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 150.75/22.32 (8) ~ (all_52_8 = all_6_2) % 150.75/22.32 (9) ~ (all_52_8 = all_52_12) % 150.75/22.32 (10) ~ (e3 = e1) % 150.75/22.32 (11) all_58_0 = all_52_12 % 150.75/22.32 (12) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 150.75/22.32 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.75/22.32 (14) all_56_9 = all_52_12 % 150.75/22.32 (15) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 150.75/22.32 (16) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.75/22.32 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.75/22.32 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.75/22.32 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.75/22.32 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.75/22.32 (all_58_27 = e0)) % 150.75/22.32 (17) ~ (e3 = e0) % 150.75/22.32 (18) ~ (all_52_12 = e1) % 150.75/22.32 (19) ~ (all_52_8 = e1) % 150.75/22.32 (20) all_58_29 = e2 % 150.75/22.32 (21) all_58_14 = all_6_2 % 150.75/22.32 (22) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 (23) all_58_25 = e1 % 150.75/22.32 (24) all_58_30 = all_6_2 % 150.75/22.32 (25) ~ (e3 = e2) % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | BETA: splitting (22) gives: % 150.75/22.32 | % 150.75/22.32 | Case 1: % 150.75/22.32 | | % 150.75/22.32 | | (26) all_58_28 = e3 % 150.75/22.32 | | % 150.75/22.32 | | REF_CLOSE: (2), (17), (26) are inconsistent by sub-proof #689. % 150.75/22.32 | | % 150.75/22.32 | Case 2: % 150.75/22.32 | | % 150.75/22.32 | | (27) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 | | % 150.75/22.32 | | BETA: splitting (27) gives: % 150.75/22.32 | | % 150.75/22.32 | | Case 1: % 150.75/22.32 | | | % 150.75/22.32 | | | (28) all_58_29 = e3 % 150.75/22.32 | | | % 150.75/22.32 | | | REF_CLOSE: (20), (25), (28) are inconsistent by sub-proof #780. % 150.75/22.32 | | | % 150.75/22.32 | | Case 2: % 150.75/22.32 | | | % 150.75/22.32 | | | (29) all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 | | | % 150.75/22.32 | | | BETA: splitting (29) gives: % 150.75/22.32 | | | % 150.75/22.32 | | | Case 1: % 150.75/22.32 | | | | % 150.75/22.32 | | | | (30) all_58_30 = e3 % 150.75/22.32 | | | | % 150.75/22.32 | | | | COMBINE_EQS: (24), (30) imply: % 150.75/22.32 | | | | (31) all_6_2 = e3 % 150.75/22.32 | | | | % 150.75/22.32 | | | | COMBINE_EQS: (21), (31) imply: % 150.75/22.32 | | | | (32) all_58_14 = e3 % 150.75/22.32 | | | | % 150.75/22.32 | | | | REDUCE: (8), (31) imply: % 150.75/22.32 | | | | (33) ~ (all_52_8 = e3) % 150.75/22.32 | | | | % 150.75/22.32 | | | | BETA: splitting (7) gives: % 150.75/22.32 | | | | % 150.75/22.32 | | | | Case 1: % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | (34) all_56_4 = e2 % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | COMBINE_EQS: (5), (34) imply: % 150.75/22.32 | | | | | (35) all_52_8 = e2 % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | SIMP: (35) implies: % 150.75/22.32 | | | | | (36) all_52_8 = e2 % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | REDUCE: (9), (36) imply: % 150.75/22.32 | | | | | (37) ~ (all_52_12 = e2) % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | SIMP: (37) implies: % 150.75/22.32 | | | | | (38) ~ (all_52_12 = e2) % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | BETA: splitting (15) gives: % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | Case 1: % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | (39) all_56_9 = e3 % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | COMBINE_EQS: (14), (39) imply: % 150.75/22.32 | | | | | | (40) all_52_12 = e3 % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | COMBINE_EQS: (11), (40) imply: % 150.75/22.32 | | | | | | (41) all_58_0 = e3 % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | BETA: splitting (16) gives: % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | Case 1: % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | (42) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = % 150.75/22.32 | | | | | | | e1) & ~ (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ % 150.75/22.32 | | | | | | | (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ (all_58_12 = % 150.75/22.32 | | | | | | | e0)) % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | REF_CLOSE: (1), (41), (42) are inconsistent by sub-proof #669. % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | Case 2: % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | (43) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 % 150.75/22.32 | | | | | | | = e1) & ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & % 150.75/22.32 | | | | | | | ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ (all_58_27 % 150.75/22.32 | | | | | | | = e0)) % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | | REF_CLOSE: (23), (32), (43) are inconsistent by sub-proof #583. % 150.75/22.32 | | | | | | | % 150.75/22.32 | | | | | | End of split % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | Case 2: % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | (44) ~ (all_56_9 = e3) % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | REDUCE: (14), (44) imply: % 150.75/22.32 | | | | | | (45) ~ (all_52_12 = e3) % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | | REF_CLOSE: (6), (13), (18), (38), (45) are inconsistent by sub-proof % 150.75/22.32 | | | | | | #612. % 150.75/22.32 | | | | | | % 150.75/22.32 | | | | | End of split % 150.75/22.32 | | | | | % 150.75/22.32 | | | | Case 2: % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | (46) ~ (all_56_4 = e2) % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | REDUCE: (5), (46) imply: % 150.75/22.32 | | | | | (47) ~ (all_52_8 = e2) % 150.75/22.32 | | | | | % 150.75/22.32 | | | | | REF_CLOSE: (3), (12), (19), (33), (47) are inconsistent by sub-proof % 150.75/22.32 | | | | | #554. % 150.75/22.32 | | | | | % 150.75/22.32 | | | | End of split % 150.75/22.32 | | | | % 150.75/22.32 | | | Case 2: % 150.75/22.32 | | | | % 150.75/22.32 | | | | (48) all_58_31 = e3 % 150.75/22.32 | | | | % 150.75/22.32 | | | | REF_CLOSE: (4), (10), (48) are inconsistent by sub-proof #656. % 150.75/22.32 | | | | % 150.75/22.32 | | | End of split % 150.75/22.32 | | | % 150.75/22.32 | | End of split % 150.75/22.32 | | % 150.75/22.32 | End of split % 150.75/22.32 | % 150.75/22.32 End of proof % 150.75/22.32 % 150.75/22.32 Sub-proof #57 shows that the following formulas are inconsistent: % 150.75/22.32 ---------------------------------------------------------------- % 150.75/22.32 (1) all_58_31 = all_4_2 % 150.75/22.32 (2) all_52_1 = e1 % 150.75/22.32 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 150.75/22.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 150.75/22.32 (4) all_58_28 = e0 % 150.75/22.32 (5) all_56_15 = all_4_2 % 150.75/22.32 (6) all_56_7 = all_52_6 % 150.75/22.32 (7) ~ (all_52_6 = all_6_2) % 150.75/22.32 (8) ~ (all_10_1 = e0) % 150.75/22.32 (9) ~ (all_52_11 = all_10_1) % 150.75/22.32 (10) all_58_15 = all_52_2 % 150.75/22.32 (11) all_58_26 = all_52_11 % 150.75/22.32 (12) ~ (all_52_8 = all_52_11) % 150.75/22.32 (13) ~ (all_52_11 = all_4_2) % 150.75/22.32 (14) all_54_7 = all_52_13 % 150.75/22.32 (15) all_58_6 = all_52_12 % 150.75/22.32 (16) ~ (all_52_6 = all_8_2) % 150.75/22.32 (17) all_56_4 = all_52_8 % 150.75/22.32 (18) ~ (all_52_4 = all_8_2) % 150.75/22.32 (19) all_54_3 = all_52_12 % 150.75/22.32 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.32 (21) all_54_1 = all_52_4 % 150.75/22.32 (22) ~ (all_6_2 = e0) % 150.75/22.32 (23) ~ (all_52_4 = all_52_6) % 150.75/22.32 (24) ~ (all_10_1 = all_4_2) % 150.75/22.32 (25) all_58_13 = all_52_13 % 150.75/22.32 (26) op(e2, e2) = all_8_2 % 150.75/22.32 (27) all_56_12 = all_10_1 % 150.75/22.32 (28) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 150.75/22.32 (29) all_58_11 = e0 % 150.75/22.32 (30) all_58_20 = e0 % 150.75/22.32 (31) ~ (all_52_8 = all_6_2) % 150.75/22.32 (32) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 150.75/22.32 (33) ~ (all_52_12 = all_52_13) % 150.75/22.32 (34) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.75/22.32 (35) all_56_13 = e0 % 150.75/22.32 (36) all_54_5 = all_8_2 % 150.75/22.32 (37) op(e3, all_52_8) = all_58_3 % 150.75/22.32 (38) ~ (all_52_8 = all_52_12) % 150.75/22.32 (39) ~ (all_52_13 = all_4_2) % 150.75/22.32 (40) all_58_19 = e0 % 150.75/22.32 (41) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 150.75/22.32 (42) ~ (all_52_13 = all_8_2) % 150.75/22.32 (43) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 150.75/22.32 (44) ~ (e3 = e1) % 150.75/22.32 (45) all_54_12 = all_10_1 % 150.75/22.32 (46) ~ (all_52_6 = e0) % 150.75/22.32 (47) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 150.75/22.32 (48) ~ (all_52_1 = all_52_13) % 150.75/22.32 (49) all_54_14 = all_52_11 % 150.75/22.32 (50) all_56_2 = e1 % 150.75/22.32 (51) ~ (all_52_12 = e0) % 150.75/22.32 (52) all_58_2 = all_52_4 % 150.75/22.32 (53) all_20_2 = all_4_2 % 150.75/22.32 (54) all_56_1 = all_52_4 % 150.75/22.32 (55) ~ (all_52_13 = e0) % 150.75/22.32 (56) all_58_24 = e0 % 150.75/22.32 (57) op(e0, e3) = all_10_1 % 150.75/22.32 (58) ~ (all_52_1 = all_8_2) % 150.75/22.32 (59) all_56_3 = all_8_2 % 150.75/22.32 (60) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 150.75/22.32 (61) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 150.75/22.32 (62) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 150.75/22.32 (63) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 150.75/22.32 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.75/22.32 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.75/22.32 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 150.75/22.32 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.75/22.32 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.75/22.32 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 150.75/22.32 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.75/22.32 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.75/22.32 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 150.75/22.32 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.75/22.32 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 150.75/22.32 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.75/22.32 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.75/22.32 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.75/22.32 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 150.75/22.32 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.75/22.32 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.75/22.32 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.32 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.75/22.32 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.75/22.32 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 150.75/22.32 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.75/22.32 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.75/22.32 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.75/22.32 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 150.75/22.32 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.75/22.32 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.75/22.32 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.75/22.32 e0) % 150.75/22.32 (64) ~ (all_52_4 = all_52_8) % 150.75/22.32 (65) all_58_21 = all_10_0 % 150.75/22.32 (66) all_56_9 = all_52_12 % 150.75/22.32 (67) all_58_29 = all_8_2 % 150.75/22.32 (68) all_58_8 = all_52_1 % 150.75/22.32 (69) ~ (e2 = e1) % 150.75/22.32 (70) ~ (all_52_2 = all_52_6) % 150.75/22.32 (71) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 150.75/22.32 (72) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.75/22.32 (73) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 150.75/22.32 (74) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 150.75/22.32 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 150.75/22.32 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 150.75/22.32 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 150.75/22.32 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 150.75/22.32 (all_58_27 = e0)) % 150.75/22.32 (75) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.75/22.32 (76) ~ (all_52_4 = e0) % 150.75/22.32 (77) ~ (all_52_11 = all_6_2) % 150.75/22.32 (78) ~ (e3 = e0) % 150.75/22.32 (79) ~ (all_52_11 = e0) % 150.75/22.32 (80) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 150.75/22.32 (81) all_56_10 = all_52_13 % 150.75/22.32 (82) all_56_5 = e0 % 150.75/22.32 (83) all_56_14 = all_52_11 % 150.75/22.32 (84) all_58_17 = all_52_6 % 150.75/22.32 (85) op(e3, e1) = all_52_8 % 150.75/22.32 (86) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 150.75/22.32 (87) ~ (e2 = e0) % 150.75/22.32 (88) ~ (all_4_2 = e0) % 150.75/22.32 (89) ~ (all_52_1 = e0) % 150.75/22.32 (90) all_56_8 = all_6_2 % 150.75/22.32 (91) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 150.75/22.32 (92) all_58_4 = all_52_8 % 150.75/22.32 (93) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.32 (94) ~ (all_52_8 = e0) % 150.75/22.32 (95) op(e0, all_10_1) = all_10_0 % 150.75/22.32 (96) all_58_30 = all_6_2 % 150.75/22.32 (97) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.75/22.32 (98) all_56_11 = e0 % 150.75/22.32 (99) ~ (e3 = e2) % 150.75/22.32 (100) ~ (all_8_2 = e0) % 150.75/22.32 (101) ~ (all_52_4 = all_52_12) % 150.75/22.32 (102) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 150.75/22.32 (103) op(e2, all_8_2) = all_58_9 % 150.75/22.32 % 150.75/22.32 Begin of proof % 150.75/22.32 | % 150.75/22.32 | COMBINE_EQS: (2), (68) imply: % 150.75/22.33 | (104) all_58_8 = e1 % 150.75/22.33 | % 150.75/22.33 | REDUCE: (2), (48) imply: % 150.75/22.33 | (105) ~ (all_52_13 = e1) % 150.75/22.33 | % 150.75/22.33 | SIMP: (105) implies: % 150.75/22.33 | (106) ~ (all_52_13 = e1) % 150.75/22.33 | % 150.75/22.33 | REDUCE: (2), (58) imply: % 150.75/22.33 | (107) ~ (all_8_2 = e1) % 150.75/22.33 | % 150.75/22.33 | SIMP: (107) implies: % 150.75/22.33 | (108) ~ (all_8_2 = e1) % 150.75/22.33 | % 150.75/22.33 | REDUCE: (2), (89) imply: % 150.75/22.33 | (109) ~ (e1 = e0) % 150.75/22.33 | % 150.75/22.33 | BETA: splitting (41) gives: % 150.75/22.33 | % 150.75/22.33 | Case 1: % 150.75/22.33 | | % 150.75/22.33 | | (110) all_56_2 = e2 % 150.75/22.33 | | % 150.75/22.33 | | REF_CLOSE: (50), (69), (110) are inconsistent by sub-proof #247. % 150.75/22.33 | | % 150.75/22.33 | Case 2: % 150.75/22.33 | | % 150.75/22.33 | | (111) ~ (all_56_2 = e2) % 150.75/22.33 | | (112) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 150.75/22.33 | | % 150.75/22.33 | | REDUCE: (50), (111) imply: % 150.75/22.33 | | (113) ~ (e2 = e1) % 150.75/22.33 | | % 150.75/22.33 | | BETA: splitting (72) gives: % 150.75/22.33 | | % 150.75/22.33 | | Case 1: % 150.75/22.33 | | | % 150.75/22.33 | | | (114) all_56_1 = e1 % 150.75/22.33 | | | % 150.75/22.33 | | | COMBINE_EQS: (54), (114) imply: % 150.75/22.33 | | | (115) all_52_4 = e1 % 150.75/22.33 | | | % 150.75/22.33 | | | REDUCE: (23), (115) imply: % 150.75/22.33 | | | (116) ~ (all_52_6 = e1) % 150.75/22.33 | | | % 150.75/22.33 | | | SIMP: (116) implies: % 150.75/22.33 | | | (117) ~ (all_52_6 = e1) % 150.75/22.33 | | | % 150.75/22.33 | | | REDUCE: (101), (115) imply: % 150.75/22.33 | | | (118) ~ (all_52_12 = e1) % 150.75/22.33 | | | % 150.75/22.33 | | | SIMP: (118) implies: % 150.75/22.33 | | | (119) ~ (all_52_12 = e1) % 150.75/22.33 | | | % 150.75/22.33 | | | BETA: splitting (75) gives: % 150.75/22.33 | | | % 150.75/22.33 | | | Case 1: % 150.75/22.33 | | | | % 150.75/22.33 | | | | (120) all_56_9 = e1 % 150.75/22.33 | | | | % 150.75/22.33 | | | | REF_CLOSE: (66), (119), (120) are inconsistent by sub-proof #486. % 150.75/22.33 | | | | % 150.75/22.33 | | | Case 2: % 150.75/22.33 | | | | % 150.75/22.33 | | | | (121) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 150.75/22.33 | | | | % 150.75/22.33 | | | | BETA: splitting (121) gives: % 150.75/22.33 | | | | % 150.75/22.33 | | | | Case 1: % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | (122) all_56_10 = e1 % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | REF_CLOSE: (81), (106), (122) are inconsistent by sub-proof #606. % 150.75/22.33 | | | | | % 150.75/22.33 | | | | Case 2: % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | (123) all_56_11 = e1 | all_56_15 = e1 % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | BETA: splitting (80) gives: % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | Case 1: % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | (124) all_56_7 = e1 % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | REF_CLOSE: (6), (117), (124) are inconsistent by sub-proof #547. % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | Case 2: % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | (125) all_56_8 = e1 | all_56_11 = e1 % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | BETA: splitting (125) gives: % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | Case 1: % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | (126) all_56_8 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | COMBINE_EQS: (90), (126) imply: % 150.75/22.33 | | | | | | | (127) all_6_2 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | SIMP: (127) implies: % 150.75/22.33 | | | | | | | (128) all_6_2 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | COMBINE_EQS: (96), (128) imply: % 150.75/22.33 | | | | | | | (129) all_58_30 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | BETA: splitting (123) gives: % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | (130) all_56_11 = e1 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | COMBINE_EQS: (98), (130) imply: % 150.75/22.33 | | | | | | | | (131) e1 = e0 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | COMBINE_EQS: (129), (131) imply: % 150.75/22.33 | | | | | | | | (132) all_58_30 = e0 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | REF_CLOSE: (1), (4), (20), (44), (53), (67), (69), (78), (86), % 150.75/22.33 | | | | | | | | (87), (93), (97), (99), (109), (132) are inconsistent % 150.75/22.33 | | | | | | | | by sub-proof #679. % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | (133) all_56_15 = e1 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | REF_CLOSE: (1), (4), (5), (20), (44), (67), (69), (78), (87), % 150.75/22.33 | | | | | | | | (90), (93), (96), (98), (99), (109), (125), (133) are % 150.75/22.33 | | | | | | | | inconsistent by sub-proof #65. % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | End of split % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | Case 2: % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | (134) all_56_11 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | COMBINE_EQS: (98), (134) imply: % 150.75/22.33 | | | | | | | (135) e1 = e0 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | REDUCE: (109), (135) imply: % 150.75/22.33 | | | | | | | (136) $false % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | CLOSE: (136) is inconsistent. % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | End of split % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | End of split % 150.75/22.33 | | | | | % 150.75/22.33 | | | | End of split % 150.75/22.33 | | | | % 150.75/22.33 | | | End of split % 150.75/22.33 | | | % 150.75/22.33 | | Case 2: % 150.75/22.33 | | | % 150.75/22.33 | | | (137) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 150.75/22.33 | | | % 150.75/22.33 | | | BETA: splitting (137) gives: % 150.75/22.33 | | | % 150.75/22.33 | | | Case 1: % 150.75/22.33 | | | | % 150.75/22.33 | | | | (138) all_56_3 = e1 % 150.75/22.33 | | | | % 150.75/22.33 | | | | COMBINE_EQS: (59), (138) imply: % 150.75/22.33 | | | | (139) all_8_2 = e1 % 150.75/22.33 | | | | % 150.75/22.33 | | | | REDUCE: (108), (139) imply: % 150.75/22.33 | | | | (140) $false % 150.75/22.33 | | | | % 150.75/22.33 | | | | CLOSE: (140) is inconsistent. % 150.75/22.33 | | | | % 150.75/22.33 | | | Case 2: % 150.75/22.33 | | | | % 150.75/22.33 | | | | (141) all_56_7 = e1 | all_56_13 = e1 % 150.75/22.33 | | | | % 150.75/22.33 | | | | BETA: splitting (141) gives: % 150.75/22.33 | | | | % 150.75/22.33 | | | | Case 1: % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | (142) all_56_7 = e1 % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | COMBINE_EQS: (6), (142) imply: % 150.75/22.33 | | | | | (143) all_52_6 = e1 % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | SIMP: (143) implies: % 150.75/22.33 | | | | | (144) all_52_6 = e1 % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | COMBINE_EQS: (84), (144) imply: % 150.75/22.33 | | | | | (145) all_58_17 = e1 % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | REDUCE: (70), (144) imply: % 150.75/22.33 | | | | | (146) ~ (all_52_2 = e1) % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | REDUCE: (23), (144) imply: % 150.75/22.33 | | | | | (147) ~ (all_52_4 = e1) % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | REDUCE: (7), (144) imply: % 150.75/22.33 | | | | | (148) ~ (all_6_2 = e1) % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | SIMP: (148) implies: % 150.75/22.33 | | | | | (149) ~ (all_6_2 = e1) % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | BETA: splitting (63) gives: % 150.75/22.33 | | | | | % 150.75/22.33 | | | | | Case 1: % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | (150) all_58_31 = e0 % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | COMBINE_EQS: (1), (150) imply: % 150.75/22.33 | | | | | | (151) all_4_2 = e0 % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | REDUCE: (88), (151) imply: % 150.75/22.33 | | | | | | (152) $false % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | CLOSE: (152) is inconsistent. % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | Case 2: % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | (153) ~ (all_58_31 = e0) % 150.75/22.33 | | | | | | (154) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 150.75/22.33 | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 % 150.75/22.33 | | | | | | = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.75/22.33 | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 150.75/22.33 | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 150.75/22.33 | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.75/22.33 | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 % 150.75/22.33 | | | | | | = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.75/22.33 | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 150.75/22.33 | | | | | | all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 150.75/22.33 | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.75/22.33 | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 % 150.75/22.33 | | | | | | & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 150.75/22.33 | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 150.75/22.33 | | | | | | all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.75/22.33 | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & % 150.75/22.33 | | | | | | all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 150.75/22.33 | | | | | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.75/22.33 | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.75/22.33 | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 150.75/22.33 | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = % 150.75/22.33 | | | | | | e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & % 150.75/22.33 | | | | | | all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.75/22.33 | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.33 | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 150.75/22.33 | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 150.75/22.33 | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = % 150.75/22.33 | | | | | | e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 150.75/22.33 | | | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.75/22.33 | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 150.75/22.33 | | | | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 150.75/22.33 | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 150.75/22.33 | | | | | | all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 150.75/22.33 | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 150.75/22.33 | | | | | | all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.75/22.33 | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = % 150.75/22.33 | | | | | | e0 & all_58_26 = e0 & e1 = e0) % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | BETA: splitting (154) gives: % 150.75/22.33 | | | | | | % 150.75/22.33 | | | | | | Case 1: % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | (155) all_58_30 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | COMBINE_EQS: (96), (155) imply: % 150.75/22.33 | | | | | | | (156) all_6_2 = e1 % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | REDUCE: (149), (156) imply: % 150.75/22.33 | | | | | | | (157) $false % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | CLOSE: (157) is inconsistent. % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | Case 2: % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | (158) ~ (all_58_30 = e1) % 150.75/22.33 | | | | | | | (159) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 150.75/22.33 | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 150.75/22.33 | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.75/22.33 | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 150.75/22.33 | | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 150.75/22.33 | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 150.75/22.33 | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 150.75/22.33 | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 150.75/22.33 | | | | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.75/22.33 | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 150.75/22.33 | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.75/22.33 | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 150.75/22.33 | | | | | | | e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.75/22.33 | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 150.75/22.33 | | | | | | | all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & % 150.75/22.33 | | | | | | | all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 150.75/22.33 | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.75/22.33 | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.75/22.33 | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 150.75/22.33 | | | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.75/22.33 | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = % 150.75/22.33 | | | | | | | e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) % 150.75/22.33 | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.75/22.33 | | | | | | | all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.75/22.33 | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 150.75/22.33 | | | | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.75/22.33 | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 150.75/22.33 | | | | | | | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) % 150.75/22.33 | | | | | | | | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 150.75/22.33 | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.75/22.33 | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 150.75/22.33 | | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.75/22.33 | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 % 150.75/22.33 | | | | | | | = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 150.75/22.33 | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 150.75/22.33 | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & % 150.75/22.33 | | | | | | | e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | BETA: splitting (159) gives: % 150.75/22.33 | | | | | | | % 150.75/22.33 | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | (160) all_58_29 = e2 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | COMBINE_EQS: (67), (160) imply: % 150.75/22.33 | | | | | | | | (161) all_8_2 = e2 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | REDUCE: (18), (161) imply: % 150.75/22.33 | | | | | | | | (162) ~ (all_52_4 = e2) % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | REDUCE: (103), (161) imply: % 150.75/22.33 | | | | | | | | (163) op(e2, e2) = all_58_9 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | REDUCE: (26), (161) imply: % 150.75/22.33 | | | | | | | | (164) op(e2, e2) = e2 % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | BETA: splitting (43) gives: % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | (165) all_56_1 = e3 % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | COMBINE_EQS: (54), (165) imply: % 150.75/22.33 | | | | | | | | | (166) all_52_4 = e3 % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | REDUCE: (64), (166) imply: % 150.75/22.33 | | | | | | | | | (167) ~ (all_52_8 = e3) % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | SIMP: (167) implies: % 150.75/22.33 | | | | | | | | | (168) ~ (all_52_8 = e3) % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | BETA: splitting (97) gives: % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | (169) all_58_28 = e1 % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | REF_CLOSE: (4), (109), (169) are inconsistent by sub-proof % 150.75/22.33 | | | | | | | | | | #690. % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | (170) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | BETA: splitting (170) gives: % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | (171) all_58_29 = e1 % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | COMBINE_EQS: (160), (171) imply: % 150.75/22.33 | | | | | | | | | | | (172) e2 = e1 % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | REDUCE: (69), (172) imply: % 150.75/22.33 | | | | | | | | | | | (173) $false % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | CLOSE: (173) is inconsistent. % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | (174) ~ (all_58_29 = e1) % 150.75/22.33 | | | | | | | | | | | (175) all_58_30 = e1 | all_58_31 = e1 % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | BETA: splitting (175) gives: % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | (176) all_58_30 = e1 % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | COMBINE_EQS: (96), (176) imply: % 150.75/22.33 | | | | | | | | | | | | (177) all_6_2 = e1 % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | REDUCE: (149), (177) imply: % 150.75/22.33 | | | | | | | | | | | | (178) $false % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | CLOSE: (178) is inconsistent. % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | (179) all_58_31 = e1 % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | COMBINE_EQS: (1), (179) imply: % 150.75/22.33 | | | | | | | | | | | | (180) all_4_2 = e1 % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | REDUCE: (13), (180) imply: % 150.75/22.33 | | | | | | | | | | | | (181) ~ (all_52_11 = e1) % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | REDUCE: (24), (180) imply: % 150.75/22.33 | | | | | | | | | | | | (182) ~ (all_10_1 = e1) % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | BETA: splitting (34) gives: % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | (183) all_56_4 = e1 % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | COMBINE_EQS: (17), (183) imply: % 150.75/22.33 | | | | | | | | | | | | | (184) all_52_8 = e1 % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | SIMP: (184) implies: % 150.75/22.33 | | | | | | | | | | | | | (185) all_52_8 = e1 % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | REDUCE: (12), (185) imply: % 150.75/22.33 | | | | | | | | | | | | | (186) ~ (all_52_11 = e1) % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | REDUCE: (168), (185) imply: % 150.75/22.33 | | | | | | | | | | | | | (187) ~ (e3 = e1) % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | REDUCE: (37), (185) imply: % 150.75/22.33 | | | | | | | | | | | | | (188) op(e3, e1) = all_58_3 % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | REDUCE: (85), (185) imply: % 150.75/22.33 | | | | | | | | | | | | | (189) op(e3, e1) = e1 % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | BETA: splitting (93) gives: % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | (190) all_58_28 = e3 % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | COMBINE_EQS: (4), (190) imply: % 150.75/22.33 | | | | | | | | | | | | | | (191) e3 = e0 % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | REDUCE: (78), (191) imply: % 150.75/22.33 | | | | | | | | | | | | | | (192) $false % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | (193) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | BETA: splitting (193) gives: % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | (194) all_58_29 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | COMBINE_EQS: (160), (194) imply: % 150.75/22.33 | | | | | | | | | | | | | | | (195) e3 = e2 % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | REDUCE: (99), (195) imply: % 150.75/22.33 | | | | | | | | | | | | | | | (196) $false % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | (197) ~ (all_58_29 = e3) % 150.75/22.33 | | | | | | | | | | | | | | | (198) all_58_30 = e3 | all_58_31 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | REDUCE: (160), (197) imply: % 150.75/22.33 | | | | | | | | | | | | | | | (199) ~ (e3 = e2) % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | (200) all_58_30 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (200) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | (201) all_6_2 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | SIMP: (201) implies: % 150.75/22.33 | | | | | | | | | | | | | | | | (202) all_6_2 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | REDUCE: (77), (202) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | (203) ~ (all_52_11 = e3) % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | BETA: splitting (62) gives: % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | (204) all_56_12 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (204) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | (205) all_10_1 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | SIMP: (205) implies: % 150.75/22.33 | | | | | | | | | | | | | | | | | (206) all_10_1 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | REDUCE: (95), (206) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | (207) op(e0, e3) = all_10_0 % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | REDUCE: (57), (206) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | (208) op(e0, e3) = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | BETA: splitting (28) gives: % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | (209) all_56_4 = e2 % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (209) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | | (210) e2 = e1 % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | REDUCE: (69), (210) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | | (211) $false % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | (212) ~ (all_56_4 = e2) % 150.75/22.33 | | | | | | | | | | | | | | | | | | (213) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | (214) all_56_5 = e2 % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (214) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | | | (215) e2 = e0 % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (215) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | | | | (216) all_58_29 = e0 % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (96), (99), % 150.75/22.33 | | | | | | | | | | | | | | | | | | | (179), (193), (216) are inconsistent by sub-proof % 150.75/22.33 | | | | | | | | | | | | | | | | | | | #654. % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_58_3, e1, e3, % 150.75/22.33 | | | | | | | | | | | | | | | | | | | simplifying with (188), (189) gives: % 150.75/22.33 | | | | | | | | | | | | | | | | | | | (217) all_58_3 = e1 % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (40), (65), (74), (163), (164), (207), (208), % 150.75/22.33 | | | | | | | | | | | | | | | | | | | (217) are inconsistent by sub-proof #417. % 150.75/22.33 | | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | (218) ~ (all_56_12 = e3) % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (27), (45), (49), (71), (102), (181), (182), % 150.75/22.33 | | | | | | | | | | | | | | | | | (203), (218) are inconsistent by sub-proof #195. % 150.75/22.33 | | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | (219) all_58_31 = e3 % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (219) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | (220) e3 = e1 % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | REDUCE: (44), (220) imply: % 150.75/22.33 | | | | | | | | | | | | | | | | (221) $false % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 150.75/22.33 | | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | (222) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (67), (69), (78), (82), (83), % 150.75/22.33 | | | | | | | | | | | | | (87), (90), (93), (96), (99), (109), (179), (181), % 150.75/22.33 | | | | | | | | | | | | | (222) are inconsistent by sub-proof #402. % 150.75/22.33 | | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | End of split % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | (223) ~ (all_56_1 = e3) % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | REDUCE: (54), (223) imply: % 150.75/22.33 | | | | | | | | | (224) ~ (all_52_4 = e3) % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | REF_CLOSE: (21), (32), (147), (162), (224) are inconsistent by % 150.75/22.33 | | | | | | | | | sub-proof #738. % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | End of split % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | (225) ~ (all_58_29 = e2) % 150.75/22.33 | | | | | | | | (226) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 150.75/22.33 | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 150.75/22.33 | | | | | | | | all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 150.75/22.33 | | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 150.75/22.33 | | | | | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.75/22.33 | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 150.75/22.33 | | | | | | | | all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 150.75/22.33 | | | | | | | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.75/22.33 | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 150.75/22.33 | | | | | | | | all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 150.75/22.33 | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 150.75/22.33 | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = % 150.75/22.33 | | | | | | | | e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 150.75/22.33 | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 150.75/22.33 | | | | | | | | all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.75/22.33 | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & % 150.75/22.33 | | | | | | | | all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 150.75/22.33 | | | | | | | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.75/22.33 | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.75/22.33 | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 150.75/22.33 | | | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 150.75/22.33 | | | | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 150.75/22.33 | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.75/22.33 | | | | | | | | all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.75/22.33 | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 150.75/22.33 | | | | | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.75/22.33 | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 % 150.75/22.33 | | | | | | | | = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 150.75/22.33 | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = % 150.75/22.33 | | | | | | | | e1 & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = % 150.75/22.33 | | | | | | | | e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.75/22.33 | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 150.75/22.33 | | | | | | | | e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 150.75/22.33 | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 150.75/22.33 | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 150.75/22.33 | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 150.75/22.33 | | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 150.75/22.33 | | | | | | | | all_58_26 = e0 & e1 = e0) % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | REDUCE: (67), (225) imply: % 150.75/22.33 | | | | | | | | (227) ~ (all_8_2 = e2) % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | BETA: splitting (97) gives: % 150.75/22.33 | | | | | | | | % 150.75/22.33 | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | (228) all_58_28 = e1 % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | REF_CLOSE: (4), (109), (228) are inconsistent by sub-proof % 150.75/22.33 | | | | | | | | | #690. % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | Case 2: % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | (229) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | BETA: splitting (91) gives: % 150.75/22.33 | | | | | | | | | % 150.75/22.33 | | | | | | | | | Case 1: % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | (230) all_56_1 = e2 % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | COMBINE_EQS: (54), (230) imply: % 150.75/22.33 | | | | | | | | | | (231) all_52_4 = e2 % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | COMBINE_EQS: (52), (231) imply: % 150.75/22.33 | | | | | | | | | | (232) all_58_2 = e2 % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | REDUCE: (64), (231) imply: % 150.75/22.33 | | | | | | | | | | (233) ~ (all_52_8 = e2) % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | SIMP: (233) implies: % 150.75/22.33 | | | | | | | | | | (234) ~ (all_52_8 = e2) % 150.75/22.33 | | | | | | | | | | % 150.75/22.33 | | | | | | | | | | REDUCE: (18), (231) imply: % 150.75/22.33 | | | | | | | | | | (235) ~ (all_8_2 = e2) % 150.75/22.34 | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | BETA: splitting (61) gives: % 150.75/22.34 | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | (236) all_54_5 = e1 % 150.75/22.34 | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | REF_CLOSE: (36), (108), (236) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | #534. % 150.75/22.34 | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | (237) ~ (all_54_5 = e1) % 150.75/22.34 | | | | | | | | | | | (238) all_54_5 = e3 | all_54_5 = e2 % 150.75/22.34 | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | BETA: splitting (238) gives: % 150.75/22.34 | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | (239) all_54_5 = e2 % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | REF_CLOSE: (36), (227), (239) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | #533. % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | (240) all_54_5 = e3 % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | COMBINE_EQS: (36), (240) imply: % 150.75/22.34 | | | | | | | | | | | | (241) all_8_2 = e3 % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | SIMP: (241) implies: % 150.75/22.34 | | | | | | | | | | | | (242) all_8_2 = e3 % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | COMBINE_EQS: (59), (242) imply: % 150.75/22.34 | | | | | | | | | | | | (243) all_56_3 = e3 % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | COMBINE_EQS: (67), (242) imply: % 150.75/22.34 | | | | | | | | | | | | (244) all_58_29 = e3 % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | REDUCE: (42), (242) imply: % 150.75/22.34 | | | | | | | | | | | | (245) ~ (all_52_13 = e3) % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | BETA: splitting (229) gives: % 150.75/22.34 | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | (246) all_58_29 = e1 % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | COMBINE_EQS: (244), (246) imply: % 150.75/22.34 | | | | | | | | | | | | | (247) e3 = e1 % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | REDUCE: (44), (247) imply: % 150.75/22.34 | | | | | | | | | | | | | (248) $false % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | CLOSE: (248) is inconsistent. % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | (249) ~ (all_58_29 = e1) % 150.75/22.34 | | | | | | | | | | | | | (250) all_58_30 = e1 | all_58_31 = e1 % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | BETA: splitting (112) gives: % 150.75/22.34 | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | (251) all_56_3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | COMBINE_EQS: (243), (251) imply: % 150.75/22.34 | | | | | | | | | | | | | | (252) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | REDUCE: (99), (252) imply: % 150.75/22.34 | | | | | | | | | | | | | | (253) $false % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | (254) all_56_5 = e2 | all_56_10 = e2 % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | BETA: splitting (254) gives: % 150.75/22.34 | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | (255) all_56_5 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | COMBINE_EQS: (82), (255) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (256) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | SIMP: (256) implies: % 150.75/22.34 | | | | | | | | | | | | | | | (257) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | REDUCE: (87), (257) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (258) $false % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent. % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | (259) all_56_10 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | COMBINE_EQS: (81), (259) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (260) all_52_13 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | SIMP: (260) implies: % 150.75/22.34 | | | | | | | | | | | | | | | (261) all_52_13 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | COMBINE_EQS: (25), (261) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (262) all_58_13 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | REDUCE: (33), (261) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (263) ~ (all_52_12 = e2) % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | REDUCE: (39), (261) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (264) ~ (all_4_2 = e2) % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | SIMP: (264) implies: % 150.75/22.34 | | | | | | | | | | | | | | | (265) ~ (all_4_2 = e2) % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | REDUCE: (245), (261) imply: % 150.75/22.34 | | | | | | | | | | | | | | | (266) ~ (e3 = e2) % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 150.75/22.34 | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | (267) all_58_30 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | REF_CLOSE: (96), (149), (267) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | | | | | #825. % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | (268) all_58_31 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (268) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | (269) all_4_2 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | SIMP: (269) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | (270) all_4_2 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | REDUCE: (13), (270) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | (271) ~ (all_52_11 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | (272) all_56_4 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (272) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | (273) all_52_8 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | SIMP: (273) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | (274) all_52_8 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (274) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | (275) all_58_4 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | REDUCE: (38), (274) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | (276) ~ (all_52_12 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | SIMP: (276) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | (277) ~ (all_52_12 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | (278) all_56_9 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (278) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | (279) all_52_12 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (279) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | (280) all_58_6 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | (281) all_58_28 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | (99), (244), (268), (281) are inconsistent by % 150.75/22.34 | | | | | | | | | | | | | | | | | | | sub-proof #64. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | (282) ~ (all_58_28 = e3) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | (283) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | e0) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | REDUCE: (4), (282) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | (284) ~ (e3 = e0) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | (285) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | = e0) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | (286) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | (287) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | = e2) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_8 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_2 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (290) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (291) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (291) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (292) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (289) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (293) e3 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (292), (293) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | #263. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (294) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (295) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_8 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_6 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (297) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (298) e3 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (296) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (299) e3 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (299) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (300) e1 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (299), (300) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #63. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_11 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_8 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_2 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (304) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (305) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (306) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (303) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (307) e3 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (302) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (308) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (309) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (307) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (310) e2 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (310) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (311) e1 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (306), (309) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #62. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | (312) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (313) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_24 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_2 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (316) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (317) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (317) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (318) e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (315) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (319) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (319) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (320) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (318), (320) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #62. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (322) all_58_8 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (322) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (323) e2 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (323) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (324) $false % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (325) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (104), (326) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | #61. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_11 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (96), (109), (149), (250), (268), (328) are % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | (329) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | = e0) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | (330) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (331) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (333) all_58_13 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_8 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (334) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (335) e2 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (333) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (336) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (337) e2 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (337) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (338) e1 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (338) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (339) all_58_31 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (109), (149), (250), (339) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (340) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (104), (340) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | #261. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (341) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (342) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (343) all_58_6 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (280), (343) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #59. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (345) all_58_11 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_4 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (346) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (347) e3 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (345) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (348) e1 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (349) e1 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (347), (349) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #63. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | (350) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (350) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (351) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (352) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (352) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_20 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_4 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (354) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (355) e3 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (353) imply: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (356) e1 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (355), (356) are inconsistent % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #63. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (357) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_15 = e1 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (146), (358) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | #593. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | (359) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (359) gives: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (360) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (361) all_58_17 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_11 = e2 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (96), (109), (145), (149), (250), (268), % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (361), (362) are inconsistent by sub-proof #58. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (363) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (363) implies: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_26 = e0 % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (79), (364) are inconsistent by sub-proof % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | #273. % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | (365) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.75/22.34 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (366) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (366) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (367) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (368) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (369) e3 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (369) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (370) $false % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (370) is inconsistent. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (371) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (372) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (373) all_58_13 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (262), (373) are inconsistent by sub-proof % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | #665. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_26 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (79), (375) are inconsistent by sub-proof % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | #273. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (376) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (377) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (378) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (379) all_58_6 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (280), (379) are inconsistent % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #59. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (380) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (381) all_58_6 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (280), (381) are inconsistent % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #59. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (382) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (382) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (383) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (384) all_58_6 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (69), (78), (87), (93), (96), % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (99), (244), (268), (280), (384) are inconsistent % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #59. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (385) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (386) all_58_17 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_13 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (387) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (388) e2 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (388) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (389) e2 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (386) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (390) e2 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (390) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (391) e1 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (391) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (392) all_58_31 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (109), (149), (250), (392) are inconsistent % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (393) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (394) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (394) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (395) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (395) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (396) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (396) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (397) all_58_17 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (398) all_58_11 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (96), (109), (145), (149), (250), (268), % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (397), (398) are inconsistent by sub-proof #58. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (399) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (399) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (400) all_58_11 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (96), (109), (149), (250), (268), (400) are % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (401) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (402) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (402) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (403) all_58_11 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (96), (109), (149), (250), (268), (403) are % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (404) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (405) all_58_11 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (96), (109), (149), (250), (268), (405) are % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (406) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (407) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (407) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (408) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (408) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (409) all_58_24 = e2 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (87), (409) are inconsistent by sub-proof % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | #413. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (410) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (411) all_58_20 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (411) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (412) e1 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (412) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (413) all_58_31 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (109), (149), (250), (413) are inconsistent % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (414) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (415) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (416) all_58_13 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (262), (416) are inconsistent by sub-proof % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | #665. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (417) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (417) implies: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (418) e1 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (418) imply: % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | (419) all_58_31 = e0 % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (109), (149), (250), (419) are inconsistent % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | (420) ~ (all_56_9 = e3) % 150.75/22.35 | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (33), (47), (60), (66), (106), (245), % 150.75/22.35 | | | | | | | | | | | | | | | | | | (277), (420) are inconsistent by sub-proof #406. % 150.75/22.35 | | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | (421) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 150.75/22.35 | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (44), (67), (69), (78), (82), (83), % 150.75/22.35 | | | | | | | | | | | | | | | | | (87), (90), (93), (96), (99), (109), (268), (271), % 150.75/22.35 | | | | | | | | | | | | | | | | | (421) are inconsistent by sub-proof #402. % 150.75/22.35 | | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | | % 150.75/22.35 | | | | | | | | | Case 2: % 150.75/22.35 | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | (422) ~ (all_56_1 = e2) % 150.75/22.35 | | | | | | | | | | % 150.75/22.35 | | | | | | | | | | REF_CLOSE: (18), (21), (32), (36), (54), (61), (108), (147), % 150.75/22.35 | | | | | | | | | | (227), (422) are inconsistent by sub-proof #198. % 150.75/22.35 | | | | | | | | | | % 150.75/22.35 | | | | | | | | | End of split % 150.75/22.35 | | | | | | | | | % 150.75/22.35 | | | | | | | | End of split % 150.75/22.35 | | | | | | | | % 150.75/22.35 | | | | | | | End of split % 150.75/22.35 | | | | | | | % 150.75/22.35 | | | | | | End of split % 150.75/22.35 | | | | | | % 150.75/22.35 | | | | | End of split % 150.75/22.35 | | | | | % 150.75/22.35 | | | | Case 2: % 150.75/22.35 | | | | | % 150.75/22.35 | | | | | (423) all_56_13 = e1 % 150.75/22.35 | | | | | % 150.75/22.35 | | | | | COMBINE_EQS: (35), (423) imply: % 150.75/22.35 | | | | | (424) e1 = e0 % 150.75/22.35 | | | | | % 150.75/22.35 | | | | | REDUCE: (109), (424) imply: % 150.75/22.35 | | | | | (425) $false % 150.75/22.35 | | | | | % 150.75/22.35 | | | | | CLOSE: (425) is inconsistent. % 150.75/22.35 | | | | | % 150.75/22.35 | | | | End of split % 150.75/22.35 | | | | % 150.75/22.35 | | | End of split % 150.75/22.35 | | | % 150.75/22.35 | | End of split % 150.75/22.35 | | % 150.75/22.35 | End of split % 150.75/22.35 | % 150.75/22.35 End of proof % 150.75/22.35 % 150.75/22.35 Sub-proof #58 shows that the following formulas are inconsistent: % 150.75/22.35 ---------------------------------------------------------------- % 150.75/22.35 (1) all_58_31 = e1 % 150.75/22.35 (2) all_58_11 = e0 % 150.75/22.35 (3) all_58_11 = e2 % 150.75/22.35 (4) all_58_17 = e1 % 150.75/22.35 (5) all_58_30 = e1 | all_58_31 = e1 % 150.75/22.35 (6) all_58_17 = e2 % 150.75/22.35 (7) ~ (e1 = e0) % 150.75/22.35 (8) ~ (all_6_2 = e1) % 150.75/22.35 (9) all_58_30 = all_6_2 % 150.75/22.35 % 150.75/22.35 Begin of proof % 150.75/22.35 | % 150.75/22.35 | COMBINE_EQS: (2), (3) imply: % 150.75/22.35 | (10) e2 = e0 % 150.75/22.35 | % 150.75/22.35 | SIMP: (10) implies: % 150.75/22.35 | (11) e2 = e0 % 150.75/22.35 | % 150.75/22.35 | COMBINE_EQS: (4), (6) imply: % 150.75/22.35 | (12) e2 = e1 % 150.75/22.35 | % 150.75/22.35 | COMBINE_EQS: (11), (12) imply: % 150.75/22.35 | (13) e1 = e0 % 150.75/22.35 | % 150.75/22.35 | SIMP: (13) implies: % 150.75/22.35 | (14) e1 = e0 % 150.75/22.35 | % 150.75/22.35 | COMBINE_EQS: (1), (14) imply: % 150.75/22.35 | (15) all_58_31 = e0 % 150.75/22.35 | % 150.75/22.35 | REF_CLOSE: (5), (7), (8), (9), (15) are inconsistent by sub-proof #512. % 150.75/22.35 | % 150.75/22.35 End of proof % 150.75/22.35 % 150.75/22.35 Sub-proof #59 shows that the following formulas are inconsistent: % 150.75/22.35 ---------------------------------------------------------------- % 150.75/22.35 (1) all_58_28 = e0 % 150.75/22.35 (2) all_58_31 = e1 % 150.75/22.35 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 150.75/22.35 (4) ~ (e3 = e1) % 150.75/22.35 (5) all_58_6 = e0 % 150.75/22.35 (6) all_58_29 = e3 % 150.75/22.35 (7) ~ (e2 = e1) % 150.75/22.35 (8) ~ (e3 = e0) % 150.75/22.35 (9) all_58_6 = e3 % 150.75/22.35 (10) ~ (e2 = e0) % 150.75/22.35 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 150.75/22.35 (12) all_58_30 = all_6_2 % 150.75/22.35 (13) ~ (e3 = e2) % 150.75/22.35 % 150.75/22.35 Begin of proof % 150.75/22.35 | % 150.75/22.35 | COMBINE_EQS: (5), (9) imply: % 150.75/22.35 | (14) e3 = e0 % 150.75/22.35 | % 150.75/22.35 | COMBINE_EQS: (6), (14) imply: % 150.75/22.35 | (15) all_58_29 = e0 % 150.75/22.35 | % 150.75/22.35 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (12), (13), (15) are % 150.75/22.35 | inconsistent by sub-proof #653. % 150.75/22.35 | % 151.07/22.35 End of proof % 151.07/22.35 % 151.07/22.35 Sub-proof #60 shows that the following formulas are inconsistent: % 151.07/22.35 ---------------------------------------------------------------- % 151.07/22.35 (1) all_58_31 = e1 % 151.07/22.35 (2) all_58_11 = e0 % 151.07/22.35 (3) all_58_11 = e1 % 151.07/22.35 (4) all_58_30 = e1 | all_58_31 = e1 % 151.07/22.35 (5) ~ (e1 = e0) % 151.07/22.35 (6) ~ (all_6_2 = e1) % 151.07/22.35 (7) all_58_30 = all_6_2 % 151.07/22.35 % 151.07/22.35 Begin of proof % 151.07/22.35 | % 151.07/22.35 | COMBINE_EQS: (2), (3) imply: % 151.07/22.35 | (8) e1 = e0 % 151.07/22.35 | % 151.07/22.35 | SIMP: (8) implies: % 151.07/22.35 | (9) e1 = e0 % 151.07/22.35 | % 151.07/22.35 | COMBINE_EQS: (1), (9) imply: % 151.07/22.35 | (10) all_58_31 = e0 % 151.07/22.35 | % 151.07/22.35 | REF_CLOSE: (4), (5), (6), (7), (10) are inconsistent by sub-proof #512. % 151.07/22.35 | % 151.07/22.35 End of proof % 151.07/22.35 % 151.07/22.35 Sub-proof #61 shows that the following formulas are inconsistent: % 151.07/22.35 ---------------------------------------------------------------- % 151.07/22.35 (1) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3 % 151.07/22.35 (2) all_58_8 = e1 % 151.07/22.35 (3) ~ (e2 = e1) % 151.07/22.35 % 151.07/22.35 Begin of proof % 151.07/22.35 | % 151.07/22.35 | ALPHA: (1) implies: % 151.07/22.35 | (4) all_58_8 = e2 % 151.07/22.35 | % 151.07/22.35 | COMBINE_EQS: (2), (4) imply: % 151.07/22.35 | (5) e2 = e1 % 151.07/22.35 | % 151.07/22.35 | REDUCE: (3), (5) imply: % 151.07/22.35 | (6) $false % 151.07/22.35 | % 151.07/22.35 | CLOSE: (6) is inconsistent. % 151.07/22.35 | % 151.07/22.35 End of proof % 151.07/22.35 % 151.07/22.35 Sub-proof #62 shows that the following formulas are inconsistent: % 151.07/22.35 ---------------------------------------------------------------- % 151.07/22.35 (1) all_58_28 = e0 % 151.07/22.35 (2) all_58_31 = e1 % 151.07/22.35 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.07/22.35 (4) ~ (e3 = e1) % 151.07/22.35 (5) all_58_29 = e3 % 151.07/22.35 (6) ~ (e2 = e1) % 151.07/22.35 (7) ~ (e3 = e0) % 151.07/22.35 (8) ~ (e2 = e0) % 151.07/22.35 (9) e2 = e0 % 151.07/22.35 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.07/22.35 (11) all_58_30 = all_6_2 % 151.07/22.35 (12) ~ (e3 = e2) % 151.07/22.35 (13) e3 = e2 % 151.07/22.35 % 151.07/22.35 Begin of proof % 151.07/22.35 | % 151.07/22.35 | COMBINE_EQS: (9), (13) imply: % 151.07/22.35 | (14) e3 = e0 % 151.07/22.35 | % 151.07/22.35 | COMBINE_EQS: (5), (14) imply: % 151.07/22.35 | (15) all_58_29 = e0 % 151.07/22.35 | % 151.07/22.35 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (15) are % 151.07/22.35 | inconsistent by sub-proof #653. % 151.07/22.35 | % 151.07/22.35 End of proof % 151.07/22.35 % 151.07/22.35 Sub-proof #63 shows that the following formulas are inconsistent: % 151.07/22.35 ---------------------------------------------------------------- % 151.07/22.35 (1) all_58_28 = e0 % 151.07/22.35 (2) all_58_31 = e1 % 151.07/22.35 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.07/22.35 (4) ~ (e3 = e1) % 151.07/22.35 (5) e3 = e1 % 151.07/22.35 (6) all_58_29 = e3 % 151.07/22.35 (7) ~ (e2 = e1) % 151.07/22.35 (8) ~ (e3 = e0) % 151.07/22.35 (9) ~ (e2 = e0) % 151.07/22.36 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.07/22.36 (11) e1 = e0 % 151.07/22.36 (12) all_58_30 = all_6_2 % 151.07/22.36 (13) ~ (e3 = e2) % 151.07/22.36 % 151.07/22.36 Begin of proof % 151.07/22.36 | % 151.07/22.36 | COMBINE_EQS: (5), (11) imply: % 151.07/22.36 | (14) e3 = e0 % 151.07/22.36 | % 151.07/22.36 | COMBINE_EQS: (6), (14) imply: % 151.07/22.36 | (15) all_58_29 = e0 % 151.07/22.36 | % 151.07/22.36 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (15) are % 151.07/22.36 | inconsistent by sub-proof #653. % 151.07/22.36 | % 151.07/22.36 End of proof % 151.07/22.36 % 151.07/22.36 Sub-proof #64 shows that the following formulas are inconsistent: % 151.07/22.36 ---------------------------------------------------------------- % 151.07/22.36 (1) all_58_28 = e0 % 151.07/22.36 (2) all_58_31 = e1 % 151.07/22.36 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.07/22.36 (4) ~ (e3 = e1) % 151.07/22.36 (5) all_58_29 = e3 % 151.07/22.36 (6) ~ (e2 = e1) % 151.07/22.36 (7) ~ (e3 = e0) % 151.07/22.36 (8) ~ (e2 = e0) % 151.07/22.36 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.07/22.36 (10) all_58_28 = e3 % 151.07/22.36 (11) all_58_30 = all_6_2 % 151.07/22.36 (12) ~ (e3 = e2) % 151.07/22.36 % 151.07/22.36 Begin of proof % 151.07/22.36 | % 151.07/22.36 | COMBINE_EQS: (1), (10) imply: % 151.07/22.36 | (13) e3 = e0 % 151.07/22.36 | % 151.07/22.36 | COMBINE_EQS: (5), (13) imply: % 151.07/22.36 | (14) all_58_29 = e0 % 151.07/22.36 | % 151.07/22.36 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (14) are % 151.07/22.36 | inconsistent by sub-proof #653. % 151.07/22.36 | % 151.07/22.36 End of proof % 151.07/22.36 % 151.07/22.36 Sub-proof #65 shows that the following formulas are inconsistent: % 151.07/22.36 ---------------------------------------------------------------- % 151.07/22.36 (1) all_58_31 = all_4_2 % 151.07/22.36 (2) all_56_8 = e1 | all_56_11 = e1 % 151.07/22.36 (3) all_58_28 = e0 % 151.07/22.36 (4) all_56_15 = all_4_2 % 151.07/22.36 (5) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.07/22.36 (6) ~ (e3 = e1) % 151.07/22.36 (7) all_58_29 = all_8_2 % 151.07/22.36 (8) ~ (e2 = e1) % 151.07/22.36 (9) ~ (e3 = e0) % 151.07/22.36 (10) ~ (e2 = e0) % 151.07/22.36 (11) all_56_8 = all_6_2 % 151.07/22.36 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.07/22.36 (13) ~ (e1 = e0) % 151.07/22.36 (14) all_58_30 = all_6_2 % 151.07/22.36 (15) all_56_11 = e0 % 151.07/22.36 (16) ~ (e3 = e2) % 151.07/22.36 (17) all_56_15 = e1 % 151.07/22.36 % 151.07/22.36 Begin of proof % 151.07/22.36 | % 151.07/22.36 | COMBINE_EQS: (4), (17) imply: % 151.07/22.36 | (18) all_4_2 = e1 % 151.07/22.36 | % 151.07/22.36 | SIMP: (18) implies: % 151.07/22.36 | (19) all_4_2 = e1 % 151.07/22.36 | % 151.07/22.36 | COMBINE_EQS: (1), (19) imply: % 151.07/22.36 | (20) all_58_31 = e1 % 151.07/22.36 | % 151.07/22.36 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 151.07/22.36 | (15), (16), (20) are inconsistent by sub-proof #495. % 151.07/22.36 | % 151.07/22.36 End of proof % 151.07/22.36 % 151.07/22.36 Sub-proof #66 shows that the following formulas are inconsistent: % 151.07/22.36 ---------------------------------------------------------------- % 151.07/22.36 (1) all_58_31 = all_4_2 % 151.07/22.36 (2) all_58_28 = e0 % 151.07/22.36 (3) all_56_15 = all_4_2 % 151.07/22.36 (4) all_56_7 = all_52_6 % 151.07/22.36 (5) ~ (all_52_6 = all_6_2) % 151.07/22.36 (6) ~ (all_10_1 = e0) % 151.07/22.36 (7) ~ (all_52_11 = all_10_1) % 151.07/22.36 (8) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.07/22.36 (9) all_58_26 = all_52_11 % 151.07/22.36 (10) all_58_6 = all_52_12 % 151.07/22.36 (11) ~ (all_52_6 = all_8_2) % 151.07/22.36 (12) all_58_15 = e1 % 151.07/22.36 (13) all_56_4 = all_52_8 % 151.07/22.36 (14) ~ (all_52_4 = all_8_2) % 151.07/22.36 (15) all_54_3 = all_52_12 % 151.07/22.36 (16) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.07/22.36 (17) all_54_1 = all_52_4 % 151.07/22.36 (18) ~ (all_6_2 = e0) % 151.07/22.36 (19) ~ (all_52_4 = all_52_6) % 151.07/22.36 (20) all_58_13 = all_52_13 % 151.07/22.36 (21) all_56_12 = all_10_1 % 151.07/22.36 (22) all_58_11 = e0 % 151.07/22.36 (23) all_58_20 = e0 % 151.07/22.36 (24) ~ (all_52_6 = e1) % 151.07/22.36 (25) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.07/22.36 (26) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 151.07/22.36 (27) ~ (all_52_12 = all_52_13) % 151.07/22.36 (28) all_56_13 = e0 % 151.07/22.36 (29) all_56_0 = e0 % 151.07/22.36 (30) all_54_9 = all_52_6 % 151.07/22.36 (31) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 151.07/22.36 (32) ~ (all_52_13 = all_8_2) % 151.07/22.36 (33) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 151.07/22.36 (34) ~ (e3 = e1) % 151.07/22.36 (35) ~ (all_52_6 = e0) % 151.07/22.36 (36) all_54_14 = all_52_11 % 151.07/22.36 (37) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 151.07/22.36 (38) ~ (all_52_12 = e0) % 151.07/22.36 (39) all_58_2 = all_52_4 % 151.07/22.36 (40) all_56_11 = all_52_14 % 151.07/22.36 (41) all_56_1 = all_52_4 % 151.07/22.36 (42) ~ (all_52_13 = e0) % 151.07/22.36 (43) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.07/22.36 (44) all_58_24 = e0 % 151.07/22.36 (45) ~ (all_52_1 = all_10_1) % 151.07/22.36 (46) ~ (all_52_1 = all_8_2) % 151.07/22.36 (47) all_56_3 = all_8_2 % 151.07/22.36 (48) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.07/22.36 (49) ~ (all_52_11 = e1) % 151.07/22.36 (50) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.07/22.36 (51) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 151.07/22.36 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 151.07/22.36 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 151.07/22.36 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 151.07/22.36 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 151.07/22.36 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 151.07/22.36 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 151.07/22.36 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 151.07/22.36 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 151.07/22.36 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 151.07/22.36 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.07/22.36 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.07/22.36 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.07/22.36 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.07/22.36 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.07/22.36 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 151.07/22.36 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.07/22.36 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.07/22.36 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.07/22.36 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.07/22.36 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.07/22.36 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 151.07/22.36 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.07/22.36 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.07/22.36 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.07/22.36 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 151.07/22.36 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 151.07/22.36 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 151.07/22.36 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.07/22.36 e0) % 151.07/22.36 (52) all_56_9 = all_52_12 % 151.07/22.36 (53) all_58_29 = all_8_2 % 151.07/22.36 (54) ~ (all_52_12 = all_52_14) % 151.07/22.36 (55) ~ (all_52_4 = e1) % 151.07/22.36 (56) all_58_8 = all_52_1 % 151.07/22.36 (57) ~ (e2 = e1) % 151.07/22.36 (58) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.07/22.36 (59) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.07/22.36 (60) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 151.07/22.36 (61) ~ (all_52_4 = e0) % 151.07/22.36 (62) ~ (all_52_11 = all_6_2) % 151.07/22.36 (63) ~ (e3 = e0) % 151.07/22.36 (64) all_56_2 = all_52_1 % 151.07/22.36 (65) ~ (all_52_11 = e0) % 151.07/22.36 (66) all_58_22 = all_10_1 % 151.07/22.36 (67) all_56_10 = all_52_13 % 151.07/22.36 (68) ~ (all_52_12 = e1) % 151.07/22.36 (69) all_56_14 = all_52_11 % 151.07/22.36 (70) all_58_28 = all_10_2 % 151.07/22.36 (71) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.07/22.36 (72) all_58_17 = all_52_6 % 151.07/22.36 (73) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.07/22.36 (74) ~ (e2 = e0) % 151.07/22.36 (75) all_56_0 = all_10_2 % 151.07/22.36 (76) all_56_8 = all_6_2 % 151.07/22.36 (77) ~ (all_10_1 = e1) % 151.07/22.36 (78) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.07/22.36 (79) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.07/22.36 (80) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.07/22.36 (81) ~ (e1 = e0) % 151.07/22.36 (82) ~ (all_52_8 = e0) % 151.07/22.36 (83) all_58_30 = all_6_2 % 151.07/22.36 (84) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.07/22.36 (85) all_56_11 = e0 % 151.07/22.36 (86) ~ (e3 = e2) % 151.07/22.36 (87) ~ (all_8_2 = e0) % 151.07/22.36 (88) ~ (all_52_4 = all_52_12) % 151.07/22.36 (89) all_54_4 = all_52_1 % 151.07/22.36 % 151.07/22.36 Begin of proof % 151.07/22.36 | % 151.07/22.36 | BETA: splitting (73) gives: % 151.07/22.36 | % 151.07/22.36 | Case 1: % 151.07/22.36 | | % 151.07/22.36 | | (90) all_56_12 = e1 % 151.07/22.36 | | % 151.07/22.36 | | REF_CLOSE: (21), (77), (90) are inconsistent by sub-proof #405. % 151.07/22.36 | | % 151.07/22.36 | Case 2: % 151.07/22.36 | | % 151.07/22.36 | | (91) ~ (all_56_12 = e1) % 151.07/22.36 | | (92) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.07/22.36 | | % 151.07/22.36 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 151.07/22.36 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 151.07/22.36 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 151.07/22.36 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 151.07/22.36 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 151.07/22.36 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 151.07/22.36 | | (68), (69), (70), (71), (72), (74), (75), (76), (77), (78), (79), % 151.07/22.36 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (92) % 151.07/22.36 | | are inconsistent by sub-proof #67. % 151.07/22.36 | | % 151.07/22.36 | End of split % 151.07/22.36 | % 151.07/22.36 End of proof % 151.07/22.36 % 151.07/22.36 Sub-proof #67 shows that the following formulas are inconsistent: % 151.07/22.36 ---------------------------------------------------------------- % 151.07/22.36 (1) all_58_31 = all_4_2 % 151.07/22.36 (2) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.07/22.36 (3) all_58_28 = e0 % 151.07/22.36 (4) all_56_15 = all_4_2 % 151.07/22.36 (5) all_56_7 = all_52_6 % 151.07/22.36 (6) ~ (all_52_6 = all_6_2) % 151.07/22.36 (7) ~ (all_10_1 = e0) % 151.07/22.36 (8) ~ (all_52_11 = all_10_1) % 151.07/22.36 (9) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.07/22.36 (10) all_58_26 = all_52_11 % 151.07/22.36 (11) all_58_6 = all_52_12 % 151.07/22.36 (12) ~ (all_52_6 = all_8_2) % 151.07/22.36 (13) all_58_15 = e1 % 151.07/22.36 (14) all_56_4 = all_52_8 % 151.07/22.36 (15) ~ (all_52_4 = all_8_2) % 151.07/22.36 (16) all_54_3 = all_52_12 % 151.07/22.36 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.07/22.36 (18) all_54_1 = all_52_4 % 151.07/22.36 (19) ~ (all_6_2 = e0) % 151.07/22.36 (20) ~ (all_52_4 = all_52_6) % 151.07/22.36 (21) all_58_13 = all_52_13 % 151.07/22.36 (22) all_56_12 = all_10_1 % 151.07/22.36 (23) all_58_11 = e0 % 151.07/22.36 (24) all_58_20 = e0 % 151.07/22.36 (25) ~ (all_52_6 = e1) % 151.07/22.36 (26) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.07/22.36 (27) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 151.07/22.36 (28) ~ (all_52_12 = all_52_13) % 151.07/22.36 (29) all_56_13 = e0 % 151.07/22.36 (30) all_56_0 = e0 % 151.07/22.36 (31) all_54_9 = all_52_6 % 151.07/22.36 (32) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 151.07/22.36 (33) ~ (all_52_13 = all_8_2) % 151.07/22.36 (34) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 151.07/22.36 (35) ~ (e3 = e1) % 151.07/22.36 (36) ~ (all_52_6 = e0) % 151.07/22.36 (37) all_54_14 = all_52_11 % 151.07/22.36 (38) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 151.07/22.36 (39) ~ (all_52_12 = e0) % 151.07/22.36 (40) all_58_2 = all_52_4 % 151.07/22.36 (41) all_56_11 = all_52_14 % 151.07/22.36 (42) all_56_1 = all_52_4 % 151.07/22.36 (43) ~ (all_52_13 = e0) % 151.07/22.36 (44) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.07/22.36 (45) all_58_24 = e0 % 151.07/22.36 (46) ~ (all_52_1 = all_10_1) % 151.07/22.36 (47) ~ (all_52_1 = all_8_2) % 151.07/22.36 (48) all_56_3 = all_8_2 % 151.07/22.36 (49) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.07/22.36 (50) ~ (all_52_11 = e1) % 151.07/22.36 (51) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.07/22.36 (52) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 151.07/22.36 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 151.07/22.36 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 151.07/22.36 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 151.07/22.36 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 151.07/22.36 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 151.07/22.36 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 151.07/22.36 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 151.07/22.36 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 151.07/22.36 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 151.07/22.36 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.07/22.36 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.07/22.36 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.07/22.36 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.07/22.36 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.07/22.36 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 151.07/22.36 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.07/22.36 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.07/22.36 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.07/22.36 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.07/22.36 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.07/22.36 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 151.07/22.36 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.07/22.36 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.07/22.36 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.07/22.36 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 151.07/22.36 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 151.07/22.36 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 151.07/22.36 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.07/22.36 e0) % 151.07/22.36 (53) all_56_9 = all_52_12 % 151.07/22.36 (54) all_58_29 = all_8_2 % 151.07/22.36 (55) ~ (all_52_12 = all_52_14) % 151.07/22.36 (56) ~ (all_52_4 = e1) % 151.07/22.36 (57) all_58_8 = all_52_1 % 151.07/22.36 (58) ~ (e2 = e1) % 151.07/22.36 (59) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.07/22.36 (60) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.07/22.36 (61) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 151.07/22.36 (62) ~ (all_52_4 = e0) % 151.07/22.36 (63) ~ (all_52_11 = all_6_2) % 151.07/22.36 (64) ~ (e3 = e0) % 151.07/22.36 (65) all_56_2 = all_52_1 % 151.07/22.36 (66) ~ (all_52_11 = e0) % 151.07/22.36 (67) all_58_22 = all_10_1 % 151.07/22.36 (68) all_56_10 = all_52_13 % 151.07/22.36 (69) ~ (all_52_12 = e1) % 151.07/22.36 (70) all_56_14 = all_52_11 % 151.07/22.36 (71) all_58_28 = all_10_2 % 151.07/22.36 (72) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.07/22.36 (73) all_58_17 = all_52_6 % 151.07/22.36 (74) ~ (e2 = e0) % 151.07/22.36 (75) all_56_0 = all_10_2 % 151.07/22.36 (76) all_56_8 = all_6_2 % 151.07/22.36 (77) ~ (all_10_1 = e1) % 151.07/22.36 (78) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.07/22.36 (79) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.07/22.36 (80) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.07/22.36 (81) ~ (e1 = e0) % 151.07/22.36 (82) ~ (all_52_8 = e0) % 151.07/22.36 (83) all_58_30 = all_6_2 % 151.07/22.36 (84) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.07/22.36 (85) all_56_11 = e0 % 151.07/22.36 (86) ~ (e3 = e2) % 151.07/22.36 (87) ~ (all_8_2 = e0) % 151.07/22.36 (88) ~ (all_52_4 = all_52_12) % 151.07/22.36 (89) all_54_4 = all_52_1 % 151.07/22.36 % 151.07/22.36 Begin of proof % 151.07/22.36 | % 151.07/22.36 | BETA: splitting (60) gives: % 151.07/22.36 | % 151.07/22.36 | Case 1: % 151.07/22.36 | | % 151.07/22.36 | | (90) all_56_1 = e1 % 151.07/22.36 | | % 151.07/22.36 | | COMBINE_EQS: (42), (90) imply: % 151.07/22.36 | | (91) all_52_4 = e1 % 151.07/22.36 | | % 151.07/22.36 | | REDUCE: (56), (91) imply: % 151.07/22.36 | | (92) $false % 151.07/22.36 | | % 151.07/22.36 | | CLOSE: (92) is inconsistent. % 151.07/22.36 | | % 151.07/22.36 | Case 2: % 151.07/22.36 | | % 151.07/22.36 | | (93) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.07/22.36 | | % 151.07/22.36 | | BETA: splitting (93) gives: % 151.07/22.36 | | % 151.07/22.36 | | Case 1: % 151.07/22.36 | | | % 151.07/22.36 | | | (94) all_56_3 = e1 % 151.07/22.36 | | | % 151.07/22.36 | | | COMBINE_EQS: (48), (94) imply: % 151.07/22.36 | | | (95) all_8_2 = e1 % 151.07/22.36 | | | % 151.07/22.36 | | | COMBINE_EQS: (54), (95) imply: % 151.07/22.36 | | | (96) all_58_29 = e1 % 151.07/22.36 | | | % 151.07/22.36 | | | REDUCE: (47), (95) imply: % 151.07/22.36 | | | (97) ~ (all_52_1 = e1) % 151.07/22.36 | | | % 151.07/22.36 | | | REDUCE: (33), (95) imply: % 151.07/22.36 | | | (98) ~ (all_52_13 = e1) % 151.07/22.36 | | | % 151.07/22.36 | | | BETA: splitting (2) gives: % 151.07/22.36 | | | % 151.07/22.36 | | | Case 1: % 151.07/22.36 | | | | % 151.07/22.36 | | | | (99) all_56_13 = e1 % 151.07/22.36 | | | | % 151.07/22.36 | | | | COMBINE_EQS: (29), (99) imply: % 151.07/22.36 | | | | (100) e1 = e0 % 151.07/22.36 | | | | % 151.07/22.36 | | | | COMBINE_EQS: (96), (100) imply: % 151.07/22.36 | | | | (101) all_58_29 = e0 % 151.07/22.36 | | | | % 151.07/22.36 | | | | REF_CLOSE: (5), (14), (17), (19), (35), (36), (38), (41), (42), (53), % 151.07/22.36 | | | | (55), (58), (62), (64), (71), (72), (74), (75), (76), (80), % 151.07/22.36 | | | | (81), (82), (83), (84), (86), (101) are inconsistent by % 151.07/22.36 | | | | sub-proof #481. % 151.07/22.36 | | | | % 151.07/22.36 | | | Case 2: % 151.07/22.36 | | | | % 151.07/22.36 | | | | (102) ~ (all_56_13 = e1) % 151.07/22.36 | | | | (103) all_56_14 = e1 | all_56_15 = e1 % 151.07/22.36 | | | | % 151.07/22.36 | | | | REDUCE: (29), (102) imply: % 151.13/22.36 | | | | (104) ~ (e1 = e0) % 151.13/22.36 | | | | % 151.13/22.36 | | | | BETA: splitting (103) gives: % 151.13/22.36 | | | | % 151.13/22.36 | | | | Case 1: % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | (105) all_56_14 = e1 % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | REF_CLOSE: (50), (70), (105) are inconsistent by sub-proof #811. % 151.13/22.36 | | | | | % 151.13/22.36 | | | | Case 2: % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | (106) all_56_15 = e1 % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | COMBINE_EQS: (4), (106) imply: % 151.13/22.36 | | | | | (107) all_4_2 = e1 % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | SIMP: (107) implies: % 151.13/22.36 | | | | | (108) all_4_2 = e1 % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | COMBINE_EQS: (1), (108) imply: % 151.13/22.36 | | | | | (109) all_58_31 = e1 % 151.13/22.36 | | | | | % 151.13/22.36 | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (13), (16), % 151.13/22.36 | | | | | (17), (18), (20), (21), (22), (23), (24), (25), (26), (27), % 151.13/22.36 | | | | | (28), (29), (30), (31), (32), (34), (35), (36), (37), (39), % 151.13/22.36 | | | | | (40), (42), (43), (44), (45), (46), (49), (50), (51), (52), % 151.13/22.36 | | | | | (53), (56), (57), (58), (59), (61), (62), (63), (64), (65), % 151.13/22.36 | | | | | (66), (67), (68), (69), (70), (73), (74), (77), (78), (79), % 151.13/22.36 | | | | | (80), (81), (83), (84), (85), (86), (88), (89), (94), (96), % 151.13/22.36 | | | | | (97), (98), (106), (109) are inconsistent by sub-proof % 151.13/22.36 | | | | | #420. % 151.13/22.36 | | | | | % 151.13/22.36 | | | | End of split % 151.13/22.36 | | | | % 151.13/22.36 | | | End of split % 151.13/22.36 | | | % 151.13/22.36 | | Case 2: % 151.13/22.36 | | | % 151.13/22.36 | | | (110) all_56_7 = e1 | all_56_13 = e1 % 151.13/22.36 | | | % 151.13/22.36 | | | REF_CLOSE: (5), (25), (29), (81), (110) are inconsistent by sub-proof % 151.13/22.36 | | | #529. % 151.13/22.36 | | | % 151.13/22.36 | | End of split % 151.13/22.36 | | % 151.13/22.36 | End of split % 151.13/22.36 | % 151.13/22.36 End of proof % 151.13/22.36 % 151.13/22.36 Sub-proof #68 shows that the following formulas are inconsistent: % 151.13/22.36 ---------------------------------------------------------------- % 151.13/22.36 (1) all_58_31 = all_4_2 % 151.13/22.36 (2) all_58_28 = e0 % 151.13/22.36 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.36 (4) all_54_10 = all_6_2 % 151.13/22.36 (5) ~ (e3 = e1) % 151.13/22.36 (6) all_20_2 = all_4_2 % 151.13/22.36 (7) all_58_29 = all_8_2 % 151.13/22.36 (8) ~ (e2 = e1) % 151.13/22.36 (9) ~ (e3 = e0) % 151.13/22.36 (10) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.13/22.36 (11) ~ (e2 = e0) % 151.13/22.36 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.36 (13) ~ (e1 = e0) % 151.13/22.36 (14) all_54_10 = e0 % 151.13/22.36 (15) all_58_30 = all_6_2 % 151.13/22.36 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.36 (17) ~ (e3 = e2) % 151.13/22.36 % 151.13/22.36 Begin of proof % 151.13/22.36 | % 151.13/22.36 | COMBINE_EQS: (4), (14) imply: % 151.13/22.36 | (18) all_6_2 = e0 % 151.13/22.36 | % 151.13/22.36 | SIMP: (18) implies: % 151.13/22.36 | (19) all_6_2 = e0 % 151.13/22.36 | % 151.13/22.36 | COMBINE_EQS: (15), (19) imply: % 151.13/22.36 | (20) all_58_30 = e0 % 151.13/22.36 | % 151.13/22.37 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 151.13/22.37 | (16), (17), (20) are inconsistent by sub-proof #679. % 151.13/22.37 | % 151.13/22.37 End of proof % 151.13/22.37 % 151.13/22.37 Sub-proof #69 shows that the following formulas are inconsistent: % 151.13/22.37 ---------------------------------------------------------------- % 151.13/22.37 (1) all_58_31 = all_4_2 % 151.13/22.37 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.37 (3) all_56_15 = all_4_2 % 151.13/22.37 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.37 (5) op(e0, all_4_2) = all_58_27 % 151.13/22.37 (6) ~ (e3 = e1) % 151.13/22.37 (7) all_56_1 = all_52_4 % 151.13/22.37 (8) all_56_3 = all_8_2 % 151.13/22.37 (9) all_58_29 = all_8_2 % 151.13/22.37 (10) ~ (e2 = e1) % 151.13/22.37 (11) all_56_13 = all_52_7 % 151.13/22.37 (12) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.13/22.37 (13) ~ (all_52_4 = e0) % 151.13/22.37 (14) ~ (e3 = e0) % 151.13/22.37 (15) all_56_15 = e0 % 151.13/22.37 (16) ~ (e2 = e0) % 151.13/22.37 (17) op(e0, e0) = all_4_2 % 151.13/22.37 (18) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.37 (19) ~ (e1 = e0) % 151.13/22.37 (20) ~ (all_52_7 = all_4_2) % 151.13/22.37 (21) op(all_4_2, all_4_1) = e1 % 151.13/22.37 (22) all_58_30 = all_6_2 % 151.13/22.37 (23) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.37 (24) ~ (e3 = e2) % 151.13/22.37 (25) op(all_4_2, e0) = all_4_1 % 151.13/22.37 % 151.13/22.37 Begin of proof % 151.13/22.37 | % 151.13/22.37 | COMBINE_EQS: (3), (15) imply: % 151.13/22.37 | (26) all_4_2 = e0 % 151.13/22.37 | % 151.13/22.37 | SIMP: (26) implies: % 151.13/22.37 | (27) all_4_2 = e0 % 151.13/22.37 | % 151.13/22.37 | COMBINE_EQS: (1), (27) imply: % 151.13/22.37 | (28) all_58_31 = e0 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (20), (27) imply: % 151.13/22.37 | (29) ~ (all_52_7 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (21), (27) imply: % 151.13/22.37 | (30) op(e0, all_4_1) = e1 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (25), (27) imply: % 151.13/22.37 | (31) op(e0, e0) = all_4_1 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (5), (27) imply: % 151.13/22.37 | (32) op(e0, e0) = all_58_27 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (17), (27) imply: % 151.13/22.37 | (33) op(e0, e0) = e0 % 151.13/22.37 | % 151.13/22.37 | BETA: splitting (12) gives: % 151.13/22.37 | % 151.13/22.37 | Case 1: % 151.13/22.37 | | % 151.13/22.37 | | (34) all_56_1 = e0 % 151.13/22.37 | | % 151.13/22.37 | | REF_CLOSE: (7), (13), (34) are inconsistent by sub-proof #244. % 151.13/22.37 | | % 151.13/22.37 | Case 2: % 151.13/22.37 | | % 151.13/22.37 | | (35) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.13/22.37 | | % 151.13/22.37 | | BETA: splitting (35) gives: % 151.13/22.37 | | % 151.13/22.37 | | Case 1: % 151.13/22.37 | | | % 151.13/22.37 | | | (36) all_56_3 = e0 % 151.13/22.37 | | | % 151.13/22.37 | | | COMBINE_EQS: (8), (36) imply: % 151.13/22.37 | | | (37) all_8_2 = e0 % 151.13/22.37 | | | % 151.13/22.37 | | | SIMP: (37) implies: % 151.13/22.37 | | | (38) all_8_2 = e0 % 151.13/22.37 | | | % 151.13/22.37 | | | COMBINE_EQS: (9), (38) imply: % 151.13/22.37 | | | (39) all_58_29 = e0 % 151.13/22.37 | | | % 151.13/22.37 | | | REF_CLOSE: (4), (6), (10), (14), (16), (18), (19), (22), (23), (24), (28), % 151.13/22.37 | | | (39) are inconsistent by sub-proof #844. % 151.13/22.37 | | | % 151.13/22.37 | | Case 2: % 151.13/22.37 | | | % 151.13/22.37 | | | (40) all_56_7 = e0 | all_56_13 = e0 % 151.13/22.37 | | | % 151.13/22.37 | | | BETA: splitting (40) gives: % 151.13/22.37 | | | % 151.13/22.37 | | | Case 1: % 151.13/22.37 | | | | % 151.13/22.37 | | | | % 151.13/22.37 | | | | GROUND_INST: instantiating (2) with all_4_1, all_58_27, e0, e0, % 151.13/22.37 | | | | simplifying with (31), (32) gives: % 151.13/22.37 | | | | (41) all_58_27 = all_4_1 % 151.13/22.37 | | | | % 151.13/22.37 | | | | REF_CLOSE: (2), (19), (30), (31), (32), (33), (41) are inconsistent by % 151.13/22.37 | | | | sub-proof #71. % 151.13/22.37 | | | | % 151.13/22.37 | | | Case 2: % 151.13/22.37 | | | | % 151.13/22.37 | | | | (42) all_56_13 = e0 % 151.13/22.37 | | | | % 151.13/22.37 | | | | REF_CLOSE: (11), (29), (42) are inconsistent by sub-proof #802. % 151.13/22.37 | | | | % 151.13/22.37 | | | End of split % 151.13/22.37 | | | % 151.13/22.37 | | End of split % 151.13/22.37 | | % 151.13/22.37 | End of split % 151.13/22.37 | % 151.13/22.37 End of proof % 151.13/22.37 % 151.13/22.37 Sub-proof #70 shows that the following formulas are inconsistent: % 151.13/22.37 ---------------------------------------------------------------- % 151.13/22.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.37 (2) op(e0, all_4_2) = all_58_27 % 151.13/22.37 (3) all_4_2 = e0 % 151.13/22.37 (4) op(e0, e0) = all_4_2 % 151.13/22.37 (5) ~ (e1 = e0) % 151.13/22.37 (6) op(all_4_2, all_4_1) = e1 % 151.13/22.37 (7) op(all_4_2, e0) = all_4_1 % 151.13/22.37 % 151.13/22.37 Begin of proof % 151.13/22.37 | % 151.13/22.37 | REDUCE: (3), (6) imply: % 151.13/22.37 | (8) op(e0, all_4_1) = e1 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (3), (7) imply: % 151.13/22.37 | (9) op(e0, e0) = all_4_1 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (2), (3) imply: % 151.13/22.37 | (10) op(e0, e0) = all_58_27 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (3), (4) imply: % 151.13/22.37 | (11) op(e0, e0) = e0 % 151.13/22.37 | % 151.13/22.37 | GROUND_INST: instantiating (1) with all_4_1, all_58_27, e0, e0, simplifying % 151.13/22.37 | with (9), (10) gives: % 151.13/22.37 | (12) all_58_27 = all_4_1 % 151.13/22.37 | % 151.13/22.37 | REF_CLOSE: (1), (5), (8), (9), (10), (11), (12) are inconsistent by sub-proof % 151.13/22.37 | #71. % 151.13/22.37 | % 151.13/22.37 End of proof % 151.13/22.37 % 151.13/22.37 Sub-proof #71 shows that the following formulas are inconsistent: % 151.13/22.37 ---------------------------------------------------------------- % 151.13/22.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.37 (2) op(e0, e0) = all_4_1 % 151.13/22.37 (3) op(e0, e0) = all_58_27 % 151.13/22.37 (4) op(e0, e0) = e0 % 151.13/22.37 (5) all_58_27 = all_4_1 % 151.13/22.37 (6) op(e0, all_4_1) = e1 % 151.13/22.37 (7) ~ (e1 = e0) % 151.13/22.37 % 151.13/22.37 Begin of proof % 151.13/22.37 | % 151.13/22.37 | GROUND_INST: instantiating (1) with e0, all_58_27, e0, e0, simplifying with % 151.13/22.37 | (3), (4) gives: % 151.13/22.37 | (8) all_58_27 = e0 % 151.13/22.37 | % 151.13/22.37 | COMBINE_EQS: (5), (8) imply: % 151.13/22.37 | (9) all_4_1 = e0 % 151.13/22.37 | % 151.13/22.37 | SIMP: (9) implies: % 151.13/22.37 | (10) all_4_1 = e0 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (6), (10) imply: % 151.13/22.37 | (11) op(e0, e0) = e1 % 151.13/22.37 | % 151.13/22.37 | REF_CLOSE: (1), (3), (4), (7), (11) are inconsistent by sub-proof #461. % 151.13/22.37 | % 151.13/22.37 End of proof % 151.13/22.37 % 151.13/22.37 Sub-proof #72 shows that the following formulas are inconsistent: % 151.13/22.37 ---------------------------------------------------------------- % 151.13/22.37 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.13/22.37 (2) all_58_31 = all_4_2 % 151.13/22.37 (3) ~ (all_52_8 = all_52_9) % 151.13/22.37 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.37 (5) all_54_13 = all_52_7 % 151.13/22.37 (6) ~ (all_52_2 = all_52_3) % 151.13/22.37 (7) all_58_11 = all_52_9 % 151.13/22.37 (8) all_56_15 = all_4_2 % 151.13/22.37 (9) all_56_7 = all_52_6 % 151.13/22.37 (10) ~ (all_52_6 = all_6_2) % 151.13/22.37 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.13/22.37 (12) all_54_2 = all_52_8 % 151.13/22.37 (13) all_54_8 = all_52_2 % 151.13/22.37 (14) op(e1, all_6_2) = all_58_18 % 151.13/22.37 (15) op(all_10_2, all_10_1) = e0 % 151.13/22.37 (16) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.13/22.37 (17) op(all_8_2, all_8_1) = all_8_0 % 151.13/22.37 (18) ~ (all_52_8 = all_10_2) % 151.13/22.37 (19) all_58_15 = all_52_2 % 151.13/22.37 (20) all_58_26 = all_52_11 % 151.13/22.37 (21) op(e1, all_52_14) = all_58_19 % 151.13/22.37 (22) ~ (all_52_8 = all_52_11) % 151.13/22.37 (23) ~ (all_52_11 = all_4_2) % 151.13/22.37 (24) all_54_7 = all_52_13 % 151.13/22.37 (25) all_58_6 = all_52_12 % 151.13/22.37 (26) ~ (all_52_6 = all_8_2) % 151.13/22.37 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 151.13/22.37 (28) all_56_4 = all_52_8 % 151.13/22.37 (29) ~ (all_52_4 = all_8_2) % 151.13/22.37 (30) all_54_3 = all_52_12 % 151.13/22.37 (31) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.37 (32) all_54_1 = all_52_4 % 151.13/22.37 (33) op(e0, all_4_2) = all_58_27 % 151.13/22.37 (34) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.37 (35) ~ (all_52_4 = all_52_6) % 151.13/22.37 (36) all_58_13 = all_52_13 % 151.13/22.37 (37) op(e0, e1) = all_52_11 % 151.13/22.37 (38) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 151.13/22.37 (39) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.13/22.37 (40) ~ (all_52_6 = all_52_7) % 151.13/22.37 (41) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.13/22.37 (42) all_54_11 = all_52_14 % 151.13/22.37 (43) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 151.13/22.37 (44) all_58_20 = all_52_14 % 151.13/22.37 (45) ~ (all_52_8 = all_6_2) % 151.13/22.37 (46) op(e2, e3) = all_52_1 % 151.13/22.37 (47) ~ (all_52_12 = all_52_13) % 151.13/22.37 (48) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 151.13/22.37 (49) all_54_10 = all_6_2 % 151.13/22.37 (50) op(e0, all_52_7) = all_58_23 % 151.13/22.37 (51) ~ (all_52_6 = all_52_14) % 151.13/22.37 (52) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.13/22.37 (53) all_54_6 = all_52_9 % 151.13/22.37 (54) all_54_15 = all_4_2 % 151.13/22.37 (55) ~ (all_52_4 = all_52_7) % 151.13/22.37 (56) ~ (all_52_2 = all_6_2) % 151.13/22.37 (57) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.13/22.37 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 151.13/22.37 (58) op(e3, e3) = all_10_2 % 151.13/22.37 (59) ~ (all_52_8 = all_52_12) % 151.13/22.37 (60) all_54_9 = all_52_6 % 151.13/22.37 (61) ~ (all_52_13 = all_4_2) % 151.13/22.37 (62) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 151.13/22.37 (63) ~ (all_52_13 = all_8_2) % 151.13/22.37 (64) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 151.13/22.37 (65) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 151.13/22.37 (66) ~ (e3 = e1) % 151.13/22.37 (67) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.13/22.37 (68) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.13/22.37 (69) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.37 (70) ~ (all_52_1 = all_52_13) % 151.13/22.37 (71) all_56_5 = all_52_9 % 151.13/22.37 (72) all_54_14 = all_52_11 % 151.13/22.37 (73) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 151.13/22.37 (74) all_56_12 = all_52_3 % 151.13/22.37 (75) ~ (all_52_3 = all_52_7) % 151.13/22.37 (76) all_58_2 = all_52_4 % 151.13/22.37 (77) all_20_2 = all_4_2 % 151.13/22.37 (78) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 151.13/22.37 (79) all_56_11 = all_52_14 % 151.13/22.37 (80) all_56_1 = all_52_4 % 151.13/22.37 (81) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.13/22.37 (82) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.13/22.37 (83) ~ (all_52_3 = all_4_2) % 151.13/22.37 (84) op(e1, e0) = all_52_14 % 151.13/22.37 (85) ~ (all_52_9 = all_52_11) % 151.13/22.37 (86) ~ (all_52_1 = all_8_2) % 151.13/22.37 (87) all_56_3 = all_8_2 % 151.13/22.37 (88) all_58_24 = all_52_7 % 151.13/22.37 (89) ~ (all_52_13 = all_52_14) % 151.13/22.37 (90) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.13/22.37 (91) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 151.13/22.37 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 151.13/22.37 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 151.13/22.37 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 151.13/22.37 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 151.13/22.37 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 151.13/22.37 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 151.13/22.37 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 151.13/22.37 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 151.13/22.37 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 151.13/22.37 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.13/22.37 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.13/22.37 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.13/22.37 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.13/22.37 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.13/22.37 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 151.13/22.37 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.13/22.37 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.13/22.37 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.13/22.37 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.13/22.37 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.13/22.37 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 151.13/22.37 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.13/22.37 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.13/22.37 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.13/22.37 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 151.13/22.37 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 151.13/22.37 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 151.13/22.37 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.13/22.37 e0) % 151.13/22.37 (92) ~ (all_52_4 = all_52_8) % 151.13/22.37 (93) op(e1, all_52_2) = all_58_14 % 151.13/22.37 (94) op(e2, e1) = all_52_9 % 151.13/22.37 (95) all_56_9 = all_52_12 % 151.13/22.37 (96) all_58_29 = all_8_2 % 151.13/22.37 (97) ~ (all_52_12 = all_52_14) % 151.13/22.37 (98) all_58_8 = all_52_1 % 151.13/22.37 (99) ~ (e2 = e1) % 151.13/22.37 (100) op(e3, e0) = all_52_12 % 151.13/22.37 (101) all_56_6 = all_52_2 % 151.13/22.37 (102) ~ (all_52_2 = all_52_6) % 151.13/22.37 (103) all_18_2 = all_6_2 % 151.13/22.37 (104) all_56_13 = all_52_7 % 151.13/22.37 (105) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.13/22.37 (106) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.13/22.37 (107) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.13/22.37 (108) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 151.13/22.37 (109) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 151.13/22.37 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 151.13/22.37 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 151.13/22.37 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 151.13/22.37 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 151.13/22.37 (all_58_27 = e0)) % 151.13/22.37 (110) ~ (all_52_9 = all_52_13) % 151.13/22.37 (111) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.13/22.37 (112) ~ (all_52_11 = all_6_2) % 151.13/22.37 (113) op(e3, all_10_2) = all_58_0 % 151.13/22.37 (114) ~ (e3 = e0) % 151.13/22.37 (115) all_56_2 = all_52_1 % 151.13/22.37 (116) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 151.13/22.37 (117) op(e3, all_52_12) = all_58_5 % 151.13/22.37 (118) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.13/22.37 (119) all_56_10 = all_52_13 % 151.13/22.37 (120) ~ (all_52_12 = all_10_2) % 151.13/22.37 (121) ~ (all_52_1 = all_52_3) % 151.13/22.37 (122) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.13/22.37 (123) ~ (all_52_9 = all_8_2) % 151.13/22.37 (124) all_56_14 = all_52_11 % 151.13/22.37 (125) all_58_28 = all_10_2 % 151.13/22.37 (126) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 151.13/22.37 (127) all_58_17 = all_52_6 % 151.13/22.37 (128) ~ (all_52_1 = all_52_9) % 151.13/22.37 (129) op(e3, e1) = all_52_8 % 151.13/22.37 (130) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.13/22.37 (131) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.13/22.37 (132) ~ (all_52_7 = all_52_11) % 151.13/22.37 (133) op(all_8_2, e2) = all_8_1 % 151.13/22.37 (134) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.13/22.37 (135) all_14_0 = all_8_0 % 151.13/22.37 (136) ~ (e2 = e0) % 151.13/22.37 (137) ~ (all_52_9 = all_6_2) % 151.13/22.37 (138) ~ (all_52_2 = all_10_2) % 151.13/22.37 (139) all_56_0 = all_10_2 % 151.13/22.37 (140) ~ (all_52_3 = all_52_11) % 151.13/22.37 (141) all_58_22 = all_52_3 % 151.13/22.37 (142) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 151.13/22.37 (143) ~ (all_52_12 = all_4_2) % 151.13/22.37 (144) ~ (all_52_3 = all_10_2) % 151.13/22.37 (145) all_56_8 = all_6_2 % 151.13/22.37 (146) op(e1, e1) = all_6_2 % 151.13/22.37 (147) ~ (all_52_1 = all_52_2) % 151.13/22.37 (148) ~ (all_52_7 = all_8_2) % 151.13/22.37 (149) op(e2, e0) = all_52_13 % 151.13/22.37 (150) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.13/22.37 (151) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.13/22.37 (152) all_58_4 = all_52_8 % 151.13/22.37 (153) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.37 (154) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 151.13/22.37 (155) all_54_0 = all_10_2 % 151.13/22.37 (156) ~ (all_52_2 = all_52_14) % 151.13/22.37 (157) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.13/22.37 (158) all_14_1 = all_8_1 % 151.13/22.37 (159) ~ (all_52_14 = all_4_2) % 151.13/22.37 (160) ~ (e1 = e0) % 151.13/22.37 (161) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 151.13/22.37 (162) ~ (all_52_7 = all_4_2) % 151.13/22.37 (163) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.37 (164) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 151.13/22.37 (165) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.13/22.37 (166) op(e0, e2) = all_52_7 % 151.13/22.37 (167) ~ (all_52_4 = all_10_2) % 151.13/22.37 (168) all_58_30 = all_6_2 % 151.13/22.37 (169) op(e2, all_52_1) = all_58_7 % 151.13/22.37 (170) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.37 (171) ~ (e3 = e2) % 151.13/22.37 (172) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 151.13/22.37 (173) ~ (all_52_14 = all_6_2) % 151.13/22.37 (174) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.13/22.37 (175) op(all_4_2, e0) = all_4_1 % 151.13/22.37 (176) op(all_10_2, e3) = all_10_1 % 151.13/22.37 (177) all_8_2 = e0 % 151.13/22.37 (178) ~ (all_52_4 = all_52_12) % 151.13/22.37 (179) all_54_12 = all_52_3 % 151.13/22.37 (180) op(e2, all_8_2) = all_58_9 % 151.13/22.37 (181) all_54_4 = all_52_1 % 151.13/22.37 (182) ~ (all_52_1 = all_10_2) % 151.13/22.37 % 151.13/22.37 Begin of proof % 151.13/22.37 | % 151.13/22.37 | COMBINE_EQS: (87), (177) imply: % 151.13/22.37 | (183) all_56_3 = e0 % 151.13/22.37 | % 151.13/22.37 | COMBINE_EQS: (96), (177) imply: % 151.13/22.37 | (184) all_58_29 = e0 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (86), (177) imply: % 151.13/22.37 | (185) ~ (all_52_1 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (29), (177) imply: % 151.13/22.37 | (186) ~ (all_52_4 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (26), (177) imply: % 151.13/22.37 | (187) ~ (all_52_6 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (148), (177) imply: % 151.13/22.37 | (188) ~ (all_52_7 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (123), (177) imply: % 151.13/22.37 | (189) ~ (all_52_9 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (63), (177) imply: % 151.13/22.37 | (190) ~ (all_52_13 = e0) % 151.13/22.37 | % 151.13/22.37 | REDUCE: (17), (177) imply: % 151.13/22.37 | (191) op(e0, all_8_1) = all_8_0 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (133), (177) imply: % 151.13/22.37 | (192) op(e0, e2) = all_8_1 % 151.13/22.37 | % 151.13/22.37 | REDUCE: (177), (180) imply: % 151.13/22.37 | (193) op(e2, e0) = all_58_9 % 151.13/22.37 | % 151.13/22.38 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 151.13/22.38 | (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), % 151.13/22.38 | (25), (27), (28), (30), (31), (32), (33), (34), (35), (36), (37), % 151.13/22.38 | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), % 151.13/22.38 | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), % 151.13/22.38 | (60), (61), (62), (64), (65), (66), (67), (68), (69), (70), (71), % 151.13/22.38 | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), % 151.13/22.38 | (83), (84), (85), (88), (89), (90), (91), (92), (93), (94), (95), % 151.13/22.38 | (96), (97), (98), (99), (100), (101), (102), (103), (104), (105), % 151.13/22.38 | (106), (107), (108), (109), (110), (111), (112), (113), (114), % 151.13/22.38 | (115), (116), (117), (118), (119), (120), (121), (122), (124), % 151.13/22.38 | (125), (126), (127), (128), (129), (130), (131), (132), (134), % 151.13/22.38 | (135), (136), (137), (138), (139), (140), (141), (142), (143), % 151.13/22.38 | (144), (145), (146), (147), (149), (150), (151), (152), (153), % 151.13/22.38 | (154), (155), (156), (157), (158), (159), (160), (161), (162), % 151.13/22.38 | (163), (164), (165), (166), (167), (168), (169), (170), (171), % 151.13/22.38 | (172), (173), (174), (175), (176), (178), (179), (181), (182), % 151.13/22.38 | (183), (184), (185), (186), (187), (188), (189), (190), (191), % 151.13/22.38 | (192), (193) are inconsistent by sub-proof #159. % 151.13/22.38 | % 151.13/22.38 End of proof % 151.13/22.38 % 151.13/22.38 Sub-proof #73 shows that the following formulas are inconsistent: % 151.13/22.38 ---------------------------------------------------------------- % 151.13/22.38 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.13/22.38 (2) all_58_31 = all_4_2 % 151.13/22.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.38 (4) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 151.13/22.38 (5) all_54_13 = all_52_7 % 151.13/22.38 (6) ~ (all_52_2 = all_52_3) % 151.13/22.38 (7) all_58_11 = all_52_9 % 151.13/22.38 (8) all_56_15 = all_4_2 % 151.13/22.38 (9) all_56_7 = all_52_6 % 151.13/22.38 (10) ~ (all_52_6 = all_6_2) % 151.13/22.38 (11) all_54_2 = all_52_8 % 151.13/22.38 (12) op(all_10_2, all_10_1) = e0 % 151.13/22.38 (13) ~ (all_52_8 = all_10_2) % 151.13/22.38 (14) all_58_15 = all_52_2 % 151.13/22.38 (15) all_58_26 = all_52_11 % 151.13/22.38 (16) ~ (all_52_8 = all_52_11) % 151.13/22.38 (17) ~ (all_52_11 = all_4_2) % 151.13/22.38 (18) all_58_6 = all_52_12 % 151.13/22.38 (19) ~ (all_52_6 = all_8_2) % 151.13/22.38 (20) all_56_4 = all_52_8 % 151.13/22.38 (21) ~ (all_52_4 = all_8_2) % 151.13/22.38 (22) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.38 (23) all_54_1 = all_52_4 % 151.13/22.38 (24) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.13/22.38 (25) ~ (all_52_4 = all_52_6) % 151.13/22.38 (26) all_58_13 = all_52_13 % 151.13/22.38 (27) op(e0, e1) = all_52_11 % 151.13/22.38 (28) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 151.13/22.38 (29) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.13/22.38 (30) ~ (all_52_6 = all_52_7) % 151.13/22.38 (31) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.13/22.38 (32) all_54_11 = all_52_14 % 151.13/22.38 (33) all_58_20 = all_52_14 % 151.13/22.38 (34) ~ (all_52_8 = all_6_2) % 151.13/22.38 (35) ~ (all_52_12 = all_52_13) % 151.13/22.38 (36) op(e0, all_52_3) = all_58_21 % 151.13/22.38 (37) all_54_5 = all_8_2 % 151.13/22.38 (38) ~ (all_52_6 = all_52_14) % 151.13/22.38 (39) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.13/22.38 (40) ~ (all_52_4 = all_52_7) % 151.13/22.38 (41) ~ (all_52_2 = all_6_2) % 151.13/22.38 (42) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.13/22.38 (43) ~ (all_52_8 = all_52_12) % 151.13/22.38 (44) all_54_9 = all_52_6 % 151.13/22.38 (45) ~ (all_52_13 = all_4_2) % 151.13/22.38 (46) ~ (all_52_13 = all_8_2) % 151.13/22.38 (47) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 151.13/22.38 (48) ~ (e3 = e1) % 151.13/22.38 (49) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.13/22.38 (50) ~ (all_52_1 = all_52_13) % 151.13/22.38 (51) all_56_5 = all_52_9 % 151.13/22.38 (52) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.13/22.38 (53) all_56_12 = all_52_3 % 151.13/22.38 (54) ~ (all_52_3 = all_52_7) % 151.13/22.38 (55) all_20_2 = all_4_2 % 151.13/22.38 (56) all_56_11 = all_52_14 % 151.13/22.38 (57) all_56_1 = all_52_4 % 151.13/22.38 (58) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.13/22.38 (59) ~ (all_52_3 = all_4_2) % 151.13/22.38 (60) ~ (all_52_9 = all_52_11) % 151.13/22.38 (61) all_56_3 = all_8_2 % 151.13/22.38 (62) all_58_24 = all_52_7 % 151.13/22.38 (63) ~ (all_52_13 = all_52_14) % 151.13/22.38 (64) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.13/22.38 (65) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 151.13/22.38 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 151.13/22.38 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 151.13/22.38 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 151.13/22.38 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 151.13/22.38 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 151.13/22.38 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 151.13/22.38 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 151.13/22.38 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 151.13/22.38 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 151.13/22.38 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.13/22.38 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.13/22.38 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.13/22.38 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.13/22.38 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.13/22.38 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 151.13/22.38 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.13/22.38 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.13/22.38 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.13/22.38 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.13/22.38 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.13/22.38 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 151.13/22.38 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.13/22.38 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.13/22.38 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.13/22.38 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 151.13/22.38 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 151.13/22.38 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 151.13/22.38 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.13/22.38 e0) % 151.13/22.38 (66) ~ (all_52_4 = all_52_8) % 151.13/22.38 (67) all_56_9 = all_52_12 % 151.13/22.38 (68) all_58_29 = all_8_2 % 151.13/22.38 (69) ~ (all_52_12 = all_52_14) % 151.13/22.38 (70) ~ (e2 = e1) % 151.13/22.38 (71) all_56_6 = all_52_2 % 151.13/22.38 (72) all_56_13 = all_52_7 % 151.13/22.38 (73) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.13/22.38 (74) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.13/22.38 (75) op(all_6_2, e1) = e0 % 151.13/22.38 (76) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 151.13/22.38 (77) ~ (all_52_9 = all_52_13) % 151.13/22.38 (78) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.13/22.38 (79) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.13/22.38 (80) ~ (all_52_11 = all_6_2) % 151.13/22.38 (81) ~ (e3 = e0) % 151.13/22.38 (82) all_56_2 = all_52_1 % 151.13/22.38 (83) op(e0, e3) = all_52_3 % 151.13/22.38 (84) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.13/22.38 (85) all_56_10 = all_52_13 % 151.13/22.38 (86) ~ (all_52_12 = all_10_2) % 151.13/22.38 (87) ~ (all_52_9 = all_8_2) % 151.13/22.38 (88) all_56_14 = all_52_11 % 151.13/22.38 (89) all_58_28 = all_10_2 % 151.13/22.38 (90) all_58_17 = all_52_6 % 151.13/22.38 (91) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.13/22.38 (92) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.13/22.38 (93) ~ (all_52_7 = all_52_11) % 151.13/22.38 (94) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.13/22.38 (95) ~ (e2 = e0) % 151.13/22.38 (96) ~ (all_4_2 = e0) % 151.13/22.38 (97) ~ (all_52_2 = all_10_2) % 151.13/22.38 (98) all_56_0 = all_10_2 % 151.13/22.38 (99) ~ (all_52_3 = all_52_11) % 151.13/22.38 (100) all_58_22 = all_52_3 % 151.13/22.38 (101) ~ (all_52_12 = all_4_2) % 151.13/22.38 (102) ~ (all_52_3 = all_10_2) % 151.13/22.38 (103) all_56_8 = all_6_2 % 151.13/22.38 (104) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.13/22.38 (105) ~ (all_52_7 = all_8_2) % 151.13/22.38 (106) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.13/22.38 (107) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.13/22.38 (108) all_58_4 = all_52_8 % 151.13/22.38 (109) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.38 (110) ~ (all_52_2 = all_52_14) % 151.13/22.38 (111) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.13/22.38 (112) ~ (all_52_14 = all_4_2) % 151.13/22.38 (113) ~ (e1 = e0) % 151.13/22.38 (114) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 151.13/22.38 (115) ~ (all_52_7 = all_4_2) % 151.13/22.38 (116) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.38 (117) ~ (all_4_2 = e1) % 151.13/22.38 (118) op(e0, e2) = all_52_7 % 151.13/22.38 (119) ~ (all_52_4 = all_10_2) % 151.13/22.38 (120) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.13/22.38 (121) all_58_30 = all_6_2 % 151.13/22.38 (122) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.38 (123) ~ (e3 = e2) % 151.13/22.38 (124) ~ (all_52_14 = all_6_2) % 151.13/22.38 (125) op(all_10_2, e3) = all_10_1 % 151.13/22.38 (126) ~ (all_8_2 = e0) % 151.13/22.38 (127) ~ (all_52_4 = all_52_12) % 151.13/22.38 (128) all_54_12 = all_52_3 % 151.13/22.38 (129) ~ (all_52_1 = all_10_2) % 151.13/22.38 % 151.13/22.38 Begin of proof % 151.13/22.38 | % 151.13/22.38 | BETA: splitting (42) gives: % 151.13/22.38 | % 151.13/22.38 | Case 1: % 151.13/22.38 | | % 151.13/22.38 | | (130) all_58_28 = e0 % 151.13/22.38 | | % 151.13/22.38 | | COMBINE_EQS: (89), (130) imply: % 151.13/22.38 | | (131) all_10_2 = e0 % 151.13/22.38 | | % 151.13/22.38 | | COMBINE_EQS: (98), (131) imply: % 151.13/22.38 | | (132) all_56_0 = e0 % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (129), (131) imply: % 151.13/22.38 | | (133) ~ (all_52_1 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (97), (131) imply: % 151.13/22.38 | | (134) ~ (all_52_2 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (102), (131) imply: % 151.13/22.38 | | (135) ~ (all_52_3 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (119), (131) imply: % 151.13/22.38 | | (136) ~ (all_52_4 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (13), (131) imply: % 151.13/22.38 | | (137) ~ (all_52_8 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (86), (131) imply: % 151.13/22.38 | | (138) ~ (all_52_12 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (12), (131) imply: % 151.13/22.38 | | (139) op(e0, all_10_1) = e0 % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (125), (131) imply: % 151.13/22.38 | | (140) op(e0, e3) = all_10_1 % 151.13/22.38 | | % 151.13/22.38 | | GROUND_INST: instantiating (3) with all_52_3, all_10_1, e3, e0, simplifying % 151.13/22.38 | | with (83), (140) gives: % 151.13/22.38 | | (141) all_52_3 = all_10_1 % 151.13/22.38 | | % 151.13/22.38 | | COMBINE_EQS: (128), (141) imply: % 151.13/22.38 | | (142) all_54_12 = all_10_1 % 151.13/22.38 | | % 151.13/22.38 | | COMBINE_EQS: (53), (141) imply: % 151.13/22.38 | | (143) all_56_12 = all_10_1 % 151.13/22.38 | | % 151.13/22.38 | | COMBINE_EQS: (100), (141) imply: % 151.13/22.38 | | (144) all_58_22 = all_10_1 % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (6), (141) imply: % 151.13/22.38 | | (145) ~ (all_52_2 = all_10_1) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (54), (141) imply: % 151.13/22.38 | | (146) ~ (all_52_7 = all_10_1) % 151.13/22.38 | | % 151.13/22.38 | | SIMP: (146) implies: % 151.13/22.38 | | (147) ~ (all_52_7 = all_10_1) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (99), (141) imply: % 151.13/22.38 | | (148) ~ (all_52_11 = all_10_1) % 151.13/22.38 | | % 151.13/22.38 | | SIMP: (148) implies: % 151.13/22.38 | | (149) ~ (all_52_11 = all_10_1) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (59), (141) imply: % 151.13/22.38 | | (150) ~ (all_10_1 = all_4_2) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (135), (141) imply: % 151.13/22.38 | | (151) ~ (all_10_1 = e0) % 151.13/22.38 | | % 151.13/22.38 | | REDUCE: (36), (141) imply: % 151.13/22.38 | | (152) op(e0, all_10_1) = all_58_21 % 151.13/22.38 | | % 151.13/22.38 | | GROUND_INST: instantiating (3) with e0, all_58_21, all_10_1, e0, simplifying % 151.13/22.38 | | with (139), (152) gives: % 151.13/22.38 | | (153) all_58_21 = e0 % 151.13/22.38 | | % 151.13/22.38 | | BETA: splitting (24) gives: % 151.13/22.38 | | % 151.13/22.38 | | Case 1: % 151.13/22.38 | | | % 151.13/22.38 | | | (154) all_56_2 = e0 % 151.13/22.38 | | | % 151.13/22.38 | | | COMBINE_EQS: (82), (154) imply: % 151.13/22.38 | | | (155) all_52_1 = e0 % 151.13/22.38 | | | % 151.13/22.38 | | | REDUCE: (133), (155) imply: % 151.13/22.38 | | | (156) $false % 151.13/22.38 | | | % 151.13/22.38 | | | CLOSE: (156) is inconsistent. % 151.13/22.38 | | | % 151.13/22.38 | | Case 2: % 151.13/22.38 | | | % 151.13/22.38 | | | (157) ~ (all_56_2 = e0) % 151.13/22.38 | | | (158) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.13/22.38 | | | % 151.13/22.38 | | | BETA: splitting (78) gives: % 151.13/22.38 | | | % 151.13/22.38 | | | Case 1: % 151.13/22.38 | | | | % 151.13/22.38 | | | | (159) all_56_1 = e0 % 151.13/22.38 | | | | % 151.13/22.38 | | | | COMBINE_EQS: (57), (159) imply: % 151.13/22.38 | | | | (160) all_52_4 = e0 % 151.13/22.38 | | | | % 151.13/22.38 | | | | REDUCE: (136), (160) imply: % 151.13/22.38 | | | | (161) $false % 151.13/22.38 | | | | % 151.13/22.38 | | | | CLOSE: (161) is inconsistent. % 151.13/22.38 | | | | % 151.13/22.38 | | | Case 2: % 151.13/22.38 | | | | % 151.13/22.38 | | | | (162) ~ (all_56_1 = e0) % 151.13/22.38 | | | | (163) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.13/22.38 | | | | % 151.13/22.38 | | | | BETA: splitting (106) gives: % 151.13/22.38 | | | | % 151.13/22.38 | | | | Case 1: % 151.13/22.38 | | | | | % 151.13/22.38 | | | | | (164) all_54_1 = e0 % 151.13/22.38 | | | | | % 151.13/22.38 | | | | | REF_CLOSE: (23), (136), (164) are inconsistent by sub-proof #798. % 151.13/22.38 | | | | | % 151.13/22.38 | | | | Case 2: % 151.13/22.38 | | | | | % 151.13/22.38 | | | | | (165) ~ (all_54_1 = e0) % 151.13/22.38 | | | | | (166) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.13/22.38 | | | | | % 151.13/22.38 | | | | | BETA: splitting (39) gives: % 151.13/22.38 | | | | | % 151.13/22.38 | | | | | Case 1: % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | (167) all_54_11 = e0 % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | COMBINE_EQS: (32), (167) imply: % 151.13/22.38 | | | | | | (168) all_52_14 = e0 % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | SIMP: (168) implies: % 151.13/22.38 | | | | | | (169) all_52_14 = e0 % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | REDUCE: (124), (169) imply: % 151.13/22.38 | | | | | | (170) ~ (all_6_2 = e0) % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | SIMP: (170) implies: % 151.13/22.38 | | | | | | (171) ~ (all_6_2 = e0) % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (14), (15), % 151.13/22.38 | | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), % 151.13/22.38 | | | | | | (25), (26), (27), (28), (29), (30), (31), (33), (34), % 151.13/22.38 | | | | | | (35), (37), (38), (40), (41), (43), (45), (46), (47), % 151.13/22.38 | | | | | | (48), (50), (51), (52), (56), (57), (58), (60), (61), % 151.13/22.38 | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (70), % 151.13/22.38 | | | | | | (71), (72), (73), (74), (76), (77), (79), (80), (81), % 151.13/22.38 | | | | | | (82), (84), (85), (87), (88), (90), (92), (93), (94), % 151.13/22.38 | | | | | | (95), (101), (103), (104), (105), (106), (107), (108), % 151.13/22.38 | | | | | | (109), (110), (112), (113), (114), (115), (116), (117), % 151.13/22.38 | | | | | | (118), (120), (121), (122), (123), (124), (127), (130), % 151.13/22.38 | | | | | | (132), (133), (136), (137), (138), (139), (140), (142), % 151.13/22.38 | | | | | | (143), (144), (145), (147), (149), (150), (151), (163), % 151.13/22.38 | | | | | | (171) are inconsistent by sub-proof #218. % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | Case 2: % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | (172) ~ (all_54_11 = e0) % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | REDUCE: (32), (172) imply: % 151.13/22.38 | | | | | | (173) ~ (all_52_14 = e0) % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | BETA: splitting (111) gives: % 151.13/22.38 | | | | | | % 151.13/22.38 | | | | | | Case 1: % 151.13/22.38 | | | | | | | % 151.13/22.38 | | | | | | | (174) all_56_6 = e0 % 151.13/22.38 | | | | | | | % 151.13/22.38 | | | | | | | COMBINE_EQS: (71), (174) imply: % 151.13/22.38 | | | | | | | (175) all_52_2 = e0 % 151.13/22.38 | | | | | | | % 151.13/22.38 | | | | | | | REDUCE: (134), (175) imply: % 151.13/22.38 | | | | | | | (176) $false % 151.13/22.38 | | | | | | | % 151.13/22.38 | | | | | | | CLOSE: (176) is inconsistent. % 151.13/22.38 | | | | | | | % 151.13/22.38 | | | | | | Case 2: % 151.13/22.38 | | | | | | | % 151.13/22.39 | | | | | | | (177) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.13/22.39 | | | | | | | % 151.13/22.39 | | | | | | | BETA: splitting (58) gives: % 151.13/22.39 | | | | | | | % 151.13/22.39 | | | | | | | Case 1: % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | (178) all_56_4 = e0 % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | COMBINE_EQS: (20), (178) imply: % 151.13/22.39 | | | | | | | | (179) all_52_8 = e0 % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | REDUCE: (137), (179) imply: % 151.13/22.39 | | | | | | | | (180) $false % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | CLOSE: (180) is inconsistent. % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | Case 2: % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | (181) ~ (all_56_4 = e0) % 151.13/22.39 | | | | | | | | (182) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | BETA: splitting (49) gives: % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | | Case 1: % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | (183) all_54_9 = e0 % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | COMBINE_EQS: (44), (183) imply: % 151.13/22.39 | | | | | | | | | (184) all_52_6 = e0 % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | SIMP: (184) implies: % 151.13/22.39 | | | | | | | | | (185) all_52_6 = e0 % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | REDUCE: (10), (185) imply: % 151.13/22.39 | | | | | | | | | (186) ~ (all_6_2 = e0) % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | SIMP: (186) implies: % 151.13/22.39 | | | | | | | | | (187) ~ (all_6_2 = e0) % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (14), % 151.13/22.39 | | | | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), % 151.13/22.39 | | | | | | | | | (23), (25), (26), (27), (28), (29), (30), (31), % 151.13/22.39 | | | | | | | | | (33), (34), (35), (37), (38), (40), (41), (43), % 151.13/22.39 | | | | | | | | | (45), (46), (47), (48), (50), (51), (52), (56), % 151.13/22.39 | | | | | | | | | (57), (60), (61), (62), (63), (64), (65), (66), % 151.13/22.39 | | | | | | | | | (67), (68), (69), (70), (71), (72), (73), (74), % 151.13/22.39 | | | | | | | | | (76), (77), (79), (80), (81), (82), (84), (85), % 151.13/22.39 | | | | | | | | | (87), (88), (90), (92), (93), (94), (95), (101), % 151.13/22.39 | | | | | | | | | (103), (104), (105), (107), (108), (109), (110), % 151.13/22.39 | | | | | | | | | (112), (113), (114), (115), (116), (117), (118), % 151.13/22.39 | | | | | | | | | (120), (121), (122), (123), (124), (127), (130), % 151.13/22.39 | | | | | | | | | (132), (137), (138), (139), (140), (142), (143), % 151.13/22.39 | | | | | | | | | (144), (145), (147), (149), (150), (151), (158), % 151.13/22.39 | | | | | | | | | (163), (166), (182), (187) are inconsistent by % 151.13/22.39 | | | | | | | | | sub-proof #219. % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | Case 2: % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | (188) ~ (all_54_9 = e0) % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | REDUCE: (44), (188) imply: % 151.13/22.39 | | | | | | | | | (189) ~ (all_52_6 = e0) % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | | REF_CLOSE: (2), (9), (22), (48), (55), (56), (68), (70), (81), % 151.13/22.39 | | | | | | | | | (91), (95), (103), (109), (113), (121), (122), % 151.13/22.39 | | | | | | | | | (123), (130), (173), (177), (189) are inconsistent % 151.13/22.39 | | | | | | | | | by sub-proof #74. % 151.13/22.39 | | | | | | | | | % 151.13/22.39 | | | | | | | | End of split % 151.13/22.39 | | | | | | | | % 151.13/22.39 | | | | | | | End of split % 151.13/22.39 | | | | | | | % 151.13/22.39 | | | | | | End of split % 151.13/22.39 | | | | | | % 151.13/22.39 | | | | | End of split % 151.13/22.39 | | | | | % 151.13/22.39 | | | | End of split % 151.13/22.39 | | | | % 151.13/22.39 | | | End of split % 151.13/22.39 | | | % 151.13/22.39 | | End of split % 151.13/22.39 | | % 151.13/22.39 | Case 2: % 151.13/22.39 | | % 151.13/22.39 | | (190) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.13/22.39 | | % 151.13/22.39 | | REF_CLOSE: (2), (3), (27), (68), (75), (80), (96), (121), (126), (190) are % 151.13/22.39 | | inconsistent by sub-proof #78. % 151.13/22.39 | | % 151.13/22.39 | End of split % 151.13/22.39 | % 151.13/22.39 End of proof % 151.13/22.39 % 151.13/22.39 Sub-proof #74 shows that the following formulas are inconsistent: % 151.13/22.39 ---------------------------------------------------------------- % 151.13/22.39 (1) all_58_31 = all_4_2 % 151.13/22.39 (2) all_58_28 = e0 % 151.13/22.39 (3) all_56_7 = all_52_6 % 151.13/22.39 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.39 (5) ~ (e3 = e1) % 151.13/22.39 (6) ~ (all_52_6 = e0) % 151.13/22.39 (7) all_20_2 = all_4_2 % 151.13/22.39 (8) all_56_11 = all_52_14 % 151.13/22.39 (9) all_58_29 = all_8_2 % 151.13/22.39 (10) ~ (e2 = e1) % 151.13/22.39 (11) ~ (e3 = e0) % 151.13/22.39 (12) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.13/22.39 (13) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.13/22.39 (14) ~ (e2 = e0) % 151.13/22.39 (15) all_56_8 = all_6_2 % 151.13/22.39 (16) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.39 (17) ~ (e1 = e0) % 151.13/22.39 (18) ~ (all_52_14 = e0) % 151.13/22.39 (19) all_58_30 = all_6_2 % 151.13/22.39 (20) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.39 (21) ~ (e3 = e2) % 151.13/22.39 % 151.13/22.39 Begin of proof % 151.13/22.39 | % 151.13/22.39 | BETA: splitting (12) gives: % 151.13/22.39 | % 151.13/22.39 | Case 1: % 151.13/22.39 | | % 151.13/22.39 | | (22) all_56_7 = e0 % 151.13/22.39 | | % 151.13/22.39 | | REF_CLOSE: (3), (6), (22) are inconsistent by sub-proof #803. % 151.13/22.39 | | % 151.13/22.39 | Case 2: % 151.13/22.39 | | % 151.13/22.39 | | (23) all_56_8 = e0 | all_56_11 = e0 % 151.13/22.39 | | % 151.13/22.39 | | BETA: splitting (23) gives: % 151.13/22.39 | | % 151.13/22.39 | | Case 1: % 151.13/22.39 | | | % 151.13/22.39 | | | (24) all_56_8 = e0 % 151.13/22.39 | | | % 151.13/22.39 | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (13), (14), (15), % 151.13/22.39 | | | (16), (17), (19), (20), (21), (24) are inconsistent by % 151.13/22.39 | | | sub-proof #75. % 151.13/22.39 | | | % 151.13/22.39 | | Case 2: % 151.13/22.39 | | | % 151.13/22.39 | | | (25) all_56_11 = e0 % 151.13/22.39 | | | % 151.13/22.39 | | | REF_CLOSE: (8), (18), (25) are inconsistent by sub-proof #220. % 151.13/22.39 | | | % 151.13/22.39 | | End of split % 151.13/22.39 | | % 151.13/22.39 | End of split % 151.13/22.39 | % 151.13/22.39 End of proof % 151.13/22.39 % 151.13/22.39 Sub-proof #75 shows that the following formulas are inconsistent: % 151.13/22.39 ---------------------------------------------------------------- % 151.13/22.39 (1) all_58_31 = all_4_2 % 151.13/22.39 (2) all_58_28 = e0 % 151.13/22.39 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.39 (4) ~ (e3 = e1) % 151.13/22.39 (5) all_56_8 = e0 % 151.13/22.39 (6) all_20_2 = all_4_2 % 151.13/22.39 (7) all_58_29 = all_8_2 % 151.13/22.39 (8) ~ (e2 = e1) % 151.13/22.39 (9) ~ (e3 = e0) % 151.13/22.39 (10) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.13/22.39 (11) ~ (e2 = e0) % 151.13/22.39 (12) all_56_8 = all_6_2 % 151.13/22.39 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.39 (14) ~ (e1 = e0) % 151.13/22.39 (15) all_58_30 = all_6_2 % 151.13/22.39 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.39 (17) ~ (e3 = e2) % 151.13/22.39 % 151.13/22.39 Begin of proof % 151.13/22.39 | % 151.13/22.39 | COMBINE_EQS: (5), (12) imply: % 151.13/22.39 | (18) all_6_2 = e0 % 151.13/22.39 | % 151.13/22.39 | SIMP: (18) implies: % 151.13/22.39 | (19) all_6_2 = e0 % 151.13/22.39 | % 151.13/22.39 | COMBINE_EQS: (15), (19) imply: % 151.13/22.39 | (20) all_58_30 = e0 % 151.13/22.39 | % 151.13/22.39 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), % 151.13/22.39 | (16), (17), (20) are inconsistent by sub-proof #679. % 151.13/22.39 | % 151.13/22.39 End of proof % 151.13/22.39 % 151.13/22.39 Sub-proof #76 shows that the following formulas are inconsistent: % 151.13/22.39 ---------------------------------------------------------------- % 151.13/22.39 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.13/22.39 (2) all_58_31 = all_4_2 % 151.13/22.39 (3) ~ (all_52_8 = all_52_9) % 151.13/22.39 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.13/22.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.13/22.39 (5) all_46_2 = all_6_2 % 151.13/22.39 (6) all_54_13 = all_52_7 % 151.13/22.39 (7) ~ (all_52_2 = all_52_3) % 151.13/22.39 (8) all_56_15 = all_4_2 % 151.13/22.39 (9) all_32_0 = all_10_0 % 151.13/22.39 (10) all_56_7 = all_52_6 % 151.13/22.39 (11) ~ (all_52_6 = all_6_2) % 151.13/22.39 (12) all_54_2 = all_52_8 % 151.13/22.39 (13) all_46_1 = all_6_1 % 151.13/22.39 (14) all_54_8 = all_52_2 % 151.13/22.39 (15) op(e1, all_6_2) = all_58_18 % 151.13/22.39 (16) op(e3, all_52_4) = all_58_1 % 151.13/22.39 (17) all_46_0 = all_6_0 % 151.13/22.39 (18) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.13/22.39 (19) op(all_8_2, all_8_1) = all_8_0 % 151.13/22.39 (20) ~ (all_52_8 = all_10_2) % 151.13/22.39 (21) ~ (all_52_8 = all_52_11) % 151.13/22.39 (22) ~ (all_52_11 = all_4_2) % 151.13/22.39 (23) all_54_7 = all_52_13 % 151.13/22.39 (24) ~ (all_52_6 = all_8_2) % 151.13/22.39 (25) all_56_4 = all_52_8 % 151.13/22.39 (26) ~ (all_52_4 = all_8_2) % 151.13/22.39 (27) all_32_2 = all_10_2 % 151.13/22.39 (28) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.39 (29) all_54_1 = all_52_4 % 151.13/22.39 (30) op(e0, all_4_2) = all_58_27 % 151.13/22.39 (31) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.13/22.39 (32) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.13/22.39 (33) ~ (all_52_4 = all_52_6) % 151.13/22.39 (34) op(e2, e2) = all_8_2 % 151.13/22.39 (35) op(e0, e1) = all_52_11 % 151.13/22.39 (36) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 151.13/22.39 (37) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.13/22.39 (38) ~ (all_52_6 = all_52_7) % 151.13/22.39 (39) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.13/22.39 (40) op(all_10_2, all_10_1) = all_10_0 % 151.13/22.39 (41) all_54_11 = all_52_14 % 151.13/22.39 (42) op(e3, e2) = all_52_4 % 151.13/22.39 (43) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 151.13/22.39 (44) ~ (all_52_8 = all_6_2) % 151.13/22.39 (45) op(e2, e3) = all_52_1 % 151.13/22.39 (46) ~ (all_52_12 = all_52_13) % 151.13/22.39 (47) ~ (all_36_0 = e3) | ~ (all_36_1 = e0) | ~ (all_36_2 = e2) % 151.13/22.39 (48) ~ (all_52_6 = all_52_14) % 151.13/22.39 (49) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 151.13/22.39 (50) all_36_2 = all_6_2 % 151.13/22.39 (51) all_54_6 = all_52_9 % 151.13/22.39 (52) ~ (all_52_4 = all_52_7) % 151.13/22.39 (53) ~ (all_10_2 = e0) % 151.13/22.39 (54) ~ (all_52_2 = all_6_2) % 151.13/22.39 (55) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.13/22.39 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 151.13/22.39 (56) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.13/22.39 (57) op(e3, e3) = all_10_2 % 151.13/22.39 (58) op(e3, all_52_8) = all_58_3 % 151.13/22.39 (59) ~ (all_52_8 = all_52_12) % 151.13/22.39 (60) all_54_9 = all_52_6 % 151.13/22.39 (61) ~ (all_52_13 = all_4_2) % 151.13/22.39 (62) op(e1, e2) = all_52_6 % 151.13/22.39 (63) ~ (all_52_13 = all_8_2) % 151.13/22.39 (64) op(e1, all_52_6) = all_58_16 % 151.13/22.39 (65) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 151.13/22.39 (66) ~ (e3 = e1) % 151.13/22.39 (67) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.13/22.39 (68) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.13/22.39 (69) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.13/22.39 (70) ~ (all_4_0 = e1) % 151.13/22.39 (71) ~ (all_52_1 = all_52_13) % 151.13/22.39 (72) all_56_5 = all_52_9 % 151.13/22.39 (73) all_56_12 = all_52_3 % 151.13/22.39 (74) ~ (all_52_3 = all_52_7) % 151.13/22.39 (75) all_56_11 = all_52_14 % 151.13/22.39 (76) all_56_1 = all_52_4 % 151.13/22.39 (77) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.13/22.39 (78) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.13/22.39 (79) ~ (all_52_3 = all_4_2) % 151.13/22.39 (80) op(e1, e3) = all_52_2 % 151.13/22.39 (81) ~ (all_6_0 = e2) | ~ (all_6_2 = e3) % 151.13/22.39 (82) op(e1, e0) = all_52_14 % 151.13/22.39 (83) ~ (all_52_9 = all_52_11) % 151.13/22.39 (84) ~ (all_52_1 = all_8_2) % 151.13/22.39 (85) all_56_3 = all_8_2 % 151.13/22.39 (86) ~ (all_52_13 = all_52_14) % 151.13/22.39 (87) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.13/22.39 (88) ~ (all_52_4 = all_52_8) % 151.13/22.39 (89) op(e1, all_52_2) = all_58_14 % 151.13/22.39 (90) op(e2, e1) = all_52_9 % 151.13/22.39 (91) all_56_9 = all_52_12 % 151.13/22.39 (92) all_58_29 = all_8_2 % 151.13/22.39 (93) ~ (all_52_12 = all_52_14) % 151.13/22.39 (94) ~ (e2 = e1) % 151.13/22.39 (95) op(e3, e0) = all_52_12 % 151.13/22.39 (96) all_56_6 = all_52_2 % 151.13/22.39 (97) ~ (all_52_2 = all_52_6) % 151.13/22.39 (98) all_36_0 = all_6_0 % 151.13/22.39 (99) all_56_13 = all_52_7 % 151.13/22.39 (100) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.13/22.39 (101) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.13/22.39 (102) op(all_6_2, all_6_1) = all_6_0 % 151.13/22.39 (103) op(all_6_2, e1) = e0 % 151.13/22.39 (104) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 151.13/22.39 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 151.13/22.39 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 151.13/22.39 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 151.13/22.39 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 151.13/22.39 (all_58_27 = e0)) % 151.13/22.39 (105) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.13/22.39 (106) op(all_6_2, e1) = all_6_1 % 151.13/22.39 (107) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.13/22.39 (108) op(e2, all_52_9) = all_58_10 % 151.13/22.39 (109) ~ (all_52_11 = all_6_2) % 151.13/22.39 (110) op(e3, all_10_2) = all_58_0 % 151.13/22.39 (111) ~ (e3 = e0) % 151.13/22.39 (112) ~ (all_40_0 = e0) | ~ (all_40_1 = e3) | ~ (all_40_2 = e2) % 151.13/22.39 (113) all_56_2 = all_52_1 % 151.13/22.39 (114) ~ (all_32_0 = e1) | ~ (all_32_1 = e0) | ~ (all_32_2 = e2) % 151.13/22.39 (115) ~ (all_46_0 = e0) | ~ (all_46_1 = e2) | ~ (all_46_2 = e3) % 151.13/22.39 (116) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.13/22.39 (117) all_56_10 = all_52_13 % 151.13/22.39 (118) ~ (all_52_12 = all_10_2) % 151.13/22.39 (119) ~ (all_52_1 = all_52_3) % 151.13/22.39 (120) all_32_1 = all_10_1 % 151.13/22.39 (121) ~ (all_52_9 = all_8_2) % 151.13/22.39 (122) all_56_14 = all_52_11 % 151.13/22.39 (123) all_58_28 = all_10_2 % 151.13/22.39 (124) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 151.13/22.39 (125) ~ (all_52_1 = all_52_9) % 151.13/22.39 (126) all_40_0 = all_6_0 % 151.13/22.39 (127) op(e3, e1) = all_52_8 % 151.13/22.39 (128) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.13/22.39 (129) op(all_8_2, e2) = all_8_1 % 151.13/22.39 (130) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.13/22.39 (131) ~ (e2 = e0) % 151.13/22.39 (132) ~ (all_52_9 = all_6_2) % 151.13/22.39 (133) ~ (all_52_2 = all_10_2) % 151.13/22.39 (134) all_56_0 = all_10_2 % 151.13/22.39 (135) op(e0, e0) = all_4_2 % 151.13/22.39 (136) op(all_6_2, e0) = all_6_0 % 151.13/22.39 (137) ~ (all_52_3 = all_52_11) % 151.13/22.39 (138) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 151.13/22.39 (139) ~ (all_52_3 = all_10_2) % 151.13/22.39 (140) all_56_8 = all_6_2 % 151.13/22.39 (141) op(e1, e1) = all_6_2 % 151.13/22.39 (142) ~ (all_52_1 = all_52_2) % 151.13/22.39 (143) ~ (all_52_7 = all_8_2) % 151.13/22.39 (144) op(all_4_2, all_4_1) = all_4_0 % 151.13/22.39 (145) op(e2, e0) = all_52_13 % 151.13/22.39 (146) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.13/22.39 (147) ~ (all_8_1 = e0) % 151.13/22.39 (148) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.13/22.39 (149) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 151.13/22.39 (150) all_54_0 = all_10_2 % 151.13/22.39 (151) ~ (all_52_2 = all_52_14) % 151.13/22.39 (152) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.13/22.39 (153) ~ (all_52_14 = all_4_2) % 151.13/22.39 (154) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 151.13/22.39 (155) ~ (all_52_7 = all_4_2) % 151.13/22.39 (156) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.13/22.39 (157) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 151.13/22.39 (158) ~ (all_4_2 = e1) % 151.13/22.39 (159) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.13/22.39 (160) ~ (all_52_4 = all_10_2) % 151.13/22.39 (161) all_58_30 = all_6_2 % 151.13/22.39 (162) op(e2, all_52_1) = all_58_7 % 151.13/22.39 (163) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.39 (164) ~ (e3 = e2) % 151.13/22.39 (165) ~ (all_52_14 = all_6_2) % 151.13/22.39 (166) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.13/22.39 (167) op(all_4_2, e0) = all_4_1 % 151.13/22.39 (168) op(all_10_2, e3) = all_10_1 % 151.13/22.39 (169) ~ (all_8_2 = e0) % 151.13/22.39 (170) ~ (all_52_4 = all_52_12) % 151.13/22.39 (171) all_54_12 = all_52_3 % 151.13/22.39 (172) op(e2, all_8_2) = all_58_9 % 151.13/22.39 (173) all_54_4 = all_52_1 % 151.13/22.39 (174) all_36_1 = e0 % 151.13/22.39 (175) ~ (all_52_1 = all_10_2) % 151.13/22.39 % 151.13/22.39 Begin of proof % 151.13/22.39 | % 151.13/22.39 | BETA: splitting (114) gives: % 151.13/22.39 | % 151.13/22.39 | Case 1: % 151.13/22.39 | | % 151.13/22.39 | | (176) ~ (all_32_1 = e0) % 151.13/22.39 | | % 151.13/22.39 | | REDUCE: (120), (176) imply: % 151.13/22.39 | | (177) ~ (all_10_1 = e0) % 151.13/22.39 | | % 151.13/22.39 | | BETA: splitting (47) gives: % 151.13/22.39 | | % 151.13/22.39 | | Case 1: % 151.13/22.39 | | | % 151.13/22.39 | | | (178) ~ (all_36_1 = e0) % 151.13/22.39 | | | % 151.13/22.39 | | | REDUCE: (174), (178) imply: % 151.13/22.39 | | | (179) $false % 151.13/22.39 | | | % 151.13/22.39 | | | CLOSE: (179) is inconsistent. % 151.13/22.39 | | | % 151.13/22.39 | | Case 2: % 151.13/22.39 | | | % 151.13/22.39 | | | (180) ~ (all_36_0 = e3) | ~ (all_36_2 = e2) % 151.13/22.39 | | | % 151.13/22.39 | | | BETA: splitting (55) gives: % 151.13/22.39 | | | % 151.13/22.39 | | | Case 1: % 151.13/22.39 | | | | % 151.13/22.39 | | | | (181) all_56_15 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | COMBINE_EQS: (8), (181) imply: % 151.13/22.40 | | | | (182) all_4_2 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | SIMP: (182) implies: % 151.13/22.40 | | | | (183) all_4_2 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | COMBINE_EQS: (2), (183) imply: % 151.13/22.40 | | | | (184) all_58_31 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (79), (183) imply: % 151.13/22.40 | | | | (185) ~ (all_52_3 = e0) % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (155), (183) imply: % 151.13/22.40 | | | | (186) ~ (all_52_7 = e0) % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (22), (183) imply: % 151.13/22.40 | | | | (187) ~ (all_52_11 = e0) % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (61), (183) imply: % 151.13/22.40 | | | | (188) ~ (all_52_13 = e0) % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (144), (183) imply: % 151.13/22.40 | | | | (189) op(e0, all_4_1) = all_4_0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (167), (183) imply: % 151.13/22.40 | | | | (190) op(e0, e0) = all_4_1 % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (30), (183) imply: % 151.13/22.40 | | | | (191) op(e0, e0) = all_58_27 % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (135), (183) imply: % 151.13/22.40 | | | | (192) op(e0, e0) = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 151.13/22.40 | | | | simplifying with (190), (191) gives: % 151.13/22.40 | | | | (193) all_58_27 = all_4_1 % 151.13/22.40 | | | | % 151.13/22.40 | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, simplifying % 151.13/22.40 | | | | with (191), (192) gives: % 151.13/22.40 | | | | (194) all_58_27 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | COMBINE_EQS: (193), (194) imply: % 151.13/22.40 | | | | (195) all_4_1 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | SIMP: (195) implies: % 151.13/22.40 | | | | (196) all_4_1 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (189), (196) imply: % 151.13/22.40 | | | | (197) op(e0, e0) = all_4_0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, simplifying % 151.13/22.40 | | | | with (192), (197) gives: % 151.13/22.40 | | | | (198) all_4_0 = e0 % 151.13/22.40 | | | | % 151.13/22.40 | | | | REDUCE: (70), (198) imply: % 151.13/22.40 | | | | (199) ~ (e1 = e0) % 151.13/22.40 | | | | % 151.13/22.40 | | | | SIMP: (199) implies: % 151.13/22.40 | | | | (200) ~ (e1 = e0) % 151.13/22.40 | | | | % 151.13/22.40 | | | | BETA: splitting (31) gives: % 151.13/22.40 | | | | % 151.13/22.40 | | | | Case 1: % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | (201) all_56_2 = e0 % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | COMBINE_EQS: (113), (201) imply: % 151.13/22.40 | | | | | (202) all_52_1 = e0 % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | REDUCE: (119), (202) imply: % 151.13/22.40 | | | | | (203) ~ (all_52_3 = e0) % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | REDUCE: (125), (202) imply: % 151.13/22.40 | | | | | (204) ~ (all_52_9 = e0) % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | SIMP: (204) implies: % 151.13/22.40 | | | | | (205) ~ (all_52_9 = e0) % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | REDUCE: (71), (202) imply: % 151.13/22.40 | | | | | (206) ~ (all_52_13 = e0) % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (14), (15), (16), % 151.13/22.40 | | | | | (18), (20), (24), (25), (26), (28), (29), (32), (35), (38), % 151.13/22.40 | | | | | (39), (40), (42), (44), (46), (51), (52), (54), (56), (58), % 151.13/22.40 | | | | | (59), (61), (62), (63), (66), (68), (72), (73), (75), (76), % 151.13/22.40 | | | | | (77), (78), (80), (81), (85), (86), (88), (89), (90), (91), % 151.13/22.40 | | | | | (92), (93), (94), (95), (96), (97), (99), (100), (103), % 151.13/22.40 | | | | | (104), (105), (106), (107), (108), (109), (111), (117), % 151.13/22.40 | | | | | (121), (122), (123), (128), (129), (131), (132), (133), % 151.13/22.40 | | | | | (134), (136), (139), (140), (141), (143), (146), (147), % 151.13/22.40 | | | | | (148), (151), (157), (158), (159), (160), (161), (163), % 151.13/22.40 | | | | | (164), (165), (168), (181), (184), (185), (186), (187), % 151.13/22.40 | | | | | (188), (194), (200), (201), (205) are inconsistent by % 151.13/22.40 | | | | | sub-proof #80. % 151.13/22.40 | | | | | % 151.13/22.40 | | | | Case 2: % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | (207) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | BETA: splitting (138) gives: % 151.13/22.40 | | | | | % 151.13/22.40 | | | | | Case 1: % 151.13/22.40 | | | | | | % 151.13/22.40 | | | | | | (208) all_56_0 = e0 % 151.13/22.40 | | | | | | % 151.13/22.40 | | | | | | REF_CLOSE: (53), (134), (208) are inconsistent by sub-proof #799. % 151.13/22.40 | | | | | | % 151.13/22.40 | | | | | Case 2: % 151.13/22.40 | | | | | | % 151.13/22.40 | | | | | | (209) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 151.13/22.40 | | | | | | % 151.13/22.40 | | | | | | BETA: splitting (207) gives: % 151.13/22.40 | | | | | | % 151.13/22.40 | | | | | | Case 1: % 151.13/22.40 | | | | | | | % 151.13/22.40 | | | | | | | (210) all_56_3 = e0 % 151.13/22.40 | | | | | | | % 151.13/22.40 | | | | | | | REF_CLOSE: (28), (66), (85), (92), (94), (111), (131), (148), % 151.13/22.40 | | | | | | | (161), (163), (164), (184), (200), (210) are % 151.13/22.40 | | | | | | | inconsistent by sub-proof #804. % 151.13/22.40 | | | | | | | % 151.13/22.40 | | | | | | Case 2: % 151.13/22.40 | | | | | | | % 151.13/22.40 | | | | | | | (211) all_56_5 = e0 | all_56_10 = e0 % 151.13/22.40 | | | | | | | % 151.13/22.40 | | | | | | | BETA: splitting (211) gives: % 151.13/22.40 | | | | | | | % 151.13/22.40 | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | (212) all_56_5 = e0 % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | COMBINE_EQS: (72), (212) imply: % 151.13/22.40 | | | | | | | | (213) all_52_9 = e0 % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | SIMP: (213) implies: % 151.13/22.40 | | | | | | | | (214) all_52_9 = e0 % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | REDUCE: (125), (214) imply: % 151.13/22.40 | | | | | | | | (215) ~ (all_52_1 = e0) % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | REDUCE: (108), (214) imply: % 151.13/22.40 | | | | | | | | (216) op(e2, e0) = all_58_10 % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | BETA: splitting (209) gives: % 151.13/22.40 | | | | | | | | % 151.13/22.40 | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | (217) all_56_2 = e0 % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | COMBINE_EQS: (113), (217) imply: % 151.13/22.40 | | | | | | | | | (218) all_52_1 = e0 % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | REDUCE: (215), (218) imply: % 151.13/22.40 | | | | | | | | | (219) $false % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | CLOSE: (219) is inconsistent. % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | (220) all_56_6 = e0 | all_56_12 = e0 % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | BETA: splitting (220) gives: % 151.13/22.40 | | | | | | | | | % 151.13/22.40 | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | (221) all_56_6 = e0 % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | COMBINE_EQS: (96), (221) imply: % 151.13/22.40 | | | | | | | | | | (222) all_52_2 = e0 % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | SIMP: (222) implies: % 151.13/22.40 | | | | | | | | | | (223) all_52_2 = e0 % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | REDUCE: (97), (223) imply: % 151.13/22.40 | | | | | | | | | | (224) ~ (all_52_6 = e0) % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | SIMP: (224) implies: % 151.13/22.40 | | | | | | | | | | (225) ~ (all_52_6 = e0) % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | REDUCE: (80), (223) imply: % 151.13/22.40 | | | | | | | | | | (226) op(e1, e3) = e0 % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | BETA: splitting (105) gives: % 151.13/22.40 | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | (227) all_56_1 = e0 % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | COMBINE_EQS: (76), (227) imply: % 151.13/22.40 | | | | | | | | | | | (228) all_52_4 = e0 % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | SIMP: (228) implies: % 151.13/22.40 | | | | | | | | | | | (229) all_52_4 = e0 % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | REDUCE: (88), (229) imply: % 151.13/22.40 | | | | | | | | | | | (230) ~ (all_52_8 = e0) % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | SIMP: (230) implies: % 151.13/22.40 | | | | | | | | | | | (231) ~ (all_52_8 = e0) % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | REDUCE: (170), (229) imply: % 151.13/22.40 | | | | | | | | | | | (232) ~ (all_52_12 = e0) % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | SIMP: (232) implies: % 151.13/22.40 | | | | | | | | | | | (233) ~ (all_52_12 = e0) % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | REDUCE: (160), (229) imply: % 151.13/22.40 | | | | | | | | | | | (234) ~ (all_10_2 = e0) % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | REDUCE: (26), (229) imply: % 151.13/22.40 | | | | | | | | | | | (235) ~ (all_8_2 = e0) % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | REDUCE: (42), (229) imply: % 151.13/22.40 | | | | | | | | | | | (236) op(e3, e2) = e0 % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, all_58_10, e0, % 151.13/22.40 | | | | | | | | | | | e2, simplifying with (145), (216) gives: % 151.13/22.40 | | | | | | | | | | | (237) all_58_10 = all_52_13 % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | BETA: splitting (69) gives: % 151.13/22.40 | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | (238) all_54_0 = e0 % 151.13/22.40 | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | REF_CLOSE: (53), (150), (238) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | #861. % 151.13/22.40 | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | (239) ~ (all_54_0 = e0) % 151.13/22.40 | | | | | | | | | | | | (240) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 151.13/22.40 | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | BETA: splitting (156) gives: % 151.13/22.40 | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | (241) all_54_2 = e0 % 151.13/22.40 | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | REF_CLOSE: (12), (231), (241) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | #860. % 151.13/22.40 | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | (242) ~ (all_54_2 = e0) % 151.13/22.40 | | | | | | | | | | | | | (243) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | BETA: splitting (101) gives: % 151.13/22.40 | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | (244) all_54_4 = e0 % 151.13/22.40 | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | REF_CLOSE: (173), (215), (244) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | #859. % 151.13/22.40 | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | (245) ~ (all_54_4 = e0) % 151.13/22.40 | | | | | | | | | | | | | | (246) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 151.13/22.40 | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | BETA: splitting (67) gives: % 151.13/22.40 | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | (247) all_54_9 = e0 % 151.13/22.40 | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | REF_CLOSE: (60), (225), (247) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | #572. % 151.13/22.40 | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | (248) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 151.13/22.40 | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | (249) all_56_9 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (249) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | (250) all_52_12 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | REDUCE: (46), (250) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | (251) ~ (all_52_13 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | SIMP: (251) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | (252) ~ (all_52_13 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | REDUCE: (93), (250) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | (253) ~ (all_52_14 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | SIMP: (253) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | (254) ~ (all_52_14 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | REDUCE: (118), (250) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | (255) ~ (all_10_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | SIMP: (255) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | (256) ~ (all_10_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | BETA: splitting (68) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | (257) all_56_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (257) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | (258) all_52_1 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | SIMP: (258) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | (259) all_52_1 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | REDUCE: (84), (259) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | (260) ~ (all_8_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | SIMP: (260) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | (261) ~ (all_8_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | (262) all_58_28 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (256), (262) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | | | | #858. % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | (263) ~ (all_58_28 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | (264) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (265) all_58_29 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (261), (265) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | | | | | #809. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (266) all_58_30 = e1 | all_58_31 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (267) all_58_30 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (267) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (268) all_6_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (12), (15), (20), (25), (28), (34), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (44), (57), (92), (104), (110), (123), (124), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (129), (134), (141), (147), (148), (150), (154), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (161), (172), (184), (194), (231), (236), (240), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (243), (256), (267), (268) are inconsistent by % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | sub-proof #812. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (269) all_58_31 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (35), (53), (56), (92), (103), (109), (123), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (161), (169), (200), (269) are inconsistent by % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | sub-proof #81. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | (270) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | (271) all_56_3 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (271) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | (272) all_8_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | SIMP: (272) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | (273) all_8_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (273) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | (274) all_58_29 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | REDUCE: (24), (273) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | (275) ~ (all_52_6 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (276) all_56_6 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (66), (94), (111), (131), (148), (161), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (163), (164), (184), (200), (221), (274), (276) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #843. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (277) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (278) all_56_7 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (278) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (279) all_52_6 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (279) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (280) $false % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (281) all_56_8 = e1 | all_56_11 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (282) all_56_8 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (282) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (283) all_6_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (283) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (284) all_58_30 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (12), (15), (20), (25), (28), (34), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (44), (57), (92), (104), (110), (123), (124), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (129), (134), (141), (147), (148), (150), (154), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (161), (172), (184), (194), (231), (236), (240), % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (243), (256), (283), (284) are inconsistent by % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | sub-proof #812. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (285) all_56_11 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (254), (285) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | #580. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | (286) all_56_5 = e1 | all_56_10 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (200), (212), (252), (286) are inconsistent % 151.13/22.40 | | | | | | | | | | | | | | | | | | by sub-proof #194. % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | End of split % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | (287) ~ (all_56_9 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | REDUCE: (91), (287) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | (288) ~ (all_52_12 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | (289) all_56_0 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (289) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | (290) all_10_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | REDUCE: (168), (290) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | (291) op(e1, e3) = all_10_1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (177), (226), (291) are inconsistent by % 151.13/22.40 | | | | | | | | | | | | | | | | | sub-proof #810. % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | (292) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | (293) all_56_1 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (293) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | (294) e1 = e0 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | REDUCE: (200), (294) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | (295) $false % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | (296) all_56_4 = e1 | all_56_9 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (297) all_56_4 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (297) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (298) all_52_8 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (299) all_52_8 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REDUCE: (21), (299) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (300) ~ (all_52_11 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (301) ~ (all_52_11 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REDUCE: (20), (299) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (302) ~ (all_10_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | SIMP: (302) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (303) ~ (all_10_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (299) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (304) ~ (all_6_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | SIMP: (304) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (305) ~ (all_6_2 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REDUCE: (58), (299) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (306) op(e3, e1) = all_58_3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | REDUCE: (127), (299) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | (307) op(e3, e1) = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (308) all_58_28 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (308) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (309) all_10_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (309) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (310) $false % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | CLOSE: (310) is inconsistent. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | (311) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (312) all_58_29 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (312) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (313) all_8_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | SIMP: (313) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (314) all_8_2 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (314) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (315) all_56_3 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (314) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (316) ~ (all_52_6 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (314) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_52_7 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (314) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (318) op(e1, all_8_1) = all_8_0 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (314) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | (319) op(e1, e2) = all_8_1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (320) all_56_12 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (320) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (321) all_52_3 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (322) all_52_3 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (322) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (323) ~ (all_52_1 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_6, all_8_1, e2, e1, % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | simplifying with (62), (319) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (324) all_52_6 = all_8_1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_58_3, e1, e3, % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | simplifying with (306), (307) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (325) all_58_3 = e1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (324) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (326) all_54_9 = all_8_1 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (324) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (327) ~ (all_8_1 = all_6_2) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (324) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (328) ~ (all_8_1 = e1) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (324) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (329) op(e1, all_8_1) = all_58_16 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_8_0, all_58_16, % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | all_8_1, e1, simplifying with (318), (329) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | (330) all_58_16 = all_8_0 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | (331) all_56_0 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (331) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | (332) all_10_2 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | (333) all_10_2 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (333) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_28 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (333) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_52_1 = e3) % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | (336) all_56_2 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (336) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | (337) all_52_1 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (335), (337) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | (338) $false % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (338) is inconsistent. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | (339) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_58_28 = e2 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (340) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | (341) e3 = e2 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (341) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | (342) $false % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (342) is inconsistent. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_56_3 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (315), (344) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | #449. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_56_5 = e3 | all_56_10 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_56_5 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (212), (346) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | #79. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_56_10 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (347) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_52_13 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_52_13 = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (349) imply: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) op(e2, e0) = e3 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_29 = e2 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (312), (351) are inconsistent by sub-proof % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #687. % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_58_30 = e2 | all_58_31 = e2 % 151.13/22.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_30 = e2 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (353) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_6_2 = e2 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (354) implies: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_6_2 = e2 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (355) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_36_2 = e2 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (355) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) op(e2, e0) = all_6_0 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) ~ (all_36_2 = e2) % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (358) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) $false % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (359) is inconsistent. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_36_0 = e3) % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (360) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_6_0 = e3) % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e3, all_6_0, e0, e2, % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (350), (357) gives: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_6_0 = e3 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (362) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) $false % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (363) is inconsistent. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_31 = e2 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (364) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) e2 = e0 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (365) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) $false % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (366) is inconsistent. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (367) ~ (all_56_0 = e3) % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (368) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (367) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_10_2 = e3) % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (45), (104), (113), (123), (148), (149), % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (150), (161), (162), (173), (175), (184), (194), % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (215), (221), (240), (246), (248), (303), (312), % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (318), (319), (320), (323), (325), (326), (327), % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (328), (330), (368), (369) are inconsistent by % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #826. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | (370) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (371) all_56_13 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (317), (371) are inconsistent by sub-proof % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | #676. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | (372) all_56_14 = e1 | all_56_15 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | (373) all_56_14 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (301), (373) are inconsistent by sub-proof % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | #811. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | (374) all_56_15 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (374) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | (375) e1 = e0 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (375) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | (376) $false % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (376) is inconsistent. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | (377) all_58_30 = e1 | all_58_31 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (184), (200), (305), (377) are inconsistent % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | by sub-proof #824. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | (378) all_56_9 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (378) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | (379) all_52_12 = e1 % 151.13/22.41 | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | REDUCE: (288), (379) imply: % 151.13/22.41 | | | | | | | | | | | | | | | | | | | (380) $false % 151.13/22.41 | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | | CLOSE: (380) is inconsistent. % 151.13/22.41 | | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | End of split % 151.13/22.41 | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | Case 2: % 151.13/22.41 | | | | | | | | | | | % 151.13/22.41 | | | | | | | | | | | (381) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.13/22.41 | | | | | | | | | | | % 151.32/22.41 | | | | | | | | | | | REF_CLOSE: (10), (28), (66), (85), (92), (94), (99), (111), % 151.32/22.41 | | | | | | | | | | | (131), (148), (161), (163), (164), (184), (186), % 151.32/22.41 | | | | | | | | | | | (200), (225), (381) are inconsistent by sub-proof % 151.32/22.41 | | | | | | | | | | | #801. % 151.32/22.41 | | | | | | | | | | | % 151.32/22.41 | | | | | | | | | | End of split % 151.32/22.41 | | | | | | | | | | % 151.32/22.41 | | | | | | | | | Case 2: % 151.32/22.41 | | | | | | | | | | % 151.32/22.41 | | | | | | | | | | (382) all_56_12 = e0 % 151.32/22.41 | | | | | | | | | | % 151.32/22.41 | | | | | | | | | | COMBINE_EQS: (73), (382) imply: % 151.32/22.41 | | | | | | | | | | (383) all_52_3 = e0 % 151.32/22.41 | | | | | | | | | | % 151.32/22.41 | | | | | | | | | | REDUCE: (185), (383) imply: % 151.32/22.41 | | | | | | | | | | (384) $false % 151.32/22.41 | | | | | | | | | | % 151.32/22.41 | | | | | | | | | | CLOSE: (384) is inconsistent. % 151.32/22.41 | | | | | | | | | | % 151.32/22.41 | | | | | | | | | End of split % 151.32/22.41 | | | | | | | | | % 151.32/22.41 | | | | | | | | End of split % 151.32/22.41 | | | | | | | | % 151.32/22.41 | | | | | | | Case 2: % 151.32/22.41 | | | | | | | | % 151.32/22.41 | | | | | | | | (385) all_56_10 = e0 % 151.32/22.41 | | | | | | | | % 151.32/22.41 | | | | | | | | COMBINE_EQS: (117), (385) imply: % 151.32/22.41 | | | | | | | | (386) all_52_13 = e0 % 151.32/22.41 | | | | | | | | % 151.32/22.41 | | | | | | | | REDUCE: (188), (386) imply: % 151.32/22.41 | | | | | | | | (387) $false % 151.32/22.41 | | | | | | | | % 151.32/22.41 | | | | | | | | CLOSE: (387) is inconsistent. % 151.32/22.41 | | | | | | | | % 151.32/22.41 | | | | | | | End of split % 151.32/22.41 | | | | | | | % 151.32/22.41 | | | | | | End of split % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | End of split % 151.32/22.41 | | | | | % 151.32/22.41 | | | | End of split % 151.32/22.41 | | | | % 151.32/22.41 | | | Case 2: % 151.32/22.41 | | | | % 151.32/22.41 | | | | (388) ~ (all_56_15 = e0) % 151.32/22.41 | | | | % 151.32/22.41 | | | | REF_CLOSE: (2), (4), (8), (35), (53), (56), (92), (103), (109), (123), % 151.32/22.41 | | | | (161), (169), (388) are inconsistent by sub-proof #77. % 151.32/22.41 | | | | % 151.32/22.41 | | | End of split % 151.32/22.41 | | | % 151.32/22.41 | | End of split % 151.32/22.41 | | % 151.32/22.41 | Case 2: % 151.32/22.41 | | % 151.32/22.41 | | (389) all_32_1 = e0 % 151.32/22.41 | | (390) ~ (all_32_0 = e1) | ~ (all_32_2 = e2) % 151.32/22.41 | | % 151.32/22.41 | | COMBINE_EQS: (120), (389) imply: % 151.32/22.41 | | (391) all_10_1 = e0 % 151.32/22.41 | | % 151.32/22.41 | | REDUCE: (40), (391) imply: % 151.32/22.41 | | (392) op(all_10_2, e0) = all_10_0 % 151.32/22.41 | | % 151.32/22.41 | | REDUCE: (168), (391) imply: % 151.32/22.41 | | (393) op(all_10_2, e3) = e0 % 151.32/22.41 | | % 151.32/22.41 | | BETA: splitting (55) gives: % 151.32/22.41 | | % 151.32/22.41 | | Case 1: % 151.32/22.41 | | | % 151.32/22.41 | | | (394) all_56_15 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | COMBINE_EQS: (8), (394) imply: % 151.32/22.41 | | | (395) all_4_2 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | SIMP: (395) implies: % 151.32/22.41 | | | (396) all_4_2 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | COMBINE_EQS: (2), (396) imply: % 151.32/22.41 | | | (397) all_58_31 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (79), (396) imply: % 151.32/22.41 | | | (398) ~ (all_52_3 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (155), (396) imply: % 151.32/22.41 | | | (399) ~ (all_52_7 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (22), (396) imply: % 151.32/22.41 | | | (400) ~ (all_52_11 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (61), (396) imply: % 151.32/22.41 | | | (401) ~ (all_52_13 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (153), (396) imply: % 151.32/22.41 | | | (402) ~ (all_52_14 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (144), (396) imply: % 151.32/22.41 | | | (403) op(e0, all_4_1) = all_4_0 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (167), (396) imply: % 151.32/22.41 | | | (404) op(e0, e0) = all_4_1 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (30), (396) imply: % 151.32/22.41 | | | (405) op(e0, e0) = all_58_27 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (135), (396) imply: % 151.32/22.41 | | | (406) op(e0, e0) = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 151.32/22.41 | | | simplifying with (404), (405) gives: % 151.32/22.41 | | | (407) all_58_27 = all_4_1 % 151.32/22.41 | | | % 151.32/22.41 | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, simplifying % 151.32/22.41 | | | with (405), (406) gives: % 151.32/22.41 | | | (408) all_58_27 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | COMBINE_EQS: (407), (408) imply: % 151.32/22.41 | | | (409) all_4_1 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | SIMP: (409) implies: % 151.32/22.41 | | | (410) all_4_1 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (403), (410) imply: % 151.32/22.41 | | | (411) op(e0, e0) = all_4_0 % 151.32/22.41 | | | % 151.32/22.41 | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, simplifying with % 151.32/22.41 | | | (406), (411) gives: % 151.32/22.41 | | | (412) all_4_0 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (70), (412) imply: % 151.32/22.41 | | | (413) ~ (e1 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | SIMP: (413) implies: % 151.32/22.41 | | | (414) ~ (e1 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | BETA: splitting (31) gives: % 151.32/22.41 | | | % 151.32/22.41 | | | Case 1: % 151.32/22.41 | | | | % 151.32/22.41 | | | | (415) all_56_2 = e0 % 151.32/22.41 | | | | % 151.32/22.41 | | | | COMBINE_EQS: (113), (415) imply: % 151.32/22.41 | | | | (416) all_52_1 = e0 % 151.32/22.41 | | | | % 151.32/22.41 | | | | REDUCE: (119), (416) imply: % 151.32/22.41 | | | | (417) ~ (all_52_3 = e0) % 151.32/22.41 | | | | % 151.32/22.41 | | | | REDUCE: (125), (416) imply: % 151.32/22.41 | | | | (418) ~ (all_52_9 = e0) % 151.32/22.41 | | | | % 151.32/22.41 | | | | SIMP: (418) implies: % 151.32/22.41 | | | | (419) ~ (all_52_9 = e0) % 151.32/22.41 | | | | % 151.32/22.41 | | | | REDUCE: (71), (416) imply: % 151.32/22.41 | | | | (420) ~ (all_52_13 = e0) % 151.32/22.41 | | | | % 151.32/22.41 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (14), (15), (16), % 151.32/22.41 | | | | (18), (20), (24), (25), (26), (28), (29), (32), (35), (38), % 151.32/22.41 | | | | (39), (40), (42), (44), (46), (51), (52), (54), (56), (58), % 151.32/22.41 | | | | (59), (61), (62), (63), (66), (68), (72), (73), (75), (76), % 151.32/22.41 | | | | (77), (78), (80), (81), (85), (86), (88), (89), (90), (91), % 151.32/22.41 | | | | (92), (93), (94), (95), (96), (97), (99), (100), (103), % 151.32/22.41 | | | | (104), (105), (106), (107), (108), (109), (111), (117), % 151.32/22.41 | | | | (121), (122), (123), (128), (129), (131), (132), (133), % 151.32/22.41 | | | | (134), (136), (139), (140), (141), (143), (146), (147), % 151.32/22.41 | | | | (148), (151), (157), (158), (159), (160), (161), (163), % 151.32/22.41 | | | | (164), (165), (168), (394), (397), (398), (399), (400), % 151.32/22.41 | | | | (401), (408), (414), (415), (419) are inconsistent by % 151.32/22.41 | | | | sub-proof #80. % 151.32/22.41 | | | | % 151.32/22.41 | | | Case 2: % 151.32/22.41 | | | | % 151.32/22.41 | | | | (421) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.32/22.41 | | | | % 151.32/22.41 | | | | BETA: splitting (421) gives: % 151.32/22.41 | | | | % 151.32/22.41 | | | | Case 1: % 151.32/22.41 | | | | | % 151.32/22.41 | | | | | (422) all_56_3 = e0 % 151.32/22.41 | | | | | % 151.32/22.41 | | | | | REF_CLOSE: (28), (66), (85), (92), (94), (111), (131), (148), (161), % 151.32/22.41 | | | | | (163), (164), (397), (414), (422) are inconsistent by % 151.32/22.41 | | | | | sub-proof #804. % 151.32/22.41 | | | | | % 151.32/22.41 | | | | Case 2: % 151.32/22.41 | | | | | % 151.32/22.41 | | | | | (423) all_56_5 = e0 | all_56_10 = e0 % 151.32/22.41 | | | | | % 151.32/22.41 | | | | | BETA: splitting (423) gives: % 151.32/22.41 | | | | | % 151.32/22.41 | | | | | Case 1: % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | (424) all_56_5 = e0 % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | COMBINE_EQS: (72), (424) imply: % 151.32/22.41 | | | | | | (425) all_52_9 = e0 % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | REDUCE: (83), (425) imply: % 151.32/22.41 | | | | | | (426) ~ (all_52_11 = e0) % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | REDUCE: (132), (425) imply: % 151.32/22.41 | | | | | | (427) ~ (all_6_2 = e0) % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | SIMP: (427) implies: % 151.32/22.41 | | | | | | (428) ~ (all_6_2 = e0) % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (10), (11), (12), (13), % 151.32/22.41 | | | | | | (17), (20), (23), (25), (26), (27), (28), (29), (33), % 151.32/22.41 | | | | | | (36), (37), (41), (42), (43), (44), (45), (46), (48), % 151.32/22.41 | | | | | | (49), (53), (54), (57), (58), (59), (62), (64), (65), % 151.32/22.41 | | | | | | (66), (69), (71), (72), (73), (74), (75), (76), (77), % 151.32/22.41 | | | | | | (78), (80), (82), (84), (85), (86), (87), (88), (91), % 151.32/22.41 | | | | | | (92), (93), (94), (95), (96), (97), (99), (101), (102), % 151.32/22.41 | | | | | | (104), (105), (106), (107), (110), (111), (112), (113), % 151.32/22.41 | | | | | | (115), (116), (117), (118), (119), (122), (123), (124), % 151.32/22.41 | | | | | | (125), (126), (127), (129), (131), (132), (134), (137), % 151.32/22.41 | | | | | | (138), (139), (140), (145), (146), (147), (148), (150), % 151.32/22.41 | | | | | | (152), (154), (156), (160), (161), (162), (163), (164), % 151.32/22.41 | | | | | | (165), (166), (170), (171), (173), (175), (390), (392), % 151.32/22.41 | | | | | | (393), (394), (397), (398), (399), (400), (402), (408), % 151.32/22.41 | | | | | | (414), (428) are inconsistent by sub-proof #734. % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | Case 2: % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | (429) all_56_10 = e0 % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | COMBINE_EQS: (117), (429) imply: % 151.32/22.41 | | | | | | (430) all_52_13 = e0 % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | REDUCE: (401), (430) imply: % 151.32/22.41 | | | | | | (431) $false % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | | CLOSE: (431) is inconsistent. % 151.32/22.41 | | | | | | % 151.32/22.41 | | | | | End of split % 151.32/22.41 | | | | | % 151.32/22.41 | | | | End of split % 151.32/22.41 | | | | % 151.32/22.41 | | | End of split % 151.32/22.41 | | | % 151.32/22.41 | | Case 2: % 151.32/22.41 | | | % 151.32/22.41 | | | (432) ~ (all_56_15 = e0) % 151.32/22.41 | | | % 151.32/22.41 | | | REF_CLOSE: (2), (4), (8), (35), (53), (56), (92), (103), (109), (123), % 151.32/22.41 | | | (161), (169), (432) are inconsistent by sub-proof #77. % 151.32/22.41 | | | % 151.32/22.41 | | End of split % 151.32/22.41 | | % 151.32/22.41 | End of split % 151.32/22.41 | % 151.32/22.41 End of proof % 151.32/22.41 % 151.32/22.41 Sub-proof #77 shows that the following formulas are inconsistent: % 151.32/22.41 ---------------------------------------------------------------- % 151.32/22.41 (1) all_58_31 = all_4_2 % 151.32/22.41 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.32/22.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.32/22.41 (3) all_56_15 = all_4_2 % 151.32/22.41 (4) op(e0, e1) = all_52_11 % 151.32/22.41 (5) ~ (all_10_2 = e0) % 151.32/22.41 (6) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.41 (7) all_58_29 = all_8_2 % 151.32/22.41 (8) op(all_6_2, e1) = e0 % 151.32/22.41 (9) ~ (all_52_11 = all_6_2) % 151.32/22.41 (10) all_58_28 = all_10_2 % 151.32/22.41 (11) ~ (all_56_15 = e0) % 151.32/22.41 (12) all_58_30 = all_6_2 % 151.32/22.41 (13) ~ (all_8_2 = e0) % 151.32/22.41 % 151.32/22.41 Begin of proof % 151.32/22.41 | % 151.32/22.41 | REDUCE: (3), (11) imply: % 151.32/22.41 | (14) ~ (all_4_2 = e0) % 151.32/22.41 | % 151.32/22.41 | BETA: splitting (6) gives: % 151.32/22.41 | % 151.32/22.41 | Case 1: % 151.32/22.41 | | % 151.32/22.41 | | (15) all_58_28 = e0 % 151.32/22.41 | | % 151.32/22.41 | | COMBINE_EQS: (10), (15) imply: % 151.32/22.41 | | (16) all_10_2 = e0 % 151.32/22.41 | | % 151.32/22.41 | | REDUCE: (5), (16) imply: % 151.32/22.41 | | (17) $false % 151.32/22.41 | | % 151.32/22.41 | | CLOSE: (17) is inconsistent. % 151.32/22.41 | | % 151.32/22.41 | Case 2: % 151.32/22.41 | | % 151.32/22.41 | | (18) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.41 | | % 151.32/22.41 | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (12), (13), (14), (18) are % 151.32/22.41 | | inconsistent by sub-proof #78. % 151.32/22.41 | | % 151.32/22.41 | End of split % 151.32/22.41 | % 151.32/22.41 End of proof % 151.32/22.41 % 151.32/22.41 Sub-proof #78 shows that the following formulas are inconsistent: % 151.32/22.41 ---------------------------------------------------------------- % 151.32/22.41 (1) all_58_31 = all_4_2 % 151.32/22.41 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.32/22.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.32/22.41 (3) op(e0, e1) = all_52_11 % 151.32/22.41 (4) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.41 (5) all_58_29 = all_8_2 % 151.32/22.41 (6) op(all_6_2, e1) = e0 % 151.32/22.41 (7) ~ (all_52_11 = all_6_2) % 151.32/22.41 (8) ~ (all_4_2 = e0) % 151.32/22.41 (9) all_58_30 = all_6_2 % 151.32/22.41 (10) ~ (all_8_2 = e0) % 151.32/22.41 % 151.32/22.41 Begin of proof % 151.32/22.41 | % 151.32/22.41 | BETA: splitting (4) gives: % 151.32/22.41 | % 151.32/22.41 | Case 1: % 151.32/22.41 | | % 151.32/22.41 | | (11) all_58_29 = e0 % 151.32/22.41 | | % 151.32/22.41 | | COMBINE_EQS: (5), (11) imply: % 151.32/22.41 | | (12) all_8_2 = e0 % 151.32/22.41 | | % 151.32/22.41 | | REDUCE: (10), (12) imply: % 151.32/22.41 | | (13) $false % 151.32/22.41 | | % 151.32/22.41 | | CLOSE: (13) is inconsistent. % 151.32/22.41 | | % 151.32/22.41 | Case 2: % 151.32/22.41 | | % 151.32/22.41 | | (14) all_58_30 = e0 | all_58_31 = e0 % 151.32/22.41 | | % 151.32/22.41 | | BETA: splitting (14) gives: % 151.32/22.41 | | % 151.32/22.41 | | Case 1: % 151.32/22.41 | | | % 151.32/22.41 | | | (15) all_58_30 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | REF_CLOSE: (2), (3), (6), (7), (9), (15) are inconsistent by sub-proof % 151.32/22.41 | | | #82. % 151.32/22.41 | | | % 151.32/22.41 | | Case 2: % 151.32/22.41 | | | % 151.32/22.41 | | | (16) all_58_31 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | COMBINE_EQS: (1), (16) imply: % 151.32/22.41 | | | (17) all_4_2 = e0 % 151.32/22.41 | | | % 151.32/22.41 | | | REDUCE: (8), (17) imply: % 151.32/22.41 | | | (18) $false % 151.32/22.41 | | | % 151.32/22.41 | | | CLOSE: (18) is inconsistent. % 151.32/22.41 | | | % 151.32/22.41 | | End of split % 151.32/22.41 | | % 151.32/22.41 | End of split % 151.32/22.41 | % 151.32/22.41 End of proof % 151.32/22.41 % 151.32/22.41 Sub-proof #79 shows that the following formulas are inconsistent: % 151.32/22.41 ---------------------------------------------------------------- % 151.32/22.41 (1) all_56_5 = e3 % 151.32/22.41 (2) all_56_5 = e0 % 151.32/22.41 (3) ~ (e3 = e0) % 151.32/22.41 % 151.32/22.41 Begin of proof % 151.32/22.41 | % 151.32/22.41 | COMBINE_EQS: (1), (2) imply: % 151.32/22.41 | (4) e3 = e0 % 151.32/22.41 | % 151.32/22.41 | SIMP: (4) implies: % 151.32/22.41 | (5) e3 = e0 % 151.32/22.41 | % 151.32/22.41 | REDUCE: (3), (5) imply: % 151.32/22.41 | (6) $false % 151.32/22.41 | % 151.32/22.41 | CLOSE: (6) is inconsistent. % 151.32/22.41 | % 151.32/22.41 End of proof % 151.32/22.41 % 151.32/22.41 Sub-proof #80 shows that the following formulas are inconsistent: % 151.32/22.41 ---------------------------------------------------------------- % 151.32/22.41 (1) all_58_31 = all_4_2 % 151.32/22.41 (2) ~ (all_52_8 = all_52_9) % 151.32/22.41 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.32/22.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.32/22.41 (4) all_54_13 = all_52_7 % 151.32/22.41 (5) ~ (all_52_2 = all_52_3) % 151.32/22.41 (6) all_56_15 = all_4_2 % 151.32/22.41 (7) all_56_7 = all_52_6 % 151.32/22.41 (8) ~ (all_52_6 = all_6_2) % 151.32/22.41 (9) all_54_8 = all_52_2 % 151.32/22.41 (10) op(e1, all_6_2) = all_58_18 % 151.32/22.41 (11) op(e3, all_52_4) = all_58_1 % 151.32/22.41 (12) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.32/22.41 (13) ~ (all_52_8 = all_10_2) % 151.32/22.41 (14) ~ (all_52_6 = all_8_2) % 151.32/22.41 (15) all_56_4 = all_52_8 % 151.32/22.41 (16) ~ (all_52_4 = all_8_2) % 151.32/22.41 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.32/22.41 (18) all_54_1 = all_52_4 % 151.32/22.41 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.32/22.41 (20) op(e0, e1) = all_52_11 % 151.32/22.41 (21) ~ (all_52_6 = all_52_7) % 151.32/22.41 (22) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.32/22.41 (23) op(all_10_2, all_10_1) = all_10_0 % 151.32/22.41 (24) op(e3, e2) = all_52_4 % 151.32/22.41 (25) ~ (all_52_8 = all_6_2) % 151.32/22.41 (26) ~ (all_52_12 = all_52_13) % 151.32/22.41 (27) all_54_6 = all_52_9 % 151.32/22.41 (28) ~ (all_52_4 = all_52_7) % 151.32/22.41 (29) ~ (all_52_2 = all_6_2) % 151.32/22.41 (30) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.41 (31) op(e3, all_52_8) = all_58_3 % 151.32/22.41 (32) ~ (all_52_8 = all_52_12) % 151.32/22.41 (33) ~ (all_52_13 = all_4_2) % 151.32/22.41 (34) op(e1, e2) = all_52_6 % 151.32/22.41 (35) ~ (all_52_3 = e0) % 151.32/22.41 (36) ~ (all_52_13 = all_8_2) % 151.32/22.41 (37) ~ (e3 = e1) % 151.32/22.41 (38) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.32/22.41 (39) all_56_5 = all_52_9 % 151.32/22.41 (40) all_56_12 = all_52_3 % 151.32/22.41 (41) all_56_11 = all_52_14 % 151.32/22.41 (42) all_56_1 = all_52_4 % 151.32/22.41 (43) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.32/22.41 (44) ~ (all_52_13 = e0) % 151.32/22.41 (45) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.32/22.42 (46) op(e1, e3) = all_52_2 % 151.32/22.42 (47) ~ (all_6_0 = e2) | ~ (all_6_2 = e3) % 151.32/22.42 (48) ~ (all_52_9 = e0) % 151.32/22.42 (49) all_56_3 = all_8_2 % 151.32/22.42 (50) ~ (all_52_13 = all_52_14) % 151.32/22.42 (51) ~ (all_52_4 = all_52_8) % 151.32/22.42 (52) op(e1, all_52_2) = all_58_14 % 151.32/22.42 (53) op(e2, e1) = all_52_9 % 151.32/22.42 (54) all_56_9 = all_52_12 % 151.32/22.42 (55) all_58_29 = all_8_2 % 151.32/22.42 (56) ~ (all_52_12 = all_52_14) % 151.32/22.42 (57) ~ (e2 = e1) % 151.32/22.42 (58) op(e3, e0) = all_52_12 % 151.32/22.42 (59) all_56_6 = all_52_2 % 151.32/22.42 (60) ~ (all_52_2 = all_52_6) % 151.32/22.42 (61) all_56_13 = all_52_7 % 151.32/22.42 (62) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.32/22.42 (63) op(all_6_2, e1) = e0 % 151.32/22.42 (64) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 151.32/22.42 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 151.32/22.42 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 151.32/22.42 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 151.32/22.42 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 151.32/22.42 (all_58_27 = e0)) % 151.32/22.42 (65) all_56_2 = e0 % 151.32/22.42 (66) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.32/22.42 (67) op(all_6_2, e1) = all_6_1 % 151.32/22.42 (68) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.32/22.42 (69) op(e2, all_52_9) = all_58_10 % 151.32/22.42 (70) ~ (all_52_11 = all_6_2) % 151.32/22.42 (71) ~ (e3 = e0) % 151.32/22.42 (72) ~ (all_52_11 = e0) % 151.32/22.42 (73) all_56_10 = all_52_13 % 151.32/22.42 (74) ~ (all_52_9 = all_8_2) % 151.32/22.42 (75) all_56_14 = all_52_11 % 151.32/22.42 (76) all_58_28 = all_10_2 % 151.32/22.42 (77) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.32/22.42 (78) op(all_8_2, e2) = all_8_1 % 151.32/22.42 (79) all_56_15 = e0 % 151.32/22.42 (80) ~ (e2 = e0) % 151.32/22.42 (81) ~ (all_52_9 = all_6_2) % 151.32/22.42 (82) ~ (all_52_2 = all_10_2) % 151.32/22.42 (83) all_56_0 = all_10_2 % 151.32/22.42 (84) op(all_6_2, e0) = all_6_0 % 151.32/22.42 (85) all_58_31 = e0 % 151.32/22.42 (86) ~ (all_52_3 = all_10_2) % 151.32/22.42 (87) all_56_8 = all_6_2 % 151.32/22.42 (88) op(e1, e1) = all_6_2 % 151.32/22.42 (89) all_58_27 = e0 % 151.32/22.42 (90) ~ (all_52_7 = all_8_2) % 151.32/22.42 (91) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.32/22.42 (92) ~ (all_8_1 = e0) % 151.32/22.42 (93) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.32/22.42 (94) ~ (all_52_2 = all_52_14) % 151.32/22.42 (95) ~ (all_52_7 = e0) % 151.32/22.42 (96) ~ (e1 = e0) % 151.32/22.42 (97) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 151.32/22.42 (98) ~ (all_4_2 = e1) % 151.32/22.42 (99) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.32/22.42 (100) ~ (all_52_4 = all_10_2) % 151.32/22.42 (101) all_58_30 = all_6_2 % 151.32/22.42 (102) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.32/22.42 (103) ~ (e3 = e2) % 151.32/22.42 (104) ~ (all_52_14 = all_6_2) % 151.32/22.42 (105) op(all_10_2, e3) = all_10_1 % 151.32/22.42 % 151.32/22.42 Begin of proof % 151.32/22.42 | % 151.32/22.42 | BETA: splitting (66) gives: % 151.32/22.42 | % 151.32/22.42 | Case 1: % 151.32/22.42 | | % 151.32/22.42 | | (106) all_56_1 = e0 % 151.32/22.42 | | % 151.32/22.42 | | COMBINE_EQS: (42), (106) imply: % 151.32/22.42 | | (107) all_52_4 = e0 % 151.32/22.42 | | % 151.32/22.42 | | REDUCE: (51), (107) imply: % 151.32/22.42 | | (108) ~ (all_52_8 = e0) % 151.32/22.42 | | % 151.32/22.42 | | SIMP: (108) implies: % 151.32/22.42 | | (109) ~ (all_52_8 = e0) % 151.32/22.42 | | % 151.32/22.42 | | BETA: splitting (43) gives: % 151.32/22.42 | | % 151.32/22.42 | | Case 1: % 151.32/22.42 | | | % 151.32/22.42 | | | (110) all_56_4 = e0 % 151.32/22.42 | | | % 151.32/22.42 | | | COMBINE_EQS: (15), (110) imply: % 151.32/22.42 | | | (111) all_52_8 = e0 % 151.32/22.42 | | | % 151.32/22.42 | | | REDUCE: (109), (111) imply: % 151.32/22.42 | | | (112) $false % 151.32/22.42 | | | % 151.32/22.42 | | | CLOSE: (112) is inconsistent. % 151.32/22.42 | | | % 151.32/22.42 | | Case 2: % 151.32/22.42 | | | % 151.32/22.42 | | | (113) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.32/22.42 | | | % 151.32/22.42 | | | BETA: splitting (113) gives: % 151.32/22.42 | | | % 151.32/22.42 | | | Case 1: % 151.32/22.42 | | | | % 151.32/22.42 | | | | (114) all_56_5 = e0 % 151.32/22.42 | | | | % 151.32/22.42 | | | | REF_CLOSE: (39), (48), (114) are inconsistent by sub-proof #767. % 151.32/22.42 | | | | % 151.32/22.42 | | | Case 2: % 151.32/22.42 | | | | % 151.32/22.42 | | | | (115) all_56_8 = e0 | all_56_14 = e0 % 151.32/22.42 | | | | % 151.32/22.42 | | | | BETA: splitting (115) gives: % 151.32/22.42 | | | | % 151.32/22.42 | | | | Case 1: % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | (116) all_56_8 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | COMBINE_EQS: (87), (116) imply: % 151.32/22.42 | | | | | (117) all_6_2 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | SIMP: (117) implies: % 151.32/22.42 | | | | | (118) all_6_2 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | COMBINE_EQS: (101), (118) imply: % 151.32/22.42 | | | | | (119) all_58_30 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REF_CLOSE: (1), (17), (37), (57), (71), (80), (85), (93), (96), (98), % 151.32/22.42 | | | | | (102), (103), (119) are inconsistent by sub-proof #710. % 151.32/22.42 | | | | | % 151.32/22.42 | | | | Case 2: % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | (120) all_56_14 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | COMBINE_EQS: (75), (120) imply: % 151.32/22.42 | | | | | (121) all_52_11 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REDUCE: (72), (121) imply: % 151.32/22.42 | | | | | (122) $false % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | CLOSE: (122) is inconsistent. % 151.32/22.42 | | | | | % 151.32/22.42 | | | | End of split % 151.32/22.42 | | | | % 151.32/22.42 | | | End of split % 151.32/22.42 | | | % 151.32/22.42 | | End of split % 151.32/22.42 | | % 151.32/22.42 | Case 2: % 151.32/22.42 | | % 151.32/22.42 | | (123) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.32/22.42 | | % 151.32/22.42 | | BETA: splitting (123) gives: % 151.32/22.42 | | % 151.32/22.42 | | Case 1: % 151.32/22.42 | | | % 151.32/22.42 | | | (124) all_56_3 = e0 % 151.32/22.42 | | | % 151.32/22.42 | | | REF_CLOSE: (17), (37), (49), (55), (57), (71), (80), (85), (93), (96), % 151.32/22.42 | | | (101), (102), (103), (124) are inconsistent by sub-proof #804. % 151.32/22.42 | | | % 151.32/22.42 | | Case 2: % 151.32/22.42 | | | % 151.32/22.42 | | | (125) all_56_7 = e0 | all_56_13 = e0 % 151.32/22.42 | | | % 151.32/22.42 | | | BETA: splitting (125) gives: % 151.32/22.42 | | | % 151.32/22.42 | | | Case 1: % 151.32/22.42 | | | | % 151.32/22.42 | | | | (126) all_56_7 = e0 % 151.32/22.42 | | | | % 151.32/22.42 | | | | COMBINE_EQS: (7), (126) imply: % 151.32/22.42 | | | | (127) all_52_6 = e0 % 151.32/22.42 | | | | % 151.32/22.42 | | | | SIMP: (127) implies: % 151.32/22.42 | | | | (128) all_52_6 = e0 % 151.32/22.42 | | | | % 151.32/22.42 | | | | REDUCE: (60), (128) imply: % 151.32/22.42 | | | | (129) ~ (all_52_2 = e0) % 151.32/22.42 | | | | % 151.32/22.42 | | | | REDUCE: (21), (128) imply: % 151.32/22.42 | | | | (130) ~ (all_52_7 = e0) % 151.32/22.42 | | | | % 151.32/22.42 | | | | REDUCE: (14), (128) imply: % 151.32/22.42 | | | | (131) ~ (all_8_2 = e0) % 151.32/22.42 | | | | % 151.32/22.42 | | | | SIMP: (131) implies: % 151.32/22.42 | | | | (132) ~ (all_8_2 = e0) % 151.32/22.42 | | | | % 151.32/22.42 | | | | REDUCE: (8), (128) imply: % 151.32/22.42 | | | | (133) ~ (all_6_2 = e0) % 151.32/22.42 | | | | % 151.32/22.42 | | | | SIMP: (133) implies: % 151.32/22.42 | | | | (134) ~ (all_6_2 = e0) % 151.32/22.42 | | | | % 151.32/22.42 | | | | REDUCE: (34), (128) imply: % 151.32/22.42 | | | | (135) op(e1, e2) = e0 % 151.32/22.42 | | | | % 151.32/22.42 | | | | BETA: splitting (43) gives: % 151.32/22.42 | | | | % 151.32/22.42 | | | | Case 1: % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | (136) all_56_4 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | COMBINE_EQS: (15), (136) imply: % 151.32/22.42 | | | | | (137) all_52_8 = e0 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REDUCE: (51), (137) imply: % 151.32/22.42 | | | | | (138) ~ (all_52_4 = e0) % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REDUCE: (2), (137) imply: % 151.32/22.42 | | | | | (139) ~ (all_52_9 = e0) % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REDUCE: (32), (137) imply: % 151.32/22.42 | | | | | (140) ~ (all_52_12 = e0) % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | SIMP: (140) implies: % 151.32/22.42 | | | | | (141) ~ (all_52_12 = e0) % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REDUCE: (13), (137) imply: % 151.32/22.42 | | | | | (142) ~ (all_10_2 = e0) % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | SIMP: (142) implies: % 151.32/22.42 | | | | | (143) ~ (all_10_2 = e0) % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | REDUCE: (31), (137) imply: % 151.32/22.42 | | | | | (144) op(e3, e0) = all_58_3 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | GROUND_INST: instantiating (3) with all_52_12, all_58_3, e0, e3, % 151.32/22.42 | | | | | simplifying with (58), (144) gives: % 151.32/22.42 | | | | | (145) all_58_3 = all_52_12 % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | BETA: splitting (22) gives: % 151.32/22.42 | | | | | % 151.32/22.42 | | | | | Case 1: % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | (146) all_54_13 = e0 % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | COMBINE_EQS: (4), (146) imply: % 151.32/22.42 | | | | | | (147) all_52_7 = e0 % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | REDUCE: (95), (147) imply: % 151.32/22.42 | | | | | | (148) $false % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | CLOSE: (148) is inconsistent. % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | Case 2: % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | (149) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | BETA: splitting (91) gives: % 151.32/22.42 | | | | | | % 151.32/22.42 | | | | | | Case 1: % 151.32/22.42 | | | | | | | % 151.32/22.42 | | | | | | | (150) all_54_1 = e0 % 151.32/22.42 | | | | | | | % 151.32/22.42 | | | | | | | REF_CLOSE: (18), (138), (150) are inconsistent by sub-proof #798. % 151.32/22.42 | | | | | | | % 151.32/22.42 | | | | | | Case 2: % 151.32/22.42 | | | | | | | % 151.32/22.42 | | | | | | | (151) ~ (all_54_1 = e0) % 151.32/22.42 | | | | | | | (152) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.32/22.42 | | | | | | | % 151.32/22.42 | | | | | | | BETA: splitting (99) gives: % 151.32/22.42 | | | | | | | % 151.32/22.42 | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | % 151.32/22.42 | | | | | | | | (153) all_54_6 = e0 % 151.32/22.42 | | | | | | | | % 151.32/22.42 | | | | | | | | REF_CLOSE: (27), (48), (153) are inconsistent by sub-proof #797. % 151.32/22.42 | | | | | | | | % 151.32/22.42 | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | % 151.32/22.42 | | | | | | | | (154) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 151.32/22.42 | | | | | | | | % 151.32/22.42 | | | | | | | | BETA: splitting (19) gives: % 151.32/22.42 | | | | | | | | % 151.32/22.42 | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | % 151.32/22.42 | | | | | | | | | (155) all_54_8 = e0 % 151.32/22.42 | | | | | | | | | % 151.32/22.42 | | | | | | | | | REF_CLOSE: (9), (129), (155) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | #731. % 151.32/22.42 | | | | | | | | | % 151.32/22.42 | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | % 151.32/22.42 | | | | | | | | | (156) ~ (all_54_8 = e0) % 151.32/22.42 | | | | | | | | | (157) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 151.32/22.42 | | | | | | | | | % 151.32/22.42 | | | | | | | | | BETA: splitting (68) gives: % 151.32/22.42 | | | | | | | | | % 151.32/22.42 | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | (158) all_56_9 = e1 % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | COMBINE_EQS: (54), (158) imply: % 151.32/22.42 | | | | | | | | | | (159) all_52_12 = e1 % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | REDUCE: (26), (159) imply: % 151.32/22.42 | | | | | | | | | | (160) ~ (all_52_13 = e1) % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | SIMP: (160) implies: % 151.32/22.42 | | | | | | | | | | (161) ~ (all_52_13 = e1) % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | REDUCE: (56), (159) imply: % 151.32/22.42 | | | | | | | | | | (162) ~ (all_52_14 = e1) % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | SIMP: (162) implies: % 151.32/22.42 | | | | | | | | | | (163) ~ (all_52_14 = e1) % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | BETA: splitting (38) gives: % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | (164) all_56_2 = e1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | COMBINE_EQS: (65), (164) imply: % 151.32/22.42 | | | | | | | | | | | (165) e1 = e0 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (96), (165) imply: % 151.32/22.42 | | | | | | | | | | | (166) $false % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | CLOSE: (166) is inconsistent. % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | (167) ~ (all_56_2 = e1) % 151.32/22.42 | | | | | | | | | | | (168) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (65), (167) imply: % 151.32/22.42 | | | | | | | | | | | (169) ~ (e1 = e0) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | BETA: splitting (77) gives: % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | (170) all_56_6 = e1 % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | COMBINE_EQS: (59), (170) imply: % 151.32/22.42 | | | | | | | | | | | | (171) all_52_2 = e1 % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | REDUCE: (82), (171) imply: % 151.32/22.42 | | | | | | | | | | | | (172) ~ (all_10_2 = e1) % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | SIMP: (172) implies: % 151.32/22.42 | | | | | | | | | | | | (173) ~ (all_10_2 = e1) % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | REDUCE: (29), (171) imply: % 151.32/22.42 | | | | | | | | | | | | (174) ~ (all_6_2 = e1) % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | SIMP: (174) implies: % 151.32/22.42 | | | | | | | | | | | | (175) ~ (all_6_2 = e1) % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | REF_CLOSE: (1), (3), (55), (76), (78), (92), (98), (101), % 151.32/22.42 | | | | | | | | | | | | (102), (135), (173), (175) are inconsistent by % 151.32/22.42 | | | | | | | | | | | | sub-proof #241. % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | (176) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | BETA: splitting (176) gives: % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | (177) all_56_7 = e1 % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | REF_CLOSE: (96), (126), (177) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | #501. % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | (178) all_56_8 = e1 | all_56_11 = e1 % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | BETA: splitting (178) gives: % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | (179) all_56_8 = e1 % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | COMBINE_EQS: (87), (179) imply: % 151.32/22.42 | | | | | | | | | | | | | | (180) all_6_2 = e1 % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | REDUCE: (81), (180) imply: % 151.32/22.42 | | | | | | | | | | | | | | (181) ~ (all_52_9 = e1) % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | BETA: splitting (168) gives: % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | (182) all_56_3 = e1 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | COMBINE_EQS: (49), (182) imply: % 151.32/22.42 | | | | | | | | | | | | | | | (183) all_8_2 = e1 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | SIMP: (183) implies: % 151.32/22.42 | | | | | | | | | | | | | | | (184) all_8_2 = e1 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | REDUCE: (78), (184) imply: % 151.32/22.42 | | | | | | | | | | | | | | | (185) op(e1, e2) = all_8_1 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | REF_CLOSE: (3), (92), (135), (185) are inconsistent by % 151.32/22.42 | | | | | | | | | | | | | | | sub-proof #795. % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | (186) all_56_5 = e1 | all_56_10 = e1 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | REF_CLOSE: (39), (73), (161), (181), (186) are inconsistent % 151.32/22.42 | | | | | | | | | | | | | | | by sub-proof #176. % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | (187) all_56_11 = e1 % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | REF_CLOSE: (41), (163), (187) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | | #580. % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | (188) ~ (all_56_9 = e1) % 151.32/22.42 | | | | | | | | | | (189) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | REDUCE: (54), (188) imply: % 151.32/22.42 | | | | | | | | | | (190) ~ (all_52_12 = e1) % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | BETA: splitting (62) gives: % 151.32/22.42 | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | (191) all_56_0 = e1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | COMBINE_EQS: (83), (191) imply: % 151.32/22.42 | | | | | | | | | | | (192) all_10_2 = e1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | COMBINE_EQS: (76), (192) imply: % 151.32/22.42 | | | | | | | | | | | (193) all_58_28 = e1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (82), (192) imply: % 151.32/22.42 | | | | | | | | | | | (194) ~ (all_52_2 = e1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (86), (192) imply: % 151.32/22.42 | | | | | | | | | | | (195) ~ (all_52_3 = e1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (100), (192) imply: % 151.32/22.42 | | | | | | | | | | | (196) ~ (all_52_4 = e1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (23), (192) imply: % 151.32/22.42 | | | | | | | | | | | (197) op(e1, all_10_1) = all_10_0 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (105), (192) imply: % 151.32/22.42 | | | | | | | | | | | (198) op(e1, e3) = all_10_1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_2, all_10_1, e3, e1, % 151.32/22.42 | | | | | | | | | | | simplifying with (46), (198) gives: % 151.32/22.42 | | | | | | | | | | | (199) all_52_2 = all_10_1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | COMBINE_EQS: (9), (199) imply: % 151.32/22.42 | | | | | | | | | | | (200) all_54_8 = all_10_1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | COMBINE_EQS: (59), (199) imply: % 151.32/22.42 | | | | | | | | | | | (201) all_56_6 = all_10_1 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (5), (199) imply: % 151.32/22.42 | | | | | | | | | | | (202) ~ (all_52_3 = all_10_1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | SIMP: (202) implies: % 151.32/22.42 | | | | | | | | | | | (203) ~ (all_52_3 = all_10_1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (94), (199) imply: % 151.32/22.42 | | | | | | | | | | | (204) ~ (all_52_14 = all_10_1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | SIMP: (204) implies: % 151.32/22.42 | | | | | | | | | | | (205) ~ (all_52_14 = all_10_1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (29), (199) imply: % 151.32/22.42 | | | | | | | | | | | (206) ~ (all_10_1 = all_6_2) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (194), (199) imply: % 151.32/22.42 | | | | | | | | | | | (207) ~ (all_10_1 = e1) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (129), (199) imply: % 151.32/22.42 | | | | | | | | | | | (208) ~ (all_10_1 = e0) % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | REDUCE: (52), (199) imply: % 151.32/22.42 | | | | | | | | | | | (209) op(e1, all_10_1) = all_58_14 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_10_0, all_58_14, % 151.32/22.42 | | | | | | | | | | | all_10_1, e1, simplifying with (197), (209) gives: % 151.32/22.42 | | | | | | | | | | | (210) all_58_14 = all_10_0 % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | BETA: splitting (45) gives: % 151.32/22.42 | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | (211) all_56_0 = e3 % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | REF_CLOSE: (37), (191), (211) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | #569. % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | (212) ~ (all_56_0 = e3) % 151.32/22.42 | | | | | | | | | | | | (213) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | REDUCE: (191), (212) imply: % 151.32/22.42 | | | | | | | | | | | | (214) ~ (e3 = e1) % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | BETA: splitting (93) gives: % 151.32/22.42 | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | (215) all_58_28 = e3 % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | COMBINE_EQS: (193), (215) imply: % 151.32/22.42 | | | | | | | | | | | | | (216) e3 = e1 % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | REDUCE: (37), (216) imply: % 151.32/22.42 | | | | | | | | | | | | | (217) $false % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | CLOSE: (217) is inconsistent. % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | (218) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | BETA: splitting (17) gives: % 151.32/22.42 | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | (219) all_58_28 = e2 % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | COMBINE_EQS: (193), (219) imply: % 151.32/22.42 | | | | | | | | | | | | | | (220) e2 = e1 % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | REDUCE: (57), (220) imply: % 151.32/22.42 | | | | | | | | | | | | | | (221) $false % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | CLOSE: (221) is inconsistent. % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | (222) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | BETA: splitting (97) gives: % 151.32/22.42 | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | (223) all_56_6 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | COMBINE_EQS: (201), (223) imply: % 151.32/22.42 | | | | | | | | | | | | | | | (224) all_10_1 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | SIMP: (224) implies: % 151.32/22.42 | | | | | | | | | | | | | | | (225) all_10_1 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | REDUCE: (206), (225) imply: % 151.32/22.42 | | | | | | | | | | | | | | | (226) ~ (all_6_2 = e3) % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | SIMP: (226) implies: % 151.32/22.42 | | | | | | | | | | | | | | | (227) ~ (all_6_2 = e3) % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | (228) all_58_29 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (228) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | (229) all_8_2 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | SIMP: (229) implies: % 151.32/22.42 | | | | | | | | | | | | | | | | (230) all_8_2 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | REDUCE: (16), (230) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | (231) ~ (all_52_4 = e3) % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | (232) all_54_1 = e1 % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (196), (232) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | | | | | #741. % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | (233) all_54_1 = e3 | all_54_1 = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | (234) all_54_1 = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (234) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (235) all_52_4 = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | SIMP: (235) implies: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (236) all_52_4 = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | REDUCE: (28), (236) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (237) ~ (all_52_7 = e2) % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | SIMP: (237) implies: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (238) ~ (all_52_7 = e2) % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | REDUCE: (231), (236) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (239) ~ (e3 = e2) % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | REDUCE: (11), (236) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (240) op(e3, e2) = all_58_1 % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | REDUCE: (24), (236) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | | | (241) op(e3, e2) = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | | (242) all_58_29 = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (228), (242) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | | | | | | | #780. % 151.32/22.42 | | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | | (243) all_58_30 = e2 | all_58_31 = e2 % 151.32/22.42 | | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (27), (53), (55), (64), (67), (69), % 151.32/22.42 | | | | | | | | | | | | | | | | | | | (74), (80), (81), (85), (89), (90), (97), (101), % 151.32/22.42 | | | | | | | | | | | | | | | | | | | (134), (149), (154), (157), (197), (198), (200), % 151.32/22.42 | | | | | | | | | | | | | | | | | | | (201), (206), (207), (208), (210), (218), (238), % 151.32/22.42 | | | | | | | | | | | | | | | | | | | (240), (241), (243) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | | | | | | | #724. % 151.32/22.42 | | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | (244) all_54_1 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (231), (244) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | | | | | | #739. % 151.32/22.42 | | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | (245) all_58_30 = e3 | all_58_31 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | REF_CLOSE: (71), (85), (101), (227), (245) are inconsistent % 151.32/22.42 | | | | | | | | | | | | | | | | by sub-proof #768. % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | End of split % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | (246) ~ (all_56_6 = e3) % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | REDUCE: (201), (246) imply: % 151.32/22.42 | | | | | | | | | | | | | | | (247) ~ (all_10_1 = e3) % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 151.32/22.42 | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | (248) all_56_2 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (248) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | (249) e3 = e0 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | REDUCE: (71), (249) imply: % 151.32/22.42 | | | | | | | | | | | | | | | | (250) $false % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | (251) all_56_6 = e3 | all_56_12 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 151.32/22.42 | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | Case 1: % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | (252) all_56_6 = e3 % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (247), (252) are inconsistent by sub-proof % 151.32/22.42 | | | | | | | | | | | | | | | | | #117. % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | Case 2: % 151.32/22.42 | | | | | | | | | | | | | | | | | % 151.32/22.42 | | | | | | | | | | | | | | | | | (253) all_56_12 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (253) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | (254) all_52_3 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | SIMP: (254) implies: % 151.32/22.43 | | | | | | | | | | | | | | | | | (255) all_52_3 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | REDUCE: (203), (255) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | (256) ~ (all_10_1 = e3) % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | (257) all_54_8 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (200), (207), (257) are inconsistent by sub-proof % 151.32/22.43 | | | | | | | | | | | | | | | | | | #728. % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | (258) ~ (all_54_8 = e1) % 151.32/22.43 | | | | | | | | | | | | | | | | | | (259) all_54_8 = e3 | all_54_8 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (260) all_54_8 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (260) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (261) all_10_1 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | SIMP: (261) implies: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (262) all_10_1 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | REDUCE: (205), (262) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (263) ~ (all_52_14 = e2) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | REDUCE: (206), (262) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (264) ~ (all_6_2 = e2) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | SIMP: (264) implies: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (265) ~ (all_6_2 = e2) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | REDUCE: (247), (262) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (266) ~ (e3 = e2) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | (267) all_58_29 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (267) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | (268) all_8_2 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | SIMP: (268) implies: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | (269) all_8_2 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (269) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | (270) ~ (all_52_13 = e2) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | (271) all_56_9 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (271) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | (272) all_52_12 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (272) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | (273) op(e3, e0) = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (274) all_58_29 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (274) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (275) e3 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (275) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (276) $false % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (276) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (277) all_58_30 = e3 | all_58_31 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_30 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (278) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (279) all_6_2 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (279) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (280) op(e3, e0) = all_6_0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | (281) ~ (all_6_0 = e2) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_6_0, e0, e3, % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (273), (280) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | (282) all_6_0 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (281), (282) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | (283) $false % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_6_2 = e3) % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (85), (101), (277), (284) are inconsistent % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #768. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_31 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (285) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (286) e3 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (287) e3 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (287) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (288) all_56_12 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (201), (247), (251), (288) are inconsistent % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #116. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | (289) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (290) all_56_10 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (290) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (291) all_52_13 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (291) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (292) $false % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | (293) all_56_11 = e2 | all_56_15 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (294) all_56_11 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (294) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (295) all_52_14 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (295) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (296) $false % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (297) all_56_15 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (297) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (298) e2 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (298) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_29 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (37), (57), (71), (80), (85), (93), (96), % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | (101), (102), (103), (299) are inconsistent by % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #844. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | (300) all_58_30 = e2 | all_58_31 = e2 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (85), (101), (265), (300) are inconsistent % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | by sub-proof #817. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | (301) all_54_8 = e3 % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (200), (247), (301) are inconsistent by sub-proof % 151.32/22.43 | | | | | | | | | | | | | | | | | | | #726. % 151.32/22.43 | | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | (302) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.32/22.43 | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | BETA: splitting (302) gives: % 151.32/22.43 | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | (303) all_56_1 = e1 % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | COMBINE_EQS: (42), (303) imply: % 151.32/22.43 | | | | | | | | | | | | (304) all_52_4 = e1 % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | REDUCE: (100), (304) imply: % 151.32/22.43 | | | | | | | | | | | | (305) ~ (all_10_2 = e1) % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | SIMP: (305) implies: % 151.32/22.43 | | | | | | | | | | | | (306) ~ (all_10_2 = e1) % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | REDUCE: (16), (304) imply: % 151.32/22.43 | | | | | | | | | | | | (307) ~ (all_8_2 = e1) % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | SIMP: (307) implies: % 151.32/22.43 | | | | | | | | | | | | (308) ~ (all_8_2 = e1) % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | BETA: splitting (102) gives: % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | (309) all_58_28 = e1 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | COMBINE_EQS: (76), (309) imply: % 151.32/22.43 | | | | | | | | | | | | | (310) all_10_2 = e1 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | REDUCE: (306), (310) imply: % 151.32/22.43 | | | | | | | | | | | | | (311) $false % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | CLOSE: (311) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | (312) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | BETA: splitting (312) gives: % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | (313) all_58_29 = e1 % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | REF_CLOSE: (55), (308), (313) are inconsistent by sub-proof % 151.32/22.43 | | | | | | | | | | | | | | #809. % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | (314) ~ (all_58_29 = e1) % 151.32/22.43 | | | | | | | | | | | | | | (315) all_58_30 = e1 | all_58_31 = e1 % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | BETA: splitting (315) gives: % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | (316) all_58_30 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | COMBINE_EQS: (101), (316) imply: % 151.32/22.43 | | | | | | | | | | | | | | | (317) all_6_2 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | SIMP: (317) implies: % 151.32/22.43 | | | | | | | | | | | | | | | (318) all_6_2 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | REDUCE: (81), (318) imply: % 151.32/22.43 | | | | | | | | | | | | | | | (319) ~ (all_52_9 = e1) % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | REDUCE: (104), (318) imply: % 151.32/22.43 | | | | | | | | | | | | | | | (320) ~ (all_52_14 = e1) % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | REDUCE: (63), (318) imply: % 151.32/22.43 | | | | | | | | | | | | | | | (321) op(e1, e1) = e0 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | REDUCE: (10), (318) imply: % 151.32/22.43 | | | | | | | | | | | | | | | (322) op(e1, e1) = all_58_18 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | REDUCE: (88), (318) imply: % 151.32/22.43 | | | | | | | | | | | | | | | (323) op(e1, e1) = e1 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | (324) all_56_2 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (324) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | (325) e1 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (33), (36), (41), (44), (55), (73), % 151.32/22.43 | | | | | | | | | | | | | | | | (98), (189), (312), (316), (320), (325) are % 151.32/22.43 | | | | | | | | | | | | | | | | inconsistent by sub-proof #83. % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | (326) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | (327) all_56_3 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (327) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | (328) all_8_2 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | SIMP: (328) implies: % 151.32/22.43 | | | | | | | | | | | | | | | | | (329) all_8_2 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | REDUCE: (308), (329) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | (330) $false % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | (331) all_56_5 = e1 | all_56_10 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | (332) all_56_5 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (319), (332) are inconsistent by sub-proof % 151.32/22.43 | | | | | | | | | | | | | | | | | | #285. % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | (333) all_56_10 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (333) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | (334) all_52_13 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | REDUCE: (50), (334) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | (335) ~ (all_52_14 = e1) % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_58_18, e1, e1, % 151.32/22.43 | | | | | | | | | | | | | | | | | | simplifying with (322), (323) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | (336) all_58_18 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_58_18, e1, e1, % 151.32/22.43 | | | | | | | | | | | | | | | | | | simplifying with (321), (322) gives: % 151.32/22.43 | | | | | | | | | | | | | | | | | | (337) all_58_18 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (337) imply: % 151.32/22.43 | | | | | | | | | | | | | | | | | | (338) e1 = e0 % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (33), (36), (41), (44), (55), (73), % 151.32/22.43 | | | | | | | | | | | | | | | | | | (98), (189), (312), (316), (320), (338) are % 151.32/22.43 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #83. % 151.32/22.43 | | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | (339) all_58_31 = e1 % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | | REF_CLOSE: (3), (20), (30), (55), (63), (70), (76), (96), % 151.32/22.43 | | | | | | | | | | | | | | | (101), (132), (143), (339) are inconsistent by % 151.32/22.43 | | | | | | | | | | | | | | | sub-proof #81. % 151.32/22.43 | | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | (340) all_56_4 = e1 | all_56_9 = e1 % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | BETA: splitting (340) gives: % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | Case 1: % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | (341) all_56_4 = e1 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | COMBINE_EQS: (136), (341) imply: % 151.32/22.43 | | | | | | | | | | | | | (342) e1 = e0 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | REDUCE: (96), (342) imply: % 151.32/22.43 | | | | | | | | | | | | | (343) $false % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | Case 2: % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | (344) all_56_9 = e1 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | COMBINE_EQS: (54), (344) imply: % 151.32/22.43 | | | | | | | | | | | | | (345) all_52_12 = e1 % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | REDUCE: (190), (345) imply: % 151.32/22.43 | | | | | | | | | | | | | (346) $false % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | | CLOSE: (346) is inconsistent. % 151.32/22.43 | | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | | % 151.32/22.43 | | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | | % 151.32/22.43 | | | | | | | | | End of split % 151.32/22.43 | | | | | | | | | % 151.32/22.43 | | | | | | | | End of split % 151.32/22.43 | | | | | | | | % 151.32/22.43 | | | | | | | End of split % 151.32/22.43 | | | | | | | % 151.32/22.43 | | | | | | End of split % 151.32/22.43 | | | | | | % 151.32/22.43 | | | | | End of split % 151.32/22.43 | | | | | % 151.32/22.43 | | | | Case 2: % 151.32/22.43 | | | | | % 151.32/22.43 | | | | | (347) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.32/22.43 | | | | | % 151.32/22.43 | | | | | REF_CLOSE: (39), (48), (72), (75), (87), (134), (347) are inconsistent % 151.32/22.43 | | | | | by sub-proof #766. % 151.32/22.43 | | | | | % 151.32/22.43 | | | | End of split % 151.32/22.43 | | | | % 151.32/22.43 | | | Case 2: % 151.32/22.43 | | | | % 151.32/22.43 | | | | (348) all_56_13 = e0 % 151.32/22.43 | | | | % 151.32/22.43 | | | | COMBINE_EQS: (61), (348) imply: % 151.32/22.43 | | | | (349) all_52_7 = e0 % 151.32/22.43 | | | | % 151.32/22.43 | | | | REDUCE: (95), (349) imply: % 151.32/22.43 | | | | (350) $false % 151.32/22.43 | | | | % 151.32/22.43 | | | | CLOSE: (350) is inconsistent. % 151.32/22.43 | | | | % 151.32/22.43 | | | End of split % 151.32/22.43 | | | % 151.32/22.43 | | End of split % 151.32/22.43 | | % 151.32/22.43 | End of split % 151.32/22.43 | % 151.32/22.43 End of proof % 151.32/22.43 % 151.32/22.43 Sub-proof #81 shows that the following formulas are inconsistent: % 151.32/22.43 ---------------------------------------------------------------- % 151.32/22.43 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.32/22.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.32/22.43 (2) all_58_31 = e1 % 151.32/22.43 (3) op(e0, e1) = all_52_11 % 151.32/22.43 (4) ~ (all_10_2 = e0) % 151.32/22.43 (5) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.43 (6) all_58_29 = all_8_2 % 151.32/22.43 (7) op(all_6_2, e1) = e0 % 151.32/22.43 (8) ~ (all_52_11 = all_6_2) % 151.32/22.43 (9) all_58_28 = all_10_2 % 151.32/22.43 (10) ~ (e1 = e0) % 151.32/22.43 (11) all_58_30 = all_6_2 % 151.32/22.43 (12) ~ (all_8_2 = e0) % 151.32/22.43 % 151.32/22.43 Begin of proof % 151.32/22.43 | % 151.32/22.43 | BETA: splitting (5) gives: % 151.32/22.43 | % 151.32/22.43 | Case 1: % 151.32/22.43 | | % 151.32/22.43 | | (13) all_58_28 = e0 % 151.32/22.43 | | % 151.32/22.43 | | REF_CLOSE: (4), (9), (13) are inconsistent by sub-proof #865. % 151.32/22.43 | | % 151.32/22.43 | Case 2: % 151.32/22.43 | | % 151.32/22.43 | | (14) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.43 | | % 151.32/22.43 | | BETA: splitting (14) gives: % 151.32/22.43 | | % 151.32/22.43 | | Case 1: % 151.32/22.43 | | | % 151.32/22.43 | | | (15) all_58_29 = e0 % 151.32/22.43 | | | % 151.32/22.43 | | | REF_CLOSE: (6), (12), (15) are inconsistent by sub-proof #864. % 151.32/22.43 | | | % 151.32/22.43 | | Case 2: % 151.32/22.43 | | | % 151.32/22.43 | | | (16) all_58_30 = e0 | all_58_31 = e0 % 151.32/22.43 | | | % 151.32/22.43 | | | BETA: splitting (16) gives: % 151.32/22.43 | | | % 151.32/22.43 | | | Case 1: % 151.32/22.43 | | | | % 151.32/22.43 | | | | (17) all_58_30 = e0 % 151.32/22.43 | | | | % 151.32/22.43 | | | | REF_CLOSE: (1), (3), (7), (8), (11), (17) are inconsistent by sub-proof % 151.32/22.43 | | | | #82. % 151.32/22.43 | | | | % 151.32/22.43 | | | Case 2: % 151.32/22.43 | | | | % 151.32/22.43 | | | | (18) all_58_31 = e0 % 151.32/22.43 | | | | % 151.32/22.43 | | | | COMBINE_EQS: (2), (18) imply: % 151.32/22.43 | | | | (19) e1 = e0 % 151.32/22.43 | | | | % 151.32/22.43 | | | | REDUCE: (10), (19) imply: % 151.32/22.43 | | | | (20) $false % 151.32/22.43 | | | | % 151.32/22.43 | | | | CLOSE: (20) is inconsistent. % 151.32/22.43 | | | | % 151.32/22.43 | | | End of split % 151.32/22.43 | | | % 151.32/22.43 | | End of split % 151.32/22.43 | | % 151.32/22.43 | End of split % 151.32/22.43 | % 151.32/22.43 End of proof % 151.32/22.43 % 151.32/22.43 Sub-proof #82 shows that the following formulas are inconsistent: % 151.32/22.43 ---------------------------------------------------------------- % 151.32/22.43 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.32/22.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.32/22.43 (2) op(e0, e1) = all_52_11 % 151.32/22.43 (3) all_58_30 = e0 % 151.32/22.43 (4) op(all_6_2, e1) = e0 % 151.32/22.43 (5) ~ (all_52_11 = all_6_2) % 151.32/22.43 (6) all_58_30 = all_6_2 % 151.32/22.43 % 151.32/22.43 Begin of proof % 151.32/22.43 | % 151.32/22.43 | COMBINE_EQS: (3), (6) imply: % 151.32/22.43 | (7) all_6_2 = e0 % 151.32/22.43 | % 151.32/22.43 | SIMP: (7) implies: % 151.32/22.43 | (8) all_6_2 = e0 % 151.32/22.43 | % 151.32/22.43 | REDUCE: (5), (8) imply: % 151.32/22.43 | (9) ~ (all_52_11 = e0) % 151.32/22.43 | % 151.32/22.43 | REDUCE: (4), (8) imply: % 151.32/22.43 | (10) op(e0, e1) = e0 % 151.32/22.43 | % 151.32/22.43 | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #238. % 151.32/22.43 | % 151.32/22.43 End of proof % 151.32/22.43 % 151.32/22.43 Sub-proof #83 shows that the following formulas are inconsistent: % 151.32/22.43 ---------------------------------------------------------------- % 151.32/22.43 (1) all_58_31 = all_4_2 % 151.32/22.43 (2) all_56_15 = all_4_2 % 151.32/22.43 (3) ~ (all_52_14 = e1) % 151.32/22.43 (4) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.32/22.43 (5) ~ (all_52_13 = all_4_2) % 151.32/22.43 (6) ~ (all_52_13 = all_8_2) % 151.32/22.43 (7) all_56_11 = all_52_14 % 151.32/22.43 (8) ~ (all_52_13 = e0) % 151.32/22.43 (9) all_58_29 = all_8_2 % 151.32/22.43 (10) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.32/22.43 (11) all_56_10 = all_52_13 % 151.32/22.43 (12) all_58_30 = e1 % 151.32/22.43 (13) e1 = e0 % 151.32/22.43 (14) ~ (all_4_2 = e1) % 151.32/22.43 % 151.32/22.43 Begin of proof % 151.32/22.43 | % 151.32/22.43 | SIMP: (13) implies: % 151.32/22.43 | (15) e1 = e0 % 151.32/22.43 | % 151.32/22.43 | COMBINE_EQS: (12), (15) imply: % 151.32/22.43 | (16) all_58_30 = e0 % 151.32/22.43 | % 151.32/22.43 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (16) % 151.32/22.43 | are inconsistent by sub-proof #578. % 151.32/22.43 | % 151.32/22.43 End of proof % 151.32/22.43 % 151.32/22.43 Sub-proof #84 shows that the following formulas are inconsistent: % 151.32/22.43 ---------------------------------------------------------------- % 151.32/22.43 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.32/22.43 (2) all_58_31 = all_4_2 % 151.32/22.43 (3) ~ (all_52_8 = all_52_9) % 151.32/22.43 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.32/22.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.32/22.43 (5) all_54_13 = all_52_7 % 151.32/22.43 (6) ~ (all_52_2 = all_52_3) % 151.32/22.43 (7) all_58_11 = all_52_9 % 151.32/22.43 (8) all_56_15 = all_4_2 % 151.32/22.43 (9) all_56_7 = all_52_6 % 151.32/22.43 (10) ~ (all_52_6 = all_6_2) % 151.32/22.43 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 151.32/22.43 (12) all_54_2 = all_52_8 % 151.32/22.43 (13) all_54_8 = all_52_2 % 151.32/22.43 (14) all_22_0 = all_8_0 % 151.32/22.43 (15) op(e1, all_6_2) = all_58_18 % 151.32/22.43 (16) op(e3, all_52_4) = all_58_1 % 151.32/22.43 (17) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.32/22.43 (18) ~ (all_52_8 = all_10_2) % 151.32/22.43 (19) all_58_15 = all_52_2 % 151.32/22.43 (20) all_58_26 = all_52_11 % 151.32/22.43 (21) op(e1, all_52_14) = all_58_19 % 151.32/22.43 (22) ~ (all_52_8 = all_52_11) % 151.32/22.43 (23) ~ (all_52_11 = all_4_2) % 151.32/22.43 (24) all_54_7 = all_52_13 % 151.32/22.43 (25) all_58_6 = all_52_12 % 151.32/22.43 (26) ~ (all_52_6 = all_8_2) % 151.32/22.43 (27) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) | ~ (all_16_2 = e0) % 151.32/22.43 (28) all_56_4 = all_52_8 % 151.32/22.43 (29) ~ (all_52_4 = all_8_2) % 151.32/22.43 (30) all_54_3 = all_52_12 % 151.32/22.43 (31) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.32/22.43 (32) all_54_1 = all_52_4 % 151.32/22.43 (33) op(e0, all_4_2) = all_58_27 % 151.32/22.43 (34) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.32/22.43 (35) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.32/22.43 (36) ~ (all_52_4 = all_52_6) % 151.32/22.43 (37) all_58_13 = all_52_13 % 151.32/22.43 (38) op(e2, e2) = all_8_2 % 151.32/22.43 (39) op(e0, e1) = all_52_11 % 151.32/22.43 (40) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 151.32/22.43 (41) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.32/22.43 (42) ~ (all_52_6 = all_52_7) % 151.32/22.43 (43) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 151.32/22.43 (44) op(all_10_2, all_10_1) = all_10_0 % 151.32/22.43 (45) op(e3, e2) = all_52_4 % 151.32/22.43 (46) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 151.32/22.43 (47) all_58_20 = all_52_14 % 151.32/22.43 (48) ~ (all_52_8 = all_6_2) % 151.32/22.43 (49) ~ (all_52_12 = all_52_13) % 151.32/22.43 (50) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 151.32/22.43 (51) op(e0, all_52_3) = all_58_21 % 151.32/22.43 (52) all_16_2 = all_10_2 % 151.32/22.43 (53) all_54_5 = all_8_2 % 151.32/22.43 (54) ~ (all_52_6 = all_52_14) % 151.32/22.43 (55) all_54_6 = all_52_9 % 151.32/22.43 (56) ~ (all_52_4 = all_52_7) % 151.32/22.43 (57) ~ (all_52_2 = all_6_2) % 151.32/22.43 (58) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.32/22.43 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 151.32/22.43 (59) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.32/22.43 (60) op(e3, e3) = all_10_2 % 151.32/22.43 (61) ~ (all_52_8 = all_52_12) % 151.32/22.43 (62) all_54_9 = all_52_6 % 151.32/22.43 (63) ~ (all_52_13 = all_4_2) % 151.32/22.43 (64) op(e1, e2) = all_52_6 % 151.32/22.43 (65) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 151.32/22.43 (66) ~ (all_52_13 = all_8_2) % 151.32/22.43 (67) op(e1, all_52_6) = all_58_16 % 151.32/22.43 (68) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 151.32/22.43 (69) ~ (e3 = e1) % 151.32/22.43 (70) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 151.32/22.43 (71) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.32/22.43 (72) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 151.32/22.43 (73) ~ (all_4_0 = e1) % 151.32/22.43 (74) ~ (all_52_1 = all_52_13) % 151.32/22.43 (75) all_56_5 = all_52_9 % 151.32/22.43 (76) all_54_14 = all_52_11 % 151.32/22.43 (77) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 151.32/22.43 (78) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.32/22.43 (79) all_56_12 = all_52_3 % 151.32/22.43 (80) ~ (all_52_3 = all_52_7) % 151.32/22.44 (81) all_58_2 = all_52_4 % 151.32/22.44 (82) all_20_2 = all_4_2 % 151.32/22.44 (83) all_56_11 = all_52_14 % 151.32/22.44 (84) all_56_1 = all_52_4 % 151.32/22.44 (85) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.32/22.44 (86) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.32/22.44 (87) ~ (all_52_3 = all_4_2) % 151.32/22.44 (88) op(e1, e3) = all_52_2 % 151.32/22.44 (89) op(e1, e0) = all_52_14 % 151.32/22.44 (90) ~ (all_52_9 = all_52_11) % 151.32/22.44 (91) ~ (all_52_1 = all_8_2) % 151.32/22.44 (92) all_56_3 = all_8_2 % 151.32/22.44 (93) all_58_24 = all_52_7 % 151.32/22.44 (94) ~ (all_52_13 = all_52_14) % 151.32/22.44 (95) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.32/22.44 (96) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 151.32/22.44 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 151.32/22.44 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 151.32/22.44 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 151.32/22.44 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 151.32/22.44 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 151.32/22.44 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 151.32/22.44 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 151.32/22.44 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 151.32/22.44 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 151.32/22.44 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.32/22.44 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.32/22.44 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.32/22.44 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.32/22.44 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.32/22.44 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 151.32/22.44 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.32/22.44 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.32/22.44 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.32/22.44 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.32/22.44 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.32/22.44 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 151.32/22.44 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.32/22.44 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.32/22.44 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.32/22.44 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 151.32/22.44 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 151.32/22.44 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 151.32/22.44 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.32/22.44 e0) % 151.32/22.44 (97) ~ (all_52_4 = all_52_8) % 151.32/22.44 (98) op(e1, all_52_2) = all_58_14 % 151.32/22.44 (99) op(e2, e1) = all_52_9 % 151.32/22.44 (100) all_56_9 = all_52_12 % 151.32/22.44 (101) all_58_29 = all_8_2 % 151.32/22.44 (102) ~ (all_52_12 = all_52_14) % 151.32/22.44 (103) all_58_8 = all_52_1 % 151.32/22.44 (104) ~ (e2 = e1) % 151.32/22.44 (105) op(e3, e0) = all_52_12 % 151.32/22.44 (106) all_56_6 = all_52_2 % 151.32/22.44 (107) ~ (all_52_2 = all_52_6) % 151.32/22.44 (108) all_18_2 = all_6_2 % 151.32/22.44 (109) op(all_8_2, e2) = e0 % 151.32/22.44 (110) all_56_13 = all_52_7 % 151.32/22.44 (111) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 151.32/22.44 (112) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 151.32/22.44 (113) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.32/22.44 (114) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 151.32/22.44 (115) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 151.32/22.44 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 151.32/22.44 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 151.32/22.44 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 151.32/22.44 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 151.32/22.44 (all_58_27 = e0)) % 151.32/22.44 (116) ~ (all_52_9 = all_52_13) % 151.32/22.44 (117) ~ (all_10_0 = e0) | ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 151.32/22.44 (118) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.32/22.44 (119) op(all_6_2, e1) = all_6_1 % 151.32/22.44 (120) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.32/22.44 (121) op(e2, all_52_9) = all_58_10 % 151.32/22.44 (122) ~ (all_52_11 = all_6_2) % 151.32/22.44 (123) op(e3, all_10_2) = all_58_0 % 151.32/22.44 (124) ~ (e3 = e0) % 151.32/22.44 (125) all_56_2 = all_52_1 % 151.32/22.44 (126) ~ (all_32_0 = e1) | ~ (all_32_1 = e0) | ~ (all_32_2 = e2) % 151.32/22.44 (127) op(e0, e3) = all_52_3 % 151.32/22.44 (128) op(e3, all_52_12) = all_58_5 % 151.32/22.44 (129) all_22_1 = e0 % 151.32/22.44 (130) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 151.32/22.44 (131) all_56_10 = all_52_13 % 151.32/22.44 (132) ~ (all_52_12 = all_10_2) % 151.32/22.44 (133) ~ (all_52_1 = all_52_3) % 151.32/22.44 (134) all_32_1 = all_10_1 % 151.32/22.44 (135) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 151.32/22.44 (136) ~ (all_52_9 = all_8_2) % 151.32/22.44 (137) all_56_14 = all_52_11 % 151.32/22.44 (138) all_58_28 = all_10_2 % 151.32/22.44 (139) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 151.32/22.44 (140) op(all_8_2, e0) = all_8_0 % 151.32/22.44 (141) all_58_17 = all_52_6 % 151.32/22.44 (142) ~ (all_52_1 = all_52_9) % 151.32/22.44 (143) op(e3, e1) = all_52_8 % 151.32/22.44 (144) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.32/22.44 (145) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 151.32/22.44 (146) ~ (all_52_7 = all_52_11) % 151.32/22.44 (147) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.32/22.44 (148) ~ (e2 = e0) % 151.32/22.44 (149) ~ (all_52_9 = all_6_2) % 151.32/22.44 (150) ~ (all_52_2 = all_10_2) % 151.32/22.44 (151) all_56_0 = all_10_2 % 151.32/22.44 (152) op(e0, e0) = all_4_2 % 151.32/22.44 (153) ~ (all_22_0 = e3) | ~ (all_22_1 = e0) | ~ (all_22_2 = e1) % 151.32/22.44 (154) ~ (all_52_3 = all_52_11) % 151.32/22.44 (155) all_58_22 = all_52_3 % 151.32/22.44 (156) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 151.32/22.44 (157) ~ (all_52_12 = all_4_2) % 151.32/22.44 (158) ~ (all_52_3 = all_10_2) % 151.32/22.44 (159) all_56_8 = all_6_2 % 151.32/22.44 (160) op(e1, e1) = all_6_2 % 151.32/22.44 (161) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.32/22.44 (162) ~ (all_52_1 = all_52_2) % 151.32/22.44 (163) ~ (all_52_7 = all_8_2) % 151.32/22.44 (164) op(all_4_2, all_4_1) = all_4_0 % 151.32/22.44 (165) op(e2, e0) = all_52_13 % 151.32/22.44 (166) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.32/22.44 (167) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.32/22.44 (168) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 151.32/22.44 (169) op(e2, all_52_13) = all_58_12 % 151.32/22.44 (170) all_58_4 = all_52_8 % 151.32/22.44 (171) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.32/22.44 (172) all_16_1 = all_10_1 % 151.32/22.44 (173) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 151.32/22.44 (174) all_16_0 = all_10_0 % 151.32/22.44 (175) all_54_0 = all_10_2 % 151.32/22.44 (176) ~ (all_52_2 = all_52_14) % 151.32/22.44 (177) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.32/22.44 (178) ~ (all_52_14 = all_4_2) % 151.32/22.44 (179) all_22_2 = all_8_2 % 151.32/22.44 (180) ~ (e1 = e0) % 151.32/22.44 (181) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 151.32/22.44 (182) ~ (all_52_7 = all_4_2) % 151.32/22.44 (183) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.32/22.44 (184) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 151.32/22.44 (185) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 151.32/22.44 (186) op(e0, e2) = all_52_7 % 151.32/22.44 (187) ~ (all_52_4 = all_10_2) % 151.32/22.44 (188) all_58_30 = all_6_2 % 151.32/22.44 (189) op(e2, all_52_1) = all_58_7 % 151.32/22.44 (190) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.32/22.44 (191) ~ (e3 = e2) % 151.32/22.44 (192) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 151.32/22.44 (193) ~ (all_52_14 = all_6_2) % 151.32/22.44 (194) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 151.32/22.44 (195) op(all_4_2, e0) = all_4_1 % 151.32/22.44 (196) op(all_10_2, e3) = all_10_1 % 151.32/22.44 (197) ~ (all_52_4 = all_52_12) % 151.32/22.44 (198) all_54_12 = all_52_3 % 151.32/22.44 (199) op(e2, all_8_2) = all_58_9 % 151.32/22.44 (200) all_54_4 = all_52_1 % 151.32/22.44 (201) ~ (all_52_1 = all_10_2) % 151.32/22.44 % 151.32/22.44 Begin of proof % 151.32/22.44 | % 151.32/22.44 | BETA: splitting (117) gives: % 151.32/22.44 | % 151.32/22.44 | Case 1: % 151.32/22.44 | | % 151.32/22.44 | | (202) ~ (all_10_0 = e0) % 151.32/22.44 | | % 151.32/22.44 | | BETA: splitting (27) gives: % 151.32/22.44 | | % 151.32/22.44 | | Case 1: % 151.32/22.44 | | | % 151.32/22.44 | | | (203) ~ (all_16_2 = e0) % 151.32/22.44 | | | % 151.32/22.44 | | | REDUCE: (52), (203) imply: % 151.32/22.44 | | | (204) ~ (all_10_2 = e0) % 151.32/22.44 | | | % 151.32/22.44 | | | BETA: splitting (68) gives: % 151.32/22.44 | | | % 151.32/22.44 | | | Case 1: % 151.32/22.44 | | | | % 151.32/22.44 | | | | (205) ~ (all_18_2 = e0) % 151.32/22.44 | | | | % 151.32/22.44 | | | | REDUCE: (108), (205) imply: % 151.32/22.44 | | | | (206) ~ (all_6_2 = e0) % 151.32/22.44 | | | | % 151.32/22.44 | | | | BETA: splitting (153) gives: % 151.32/22.44 | | | | % 151.32/22.44 | | | | Case 1: % 151.32/22.44 | | | | | % 151.32/22.44 | | | | | (207) ~ (all_22_1 = e0) % 151.32/22.44 | | | | | % 151.32/22.44 | | | | | REDUCE: (129), (207) imply: % 151.32/22.44 | | | | | (208) $false % 151.32/22.44 | | | | | % 151.32/22.44 | | | | | CLOSE: (208) is inconsistent. % 151.32/22.44 | | | | | % 151.32/22.44 | | | | Case 2: % 151.32/22.44 | | | | | % 151.32/22.44 | | | | | (209) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 151.32/22.44 | | | | | % 151.32/22.44 | | | | | BETA: splitting (126) gives: % 151.32/22.44 | | | | | % 151.32/22.44 | | | | | Case 1: % 151.32/22.44 | | | | | | % 151.32/22.44 | | | | | | (210) ~ (all_32_1 = e0) % 151.32/22.44 | | | | | | % 151.32/22.44 | | | | | | REDUCE: (134), (210) imply: % 151.32/22.44 | | | | | | (211) ~ (all_10_1 = e0) % 151.32/22.44 | | | | | | % 151.32/22.44 | | | | | | BETA: splitting (58) gives: % 151.32/22.44 | | | | | | % 151.32/22.44 | | | | | | Case 1: % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | (212) all_56_15 = e0 % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | COMBINE_EQS: (8), (212) imply: % 151.32/22.44 | | | | | | | (213) all_4_2 = e0 % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | SIMP: (213) implies: % 151.32/22.44 | | | | | | | (214) all_4_2 = e0 % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | COMBINE_EQS: (2), (214) imply: % 151.32/22.44 | | | | | | | (215) all_58_31 = e0 % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | REDUCE: (182), (214) imply: % 151.32/22.44 | | | | | | | (216) ~ (all_52_7 = e0) % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | REDUCE: (157), (214) imply: % 151.32/22.44 | | | | | | | (217) ~ (all_52_12 = e0) % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | REDUCE: (63), (214) imply: % 151.32/22.44 | | | | | | | (218) ~ (all_52_13 = e0) % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | REDUCE: (178), (214) imply: % 151.32/22.44 | | | | | | | (219) ~ (all_52_14 = e0) % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | REDUCE: (164), (214) imply: % 151.32/22.44 | | | | | | | (220) op(e0, all_4_1) = all_4_0 % 151.32/22.44 | | | | | | | % 151.32/22.44 | | | | | | | REDUCE: (195), (214) imply: % 151.32/22.44 | | | | | | | (221) op(e0, e0) = all_4_1 % 151.32/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (33), (214) imply: % 151.45/22.44 | | | | | | | (222) op(e0, e0) = all_58_27 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (152), (214) imply: % 151.45/22.44 | | | | | | | (223) op(e0, e0) = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 151.45/22.44 | | | | | | | simplifying with (221), (222) gives: % 151.45/22.44 | | | | | | | (224) all_58_27 = all_4_1 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, % 151.45/22.44 | | | | | | | simplifying with (222), (223) gives: % 151.45/22.44 | | | | | | | (225) all_58_27 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | COMBINE_EQS: (224), (225) imply: % 151.45/22.44 | | | | | | | (226) all_4_1 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | SIMP: (226) implies: % 151.45/22.44 | | | | | | | (227) all_4_1 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (220), (227) imply: % 151.45/22.44 | | | | | | | (228) op(e0, e0) = all_4_0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, % 151.45/22.44 | | | | | | | simplifying with (223), (228) gives: % 151.45/22.44 | | | | | | | (229) all_4_0 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (73), (229) imply: % 151.45/22.44 | | | | | | | (230) ~ (e1 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REF_CLOSE: (3), (4), (9), (10), (11), (12), (14), (15), (16), % 151.45/22.44 | | | | | | | (18), (24), (26), (28), (29), (30), (31), (32), (34), % 151.45/22.44 | | | | | | | (36), (38), (41), (44), (45), (48), (49), (50), (53), % 151.45/22.44 | | | | | | | (57), (60), (61), (62), (64), (66), (67), (69), (70), % 151.45/22.44 | | | | | | | (71), (72), (75), (77), (78), (79), (80), (83), (84), % 151.45/22.44 | | | | | | | (86), (88), (89), (91), (92), (97), (98), (100), (101), % 151.45/22.44 | | | | | | | (104), (105), (106), (107), (109), (110), (111), (112), % 151.45/22.44 | | | | | | | (113), (114), (115), (116), (118), (120), (121), (123), % 151.45/22.44 | | | | | | | (124), (125), (128), (131), (132), (133), (136), (137), % 151.45/22.44 | | | | | | | (138), (139), (140), (142), (143), (147), (148), (150), % 151.45/22.44 | | | | | | | (151), (154), (159), (160), (161), (162), (163), (165), % 151.45/22.44 | | | | | | | (166), (168), (171), (175), (176), (177), (179), (180), % 151.45/22.44 | | | | | | | (181), (183), (184), (186), (187), (188), (189), (190), % 151.45/22.44 | | | | | | | (191), (192), (193), (194), (196), (197), (199), (200), % 151.45/22.44 | | | | | | | (201), (202), (204), (206), (209), (211), (212), (215), % 151.45/22.44 | | | | | | | (216), (217), (218), (219), (225) are inconsistent by % 151.45/22.44 | | | | | | | sub-proof #134. % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | Case 2: % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | (231) ~ (all_56_15 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REF_CLOSE: (2), (4), (8), (59), (101), (109), (138), (163), (186), % 151.45/22.44 | | | | | | | (188), (204), (206), (231) are inconsistent by % 151.45/22.44 | | | | | | | sub-proof #132. % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | End of split % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | Case 2: % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | | (232) all_32_1 = e0 % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | | COMBINE_EQS: (134), (232) imply: % 151.45/22.44 | | | | | | (233) all_10_1 = e0 % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | | REDUCE: (44), (233) imply: % 151.45/22.44 | | | | | | (234) op(all_10_2, e0) = all_10_0 % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | | BETA: splitting (58) gives: % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | | Case 1: % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | (235) all_56_15 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | COMBINE_EQS: (8), (235) imply: % 151.45/22.44 | | | | | | | (236) all_4_2 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | SIMP: (236) implies: % 151.45/22.44 | | | | | | | (237) all_4_2 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | COMBINE_EQS: (2), (237) imply: % 151.45/22.44 | | | | | | | (238) all_58_31 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (182), (237) imply: % 151.45/22.44 | | | | | | | (239) ~ (all_52_7 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (157), (237) imply: % 151.45/22.44 | | | | | | | (240) ~ (all_52_12 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (63), (237) imply: % 151.45/22.44 | | | | | | | (241) ~ (all_52_13 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (178), (237) imply: % 151.45/22.44 | | | | | | | (242) ~ (all_52_14 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (164), (237) imply: % 151.45/22.44 | | | | | | | (243) op(e0, all_4_1) = all_4_0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (195), (237) imply: % 151.45/22.44 | | | | | | | (244) op(e0, e0) = all_4_1 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (33), (237) imply: % 151.45/22.44 | | | | | | | (245) op(e0, e0) = all_58_27 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (152), (237) imply: % 151.45/22.44 | | | | | | | (246) op(e0, e0) = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 151.45/22.44 | | | | | | | simplifying with (244), (245) gives: % 151.45/22.44 | | | | | | | (247) all_58_27 = all_4_1 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, % 151.45/22.44 | | | | | | | simplifying with (245), (246) gives: % 151.45/22.44 | | | | | | | (248) all_58_27 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | COMBINE_EQS: (247), (248) imply: % 151.45/22.44 | | | | | | | (249) all_4_1 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | SIMP: (249) implies: % 151.45/22.44 | | | | | | | (250) all_4_1 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (243), (250) imply: % 151.45/22.44 | | | | | | | (251) op(e0, e0) = all_4_0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, % 151.45/22.44 | | | | | | | simplifying with (246), (251) gives: % 151.45/22.44 | | | | | | | (252) all_4_0 = e0 % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REDUCE: (73), (252) imply: % 151.45/22.44 | | | | | | | (253) ~ (e1 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REF_CLOSE: (3), (4), (9), (10), (11), (12), (14), (15), (16), % 151.45/22.44 | | | | | | | (17), (18), (24), (26), (28), (29), (30), (31), (32), % 151.45/22.44 | | | | | | | (34), (36), (38), (41), (44), (45), (48), (49), (50), % 151.45/22.44 | | | | | | | (53), (57), (60), (61), (62), (64), (66), (67), (69), % 151.45/22.44 | | | | | | | (70), (71), (72), (75), (77), (78), (79), (80), (83), % 151.45/22.44 | | | | | | | (84), (86), (89), (91), (92), (97), (98), (100), (101), % 151.45/22.44 | | | | | | | (104), (105), (106), (107), (109), (110), (111), (112), % 151.45/22.44 | | | | | | | (113), (114), (115), (116), (118), (120), (121), (123), % 151.45/22.44 | | | | | | | (124), (125), (128), (131), (132), (133), (136), (137), % 151.45/22.44 | | | | | | | (138), (139), (140), (142), (143), (147), (148), (150), % 151.45/22.44 | | | | | | | (151), (154), (159), (160), (161), (162), (163), (165), % 151.45/22.44 | | | | | | | (166), (168), (171), (175), (176), (177), (179), (180), % 151.45/22.44 | | | | | | | (181), (183), (184), (186), (187), (188), (189), (190), % 151.45/22.44 | | | | | | | (191), (192), (193), (194), (196), (197), (199), (200), % 151.45/22.44 | | | | | | | (201), (202), (204), (206), (209), (234), (235), (238), % 151.45/22.44 | | | | | | | (239), (240), (241), (242), (248) are inconsistent by % 151.45/22.44 | | | | | | | sub-proof #130. % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | Case 2: % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | (254) ~ (all_56_15 = e0) % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | | REF_CLOSE: (2), (4), (8), (59), (101), (109), (138), (163), (186), % 151.45/22.44 | | | | | | | (188), (204), (206), (254) are inconsistent by % 151.45/22.44 | | | | | | | sub-proof #132. % 151.45/22.44 | | | | | | | % 151.45/22.44 | | | | | | End of split % 151.45/22.44 | | | | | | % 151.45/22.44 | | | | | End of split % 151.45/22.44 | | | | | % 151.45/22.44 | | | | End of split % 151.45/22.44 | | | | % 151.45/22.44 | | | Case 2: % 151.45/22.44 | | | | % 151.45/22.44 | | | | (255) all_18_2 = e0 % 151.45/22.44 | | | | % 151.45/22.44 | | | | COMBINE_EQS: (108), (255) imply: % 151.45/22.44 | | | | (256) all_6_2 = e0 % 151.45/22.44 | | | | % 151.45/22.44 | | | | SIMP: (256) implies: % 151.45/22.44 | | | | (257) all_6_2 = e0 % 151.45/22.44 | | | | % 151.45/22.44 | | | | COMBINE_EQS: (159), (257) imply: % 151.45/22.44 | | | | (258) all_56_8 = e0 % 151.45/22.44 | | | | % 151.45/22.44 | | | | COMBINE_EQS: (188), (257) imply: % 151.45/22.44 | | | | (259) all_58_30 = e0 % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (57), (257) imply: % 151.45/22.44 | | | | (260) ~ (all_52_2 = e0) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (10), (257) imply: % 151.45/22.44 | | | | (261) ~ (all_52_6 = e0) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (48), (257) imply: % 151.45/22.44 | | | | (262) ~ (all_52_8 = e0) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (149), (257) imply: % 151.45/22.44 | | | | (263) ~ (all_52_9 = e0) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (122), (257) imply: % 151.45/22.44 | | | | (264) ~ (all_52_11 = e0) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (193), (257) imply: % 151.45/22.44 | | | | (265) ~ (all_52_14 = e0) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (119), (257) imply: % 151.45/22.44 | | | | (266) op(e0, e1) = all_6_1 % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (15), (257) imply: % 151.45/22.44 | | | | (267) op(e1, e0) = all_58_18 % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (160), (257) imply: % 151.45/22.44 | | | | (268) op(e1, e1) = e0 % 151.45/22.44 | | | | % 151.45/22.44 | | | | GROUND_INST: instantiating (4) with all_52_11, all_6_1, e1, e0, % 151.45/22.44 | | | | simplifying with (39), (266) gives: % 151.45/22.44 | | | | (269) all_52_11 = all_6_1 % 151.45/22.44 | | | | % 151.45/22.44 | | | | GROUND_INST: instantiating (4) with all_52_14, all_58_18, e0, e1, % 151.45/22.44 | | | | simplifying with (89), (267) gives: % 151.45/22.44 | | | | (270) all_58_18 = all_52_14 % 151.45/22.44 | | | | % 151.45/22.44 | | | | COMBINE_EQS: (76), (269) imply: % 151.45/22.44 | | | | (271) all_54_14 = all_6_1 % 151.45/22.44 | | | | % 151.45/22.44 | | | | COMBINE_EQS: (137), (269) imply: % 151.45/22.44 | | | | (272) all_56_14 = all_6_1 % 151.45/22.44 | | | | % 151.45/22.44 | | | | COMBINE_EQS: (20), (269) imply: % 151.45/22.44 | | | | (273) all_58_26 = all_6_1 % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (154), (269) imply: % 151.45/22.44 | | | | (274) ~ (all_52_3 = all_6_1) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (146), (269) imply: % 151.45/22.44 | | | | (275) ~ (all_52_7 = all_6_1) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (22), (269) imply: % 151.45/22.44 | | | | (276) ~ (all_52_8 = all_6_1) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (90), (269) imply: % 151.45/22.44 | | | | (277) ~ (all_52_9 = all_6_1) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (23), (269) imply: % 151.45/22.44 | | | | (278) ~ (all_6_1 = all_4_2) % 151.45/22.44 | | | | % 151.45/22.44 | | | | REDUCE: (264), (269) imply: % 151.45/22.44 | | | | (279) ~ (all_6_1 = e0) % 151.45/22.44 | | | | % 151.45/22.45 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), % 151.45/22.45 | | | | (16), (17), (18), (19), (21), (24), (25), (26), (28), (29), % 151.45/22.45 | | | | (30), (31), (32), (34), (36), (37), (38), (40), (41), (42), % 151.45/22.45 | | | | (45), (46), (47), (48), (49), (50), (51), (53), (54), (55), % 151.45/22.45 | | | | (56), (58), (61), (62), (63), (64), (66), (67), (69), (70), % 151.45/22.45 | | | | (71), (72), (74), (75), (77), (78), (79), (80), (81), (82), % 151.45/22.45 | | | | (83), (84), (86), (87), (88), (89), (91), (92), (93), (94), % 151.45/22.45 | | | | (95), (96), (97), (100), (101), (102), (103), (104), (105), % 151.45/22.45 | | | | (106), (107), (109), (110), (111), (112), (113), (114), % 151.45/22.45 | | | | (115), (116), (118), (120), (124), (125), (130), (131), % 151.45/22.45 | | | | (132), (133), (135), (136), (138), (139), (140), (141), % 151.45/22.45 | | | | (142), (144), (145), (147), (148), (150), (151), (152), % 151.45/22.45 | | | | (155), (156), (157), (158), (161), (162), (163), (165), % 151.45/22.45 | | | | (166), (168), (169), (170), (171), (173), (175), (176), % 151.45/22.45 | | | | (178), (180), (181), (182), (183), (184), (185), (186), % 151.45/22.45 | | | | (187), (188), (190), (191), (192), (194), (195), (196), % 151.45/22.45 | | | | (197), (198), (199), (200), (201), (204), (258), (259), % 151.45/22.45 | | | | (260), (261), (262), (263), (265), (268), (271), (272), % 151.45/22.45 | | | | (273), (274), (275), (276), (277), (278), (279) are % 151.45/22.45 | | | | inconsistent by sub-proof #102. % 151.45/22.45 | | | | % 151.45/22.45 | | | End of split % 151.45/22.45 | | | % 151.45/22.45 | | Case 2: % 151.45/22.45 | | | % 151.45/22.45 | | | (280) all_16_2 = e0 % 151.45/22.45 | | | (281) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 151.45/22.45 | | | % 151.45/22.45 | | | COMBINE_EQS: (52), (280) imply: % 151.45/22.45 | | | (282) all_10_2 = e0 % 151.45/22.45 | | | % 151.45/22.45 | | | SIMP: (282) implies: % 151.45/22.45 | | | (283) all_10_2 = e0 % 151.45/22.45 | | | % 151.45/22.45 | | | COMBINE_EQS: (151), (283) imply: % 151.45/22.45 | | | (284) all_56_0 = e0 % 151.45/22.45 | | | % 151.45/22.45 | | | COMBINE_EQS: (138), (283) imply: % 151.45/22.45 | | | (285) all_58_28 = e0 % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (201), (283) imply: % 151.45/22.45 | | | (286) ~ (all_52_1 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (150), (283) imply: % 151.45/22.45 | | | (287) ~ (all_52_2 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (158), (283) imply: % 151.45/22.45 | | | (288) ~ (all_52_3 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (187), (283) imply: % 151.45/22.45 | | | (289) ~ (all_52_4 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (18), (283) imply: % 151.45/22.45 | | | (290) ~ (all_52_8 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (132), (283) imply: % 151.45/22.45 | | | (291) ~ (all_52_12 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (44), (283) imply: % 151.45/22.45 | | | (292) op(e0, all_10_1) = all_10_0 % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (196), (283) imply: % 151.45/22.45 | | | (293) op(e0, e3) = all_10_1 % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (123), (283) imply: % 151.45/22.45 | | | (294) op(e3, e0) = all_58_0 % 151.45/22.45 | | | % 151.45/22.45 | | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, % 151.45/22.45 | | | simplifying with (127), (293) gives: % 151.45/22.45 | | | (295) all_52_3 = all_10_1 % 151.45/22.45 | | | % 151.45/22.45 | | | GROUND_INST: instantiating (4) with all_52_12, all_58_0, e0, e3, % 151.45/22.45 | | | simplifying with (105), (294) gives: % 151.45/22.45 | | | (296) all_58_0 = all_52_12 % 151.45/22.45 | | | % 151.45/22.45 | | | COMBINE_EQS: (79), (295) imply: % 151.45/22.45 | | | (297) all_56_12 = all_10_1 % 151.45/22.45 | | | % 151.45/22.45 | | | COMBINE_EQS: (155), (295) imply: % 151.45/22.45 | | | (298) all_58_22 = all_10_1 % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (133), (295) imply: % 151.45/22.45 | | | (299) ~ (all_52_1 = all_10_1) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (6), (295) imply: % 151.45/22.45 | | | (300) ~ (all_52_2 = all_10_1) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (80), (295) imply: % 151.45/22.45 | | | (301) ~ (all_52_7 = all_10_1) % 151.45/22.45 | | | % 151.45/22.45 | | | SIMP: (301) implies: % 151.45/22.45 | | | (302) ~ (all_52_7 = all_10_1) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (154), (295) imply: % 151.45/22.45 | | | (303) ~ (all_52_11 = all_10_1) % 151.45/22.45 | | | % 151.45/22.45 | | | SIMP: (303) implies: % 151.45/22.45 | | | (304) ~ (all_52_11 = all_10_1) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (87), (295) imply: % 151.45/22.45 | | | (305) ~ (all_10_1 = all_4_2) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (288), (295) imply: % 151.45/22.45 | | | (306) ~ (all_10_1 = e0) % 151.45/22.45 | | | % 151.45/22.45 | | | REDUCE: (51), (295) imply: % 151.45/22.45 | | | (307) op(e0, all_10_1) = all_58_21 % 151.45/22.45 | | | % 151.45/22.45 | | | GROUND_INST: instantiating (4) with all_10_0, all_58_21, all_10_1, e0, % 151.45/22.45 | | | simplifying with (292), (307) gives: % 151.45/22.45 | | | (308) all_58_21 = all_10_0 % 151.45/22.45 | | | % 151.45/22.45 | | | BETA: splitting (144) gives: % 151.45/22.45 | | | % 151.45/22.45 | | | Case 1: % 151.45/22.45 | | | | % 151.45/22.45 | | | | (309) ~ (all_20_2 = e1) % 151.45/22.45 | | | | % 151.45/22.45 | | | | REDUCE: (82), (309) imply: % 151.45/22.45 | | | | (310) ~ (all_4_2 = e1) % 151.45/22.45 | | | | % 151.45/22.45 | | | | BETA: splitting (58) gives: % 151.45/22.45 | | | | % 151.45/22.45 | | | | Case 1: % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | (311) all_56_15 = e0 % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | COMBINE_EQS: (8), (311) imply: % 151.45/22.45 | | | | | (312) all_4_2 = e0 % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | SIMP: (312) implies: % 151.45/22.45 | | | | | (313) all_4_2 = e0 % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | COMBINE_EQS: (2), (313) imply: % 151.45/22.45 | | | | | (314) all_58_31 = e0 % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | REDUCE: (182), (313) imply: % 151.45/22.45 | | | | | (315) ~ (all_52_7 = e0) % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | REDUCE: (63), (313) imply: % 151.45/22.45 | | | | | (316) ~ (all_52_13 = e0) % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | REDUCE: (310), (313) imply: % 151.45/22.45 | | | | | (317) ~ (e1 = e0) % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | BETA: splitting (85) gives: % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | Case 1: % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | (318) all_56_4 = e0 % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | COMBINE_EQS: (28), (318) imply: % 151.45/22.45 | | | | | | (319) all_52_8 = e0 % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | REDUCE: (290), (319) imply: % 151.45/22.45 | | | | | | (320) $false % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | CLOSE: (320) is inconsistent. % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | Case 2: % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | (321) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | BETA: splitting (321) gives: % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | Case 1: % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | (322) all_56_5 = e0 % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | COMBINE_EQS: (75), (322) imply: % 151.45/22.45 | | | | | | | (323) all_52_9 = e0 % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | REDUCE: (90), (323) imply: % 151.45/22.45 | | | | | | | (324) ~ (all_52_11 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | SIMP: (324) implies: % 151.45/22.45 | | | | | | | (325) ~ (all_52_11 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | REDUCE: (136), (323) imply: % 151.45/22.45 | | | | | | | (326) ~ (all_8_2 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | SIMP: (326) implies: % 151.45/22.45 | | | | | | | (327) ~ (all_8_2 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | REDUCE: (149), (323) imply: % 151.45/22.45 | | | | | | | (328) ~ (all_6_2 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | SIMP: (328) implies: % 151.45/22.45 | | | | | | | (329) ~ (all_6_2 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | BETA: splitting (135) gives: % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | (330) all_54_14 = e0 % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | REF_CLOSE: (76), (325), (330) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | #517. % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | (331) ~ (all_54_14 = e0) % 151.45/22.45 | | | | | | | | (332) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | BETA: splitting (166) gives: % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | (333) all_54_1 = e0 % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | REF_CLOSE: (32), (289), (333) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | #798. % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | (334) ~ (all_54_1 = e0) % 151.45/22.45 | | | | | | | | | (335) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | BETA: splitting (183) gives: % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | (336) all_54_2 = e0 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | COMBINE_EQS: (12), (336) imply: % 151.45/22.45 | | | | | | | | | | (337) all_52_8 = e0 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | REDUCE: (290), (337) imply: % 151.45/22.45 | | | | | | | | | | (338) $false % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | CLOSE: (338) is inconsistent. % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | (339) ~ (all_54_2 = e0) % 151.45/22.45 | | | | | | | | | | (340) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | BETA: splitting (171) gives: % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | (341) all_58_28 = e3 % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | REF_CLOSE: (124), (285), (341) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | | | #689. % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | (342) ~ (all_58_28 = e3) % 151.45/22.45 | | | | | | | | | | | (343) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | REDUCE: (285), (342) imply: % 151.45/22.45 | | | | | | | | | | | (344) ~ (e3 = e0) % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | BETA: splitting (31) gives: % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | (345) all_58_28 = e2 % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | REF_CLOSE: (148), (285), (345) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | | | | #688. % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | (346) ~ (all_58_28 = e2) % 151.45/22.45 | | | | | | | | | | | | (347) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | REDUCE: (285), (346) imply: % 151.45/22.45 | | | | | | | | | | | | (348) ~ (e2 = e0) % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | BETA: splitting (190) gives: % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | (349) all_58_28 = e1 % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | REF_CLOSE: (180), (285), (349) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | | | | | #690. % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | (350) ~ (all_58_28 = e1) % 151.45/22.45 | | | | | | | | | | | | | (351) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | BETA: splitting (147) gives: % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | (352) all_56_12 = e1 % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | COMBINE_EQS: (297), (352) imply: % 151.45/22.45 | | | | | | | | | | | | | | (353) all_10_1 = e1 % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | COMBINE_EQS: (172), (353) imply: % 151.45/22.45 | | | | | | | | | | | | | | (354) all_16_1 = e1 % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | REDUCE: (304), (353) imply: % 151.45/22.45 | | | | | | | | | | | | | | (355) ~ (all_52_11 = e1) % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | REDUCE: (292), (353) imply: % 151.45/22.45 | | | | | | | | | | | | | | (356) op(e0, e1) = all_10_0 % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | BETA: splitting (281) gives: % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | (357) ~ (all_16_1 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REDUCE: (354), (357) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (358) $false % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | (359) ~ (all_16_0 = e2) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REDUCE: (174), (359) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (360) ~ (all_10_0 = e2) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_11, all_10_0, e1, % 151.45/22.45 | | | | | | | | | | | | | | | e0, simplifying with (39), (356) gives: % 151.45/22.45 | | | | | | | | | | | | | | | (361) all_52_11 = all_10_0 % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | COMBINE_EQS: (76), (361) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (362) all_54_14 = all_10_0 % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | COMBINE_EQS: (137), (361) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (363) all_56_14 = all_10_0 % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REDUCE: (146), (361) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (364) ~ (all_52_7 = all_10_0) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REDUCE: (22), (361) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (365) ~ (all_52_8 = all_10_0) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REDUCE: (122), (361) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (366) ~ (all_10_0 = all_6_2) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REDUCE: (355), (361) imply: % 151.45/22.45 | | | | | | | | | | | | | | | (367) ~ (all_10_0 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | (368) all_56_12 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (368) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | (369) e2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | SIMP: (369) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | (370) e2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | REDUCE: (104), (370) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | (371) $false % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | CLOSE: (371) is inconsistent. % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | (372) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | (373) all_56_13 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (373) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (374) all_52_7 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REDUCE: (56), (374) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (375) ~ (all_52_4 = e2) % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REDUCE: (364), (374) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (376) ~ (all_10_0 = e2) % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | (377) all_54_14 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (362), (367), (377) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | | | | | | | | | | #101. % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | (378) all_54_14 = e3 | all_54_14 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (379) all_54_14 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (360), (362), (379) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | | | | | | | | | | | #100. % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (380) all_54_14 = e3 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (362), (380) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (381) all_10_0 = e3 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | SIMP: (381) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (382) all_10_0 = e3 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | REDUCE: (365), (382) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (383) ~ (all_52_8 = e3) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | REDUCE: (366), (382) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (384) ~ (all_6_2 = e3) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | SIMP: (384) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | (385) ~ (all_6_2 = e3) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | (386) all_58_29 = e3 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (386) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | (387) all_8_2 = e3 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (387) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | (388) ~ (all_52_4 = e3) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (389) all_56_1 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (389) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (390) all_52_4 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (390) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_52_8 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | SIMP: (391) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (392) ~ (all_52_8 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (38), (48), (101), (109), (188), (199), % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (290), (314), (327), (340), (347), (383), (392) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #152. % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (393) ~ (all_56_1 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (393) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_52_4 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (335), (375), (388), (394) are inconsistent % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | (395) all_58_30 = e3 | all_58_31 = e3 % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (188), (314), (385), (395) are inconsistent % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | by sub-proof #768. % 151.45/22.45 | | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | (396) all_56_14 = e2 | all_56_15 = e2 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (311), (360), (363), (396) are inconsistent % 151.45/22.45 | | | | | | | | | | | | | | | | | by sub-proof #515. % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | (397) ~ (all_56_12 = e1) % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | REDUCE: (297), (397) imply: % 151.45/22.45 | | | | | | | | | | | | | | (398) ~ (all_10_1 = e1) % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | BETA: splitting (41) gives: % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | (399) all_56_0 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | REF_CLOSE: (180), (284), (399) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | | | | | | | #516. % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | (400) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | (401) all_56_6 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (401) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | (402) all_52_2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | SIMP: (402) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | (403) all_52_2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | REDUCE: (57), (403) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | (404) ~ (all_6_2 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | SIMP: (404) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | (405) ~ (all_6_2 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | BETA: splitting (351) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | (406) all_58_29 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (406) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (407) all_8_2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | SIMP: (407) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | | (408) all_8_2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REDUCE: (29), (408) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (409) ~ (all_52_4 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (29), (32), (38), (45), (84), (101), % 151.45/22.45 | | | | | | | | | | | | | | | | | (109), (124), (148), (161), (188), (191), (199), % 151.45/22.45 | | | | | | | | | | | | | | | | | (289), (314), (327), (335), (343), (347), (409) % 151.45/22.45 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138. % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | (410) all_58_30 = e1 | all_58_31 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (188), (310), (405), (410) are inconsistent % 151.45/22.45 | | | | | | | | | | | | | | | | | by sub-proof #673. % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | (411) ~ (all_56_6 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | REDUCE: (106), (411) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | (412) ~ (all_52_2 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | BETA: splitting (400) gives: % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | (413) all_56_2 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (413) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (414) all_52_1 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REDUCE: (299), (414) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (415) ~ (all_10_1 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REDUCE: (91), (414) imply: % 151.45/22.45 | | | | | | | | | | | | | | | | | (416) ~ (all_8_2 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | SIMP: (416) implies: % 151.45/22.45 | | | | | | | | | | | | | | | | | (417) ~ (all_8_2 = e1) % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (12), (28), (29), (32), (38), % 151.45/22.45 | | | | | | | | | | | | | | | | | (41), (46), (53), (57), (61), (74), (78), (83), % 151.45/22.45 | | | | | | | | | | | | | | | | | (84), (91), (92), (97), (100), (101), (105), % 151.45/22.45 | | | | | | | | | | | | | | | | | (106), (109), (120), (124), (125), (131), (140), % 151.45/22.45 | | | | | | | | | | | | | | | | | (148), (161), (168), (173), (181), (186), (188), % 151.45/22.45 | | | | | | | | | | | | | | | | | (193), (197), (199), (284), (297), (310), (315), % 151.45/22.45 | | | | | | | | | | | | | | | | | (329), (335), (340), (351), (398), (417) are % 151.45/22.45 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #99. % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | (418) all_56_6 = e1 | all_56_12 = e1 % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (297), (398), (412), (418) are inconsistent % 151.45/22.45 | | | | | | | | | | | | | | | | | by sub-proof #404. % 151.45/22.45 | | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | End of split % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | End of split % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | End of split % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | Case 2: % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | (419) ~ (all_56_5 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | REDUCE: (75), (419) imply: % 151.45/22.45 | | | | | | | (420) ~ (all_52_9 = e0) % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | REF_CLOSE: (4), (34), (75), (92), (109), (125), (131), (163), % 151.45/22.45 | | | | | | | (186), (286), (316), (420) are inconsistent by % 151.45/22.45 | | | | | | | sub-proof #125. % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | End of split % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | End of split % 151.45/22.45 | | | | | % 151.45/22.45 | | | | Case 2: % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | (421) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.45 | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | ALPHA: (421) implies: % 151.45/22.45 | | | | | (422) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.45/22.45 | | | | | (423) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | BETA: splitting (85) gives: % 151.45/22.45 | | | | | % 151.45/22.45 | | | | | Case 1: % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | (424) all_56_4 = e0 % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | COMBINE_EQS: (28), (424) imply: % 151.45/22.45 | | | | | | (425) all_52_8 = e0 % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | REDUCE: (290), (425) imply: % 151.45/22.45 | | | | | | (426) $false % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | CLOSE: (426) is inconsistent. % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | Case 2: % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | (427) ~ (all_56_4 = e0) % 151.45/22.45 | | | | | | (428) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | BETA: splitting (177) gives: % 151.45/22.45 | | | | | | % 151.45/22.45 | | | | | | Case 1: % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | (429) all_56_6 = e0 % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | COMBINE_EQS: (106), (429) imply: % 151.45/22.45 | | | | | | | (430) all_52_2 = e0 % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | REDUCE: (287), (430) imply: % 151.45/22.45 | | | | | | | (431) $false % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | CLOSE: (431) is inconsistent. % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | Case 2: % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | (432) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | BETA: splitting (166) gives: % 151.45/22.45 | | | | | | | % 151.45/22.45 | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | (433) all_54_1 = e0 % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | REF_CLOSE: (32), (289), (433) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | #798. % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | (434) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | BETA: splitting (183) gives: % 151.45/22.45 | | | | | | | | % 151.45/22.45 | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | (435) all_54_2 = e0 % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | REF_CLOSE: (12), (290), (435) are inconsistent by sub-proof % 151.45/22.45 | | | | | | | | | #860. % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | Case 2: % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | (436) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | BETA: splitting (43) gives: % 151.45/22.45 | | | | | | | | | % 151.45/22.45 | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | (437) all_54_13 = e0 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | COMBINE_EQS: (5), (437) imply: % 151.45/22.45 | | | | | | | | | | (438) all_52_7 = e0 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | SIMP: (438) implies: % 151.45/22.45 | | | | | | | | | | (439) all_52_7 = e0 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | COMBINE_EQS: (110), (439) imply: % 151.45/22.45 | | | | | | | | | | (440) all_56_13 = e0 % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | REDUCE: (42), (439) imply: % 151.45/22.45 | | | | | | | | | | (441) ~ (all_52_6 = e0) % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | REDUCE: (302), (439) imply: % 151.45/22.45 | | | | | | | | | | (442) ~ (all_10_1 = e0) % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | BETA: splitting (428) gives: % 151.45/22.45 | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | Case 1: % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | (443) all_56_5 = e0 % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | COMBINE_EQS: (75), (443) imply: % 151.45/22.45 | | | | | | | | | | | (444) all_52_9 = e0 % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | REDUCE: (90), (444) imply: % 151.45/22.45 | | | | | | | | | | | (445) ~ (all_52_11 = e0) % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | SIMP: (445) implies: % 151.45/22.45 | | | | | | | | | | | (446) ~ (all_52_11 = e0) % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | REDUCE: (116), (444) imply: % 151.45/22.45 | | | | | | | | | | | (447) ~ (all_52_13 = e0) % 151.45/22.45 | | | | | | | | | | | % 151.45/22.45 | | | | | | | | | | | SIMP: (447) implies: % 151.45/22.46 | | | | | | | | | | | (448) ~ (all_52_13 = e0) % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | REDUCE: (99), (444) imply: % 151.45/22.46 | | | | | | | | | | | (449) op(e2, e1) = e0 % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | BETA: splitting (423) gives: % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | (450) all_56_9 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | COMBINE_EQS: (100), (450) imply: % 151.45/22.46 | | | | | | | | | | | | (451) all_52_12 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | REDUCE: (291), (451) imply: % 151.45/22.46 | | | | | | | | | | | | (452) $false % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | CLOSE: (452) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | (453) all_56_10 = e0 | all_56_11 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | BETA: splitting (453) gives: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | (454) all_56_10 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | COMBINE_EQS: (131), (454) imply: % 151.45/22.46 | | | | | | | | | | | | | (455) all_52_13 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REDUCE: (448), (455) imply: % 151.45/22.46 | | | | | | | | | | | | | (456) $false % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | CLOSE: (456) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | (457) all_56_11 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | COMBINE_EQS: (83), (457) imply: % 151.45/22.46 | | | | | | | | | | | | | (458) all_52_14 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REDUCE: (193), (458) imply: % 151.45/22.46 | | | | | | | | | | | | | (459) ~ (all_6_2 = e0) % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | SIMP: (459) implies: % 151.45/22.46 | | | | | | | | | | | | | (460) ~ (all_6_2 = e0) % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REDUCE: (21), (458) imply: % 151.45/22.46 | | | | | | | | | | | | | (461) op(e1, e0) = all_58_19 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REDUCE: (89), (458) imply: % 151.45/22.46 | | | | | | | | | | | | | (462) op(e1, e0) = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_19, e0, e1, % 151.45/22.46 | | | | | | | | | | | | | simplifying with (461), (462) gives: % 151.45/22.46 | | | | | | | | | | | | | (463) all_58_19 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | BETA: splitting (120) gives: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | (464) all_56_9 = e1 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | COMBINE_EQS: (100), (464) imply: % 151.45/22.46 | | | | | | | | | | | | | | (465) all_52_12 = e1 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | SIMP: (465) implies: % 151.45/22.46 | | | | | | | | | | | | | | (466) all_52_12 = e1 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | REDUCE: (197), (466) imply: % 151.45/22.46 | | | | | | | | | | | | | | (467) ~ (all_52_4 = e1) % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | REDUCE: (61), (466) imply: % 151.45/22.46 | | | | | | | | | | | | | | (468) ~ (all_52_8 = e1) % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | REDUCE: (157), (466) imply: % 151.45/22.46 | | | | | | | | | | | | | | (469) ~ (all_4_2 = e1) % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | BETA: splitting (147) gives: % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | (470) all_56_12 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | COMBINE_EQS: (297), (470) imply: % 151.45/22.46 | | | | | | | | | | | | | | | (471) all_10_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | SIMP: (471) implies: % 151.45/22.46 | | | | | | | | | | | | | | | (472) all_10_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | REDUCE: (304), (472) imply: % 151.45/22.46 | | | | | | | | | | | | | | | (473) ~ (all_52_11 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | BETA: splitting (50) gives: % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | (474) all_56_4 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (474) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | (475) all_52_8 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | REDUCE: (468), (475) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | (476) $false % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | CLOSE: (476) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | (477) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | BETA: splitting (477) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | (478) all_56_5 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (180), (443), (478) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | | #305. % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | (479) all_56_8 = e1 | all_56_14 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | (480) all_56_8 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (480) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (481) all_6_2 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | SIMP: (481) implies: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (482) all_6_2 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | REDUCE: (10), (482) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (483) ~ (all_52_6 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (484) all_56_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (484) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (485) all_52_4 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | REDUCE: (467), (485) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (486) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | CLOSE: (486) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (487) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (487) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (488) all_56_3 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (488) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (489) all_8_2 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (64), (109), (441), (489) are inconsistent by % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | sub-proof #129. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (490) all_56_7 = e1 | all_56_13 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (180), (440), (483), (490) are inconsistent % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | by sub-proof #529. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | (491) all_56_14 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (473), (491) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | | | #811. % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | (492) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (23), (64), (101), (109), (122), % 151.45/22.46 | | | | | | | | | | | | | | | (137), (180), (188), (190), (285), (310), (440), % 151.45/22.46 | | | | | | | | | | | | | | | (441), (446), (492) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | #97. % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | (493) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | BETA: splitting (493) gives: % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | (494) all_56_10 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | COMBINE_EQS: (131), (494) imply: % 151.45/22.46 | | | | | | | | | | | | | | | (495) all_52_13 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | SIMP: (495) implies: % 151.45/22.46 | | | | | | | | | | | | | | | (496) all_52_13 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | REDUCE: (66), (496) imply: % 151.45/22.46 | | | | | | | | | | | | | | | (497) ~ (all_8_2 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | SIMP: (497) implies: % 151.45/22.46 | | | | | | | | | | | | | | | (498) ~ (all_8_2 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | REDUCE: (63), (496) imply: % 151.45/22.46 | | | | | | | | | | | | | | | (499) ~ (all_4_2 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | REDUCE: (169), (496) imply: % 151.45/22.46 | | | | | | | | | | | | | | | (500) op(e2, e1) = all_58_12 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | (501) all_58_28 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | REF_CLOSE: (180), (285), (501) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | #690. % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | (502) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | BETA: splitting (502) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | (503) all_58_29 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (503) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | (504) all_8_2 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | REDUCE: (498), (504) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | (505) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | CLOSE: (505) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | (506) ~ (all_58_29 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | (507) all_58_30 = e1 | all_58_31 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | BETA: splitting (507) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | (508) all_58_30 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (508) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (509) all_6_2 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (509) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (510) all_56_8 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | REDUCE: (10), (509) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (511) ~ (all_52_6 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (512) all_56_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (512) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (513) all_52_4 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | REDUCE: (97), (513) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (514) ~ (all_52_8 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | SIMP: (514) implies: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (515) ~ (all_52_8 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | REDUCE: (16), (513) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (516) op(e3, e1) = all_58_1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (517) all_56_12 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (517) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (518) all_10_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | SIMP: (518) implies: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (519) all_10_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (519) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (520) all_16_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (304), (519) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (521) ~ (all_52_11 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | REDUCE: (292), (519) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (522) op(e0, e1) = all_10_0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (523) ~ (all_16_1 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (520), (523) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (524) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | CLOSE: (524) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (525) ~ (all_16_0 = e2) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (525) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_10_0 = e2) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_11, all_10_0, e1, % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (39), (522) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (527) all_52_11 = all_10_0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e1, e2, % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | simplifying with (449), (500) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (528) all_58_12 = e0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_8, all_58_1, e1, e3, % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | simplifying with (143), (516) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (529) all_58_1 = all_52_8 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (527) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (530) all_54_14 = all_10_0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (527) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (531) all_56_14 = all_10_0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (527) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (532) ~ (all_52_8 = all_10_0) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | REDUCE: (521), (527) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | (533) ~ (all_10_0 = e1) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | (534) all_54_14 = e0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (530), (534) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | #479. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | (535) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | (536) all_54_14 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (533), (536) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | #101. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | (537) all_54_14 = e3 | all_54_14 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (538) all_56_4 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (538) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (539) all_52_8 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (539) implies: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (540) all_52_8 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (540) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (541) all_58_1 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_56_4 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (542) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (543) e3 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (543) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (544) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (544) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_56_5 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (443), (546) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (547) e3 = e0 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (547) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (548) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (548) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_56_8 = e3 | all_56_14 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_56_8 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (510), (550) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) e3 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (551) implies: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) e3 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (552) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (553) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_56_14 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (554) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_10_0 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (555) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_58_21 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (463), (528), (541), (556) are inconsistent % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #615. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (557) ~ (all_56_4 = e2) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (557) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | (558) ~ (all_52_8 = e2) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (537) gives: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_54_14 = e2 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (526), (530), (559) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | #100. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_54_14 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (560) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_10_0 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (561) implies: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_10_0 = e3 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (532), (562) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | (563) ~ (all_52_8 = e3) % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (436), (515), (558), (563) are inconsistent % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #554. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (564) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (23), (64), (101), (109), (122), % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (137), (180), (188), (190), (285), (310), (440), % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | (441), (446), (564) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | #97. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | (565) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (92), (180), (440), (498), (511), (565) are % 151.45/22.46 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #528. % 151.45/22.46 | | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | (566) all_58_31 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (566) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (567) all_4_2 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | REDUCE: (310), (567) imply: % 151.45/22.46 | | | | | | | | | | | | | | | | | | (568) $false % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | | CLOSE: (568) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | (569) all_56_11 = e1 | all_56_15 = e1 % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | | REF_CLOSE: (8), (180), (310), (457), (569) are inconsistent % 151.45/22.46 | | | | | | | | | | | | | | | by sub-proof #334. % 151.45/22.46 | | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | (570) ~ (all_56_5 = e0) % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | REDUCE: (75), (570) imply: % 151.45/22.46 | | | | | | | | | | | (571) ~ (all_52_9 = e0) % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | BETA: splitting (34) gives: % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | (572) all_56_2 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | COMBINE_EQS: (125), (572) imply: % 151.45/22.46 | | | | | | | | | | | | (573) all_52_1 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | REDUCE: (286), (573) imply: % 151.45/22.46 | | | | | | | | | | | | (574) $false % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | CLOSE: (574) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | (575) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | BETA: splitting (432) gives: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | (576) all_56_7 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | COMBINE_EQS: (9), (576) imply: % 151.45/22.46 | | | | | | | | | | | | | (577) all_52_6 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REDUCE: (441), (577) imply: % 151.45/22.46 | | | | | | | | | | | | | (578) $false % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | CLOSE: (578) is inconsistent. % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | (579) ~ (all_56_7 = e0) % 151.45/22.46 | | | | | | | | | | | | | (580) all_56_8 = e0 | all_56_11 = e0 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | BETA: splitting (580) gives: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | (581) all_56_8 = e0 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | COMBINE_EQS: (159), (581) imply: % 151.45/22.46 | | | | | | | | | | | | | | (582) all_6_2 = e0 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | COMBINE_EQS: (188), (582) imply: % 151.45/22.46 | | | | | | | | | | | | | | (583) all_58_30 = e0 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (64), (101), (109), (180), (190), (285), % 151.45/22.46 | | | | | | | | | | | | | | (310), (441), (583) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | #96. % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | (584) all_56_11 = e0 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | COMBINE_EQS: (83), (584) imply: % 151.45/22.46 | | | | | | | | | | | | | | (585) all_52_14 = e0 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | SIMP: (585) implies: % 151.45/22.46 | | | | | | | | | | | | | | (586) all_52_14 = e0 % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | REDUCE: (94), (586) imply: % 151.45/22.46 | | | | | | | | | | | | | | (587) ~ (all_52_13 = e0) % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | | REF_CLOSE: (4), (75), (92), (109), (131), (163), (186), % 151.45/22.46 | | | | | | | | | | | | | | (571), (575), (587) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | | | #126. % 151.45/22.46 | | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | % 151.45/22.46 | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | (588) ~ (all_54_13 = e0) % 151.45/22.46 | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | REDUCE: (5), (588) imply: % 151.45/22.46 | | | | | | | | | | (589) ~ (all_52_7 = e0) % 151.45/22.46 | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | BETA: splitting (422) gives: % 151.45/22.46 | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | (590) all_56_12 = e0 % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | REF_CLOSE: (297), (306), (590) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | #230. % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | (591) all_56_13 = e0 | all_56_14 = e0 % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | BETA: splitting (591) gives: % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | (592) all_56_13 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | REF_CLOSE: (110), (589), (592) are inconsistent by sub-proof % 151.45/22.46 | | | | | | | | | | | | #802. % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | (593) all_56_14 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | COMBINE_EQS: (137), (593) imply: % 151.45/22.46 | | | | | | | | | | | | (594) all_52_11 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | SIMP: (594) implies: % 151.45/22.46 | | | | | | | | | | | | (595) all_52_11 = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | REDUCE: (122), (595) imply: % 151.45/22.46 | | | | | | | | | | | | (596) ~ (all_6_2 = e0) % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | SIMP: (596) implies: % 151.45/22.46 | | | | | | | | | | | | (597) ~ (all_6_2 = e0) % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | REDUCE: (39), (595) imply: % 151.45/22.46 | | | | | | | | | | | | (598) op(e0, e1) = e0 % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | BETA: splitting (147) gives: % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | Case 1: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | (599) all_56_12 = e1 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | COMBINE_EQS: (297), (599) imply: % 151.45/22.46 | | | | | | | | | | | | | (600) all_10_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | SIMP: (600) implies: % 151.45/22.46 | | | | | | | | | | | | | (601) all_10_1 = e1 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REF_CLOSE: (4), (202), (292), (598), (601) are inconsistent % 151.45/22.46 | | | | | | | | | | | | | by sub-proof #491. % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | Case 2: % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | (602) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (9), (12), (28), (29), (32), % 151.45/22.46 | | | | | | | | | | | | | (38), (41), (42), (46), (53), (56), (57), (61), % 151.45/22.46 | | | | | | | | | | | | | (74), (78), (83), (84), (91), (92), (97), (100), % 151.45/22.46 | | | | | | | | | | | | | (101), (105), (106), (109), (110), (113), (120), % 151.45/22.46 | | | | | | | | | | | | | (124), (125), (131), (140), (148), (161), (163), % 151.45/22.46 | | | | | | | | | | | | | (168), (173), (180), (181), (182), (186), (188), % 151.45/22.46 | | | | | | | | | | | | | (190), (193), (197), (199), (284), (285), (297), % 151.45/22.46 | | | | | | | | | | | | | (302), (310), (434), (436), (589), (593), (597), % 151.45/22.46 | | | | | | | | | | | | | (602) are inconsistent by sub-proof #95. % 151.45/22.46 | | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | | % 151.45/22.46 | | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | | % 151.45/22.46 | | | | | | | | | End of split % 151.45/22.46 | | | | | | | | | % 151.45/22.46 | | | | | | | | End of split % 151.45/22.46 | | | | | | | | % 151.45/22.46 | | | | | | | End of split % 151.45/22.46 | | | | | | | % 151.45/22.46 | | | | | | End of split % 151.45/22.46 | | | | | | % 151.45/22.46 | | | | | End of split % 151.45/22.46 | | | | | % 151.45/22.46 | | | | End of split % 151.45/22.46 | | | | % 151.45/22.46 | | | Case 2: % 151.45/22.46 | | | | % 151.45/22.46 | | | | (603) all_20_2 = e1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | COMBINE_EQS: (82), (603) imply: % 151.45/22.46 | | | | (604) all_4_2 = e1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | COMBINE_EQS: (8), (604) imply: % 151.45/22.46 | | | | (605) all_56_15 = e1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | COMBINE_EQS: (2), (604) imply: % 151.45/22.46 | | | | (606) all_58_31 = e1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (182), (604) imply: % 151.45/22.46 | | | | (607) ~ (all_52_7 = e1) % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (23), (604) imply: % 151.45/22.46 | | | | (608) ~ (all_52_11 = e1) % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (157), (604) imply: % 151.45/22.46 | | | | (609) ~ (all_52_12 = e1) % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (63), (604) imply: % 151.45/22.46 | | | | (610) ~ (all_52_13 = e1) % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (305), (604) imply: % 151.45/22.46 | | | | (611) ~ (all_10_1 = e1) % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (164), (604) imply: % 151.45/22.46 | | | | (612) op(e1, all_4_1) = all_4_0 % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (195), (604) imply: % 151.45/22.46 | | | | (613) op(e1, e0) = all_4_1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, % 151.45/22.46 | | | | simplifying with (89), (613) gives: % 151.45/22.46 | | | | (614) all_52_14 = all_4_1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | COMBINE_EQS: (83), (614) imply: % 151.45/22.46 | | | | (615) all_56_11 = all_4_1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | COMBINE_EQS: (47), (614) imply: % 151.45/22.46 | | | | (616) all_58_20 = all_4_1 % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (94), (614) imply: % 151.45/22.46 | | | | (617) ~ (all_52_13 = all_4_1) % 151.45/22.46 | | | | % 151.45/22.46 | | | | REDUCE: (21), (614) imply: % 151.45/22.46 | | | | (618) op(e1, all_4_1) = all_58_19 % 151.45/22.46 | | | | % 151.45/22.46 | | | | GROUND_INST: instantiating (4) with all_4_0, all_58_19, all_4_1, e1, % 151.45/22.46 | | | | simplifying with (612), (618) gives: % 151.45/22.46 | | | | (619) all_58_19 = all_4_0 % 151.45/22.46 | | | | % 151.45/22.46 | | | | BETA: splitting (11) gives: % 151.45/22.46 | | | | % 151.45/22.46 | | | | Case 1: % 151.45/22.46 | | | | | % 151.45/22.46 | | | | | (620) all_54_3 = e0 % 151.45/22.46 | | | | | % 151.45/22.46 | | | | | REF_CLOSE: (30), (291), (620) are inconsistent by sub-proof #733. % 151.45/22.46 | | | | | % 151.45/22.46 | | | | Case 2: % 151.45/22.46 | | | | | % 151.45/22.46 | | | | | (621) ~ (all_54_3 = e0) % 151.45/22.47 | | | | | (622) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.45/22.47 | | | | | % 151.45/22.47 | | | | | BETA: splitting (85) gives: % 151.45/22.47 | | | | | % 151.45/22.47 | | | | | Case 1: % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | (623) all_56_4 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | COMBINE_EQS: (28), (623) imply: % 151.45/22.47 | | | | | | (624) all_52_8 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (290), (624) imply: % 151.45/22.47 | | | | | | (625) $false % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | CLOSE: (625) is inconsistent. % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | Case 2: % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | (626) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | BETA: splitting (135) gives: % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | Case 1: % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | (627) all_54_14 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | COMBINE_EQS: (76), (627) imply: % 151.45/22.47 | | | | | | | (628) all_52_11 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | SIMP: (628) implies: % 151.45/22.47 | | | | | | | (629) all_52_11 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | COMBINE_EQS: (137), (629) imply: % 151.45/22.47 | | | | | | | (630) all_56_14 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | COMBINE_EQS: (20), (629) imply: % 151.45/22.47 | | | | | | | (631) all_58_26 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (146), (629) imply: % 151.45/22.47 | | | | | | | (632) ~ (all_52_7 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (90), (629) imply: % 151.45/22.47 | | | | | | | (633) ~ (all_52_9 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (304), (629) imply: % 151.45/22.47 | | | | | | | (634) ~ (all_10_1 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (122), (629) imply: % 151.45/22.47 | | | | | | | (635) ~ (all_6_2 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | SIMP: (635) implies: % 151.45/22.47 | | | | | | | (636) ~ (all_6_2 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | BETA: splitting (43) gives: % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | (637) all_54_13 = e0 % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | REF_CLOSE: (5), (632), (637) are inconsistent by sub-proof #732. % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | (638) ~ (all_54_13 = e0) % 151.45/22.47 | | | | | | | | (639) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | REF_CLOSE: (4), (5), (7), (12), (13), (17), (19), (25), (28), % 151.45/22.47 | | | | | | | | (30), (31), (32), (34), (35), (37), (38), (48), (49), % 151.45/22.47 | | | | | | | | (50), (56), (57), (61), (65), (69), (75), (92), (93), % 151.45/22.47 | | | | | | | | (95), (96), (97), (100), (101), (103), (104), (107), % 151.45/22.47 | | | | | | | | (109), (110), (124), (125), (131), (141), (148), % 151.45/22.47 | | | | | | | | (149), (163), (166), (167), (171), (183), (186), % 151.45/22.47 | | | | | | | | (188), (191), (197), (199), (285), (286), (287), % 151.45/22.47 | | | | | | | | (289), (290), (291), (297), (298), (300), (302), % 151.45/22.47 | | | | | | | | (306), (605), (606), (607), (609), (611), (616), % 151.45/22.47 | | | | | | | | (617), (622), (630), (631), (632), (633), (636), % 151.45/22.47 | | | | | | | | (639) are inconsistent by sub-proof #89. % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | End of split % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | Case 2: % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | (640) ~ (all_54_14 = e0) % 151.45/22.47 | | | | | | | (641) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (76), (640) imply: % 151.45/22.47 | | | | | | | (642) ~ (all_52_11 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REF_CLOSE: (3), (4), (12), (16), (22), (28), (29), (31), (32), % 151.45/22.47 | | | | | | | (38), (42), (45), (48), (50), (53), (56), (58), (64), % 151.45/22.47 | | | | | | | (69), (71), (73), (75), (76), (78), (84), (90), (91), % 151.45/22.47 | | | | | | | (92), (95), (97), (100), (101), (104), (109), (110), % 151.45/22.47 | | | | | | | (116), (122), (124), (125), (131), (137), (146), (148), % 151.45/22.47 | | | | | | | (159), (161), (163), (166), (171), (180), (183), (188), % 151.45/22.47 | | | | | | | (191), (199), (285), (291), (297), (304), (306), (605), % 151.45/22.47 | | | | | | | (606), (608), (610), (612), (613), (615), (626), (641), % 151.45/22.47 | | | | | | | (642) are inconsistent by sub-proof #87. % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | End of split % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | End of split % 151.45/22.47 | | | | | % 151.45/22.47 | | | | End of split % 151.45/22.47 | | | | % 151.45/22.47 | | | End of split % 151.45/22.47 | | | % 151.45/22.47 | | End of split % 151.45/22.47 | | % 151.45/22.47 | Case 2: % 151.45/22.47 | | % 151.45/22.47 | | (643) all_10_0 = e0 % 151.45/22.47 | | % 151.45/22.47 | | REDUCE: (44), (643) imply: % 151.45/22.47 | | (644) op(all_10_2, all_10_1) = e0 % 151.45/22.47 | | % 151.45/22.47 | | BETA: splitting (68) gives: % 151.45/22.47 | | % 151.45/22.47 | | Case 1: % 151.45/22.47 | | | % 151.45/22.47 | | | (645) ~ (all_18_2 = e0) % 151.45/22.47 | | | % 151.45/22.47 | | | REDUCE: (108), (645) imply: % 151.45/22.47 | | | (646) ~ (all_6_2 = e0) % 151.45/22.47 | | | % 151.45/22.47 | | | BETA: splitting (153) gives: % 151.45/22.47 | | | % 151.45/22.47 | | | Case 1: % 151.45/22.47 | | | | % 151.45/22.47 | | | | (647) ~ (all_22_1 = e0) % 151.45/22.47 | | | | % 151.45/22.47 | | | | REDUCE: (129), (647) imply: % 151.45/22.47 | | | | (648) $false % 151.45/22.47 | | | | % 151.45/22.47 | | | | CLOSE: (648) is inconsistent. % 151.45/22.47 | | | | % 151.45/22.47 | | | Case 2: % 151.45/22.47 | | | | % 151.45/22.47 | | | | (649) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 151.45/22.47 | | | | % 151.45/22.47 | | | | BETA: splitting (144) gives: % 151.45/22.47 | | | | % 151.45/22.47 | | | | Case 1: % 151.45/22.47 | | | | | % 151.45/22.47 | | | | | (650) ~ (all_20_2 = e1) % 151.45/22.47 | | | | | % 151.45/22.47 | | | | | REDUCE: (82), (650) imply: % 151.45/22.47 | | | | | (651) ~ (all_4_2 = e1) % 151.45/22.47 | | | | | % 151.45/22.47 | | | | | BETA: splitting (58) gives: % 151.45/22.47 | | | | | % 151.45/22.47 | | | | | Case 1: % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | (652) all_56_15 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | COMBINE_EQS: (8), (652) imply: % 151.45/22.47 | | | | | | (653) all_4_2 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | SIMP: (653) implies: % 151.45/22.47 | | | | | | (654) all_4_2 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | COMBINE_EQS: (2), (654) imply: % 151.45/22.47 | | | | | | (655) all_58_31 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (182), (654) imply: % 151.45/22.47 | | | | | | (656) ~ (all_52_7 = e0) % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (157), (654) imply: % 151.45/22.47 | | | | | | (657) ~ (all_52_12 = e0) % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (63), (654) imply: % 151.45/22.47 | | | | | | (658) ~ (all_52_13 = e0) % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (178), (654) imply: % 151.45/22.47 | | | | | | (659) ~ (all_52_14 = e0) % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (164), (654) imply: % 151.45/22.47 | | | | | | (660) op(e0, all_4_1) = all_4_0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (195), (654) imply: % 151.45/22.47 | | | | | | (661) op(e0, e0) = all_4_1 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (33), (654) imply: % 151.45/22.47 | | | | | | (662) op(e0, e0) = all_58_27 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (152), (654) imply: % 151.45/22.47 | | | | | | (663) op(e0, e0) = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 151.45/22.47 | | | | | | simplifying with (661), (662) gives: % 151.45/22.47 | | | | | | (664) all_58_27 = all_4_1 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, % 151.45/22.47 | | | | | | simplifying with (662), (663) gives: % 151.45/22.47 | | | | | | (665) all_58_27 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | COMBINE_EQS: (664), (665) imply: % 151.45/22.47 | | | | | | (666) all_4_1 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | SIMP: (666) implies: % 151.45/22.47 | | | | | | (667) all_4_1 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (660), (667) imply: % 151.45/22.47 | | | | | | (668) op(e0, e0) = all_4_0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, simplifying % 151.45/22.47 | | | | | | with (663), (668) gives: % 151.45/22.47 | | | | | | (669) all_4_0 = e0 % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | REDUCE: (73), (669) imply: % 151.45/22.47 | | | | | | (670) ~ (e1 = e0) % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | BETA: splitting (177) gives: % 151.45/22.47 | | | | | | % 151.45/22.47 | | | | | | Case 1: % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | (671) all_56_6 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | COMBINE_EQS: (106), (671) imply: % 151.45/22.47 | | | | | | | (672) all_52_2 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | SIMP: (672) implies: % 151.45/22.47 | | | | | | | (673) all_52_2 = e0 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (162), (673) imply: % 151.45/22.47 | | | | | | | (674) ~ (all_52_1 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (107), (673) imply: % 151.45/22.47 | | | | | | | (675) ~ (all_52_6 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | SIMP: (675) implies: % 151.45/22.47 | | | | | | | (676) ~ (all_52_6 = e0) % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | REDUCE: (98), (673) imply: % 151.45/22.47 | | | | | | | (677) op(e1, e0) = all_58_14 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | GROUND_INST: instantiating (4) with all_52_14, all_58_14, e0, e1, % 151.45/22.47 | | | | | | | simplifying with (89), (677) gives: % 151.45/22.47 | | | | | | | (678) all_58_14 = all_52_14 % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | BETA: splitting (85) gives: % 151.45/22.47 | | | | | | | % 151.45/22.47 | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | (679) all_56_4 = e0 % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | COMBINE_EQS: (28), (679) imply: % 151.45/22.47 | | | | | | | | (680) all_52_8 = e0 % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | REDUCE: (3), (680) imply: % 151.45/22.47 | | | | | | | | (681) ~ (all_52_9 = e0) % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | SIMP: (681) implies: % 151.45/22.47 | | | | | | | | (682) ~ (all_52_9 = e0) % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | REF_CLOSE: (4), (34), (75), (92), (109), (125), (131), (163), % 151.45/22.47 | | | | | | | | (186), (658), (674), (682) are inconsistent by % 151.45/22.47 | | | | | | | | sub-proof #125. % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | (683) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | BETA: splitting (683) gives: % 151.45/22.47 | | | | | | | | % 151.45/22.47 | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | (684) all_56_5 = e0 % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | COMBINE_EQS: (75), (684) imply: % 151.45/22.47 | | | | | | | | | (685) all_52_9 = e0 % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | SIMP: (685) implies: % 151.45/22.47 | | | | | | | | | (686) all_52_9 = e0 % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | REDUCE: (149), (686) imply: % 151.45/22.47 | | | | | | | | | (687) ~ (all_6_2 = e0) % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | REDUCE: (121), (686) imply: % 151.45/22.47 | | | | | | | | | (688) op(e2, e0) = all_58_10 % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | BETA: splitting (118) gives: % 151.45/22.47 | | | | | | | | | % 151.45/22.47 | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | (689) all_56_1 = e0 % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | COMBINE_EQS: (84), (689) imply: % 151.45/22.47 | | | | | | | | | | (690) all_52_4 = e0 % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | REDUCE: (97), (690) imply: % 151.45/22.47 | | | | | | | | | | (691) ~ (all_52_8 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | SIMP: (691) implies: % 151.45/22.47 | | | | | | | | | | (692) ~ (all_52_8 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | REDUCE: (197), (690) imply: % 151.45/22.47 | | | | | | | | | | (693) ~ (all_52_12 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | REDUCE: (187), (690) imply: % 151.45/22.47 | | | | | | | | | | (694) ~ (all_10_2 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | SIMP: (694) implies: % 151.45/22.47 | | | | | | | | | | (695) ~ (all_10_2 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | REDUCE: (29), (690) imply: % 151.45/22.47 | | | | | | | | | | (696) ~ (all_8_2 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | SIMP: (696) implies: % 151.45/22.47 | | | | | | | | | | (697) ~ (all_8_2 = e0) % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | REDUCE: (16), (690) imply: % 151.45/22.47 | | | | | | | | | | (698) op(e3, e0) = all_58_1 % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, all_58_10, e0, % 151.45/22.47 | | | | | | | | | | e2, simplifying with (165), (688) gives: % 151.45/22.47 | | | | | | | | | | (699) all_58_10 = all_52_13 % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_12, all_58_1, e0, % 151.45/22.47 | | | | | | | | | | e3, simplifying with (105), (698) gives: % 151.45/22.47 | | | | | | | | | | (700) all_58_1 = all_52_12 % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | BETA: splitting (11) gives: % 151.45/22.47 | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | (701) all_54_3 = e0 % 151.45/22.47 | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | REF_CLOSE: (30), (657), (701) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | #733. % 151.45/22.47 | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | (702) ~ (all_54_3 = e0) % 151.45/22.47 | | | | | | | | | | | (703) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.45/22.47 | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | BETA: splitting (183) gives: % 151.45/22.47 | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | (704) all_54_2 = e0 % 151.45/22.47 | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | REF_CLOSE: (12), (692), (704) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | #860. % 151.45/22.47 | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | (705) ~ (all_54_2 = e0) % 151.45/22.47 | | | | | | | | | | | | (706) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.45/22.47 | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | BETA: splitting (70) gives: % 151.45/22.47 | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | (707) all_54_9 = e0 % 151.45/22.47 | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | REF_CLOSE: (62), (676), (707) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | #572. % 151.45/22.47 | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | (708) ~ (all_54_9 = e0) % 151.45/22.47 | | | | | | | | | | | | | (709) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 151.45/22.47 | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | BETA: splitting (112) gives: % 151.45/22.47 | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | (710) all_54_4 = e0 % 151.45/22.47 | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | REF_CLOSE: (200), (674), (710) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | | #859. % 151.45/22.47 | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | (711) ~ (all_54_4 = e0) % 151.45/22.47 | | | | | | | | | | | | | | (712) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 151.45/22.47 | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | BETA: splitting (78) gives: % 151.45/22.47 | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | (713) all_54_5 = e0 % 151.45/22.47 | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | REF_CLOSE: (53), (697), (713) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | | | #158. % 151.45/22.47 | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | (714) ~ (all_54_5 = e0) % 151.45/22.47 | | | | | | | | | | | | | | | (715) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | BETA: splitting (86) gives: % 151.45/22.47 | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | (716) all_56_0 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (716) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | (717) all_10_2 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | REDUCE: (644), (717) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | (718) op(e3, all_10_1) = e0 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | REDUCE: (196), (717) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | (719) op(e3, e3) = all_10_1 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | REDUCE: (123), (717) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | (720) op(e3, e3) = all_58_0 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | REDUCE: (60), (717) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | (721) op(e3, e3) = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (124), (718), (719), (720), (721) are % 151.45/22.47 | | | | | | | | | | | | | | | | inconsistent by sub-proof #252. % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | (722) ~ (all_56_0 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | (723) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | REDUCE: (151), (722) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | (724) ~ (all_10_2 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | BETA: splitting (723) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | (725) all_56_2 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (725) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | (726) all_52_1 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | REDUCE: (201), (726) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | (727) ~ (all_10_2 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | REDUCE: (91), (726) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | (728) ~ (all_8_2 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | SIMP: (728) implies: % 151.45/22.47 | | | | | | | | | | | | | | | | | (729) ~ (all_8_2 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | (730) all_58_28 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (730) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | (731) all_10_2 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | REDUCE: (724), (731) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | (732) $false % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | CLOSE: (732) is inconsistent. % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | (733) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (734) all_58_29 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (729), (734) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | | | | | | | #756. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (735) ~ (all_58_29 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (736) all_58_30 = e3 | all_58_31 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (736) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | (737) all_58_30 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | (738) all_56_0 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (738) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | (739) all_10_2 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (739) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | (740) all_58_28 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (741) all_58_28 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (740), (741) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (742) e2 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (742) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (743) $false % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (743) is inconsistent. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (744) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | (745) all_58_29 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (745) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | (746) all_8_2 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (64), (109), (676), (746) are inconsistent by % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #129. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | (747) ~ (all_58_29 = e1) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (747) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | (748) ~ (all_8_2 = e1) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (53), (109), (199), (697), (715), % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | (729), (748) are inconsistent by sub-proof #88. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | (749) ~ (all_56_0 = e2) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (749) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | (750) ~ (all_10_2 = e2) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (751) all_58_28 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (751) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (752) all_10_2 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (750), (752) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (753) $false % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (753) is inconsistent. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (754) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (101), (109), (148), (191), (199), % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | (655), (697), (737), (754) are inconsistent by % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | sub-proof #141. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | (755) all_58_31 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (655), (755) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | #853. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | End of split % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | (756) ~ (all_56_2 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | | (757) all_56_6 = e3 | all_56_12 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | REDUCE: (125), (756) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | (758) ~ (all_52_1 = e3) % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | BETA: splitting (757) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | (759) all_56_6 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (671), (759) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | (760) e3 = e0 % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | REDUCE: (124), (760) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | (761) $false % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | CLOSE: (761) is inconsistent. % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | (762) all_56_12 = e3 % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (763) all_56_0 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (763) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (764) all_10_2 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (764) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (765) all_58_28 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | REDUCE: (201), (764) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (766) ~ (all_52_1 = e1) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | REDUCE: (18), (764) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (767) ~ (all_52_8 = e1) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | REDUCE: (132), (764) imply: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | (768) ~ (all_52_12 = e1) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (712) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | (769) all_54_4 = e1 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (200), (766), (769) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | #832. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | (770) ~ (all_54_4 = e1) % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | (771) all_54_4 = e3 | all_54_4 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | (772) all_56_0 = e2 % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (763), (772) are inconsistent by sub-proof % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | #796. % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.47 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | (773) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (774) all_56_2 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (774) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (775) all_52_1 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | SIMP: (775) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (776) all_52_1 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (776) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (777) ~ (all_8_2 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | SIMP: (777) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (778) ~ (all_8_2 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (779) all_58_28 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (765), (779) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (780) e2 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (780) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (781) $false % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (781) is inconsistent. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (782) ~ (all_58_28 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (783) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (765), (782) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (784) ~ (e2 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (785) all_58_29 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (778), (785) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | #634. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (786) ~ (all_58_29 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (787) all_58_30 = e2 | all_58_31 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (787) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_58_30 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (788) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_6_2 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (789) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_56_8 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_56_4 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (791) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_52_8 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (792) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_52_8 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (793) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (794) ~ (all_52_12 = e3) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (794) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (795) ~ (all_52_12 = e3) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_56_9 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (796) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_52_12 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (700), (797) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_58_1 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (795), (797) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) ~ (e3 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_58_28 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (765), (800) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #857. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) ~ (all_58_28 = e3) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (765), (801) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) ~ (e3 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (802) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_58_29 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (804) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) all_8_2 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (805) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_8_2 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (806) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_56_3 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (806) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) ~ (all_52_6 = e3) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) all_56_6 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (671), (809) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #839. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_56_2 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (774), (811) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) e2 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (788), (812) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) all_58_30 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (101), (104), (109), (148), (199), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655), (697), (783), (813) are inconsistent by % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #146. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) all_56_3 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (807), (815) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) e3 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (816) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) $false % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (817) is inconsistent. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_56_5 = e1 | all_56_10 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_56_7 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (819) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_52_6 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (808), (820) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) $false % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (821) is inconsistent. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) all_56_8 = e3 | all_56_11 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (822) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_56_8 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (790), (823) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) e3 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (824) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) e3 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (825) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) $false % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (826) is inconsistent. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_56_11 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (827) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_52_14 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (131), (180), (665), (678), (684), (699), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798), (818), (828) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #246. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_58_30 = e3 | all_58_31 = e3 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (101), (109), (124), (148), (188), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (199), (655), (697), (783), (829) are % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) ~ (all_56_9 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (30), (31), (38), (48), (61), (100), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (101), (104), (109), (188), (199), (655), (692), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (697), (703), (706), (765), (767), (768), (830) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #131. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (831) ~ (all_56_4 = e3) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (831) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (832) ~ (all_52_8 = e3) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (38), (48), (101), (109), (188), (199), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (655), (692), (697), (706), (767), (783), (832) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #152. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_58_31 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (655), (833) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | #855. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (834) ~ (all_56_2 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (834) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (835) ~ (all_52_1 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (200), (758), (771), (835) are inconsistent by % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | sub-proof #329. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | (836) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (836) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (837) all_56_2 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (837) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (838) all_52_1 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | SIMP: (838) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (839) all_52_1 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (839) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (840) ~ (all_10_2 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | SIMP: (840) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (841) ~ (all_10_2 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (839) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (842) ~ (all_8_2 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | SIMP: (842) implies: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (843) ~ (all_8_2 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (758), (839) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (844) ~ (e3 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | (845) all_58_28 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (841), (845) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | #858. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | (846) ~ (all_58_28 = e1) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | (847) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (847) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (848) all_58_29 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (843), (848) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | #809. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | (849) all_58_30 = e1 | all_58_31 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (850) all_56_0 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (850) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (851) all_10_2 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (851) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (852) all_58_28 = e2 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (851) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (853) ~ (all_52_12 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (724), (851) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (854) ~ (e3 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (10), (26), (28), (30), (48), (61), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (62), (64), (67), (69), (100), (101), (104), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (105), (109), (111), (114), (124), (140), (148), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (168), (171), (180), (181), (188), (190), (191), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (192), (655), (657), (671), (676), (689), (692), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (703), (709), (850), (852), (853) are inconsistent % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (855) ~ (all_56_0 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (855) imply: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | (856) ~ (all_10_2 = e2) % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (849) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (857) all_58_30 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (31), (38), (101), (104), (109), (138), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (148), (199), (655), (697), (856), (857) are % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #144. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (858) all_58_31 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (59), (101), (109), (138), (163), (180), % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | (186), (188), (646), (695), (858) are inconsistent % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #86. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | (859) all_56_6 = e1 | all_56_12 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | (860) all_56_6 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (180), (671), (860) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | #253. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | (861) all_56_12 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (762), (861) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | #792. % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | (862) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | REF_CLOSE: (4), (9), (92), (109), (110), (163), (186), (656), % 151.45/22.48 | | | | | | | | | | (676), (862) are inconsistent by sub-proof #148. % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | (863) ~ (all_56_5 = e0) % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | REDUCE: (75), (863) imply: % 151.45/22.48 | | | | | | | | | (864) ~ (all_52_9 = e0) % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | REF_CLOSE: (4), (34), (75), (92), (109), (125), (131), (163), % 151.45/22.48 | | | | | | | | | (186), (658), (674), (864) are inconsistent by % 151.45/22.48 | | | | | | | | | sub-proof #125. % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | End of split % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | End of split % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | Case 2: % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | (865) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | BETA: splitting (865) gives: % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | (866) all_56_7 = e0 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | COMBINE_EQS: (9), (866) imply: % 151.45/22.48 | | | | | | | | (867) all_52_6 = e0 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | SIMP: (867) implies: % 151.45/22.48 | | | | | | | | (868) all_52_6 = e0 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | REDUCE: (36), (868) imply: % 151.45/22.48 | | | | | | | | (869) ~ (all_52_4 = e0) % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | REDUCE: (26), (868) imply: % 151.45/22.48 | | | | | | | | (870) ~ (all_8_2 = e0) % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | SIMP: (870) implies: % 151.45/22.48 | | | | | | | | (871) ~ (all_8_2 = e0) % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | REDUCE: (67), (868) imply: % 151.45/22.48 | | | | | | | | (872) op(e1, e0) = all_58_16 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | GROUND_INST: instantiating (4) with all_52_14, all_58_16, e0, % 151.45/22.48 | | | | | | | | e1, simplifying with (89), (872) gives: % 151.45/22.48 | | | | | | | | (873) all_58_16 = all_52_14 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | BETA: splitting (156) gives: % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | (874) all_56_0 = e0 % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | COMBINE_EQS: (151), (874) imply: % 151.45/22.48 | | | | | | | | | (875) all_10_2 = e0 % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | SIMP: (875) implies: % 151.45/22.48 | | | | | | | | | (876) all_10_2 = e0 % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | COMBINE_EQS: (138), (876) imply: % 151.45/22.48 | | | | | | | | | (877) all_58_28 = e0 % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | BETA: splitting (190) gives: % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | (878) all_58_28 = e1 % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | COMBINE_EQS: (877), (878) imply: % 151.45/22.48 | | | | | | | | | | (879) e1 = e0 % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | REDUCE: (180), (879) imply: % 151.45/22.48 | | | | | | | | | | (880) $false % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | CLOSE: (880) is inconsistent. % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | (881) ~ (all_58_28 = e1) % 151.45/22.48 | | | | | | | | | | (882) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | BETA: splitting (171) gives: % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | (883) all_58_28 = e3 % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | COMBINE_EQS: (877), (883) imply: % 151.45/22.48 | | | | | | | | | | | (884) e3 = e0 % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | REDUCE: (124), (884) imply: % 151.45/22.48 | | | | | | | | | | | (885) $false % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | CLOSE: (885) is inconsistent. % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | (886) ~ (all_58_28 = e3) % 151.45/22.48 | | | | | | | | | | | (887) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | REDUCE: (877), (886) imply: % 151.45/22.48 | | | | | | | | | | | (888) ~ (e3 = e0) % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | BETA: splitting (31) gives: % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | (889) all_58_28 = e2 % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | COMBINE_EQS: (877), (889) imply: % 151.45/22.48 | | | | | | | | | | | | (890) e2 = e0 % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | REDUCE: (148), (890) imply: % 151.45/22.48 | | | | | | | | | | | | (891) $false % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | CLOSE: (891) is inconsistent. % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | (892) ~ (all_58_28 = e2) % 151.45/22.48 | | | | | | | | | | | | (893) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | REDUCE: (877), (892) imply: % 151.45/22.48 | | | | | | | | | | | | (894) ~ (e2 = e0) % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | BETA: splitting (887) gives: % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | (895) all_58_29 = e3 % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | BETA: splitting (882) gives: % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | (896) all_58_29 = e1 % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | REF_CLOSE: (69), (895), (896) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | #686. % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | (897) all_58_30 = e1 | all_58_31 = e1 % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | BETA: splitting (897) gives: % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | (898) all_58_30 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (101), (104), (109), (148), (199), % 151.45/22.48 | | | | | | | | | | | | | | | (655), (871), (893), (898) are inconsistent by % 151.45/22.48 | | | | | | | | | | | | | | | sub-proof #146. % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | (899) all_58_31 = e1 % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | | REF_CLOSE: (180), (655), (899) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | | | | | | #845. % 151.45/22.48 | | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | (900) all_58_30 = e3 | all_58_31 = e3 % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | | REF_CLOSE: (4), (38), (101), (109), (124), (148), (188), % 151.45/22.48 | | | | | | | | | | | | | (191), (199), (655), (871), (893), (900) are % 151.45/22.48 | | | | | | | | | | | | | inconsistent by sub-proof #140. % 151.45/22.48 | | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | (901) ~ (all_56_0 = e0) % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | REDUCE: (151), (901) imply: % 151.45/22.48 | | | | | | | | | (902) ~ (all_10_2 = e0) % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | BETA: splitting (77) gives: % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | (903) all_56_0 = e0 % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | REF_CLOSE: (151), (902), (903) are inconsistent by sub-proof % 151.45/22.48 | | | | | | | | | | #799. % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | (904) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | | REF_CLOSE: (3), (4), (14), (16), (28), (29), (31), (32), % 151.45/22.48 | | | | | | | | | | (34), (38), (41), (45), (48), (50), (57), (66), % 151.45/22.48 | | | | | | | | | | (69), (75), (79), (80), (83), (84), (86), (89), % 151.45/22.48 | | | | | | | | | | (91), (92), (97), (98), (100), (101), (104), % 151.45/22.48 | | | | | | | | | | (106), (109), (110), (113), (114), (115), (120), % 151.45/22.48 | | | | | | | | | | (123), (124), (125), (128), (131), (133), (136), % 151.45/22.48 | | | | | | | | | | (137), (138), (139), (140), (143), (147), (148), % 151.45/22.48 | | | | | | | | | | (150), (151), (154), (159), (160), (161), (162), % 151.45/22.48 | | | | | | | | | | (165), (166), (171), (176), (179), (180), (184), % 151.45/22.48 | | | | | | | | | | (187), (188), (189), (190), (191), (193), (199), % 151.45/22.48 | | | | | | | | | | (201), (649), (652), (655), (657), (658), (665), % 151.45/22.48 | | | | | | | | | | (866), (869), (871), (872), (904) are inconsistent % 151.45/22.48 | | | | | | | | | | by sub-proof #136. % 151.45/22.48 | | | | | | | | | | % 151.45/22.48 | | | | | | | | | End of split % 151.45/22.48 | | | | | | | | | % 151.45/22.48 | | | | | | | | End of split % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | (905) all_56_8 = e0 | all_56_11 = e0 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | REF_CLOSE: (83), (159), (646), (659), (905) are inconsistent by % 151.45/22.48 | | | | | | | | sub-proof #763. % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | End of split % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | End of split % 151.45/22.48 | | | | | | % 151.45/22.48 | | | | | Case 2: % 151.45/22.48 | | | | | | % 151.45/22.48 | | | | | | (906) ~ (all_56_15 = e0) % 151.45/22.48 | | | | | | (907) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.48 | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.48 | | | | | | % 151.45/22.48 | | | | | | ALPHA: (907) implies: % 151.45/22.48 | | | | | | (908) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.45/22.48 | | | | | | % 151.45/22.48 | | | | | | REDUCE: (8), (906) imply: % 151.45/22.48 | | | | | | (909) ~ (all_4_2 = e0) % 151.45/22.48 | | | | | | % 151.45/22.48 | | | | | | BETA: splitting (59) gives: % 151.45/22.48 | | | | | | % 151.45/22.48 | | | | | | Case 1: % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | (910) all_58_28 = e0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | COMBINE_EQS: (138), (910) imply: % 151.45/22.48 | | | | | | | (911) all_10_2 = e0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | COMBINE_EQS: (151), (911) imply: % 151.45/22.48 | | | | | | | (912) all_56_0 = e0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (201), (911) imply: % 151.45/22.48 | | | | | | | (913) ~ (all_52_1 = e0) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (158), (911) imply: % 151.45/22.48 | | | | | | | (914) ~ (all_52_3 = e0) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (187), (911) imply: % 151.45/22.48 | | | | | | | (915) ~ (all_52_4 = e0) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (18), (911) imply: % 151.45/22.48 | | | | | | | (916) ~ (all_52_8 = e0) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (644), (911) imply: % 151.45/22.48 | | | | | | | (917) op(e0, all_10_1) = e0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (196), (911) imply: % 151.45/22.48 | | | | | | | (918) op(e0, e3) = all_10_1 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (123), (911) imply: % 151.45/22.48 | | | | | | | (919) op(e3, e0) = all_58_0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, % 151.45/22.48 | | | | | | | simplifying with (127), (918) gives: % 151.45/22.48 | | | | | | | (920) all_52_3 = all_10_1 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | GROUND_INST: instantiating (4) with all_52_12, all_58_0, e0, e3, % 151.45/22.48 | | | | | | | simplifying with (105), (919) gives: % 151.45/22.48 | | | | | | | (921) all_58_0 = all_52_12 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | COMBINE_EQS: (79), (920) imply: % 151.45/22.48 | | | | | | | (922) all_56_12 = all_10_1 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | COMBINE_EQS: (155), (920) imply: % 151.45/22.48 | | | | | | | (923) all_58_22 = all_10_1 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (6), (920) imply: % 151.45/22.48 | | | | | | | (924) ~ (all_52_2 = all_10_1) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (80), (920) imply: % 151.45/22.48 | | | | | | | (925) ~ (all_52_7 = all_10_1) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | SIMP: (925) implies: % 151.45/22.48 | | | | | | | (926) ~ (all_52_7 = all_10_1) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (154), (920) imply: % 151.45/22.48 | | | | | | | (927) ~ (all_52_11 = all_10_1) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | SIMP: (927) implies: % 151.45/22.48 | | | | | | | (928) ~ (all_52_11 = all_10_1) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (87), (920) imply: % 151.45/22.48 | | | | | | | (929) ~ (all_10_1 = all_4_2) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (914), (920) imply: % 151.45/22.48 | | | | | | | (930) ~ (all_10_1 = e0) % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | REDUCE: (51), (920) imply: % 151.45/22.48 | | | | | | | (931) op(e0, all_10_1) = all_58_21 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_21, all_10_1, e0, % 151.45/22.48 | | | | | | | simplifying with (917), (931) gives: % 151.45/22.48 | | | | | | | (932) all_58_21 = e0 % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | BETA: splitting (85) gives: % 151.45/22.48 | | | | | | | % 151.45/22.48 | | | | | | | Case 1: % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | (933) all_56_4 = e0 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | COMBINE_EQS: (28), (933) imply: % 151.45/22.48 | | | | | | | | (934) all_52_8 = e0 % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | REDUCE: (916), (934) imply: % 151.45/22.48 | | | | | | | | (935) $false % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | CLOSE: (935) is inconsistent. % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | Case 2: % 151.45/22.48 | | | | | | | | % 151.45/22.48 | | | | | | | | (936) ~ (all_56_4 = e0) % 151.45/22.49 | | | | | | | | (937) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | BETA: splitting (166) gives: % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | (938) all_54_1 = e0 % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | REF_CLOSE: (32), (915), (938) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | #798. % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | (939) ~ (all_54_1 = e0) % 151.45/22.49 | | | | | | | | | (940) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | BETA: splitting (183) gives: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | (941) all_54_2 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REF_CLOSE: (12), (916), (941) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | #860. % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | (942) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | BETA: splitting (34) gives: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | (943) all_56_2 = e0 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | COMBINE_EQS: (125), (943) imply: % 151.45/22.49 | | | | | | | | | | | (944) all_52_1 = e0 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | REDUCE: (913), (944) imply: % 151.45/22.49 | | | | | | | | | | | (945) $false % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | CLOSE: (945) is inconsistent. % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | (946) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | BETA: splitting (185) gives: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | (947) all_54_6 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | COMBINE_EQS: (55), (947) imply: % 151.45/22.49 | | | | | | | | | | | | (948) all_52_9 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | SIMP: (948) implies: % 151.45/22.49 | | | | | | | | | | | | (949) all_52_9 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REDUCE: (90), (949) imply: % 151.45/22.49 | | | | | | | | | | | | (950) ~ (all_52_11 = e0) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | SIMP: (950) implies: % 151.45/22.49 | | | | | | | | | | | | (951) ~ (all_52_11 = e0) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | BETA: splitting (908) gives: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | (952) all_56_12 = e0 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | REF_CLOSE: (922), (930), (952) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | | | | #230. % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | (953) all_56_13 = e0 | all_56_14 = e0 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | BETA: splitting (953) gives: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | (954) all_56_13 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | COMBINE_EQS: (110), (954) imply: % 151.45/22.49 | | | | | | | | | | | | | | (955) all_52_7 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | SIMP: (955) implies: % 151.45/22.49 | | | | | | | | | | | | | | (956) all_52_7 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | REDUCE: (42), (956) imply: % 151.45/22.49 | | | | | | | | | | | | | | (957) ~ (all_52_6 = e0) % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | BETA: splitting (147) gives: % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | (958) all_56_12 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | COMBINE_EQS: (922), (958) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (959) all_10_1 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | SIMP: (959) implies: % 151.45/22.49 | | | | | | | | | | | | | | | (960) all_10_1 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REDUCE: (917), (960) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (961) op(e0, e1) = e0 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_11, e0, e1, e0, % 151.45/22.49 | | | | | | | | | | | | | | | simplifying with (39), (961) gives: % 151.45/22.49 | | | | | | | | | | | | | | | (962) all_52_11 = e0 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REDUCE: (951), (962) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (963) $false % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | CLOSE: (963) is inconsistent. % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | (964) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (23), (64), (101), (109), (122), % 151.45/22.49 | | | | | | | | | | | | | | | (137), (180), (188), (190), (651), (910), (951), % 151.45/22.49 | | | | | | | | | | | | | | | (954), (957), (964) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | | | | | | #97. % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | (965) all_56_14 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | REF_CLOSE: (137), (951), (965) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | | | | | #806. % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | (966) ~ (all_54_6 = e0) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REDUCE: (55), (966) imply: % 151.45/22.49 | | | | | | | | | | | | (967) ~ (all_52_9 = e0) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | BETA: splitting (937) gives: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | (968) all_56_5 = e0 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | COMBINE_EQS: (75), (968) imply: % 151.45/22.49 | | | | | | | | | | | | | (969) all_52_9 = e0 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | REDUCE: (967), (969) imply: % 151.45/22.49 | | | | | | | | | | | | | (970) $false % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | CLOSE: (970) is inconsistent. % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | (971) all_56_8 = e0 | all_56_14 = e0 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | BETA: splitting (971) gives: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | (972) all_56_8 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | COMBINE_EQS: (159), (972) imply: % 151.45/22.49 | | | | | | | | | | | | | | (973) all_6_2 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | REDUCE: (646), (973) imply: % 151.45/22.49 | | | | | | | | | | | | | | (974) $false % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | CLOSE: (974) is inconsistent. % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | (975) all_56_14 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | COMBINE_EQS: (137), (975) imply: % 151.45/22.49 | | | | | | | | | | | | | | (976) all_52_11 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | SIMP: (976) implies: % 151.45/22.49 | | | | | | | | | | | | | | (977) all_52_11 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | COMBINE_EQS: (20), (977) imply: % 151.45/22.49 | | | | | | | | | | | | | | (978) all_58_26 = e0 % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | REDUCE: (146), (977) imply: % 151.45/22.49 | | | | | | | | | | | | | | (979) ~ (all_52_7 = e0) % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | REDUCE: (928), (977) imply: % 151.45/22.49 | | | | | | | | | | | | | | (980) ~ (all_10_1 = e0) % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | REDUCE: (122), (977) imply: % 151.45/22.49 | | | | | | | | | | | | | | (981) ~ (all_6_2 = e0) % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | BETA: splitting (147) gives: % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | (982) all_56_12 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | COMBINE_EQS: (922), (982) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (983) all_10_1 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | SIMP: (983) implies: % 151.45/22.49 | | | | | | | | | | | | | | | (984) all_10_1 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | COMBINE_EQS: (923), (984) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (985) all_58_22 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REDUCE: (924), (984) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (986) ~ (all_52_2 = e1) % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REDUCE: (926), (984) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (987) ~ (all_52_7 = e1) % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REDUCE: (929), (984) imply: % 151.45/22.49 | | | | | | | | | | | | | | | (988) ~ (all_4_2 = e1) % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | (989) all_54_9 = e0 % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (989) imply: % 151.45/22.49 | | | | | | | | | | | | | | | | (990) all_52_6 = e0 % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (990) imply: % 151.45/22.49 | | | | | | | | | | | | | | | | (991) all_56_7 = e0 % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (990) imply: % 151.45/22.49 | | | | | | | | | | | | | | | | (992) all_58_17 = e0 % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | REDUCE: (42), (990) imply: % 151.45/22.49 | | | | | | | | | | | | | | | | (993) ~ (all_52_7 = e0) % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | REDUCE: (26), (990) imply: % 151.45/22.49 | | | | | | | | | | | | | | | | (994) ~ (all_8_2 = e0) % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | SIMP: (994) implies: % 151.45/22.49 | | | | | | | | | | | | | | | | (995) ~ (all_8_2 = e0) % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (19), (28), (29), (31), (37), (47), % 151.45/22.49 | | | | | | | | | | | | | | | | (49), (63), (66), (69), (75), (83), (84), (92), % 151.45/22.49 | | | | | | | | | | | | | | | | (93), (94), (96), (100), (101), (102), (104), % 151.45/22.49 | | | | | | | | | | | | | | | | (106), (110), (111), (113), (120), (124), (131), % 151.45/22.49 | | | | | | | | | | | | | | | | (145), (148), (159), (170), (171), (176), (178), % 151.45/22.49 | | | | | | | | | | | | | | | | (180), (188), (190), (191), (193), (197), (651), % 151.45/22.49 | | | | | | | | | | | | | | | | (910), (912), (946), (967), (978), (979), (985), % 151.45/22.49 | | | | | | | | | | | | | | | | (986), (987), (991), (992), (995) are inconsistent % 151.45/22.49 | | | | | | | | | | | | | | | | by sub-proof #223. % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | (996) ~ (all_54_9 = e0) % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | REDUCE: (62), (996) imply: % 151.45/22.49 | | | | | | | | | | | | | | | | (997) ~ (all_52_6 = e0) % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (84), (92), (109), (110), (118), (163), % 151.45/22.49 | | | | | | | | | | | | | | | | (186), (915), (979), (997) are inconsistent by % 151.45/22.49 | | | | | | | | | | | | | | | | sub-proof #147. % 151.45/22.49 | | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | (998) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (9), (12), (28), (29), (32), % 151.45/22.49 | | | | | | | | | | | | | | | (38), (41), (42), (46), (53), (56), (57), (61), % 151.45/22.49 | | | | | | | | | | | | | | | (74), (78), (83), (84), (91), (92), (97), (100), % 151.45/22.49 | | | | | | | | | | | | | | | (101), (105), (106), (109), (110), (113), (120), % 151.45/22.49 | | | | | | | | | | | | | | | (124), (125), (131), (140), (148), (161), (163), % 151.45/22.49 | | | | | | | | | | | | | | | (168), (173), (180), (181), (182), (186), (188), % 151.45/22.49 | | | | | | | | | | | | | | | (190), (193), (197), (199), (646), (651), (910), % 151.45/22.49 | | | | | | | | | | | | | | | (912), (922), (926), (940), (942), (975), (979), % 151.45/22.49 | | | | | | | | | | | | | | | (998) are inconsistent by sub-proof #95. % 151.45/22.49 | | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | End of split % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | End of split % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | Case 2: % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | (999) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REF_CLOSE: (2), (4), (101), (109), (163), (186), (188), (646), % 151.45/22.49 | | | | | | | (909), (999) are inconsistent by sub-proof #133. % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | End of split % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | End of split % 151.45/22.49 | | | | | % 151.45/22.49 | | | | Case 2: % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | (1000) all_20_2 = e1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | COMBINE_EQS: (82), (1000) imply: % 151.45/22.49 | | | | | (1001) all_4_2 = e1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | COMBINE_EQS: (8), (1001) imply: % 151.45/22.49 | | | | | (1002) all_56_15 = e1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | COMBINE_EQS: (2), (1001) imply: % 151.45/22.49 | | | | | (1003) all_58_31 = e1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (87), (1001) imply: % 151.45/22.49 | | | | | (1004) ~ (all_52_3 = e1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (182), (1001) imply: % 151.45/22.49 | | | | | (1005) ~ (all_52_7 = e1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (23), (1001) imply: % 151.45/22.49 | | | | | (1006) ~ (all_52_11 = e1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (157), (1001) imply: % 151.45/22.49 | | | | | (1007) ~ (all_52_12 = e1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (63), (1001) imply: % 151.45/22.49 | | | | | (1008) ~ (all_52_13 = e1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (164), (1001) imply: % 151.45/22.49 | | | | | (1009) op(e1, all_4_1) = all_4_0 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (195), (1001) imply: % 151.45/22.49 | | | | | (1010) op(e1, e0) = all_4_1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, % 151.45/22.49 | | | | | simplifying with (89), (1010) gives: % 151.45/22.49 | | | | | (1011) all_52_14 = all_4_1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | COMBINE_EQS: (83), (1011) imply: % 151.45/22.49 | | | | | (1012) all_56_11 = all_4_1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | COMBINE_EQS: (47), (1011) imply: % 151.45/22.49 | | | | | (1013) all_58_20 = all_4_1 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (102), (1011) imply: % 151.45/22.49 | | | | | (1014) ~ (all_52_12 = all_4_1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (94), (1011) imply: % 151.45/22.49 | | | | | (1015) ~ (all_52_13 = all_4_1) % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | REDUCE: (21), (1011) imply: % 151.45/22.49 | | | | | (1016) op(e1, all_4_1) = all_58_19 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | GROUND_INST: instantiating (4) with all_4_0, all_58_19, all_4_1, e1, % 151.45/22.49 | | | | | simplifying with (1009), (1016) gives: % 151.45/22.49 | | | | | (1017) all_58_19 = all_4_0 % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | BETA: splitting (194) gives: % 151.45/22.49 | | | | | % 151.45/22.49 | | | | | Case 1: % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | (1018) all_54_7 = e0 % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | COMBINE_EQS: (24), (1018) imply: % 151.45/22.49 | | | | | | (1019) all_52_13 = e0 % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | SIMP: (1019) implies: % 151.45/22.49 | | | | | | (1020) all_52_13 = e0 % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | REDUCE: (116), (1020) imply: % 151.45/22.49 | | | | | | (1021) ~ (all_52_9 = e0) % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | REDUCE: (66), (1020) imply: % 151.45/22.49 | | | | | | (1022) ~ (all_8_2 = e0) % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | SIMP: (1022) implies: % 151.45/22.49 | | | | | | (1023) ~ (all_8_2 = e0) % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | REDUCE: (1008), (1020) imply: % 151.45/22.49 | | | | | | (1024) ~ (e1 = e0) % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | BETA: splitting (59) gives: % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | Case 1: % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | (1025) all_58_28 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | COMBINE_EQS: (138), (1025) imply: % 151.45/22.49 | | | | | | | (1026) all_10_2 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (201), (1026) imply: % 151.45/22.49 | | | | | | | (1027) ~ (all_52_1 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (150), (1026) imply: % 151.45/22.49 | | | | | | | (1028) ~ (all_52_2 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (187), (1026) imply: % 151.45/22.49 | | | | | | | (1029) ~ (all_52_4 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (18), (1026) imply: % 151.45/22.49 | | | | | | | (1030) ~ (all_52_8 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (132), (1026) imply: % 151.45/22.49 | | | | | | | (1031) ~ (all_52_12 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (196), (1026) imply: % 151.45/22.49 | | | | | | | (1032) op(e0, e3) = all_10_1 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | BETA: splitting (85) gives: % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | (1033) all_56_4 = e0 % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | REF_CLOSE: (28), (1030), (1033) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | #862. % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | (1034) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | BETA: splitting (1034) gives: % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | (1035) all_56_5 = e0 % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | REF_CLOSE: (75), (1021), (1035) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | #767. % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | (1036) all_56_8 = e0 | all_56_14 = e0 % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | BETA: splitting (1036) gives: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | (1037) all_56_8 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | COMBINE_EQS: (159), (1037) imply: % 151.45/22.49 | | | | | | | | | | (1038) all_6_2 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | SIMP: (1038) implies: % 151.45/22.49 | | | | | | | | | | (1039) all_6_2 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | COMBINE_EQS: (188), (1039) imply: % 151.45/22.49 | | | | | | | | | | (1040) all_58_30 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REF_CLOSE: (31), (69), (101), (104), (124), (148), (171), % 151.45/22.49 | | | | | | | | | | (191), (1003), (1025), (1040) are inconsistent by % 151.45/22.49 | | | | | | | | | | sub-proof #680. % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | (1041) all_56_14 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | COMBINE_EQS: (137), (1041) imply: % 151.45/22.49 | | | | | | | | | | (1042) all_52_11 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | SIMP: (1042) implies: % 151.45/22.49 | | | | | | | | | | (1043) all_52_11 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | COMBINE_EQS: (20), (1043) imply: % 151.45/22.49 | | | | | | | | | | (1044) all_58_26 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (154), (1043) imply: % 151.45/22.49 | | | | | | | | | | (1045) ~ (all_52_3 = e0) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (146), (1043) imply: % 151.45/22.49 | | | | | | | | | | (1046) ~ (all_52_7 = e0) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (122), (1043) imply: % 151.45/22.49 | | | | | | | | | | (1047) ~ (all_6_2 = e0) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, % 151.45/22.49 | | | | | | | | | | simplifying with (127), (1032) gives: % 151.45/22.49 | | | | | | | | | | (1048) all_52_3 = all_10_1 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | COMBINE_EQS: (79), (1048) imply: % 151.45/22.49 | | | | | | | | | | (1049) all_56_12 = all_10_1 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | COMBINE_EQS: (155), (1048) imply: % 151.45/22.49 | | | | | | | | | | (1050) all_58_22 = all_10_1 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (6), (1048) imply: % 151.45/22.49 | | | | | | | | | | (1051) ~ (all_52_2 = all_10_1) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (80), (1048) imply: % 151.45/22.49 | | | | | | | | | | (1052) ~ (all_52_7 = all_10_1) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | SIMP: (1052) implies: % 151.45/22.49 | | | | | | | | | | (1053) ~ (all_52_7 = all_10_1) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (1004), (1048) imply: % 151.45/22.49 | | | | | | | | | | (1054) ~ (all_10_1 = e1) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REDUCE: (1045), (1048) imply: % 151.45/22.49 | | | | | | | | | | (1055) ~ (all_10_1 = e0) % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | BETA: splitting (43) gives: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | (1056) all_54_13 = e0 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | REF_CLOSE: (5), (1046), (1056) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | | #732. % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | (1057) ~ (all_54_13 = e0) % 151.45/22.49 | | | | | | | | | | | (1058) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | BETA: splitting (11) gives: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | (1059) all_54_3 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REF_CLOSE: (30), (1031), (1059) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | | | #733. % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | (1060) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (12), (13), (17), (19), (25), (28), % 151.45/22.49 | | | | | | | | | | | | (30), (31), (32), (34), (35), (37), (38), (48), % 151.45/22.49 | | | | | | | | | | | | (49), (50), (56), (57), (61), (65), (69), (75), % 151.45/22.49 | | | | | | | | | | | | (92), (93), (95), (96), (97), (100), (101), (103), % 151.45/22.49 | | | | | | | | | | | | (104), (107), (109), (110), (124), (125), (131), % 151.45/22.49 | | | | | | | | | | | | (141), (148), (149), (163), (166), (167), (171), % 151.45/22.49 | | | | | | | | | | | | (183), (186), (188), (191), (197), (199), (646), % 151.45/22.49 | | | | | | | | | | | | (1002), (1003), (1005), (1007), (1013), (1015), % 151.45/22.49 | | | | | | | | | | | | (1021), (1025), (1027), (1028), (1029), (1030), % 151.45/22.49 | | | | | | | | | | | | (1031), (1041), (1044), (1046), (1049), (1050), % 151.45/22.49 | | | | | | | | | | | | (1051), (1053), (1054), (1055), (1058), (1060) are % 151.45/22.49 | | | | | | | | | | | | inconsistent by sub-proof #89. % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | End of split % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | End of split % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | End of split % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | Case 2: % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | (1061) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REF_CLOSE: (101), (180), (188), (646), (1003), (1023), (1061) are % 151.45/22.49 | | | | | | | inconsistent by sub-proof #192. % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | End of split % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | Case 2: % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | (1062) ~ (all_54_7 = e0) % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | REDUCE: (24), (1062) imply: % 151.45/22.49 | | | | | | (1063) ~ (all_52_13 = e0) % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | BETA: splitting (43) gives: % 151.45/22.49 | | | | | | % 151.45/22.49 | | | | | | Case 1: % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | (1064) all_54_13 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | COMBINE_EQS: (5), (1064) imply: % 151.45/22.49 | | | | | | | (1065) all_52_7 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | SIMP: (1065) implies: % 151.45/22.49 | | | | | | | (1066) all_52_7 = e0 % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (146), (1066) imply: % 151.45/22.49 | | | | | | | (1067) ~ (all_52_11 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | SIMP: (1067) implies: % 151.45/22.49 | | | | | | | (1068) ~ (all_52_11 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (163), (1066) imply: % 151.45/22.49 | | | | | | | (1069) ~ (all_8_2 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | SIMP: (1069) implies: % 151.45/22.49 | | | | | | | (1070) ~ (all_8_2 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | REDUCE: (1005), (1066) imply: % 151.45/22.49 | | | | | | | (1071) ~ (e1 = e0) % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | BETA: splitting (59) gives: % 151.45/22.49 | | | | | | | % 151.45/22.49 | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | (1072) all_58_28 = e0 % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | COMBINE_EQS: (138), (1072) imply: % 151.45/22.49 | | | | | | | | (1073) all_10_2 = e0 % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | REDUCE: (158), (1073) imply: % 151.45/22.49 | | | | | | | | (1074) ~ (all_52_3 = e0) % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | REDUCE: (18), (1073) imply: % 151.45/22.49 | | | | | | | | (1075) ~ (all_52_8 = e0) % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | REDUCE: (132), (1073) imply: % 151.45/22.49 | | | | | | | | (1076) ~ (all_52_12 = e0) % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | REDUCE: (196), (1073) imply: % 151.45/22.49 | | | | | | | | (1077) op(e0, e3) = all_10_1 % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | BETA: splitting (58) gives: % 151.45/22.49 | | | | | | | | % 151.45/22.49 | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | (1078) all_56_15 = e0 % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | REF_CLOSE: (180), (1002), (1078) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | #550. % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | (1079) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.49 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | ALPHA: (1079) implies: % 151.45/22.49 | | | | | | | | | (1080) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | BETA: splitting (85) gives: % 151.45/22.49 | | | | | | | | | % 151.45/22.49 | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | (1081) all_56_4 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | REF_CLOSE: (28), (1075), (1081) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | #862. % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | (1082) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | BETA: splitting (1080) gives: % 151.45/22.49 | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | (1083) all_56_9 = e0 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | REF_CLOSE: (100), (1076), (1083) are inconsistent by % 151.45/22.49 | | | | | | | | | | | sub-proof #521. % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | (1084) all_56_10 = e0 | all_56_11 = e0 % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | BETA: splitting (1084) gives: % 151.45/22.49 | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | (1085) all_56_10 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REF_CLOSE: (131), (1063), (1085) are inconsistent by % 151.45/22.49 | | | | | | | | | | | | sub-proof #526. % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | (1086) all_56_11 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | COMBINE_EQS: (1012), (1086) imply: % 151.45/22.49 | | | | | | | | | | | | (1087) all_4_1 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | SIMP: (1087) implies: % 151.45/22.49 | | | | | | | | | | | | (1088) all_4_1 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REDUCE: (1009), (1088) imply: % 151.45/22.49 | | | | | | | | | | | | (1089) op(e1, e0) = all_4_0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REDUCE: (1010), (1088) imply: % 151.45/22.49 | | | | | | | | | | | | (1090) op(e1, e0) = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, % 151.45/22.49 | | | | | | | | | | | | simplifying with (127), (1077) gives: % 151.45/22.49 | | | | | | | | | | | | (1091) all_52_3 = all_10_1 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e1, % 151.45/22.49 | | | | | | | | | | | | simplifying with (1089), (1090) gives: % 151.45/22.49 | | | | | | | | | | | | (1092) all_4_0 = e0 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | COMBINE_EQS: (79), (1091) imply: % 151.45/22.49 | | | | | | | | | | | | (1093) all_56_12 = all_10_1 % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REDUCE: (154), (1091) imply: % 151.45/22.49 | | | | | | | | | | | | (1094) ~ (all_52_11 = all_10_1) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | SIMP: (1094) implies: % 151.45/22.49 | | | | | | | | | | | | (1095) ~ (all_52_11 = all_10_1) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | REDUCE: (1074), (1091) imply: % 151.45/22.49 | | | | | | | | | | | | (1096) ~ (all_10_1 = e0) % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | BETA: splitting (135) gives: % 151.45/22.49 | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | Case 1: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | (1097) all_54_14 = e0 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | REF_CLOSE: (76), (1068), (1097) are inconsistent by sub-proof % 151.45/22.49 | | | | | | | | | | | | | #517. % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | Case 2: % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.49 | | | | | | | | | | | | | (1098) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.45/22.49 | | | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | | | REF_CLOSE: (3), (4), (12), (16), (22), (28), (29), (31), % 151.45/22.50 | | | | | | | | | | | | | (32), (38), (42), (45), (48), (50), (53), (56), % 151.45/22.50 | | | | | | | | | | | | | (58), (64), (69), (71), (73), (75), (76), (78), % 151.45/22.50 | | | | | | | | | | | | | (84), (90), (91), (92), (95), (97), (100), (101), % 151.45/22.50 | | | | | | | | | | | | | (104), (109), (110), (116), (122), (124), (125), % 151.45/22.50 | | | | | | | | | | | | | (131), (137), (146), (148), (159), (161), (163), % 151.45/22.50 | | | | | | | | | | | | | (166), (171), (180), (183), (188), (191), (199), % 151.45/22.50 | | | | | | | | | | | | | (1002), (1003), (1006), (1008), (1009), (1010), % 151.45/22.50 | | | | | | | | | | | | | (1012), (1068), (1072), (1076), (1082), (1093), % 151.45/22.50 | | | | | | | | | | | | | (1095), (1096), (1098) are inconsistent by % 151.45/22.50 | | | | | | | | | | | | | sub-proof #87. % 151.45/22.50 | | | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | | End of split % 151.45/22.50 | | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | End of split % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | End of split % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | End of split % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | End of split % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | (1099) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REF_CLOSE: (101), (180), (188), (646), (1003), (1070), (1099) % 151.45/22.50 | | | | | | | | are inconsistent by sub-proof #192. % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | End of split % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | Case 2: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | (1100) ~ (all_54_13 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REDUCE: (5), (1100) imply: % 151.45/22.50 | | | | | | | (1101) ~ (all_52_7 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | BETA: splitting (135) gives: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | (1102) all_54_14 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | COMBINE_EQS: (76), (1102) imply: % 151.45/22.50 | | | | | | | | (1103) all_52_11 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | SIMP: (1103) implies: % 151.45/22.50 | | | | | | | | (1104) all_52_11 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (90), (1104) imply: % 151.45/22.50 | | | | | | | | (1105) ~ (all_52_9 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (122), (1104) imply: % 151.45/22.50 | | | | | | | | (1106) ~ (all_6_2 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (1006), (1104) imply: % 151.45/22.50 | | | | | | | | (1107) ~ (e1 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | BETA: splitting (34) gives: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | (1108) all_56_2 = e0 % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | COMBINE_EQS: (125), (1108) imply: % 151.45/22.50 | | | | | | | | | (1109) all_52_1 = e0 % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | REDUCE: (201), (1109) imply: % 151.45/22.50 | | | | | | | | | (1110) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | SIMP: (1110) implies: % 151.45/22.50 | | | | | | | | | (1111) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | REF_CLOSE: (4), (59), (101), (109), (138), (163), (180), % 151.45/22.50 | | | | | | | | | (186), (188), (646), (1003), (1111) are % 151.45/22.50 | | | | | | | | | inconsistent by sub-proof #86. % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | (1112) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | REF_CLOSE: (4), (75), (92), (109), (131), (163), (186), % 151.45/22.50 | | | | | | | | | (1063), (1105), (1112) are inconsistent by % 151.45/22.50 | | | | | | | | | sub-proof #126. % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | End of split % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | (1113) ~ (all_54_14 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (76), (1113) imply: % 151.45/22.50 | | | | | | | | (1114) ~ (all_52_11 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | BETA: splitting (58) gives: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | (1115) all_56_15 = e0 % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | REF_CLOSE: (180), (1002), (1115) are inconsistent by sub-proof % 151.45/22.50 | | | | | | | | | #550. % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | (1116) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.50 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | ALPHA: (1116) implies: % 151.45/22.50 | | | | | | | | | (1117) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | BETA: splitting (1117) gives: % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | (1118) all_56_12 = e0 % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | COMBINE_EQS: (79), (1118) imply: % 151.45/22.50 | | | | | | | | | | (1119) all_52_3 = e0 % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | SIMP: (1119) implies: % 151.45/22.50 | | | | | | | | | | (1120) all_52_3 = e0 % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | REDUCE: (158), (1120) imply: % 151.45/22.50 | | | | | | | | | | (1121) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | SIMP: (1121) implies: % 151.45/22.50 | | | | | | | | | | (1122) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | REDUCE: (1004), (1120) imply: % 151.45/22.50 | | | | | | | | | | (1123) ~ (e1 = e0) % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | REF_CLOSE: (4), (59), (101), (109), (138), (163), (180), % 151.45/22.50 | | | | | | | | | | (186), (188), (646), (1003), (1122) are % 151.45/22.50 | | | | | | | | | | inconsistent by sub-proof #86. % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | (1124) all_56_13 = e0 | all_56_14 = e0 % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | BETA: splitting (1124) gives: % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | (1125) all_56_13 = e0 % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | REF_CLOSE: (110), (1101), (1125) are inconsistent by % 151.45/22.50 | | | | | | | | | | | sub-proof #802. % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | (1126) all_56_14 = e0 % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | | REF_CLOSE: (137), (1114), (1126) are inconsistent by % 151.45/22.50 | | | | | | | | | | | sub-proof #806. % 151.45/22.50 | | | | | | | | | | | % 151.45/22.50 | | | | | | | | | | End of split % 151.45/22.50 | | | | | | | | | | % 151.45/22.50 | | | | | | | | | End of split % 151.45/22.50 | | | | | | | | | % 151.45/22.50 | | | | | | | | End of split % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | End of split % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | End of split % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | End of split % 151.45/22.50 | | | | | % 151.45/22.50 | | | | End of split % 151.45/22.50 | | | | % 151.45/22.50 | | | End of split % 151.45/22.50 | | | % 151.45/22.50 | | Case 2: % 151.45/22.50 | | | % 151.45/22.50 | | | (1127) all_18_2 = e0 % 151.45/22.50 | | | % 151.45/22.50 | | | COMBINE_EQS: (108), (1127) imply: % 151.45/22.50 | | | (1128) all_6_2 = e0 % 151.45/22.50 | | | % 151.45/22.50 | | | COMBINE_EQS: (159), (1128) imply: % 151.45/22.50 | | | (1129) all_56_8 = e0 % 151.45/22.50 | | | % 151.45/22.50 | | | COMBINE_EQS: (188), (1128) imply: % 151.45/22.50 | | | (1130) all_58_30 = e0 % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (57), (1128) imply: % 151.45/22.50 | | | (1131) ~ (all_52_2 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (10), (1128) imply: % 151.45/22.50 | | | (1132) ~ (all_52_6 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (48), (1128) imply: % 151.45/22.50 | | | (1133) ~ (all_52_8 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (149), (1128) imply: % 151.45/22.50 | | | (1134) ~ (all_52_9 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (122), (1128) imply: % 151.45/22.50 | | | (1135) ~ (all_52_11 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (193), (1128) imply: % 151.45/22.50 | | | (1136) ~ (all_52_14 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (119), (1128) imply: % 151.45/22.50 | | | (1137) op(e0, e1) = all_6_1 % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (15), (1128) imply: % 151.45/22.50 | | | (1138) op(e1, e0) = all_58_18 % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (160), (1128) imply: % 151.45/22.50 | | | (1139) op(e1, e1) = e0 % 151.45/22.50 | | | % 151.45/22.50 | | | GROUND_INST: instantiating (4) with all_52_11, all_6_1, e1, e0, % 151.45/22.50 | | | simplifying with (39), (1137) gives: % 151.45/22.50 | | | (1140) all_52_11 = all_6_1 % 151.45/22.50 | | | % 151.45/22.50 | | | GROUND_INST: instantiating (4) with all_52_14, all_58_18, e0, e1, % 151.45/22.50 | | | simplifying with (89), (1138) gives: % 151.45/22.50 | | | (1141) all_58_18 = all_52_14 % 151.45/22.50 | | | % 151.45/22.50 | | | COMBINE_EQS: (76), (1140) imply: % 151.45/22.50 | | | (1142) all_54_14 = all_6_1 % 151.45/22.50 | | | % 151.45/22.50 | | | COMBINE_EQS: (137), (1140) imply: % 151.45/22.50 | | | (1143) all_56_14 = all_6_1 % 151.45/22.50 | | | % 151.45/22.50 | | | COMBINE_EQS: (20), (1140) imply: % 151.45/22.50 | | | (1144) all_58_26 = all_6_1 % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (154), (1140) imply: % 151.45/22.50 | | | (1145) ~ (all_52_3 = all_6_1) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (146), (1140) imply: % 151.45/22.50 | | | (1146) ~ (all_52_7 = all_6_1) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (22), (1140) imply: % 151.45/22.50 | | | (1147) ~ (all_52_8 = all_6_1) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (90), (1140) imply: % 151.45/22.50 | | | (1148) ~ (all_52_9 = all_6_1) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (23), (1140) imply: % 151.45/22.50 | | | (1149) ~ (all_6_1 = all_4_2) % 151.45/22.50 | | | % 151.45/22.50 | | | REDUCE: (1135), (1140) imply: % 151.45/22.50 | | | (1150) ~ (all_6_1 = e0) % 151.45/22.50 | | | % 151.45/22.50 | | | BETA: splitting (144) gives: % 151.45/22.50 | | | % 151.45/22.50 | | | Case 1: % 151.45/22.50 | | | | % 151.45/22.50 | | | | (1151) ~ (all_20_2 = e1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (82), (1151) imply: % 151.45/22.50 | | | | (1152) ~ (all_4_2 = e1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | BETA: splitting (58) gives: % 151.45/22.50 | | | | % 151.45/22.50 | | | | Case 1: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | (1153) all_56_15 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | COMBINE_EQS: (8), (1153) imply: % 151.45/22.50 | | | | | (1154) all_4_2 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | SIMP: (1154) implies: % 151.45/22.50 | | | | | (1155) all_4_2 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | COMBINE_EQS: (2), (1155) imply: % 151.45/22.50 | | | | | (1156) all_58_31 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (63), (1155) imply: % 151.45/22.50 | | | | | (1157) ~ (all_52_13 = e0) % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (164), (1155) imply: % 151.45/22.50 | | | | | (1158) op(e0, all_4_1) = all_4_0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (195), (1155) imply: % 151.45/22.50 | | | | | (1159) op(e0, e0) = all_4_1 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (33), (1155) imply: % 151.45/22.50 | | | | | (1160) op(e0, e0) = all_58_27 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (152), (1155) imply: % 151.45/22.50 | | | | | (1161) op(e0, e0) = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 151.45/22.50 | | | | | simplifying with (1159), (1160) gives: % 151.45/22.50 | | | | | (1162) all_58_27 = all_4_1 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, simplifying % 151.45/22.50 | | | | | with (1160), (1161) gives: % 151.45/22.50 | | | | | (1163) all_58_27 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | COMBINE_EQS: (1162), (1163) imply: % 151.45/22.50 | | | | | (1164) all_4_1 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | SIMP: (1164) implies: % 151.45/22.50 | | | | | (1165) all_4_1 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (1158), (1165) imply: % 151.45/22.50 | | | | | (1166) op(e0, e0) = all_4_0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, simplifying % 151.45/22.50 | | | | | with (1161), (1166) gives: % 151.45/22.50 | | | | | (1167) all_4_0 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REDUCE: (73), (1167) imply: % 151.45/22.50 | | | | | (1168) ~ (e1 = e0) % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | BETA: splitting (34) gives: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | Case 1: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | (1169) all_56_2 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REF_CLOSE: (2), (4), (31), (38), (64), (91), (101), (104), (109), % 151.45/22.50 | | | | | | (125), (148), (180), (190), (199), (1130), (1132), % 151.45/22.50 | | | | | | (1152), (1156), (1169) are inconsistent by sub-proof % 151.45/22.50 | | | | | | #127. % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | Case 2: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | (1170) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REF_CLOSE: (4), (75), (92), (109), (131), (163), (186), (1134), % 151.45/22.50 | | | | | | (1157), (1170) are inconsistent by sub-proof #126. % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | End of split % 151.45/22.50 | | | | | % 151.45/22.50 | | | | Case 2: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | (1171) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.50 | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | ALPHA: (1171) implies: % 151.45/22.50 | | | | | (1172) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.45/22.50 | | | | | (1173) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | BETA: splitting (156) gives: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | Case 1: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | (1174) all_56_0 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | COMBINE_EQS: (151), (1174) imply: % 151.45/22.50 | | | | | | (1175) all_10_2 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | COMBINE_EQS: (138), (1175) imply: % 151.45/22.50 | | | | | | (1176) all_58_28 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REF_CLOSE: (2), (4), (64), (101), (109), (180), (190), (1130), % 151.45/22.50 | | | | | | (1132), (1152), (1176) are inconsistent by sub-proof #96. % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | Case 2: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | (1177) ~ (all_56_0 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REDUCE: (151), (1177) imply: % 151.45/22.50 | | | | | | (1178) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (16), % 151.45/22.50 | | | | | | (17), (19), (21), (24), (25), (28), (29), (30), (31), % 151.45/22.50 | | | | | | (32), (34), (37), (38), (45), (46), (47), (49), (51), % 151.45/22.50 | | | | | | (54), (55), (56), (61), (62), (63), (64), (66), (69), % 151.45/22.50 | | | | | | (70), (74), (77), (79), (80), (81), (83), (84), (86), % 151.45/22.50 | | | | | | (88), (91), (92), (93), (94), (95), (96), (100), (101), % 151.45/22.50 | | | | | | (102), (103), (104), (105), (106), (107), (109), (110), % 151.45/22.50 | | | | | | (112), (114), (115), (116), (118), (120), (124), (125), % 151.45/22.50 | | | | | | (131), (132), (136), (138), (139), (141), (142), (147), % 151.45/22.50 | | | | | | (148), (150), (151), (152), (155), (156), (157), (158), % 151.45/22.50 | | | | | | (161), (162), (163), (165), (166), (169), (170), (171), % 151.45/22.50 | | | | | | (176), (178), (180), (182), (183), (184), (185), (186), % 151.45/22.50 | | | | | | (187), (188), (190), (191), (194), (196), (197), (199), % 151.45/22.50 | | | | | | (200), (201), (1130), (1131), (1132), (1133), (1134), % 151.45/22.50 | | | | | | (1136), (1139), (1143), (1144), (1145), (1147), (1148), % 151.45/22.50 | | | | | | (1152), (1172), (1173), (1178) are inconsistent by % 151.45/22.50 | | | | | | sub-proof #115. % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | End of split % 151.45/22.50 | | | | | % 151.45/22.50 | | | | End of split % 151.45/22.50 | | | | % 151.45/22.50 | | | Case 2: % 151.45/22.50 | | | | % 151.45/22.50 | | | | (1179) all_20_2 = e1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | COMBINE_EQS: (82), (1179) imply: % 151.45/22.50 | | | | (1180) all_4_2 = e1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | SIMP: (1180) implies: % 151.45/22.50 | | | | (1181) all_4_2 = e1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | COMBINE_EQS: (8), (1181) imply: % 151.45/22.50 | | | | (1182) all_56_15 = e1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | COMBINE_EQS: (2), (1181) imply: % 151.45/22.50 | | | | (1183) all_58_31 = e1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (87), (1181) imply: % 151.45/22.50 | | | | (1184) ~ (all_52_3 = e1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (182), (1181) imply: % 151.45/22.50 | | | | (1185) ~ (all_52_7 = e1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (1149), (1181) imply: % 151.45/22.50 | | | | (1186) ~ (all_6_1 = e1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (195), (1181) imply: % 151.45/22.50 | | | | (1187) op(e1, e0) = all_4_1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, % 151.45/22.50 | | | | simplifying with (89), (1187) gives: % 151.45/22.50 | | | | (1188) all_52_14 = all_4_1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | COMBINE_EQS: (83), (1188) imply: % 151.45/22.50 | | | | (1189) all_56_11 = all_4_1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | COMBINE_EQS: (47), (1188) imply: % 151.45/22.50 | | | | (1190) all_58_20 = all_4_1 % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (54), (1188) imply: % 151.45/22.50 | | | | (1191) ~ (all_52_6 = all_4_1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (102), (1188) imply: % 151.45/22.50 | | | | (1192) ~ (all_52_12 = all_4_1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (94), (1188) imply: % 151.45/22.50 | | | | (1193) ~ (all_52_13 = all_4_1) % 151.45/22.50 | | | | % 151.45/22.50 | | | | REDUCE: (1136), (1188) imply: % 151.45/22.50 | | | | (1194) ~ (all_4_1 = e0) % 151.45/22.50 | | | | % 151.45/22.50 | | | | BETA: splitting (135) gives: % 151.45/22.50 | | | | % 151.45/22.50 | | | | Case 1: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | (1195) all_54_14 = e0 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | REF_CLOSE: (1142), (1150), (1195) are inconsistent by sub-proof #114. % 151.45/22.50 | | | | | % 151.45/22.50 | | | | Case 2: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | (1196) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | BETA: splitting (43) gives: % 151.45/22.50 | | | | | % 151.45/22.50 | | | | | Case 1: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | (1197) all_54_13 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | COMBINE_EQS: (5), (1197) imply: % 151.45/22.50 | | | | | | (1198) all_52_7 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | SIMP: (1198) implies: % 151.45/22.50 | | | | | | (1199) all_52_7 = e0 % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REDUCE: (56), (1199) imply: % 151.45/22.50 | | | | | | (1200) ~ (all_52_4 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REDUCE: (1146), (1199) imply: % 151.45/22.50 | | | | | | (1201) ~ (all_6_1 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REDUCE: (1185), (1199) imply: % 151.45/22.50 | | | | | | (1202) ~ (e1 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | BETA: splitting (34) gives: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | Case 1: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | (1203) all_56_2 = e0 % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | COMBINE_EQS: (125), (1203) imply: % 151.45/22.50 | | | | | | | (1204) all_52_1 = e0 % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REDUCE: (162), (1204) imply: % 151.45/22.50 | | | | | | | (1205) ~ (all_52_2 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REDUCE: (142), (1204) imply: % 151.45/22.50 | | | | | | | (1206) ~ (all_52_9 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REDUCE: (201), (1204) imply: % 151.45/22.50 | | | | | | | (1207) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | SIMP: (1207) implies: % 151.45/22.50 | | | | | | | (1208) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (16), % 151.45/22.50 | | | | | | | (17), (18), (19), (24), (25), (26), (28), (29), (30), % 151.45/22.50 | | | | | | | (31), (32), (34), (36), (37), (38), (40), (41), (42), % 151.45/22.50 | | | | | | | (48), (50), (53), (55), (56), (58), (61), (62), (64), % 151.45/22.50 | | | | | | | (67), (69), (70), (71), (72), (74), (75), (77), (78), % 151.45/22.50 | | | | | | | (79), (80), (81), (84), (86), (91), (92), (93), (95), % 151.45/22.50 | | | | | | | (96), (97), (100), (101), (103), (104), (105), (106), % 151.45/22.50 | | | | | | | (107), (109), (110), (111), (113), (114), (116), (118), % 151.45/22.50 | | | | | | | (124), (125), (130), (131), (132), (133), (136), (138), % 151.45/22.50 | | | | | | | (140), (141), (142), (145), (148), (150), (151), (155), % 151.45/22.50 | | | | | | | (156), (158), (161), (162), (163), (166), (168), (170), % 151.45/22.50 | | | | | | | (171), (173), (175), (180), (181), (183), (184), (185), % 151.45/22.50 | | | | | | | (186), (187), (188), (190), (191), (192), (194), (197), % 151.45/22.50 | | | | | | | (198), (199), (1129), (1130), (1131), (1132), (1133), % 151.45/22.50 | | | | | | | (1134), (1142), (1143), (1144), (1145), (1146), (1147), % 151.45/22.50 | | | | | | | (1148), (1150), (1182), (1183), (1184), (1185), (1186), % 151.45/22.50 | | | | | | | (1189), (1190), (1191), (1192), (1193), (1194), (1196), % 151.45/22.50 | | | | | | | (1208) are inconsistent by sub-proof #103. % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | Case 2: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | (1209) ~ (all_56_2 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REDUCE: (125), (1209) imply: % 151.45/22.50 | | | | | | | (1210) ~ (all_52_1 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | BETA: splitting (156) gives: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | (1211) all_56_0 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | COMBINE_EQS: (151), (1211) imply: % 151.45/22.50 | | | | | | | | (1212) all_10_2 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | COMBINE_EQS: (138), (1212) imply: % 151.45/22.50 | | | | | | | | (1213) all_58_28 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REF_CLOSE: (2), (4), (31), (64), (69), (82), (101), (104), % 151.45/22.50 | | | | | | | | (109), (124), (144), (148), (171), (180), (190), % 151.45/22.50 | | | | | | | | (191), (1130), (1132), (1213) are inconsistent by % 151.45/22.50 | | | | | | | | sub-proof #85. % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | Case 2: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | (1214) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REF_CLOSE: (4), (9), (79), (80), (84), (92), (106), (109), % 151.45/22.50 | | | | | | | | (110), (118), (125), (163), (186), (1131), (1132), % 151.45/22.50 | | | | | | | | (1200), (1210), (1214) are inconsistent by sub-proof % 151.45/22.50 | | | | | | | | #118. % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | End of split % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | End of split % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | Case 2: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | (1215) ~ (all_54_13 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | REDUCE: (5), (1215) imply: % 151.45/22.50 | | | | | | (1216) ~ (all_52_7 = e0) % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | BETA: splitting (58) gives: % 151.45/22.50 | | | | | | % 151.45/22.50 | | | | | | Case 1: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | (1217) all_56_15 = e0 % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | REF_CLOSE: (180), (1182), (1217) are inconsistent by sub-proof % 151.45/22.50 | | | | | | | #550. % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | Case 2: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | (1218) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.50 | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | ALPHA: (1218) implies: % 151.45/22.50 | | | | | | | (1219) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | BETA: splitting (1219) gives: % 151.45/22.50 | | | | | | | % 151.45/22.50 | | | | | | | Case 1: % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | (1220) all_56_12 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | COMBINE_EQS: (79), (1220) imply: % 151.45/22.50 | | | | | | | | (1221) all_52_3 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | SIMP: (1221) implies: % 151.45/22.50 | | | | | | | | (1222) all_52_3 = e0 % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (158), (1222) imply: % 151.45/22.50 | | | | | | | | (1223) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | SIMP: (1223) implies: % 151.45/22.50 | | | | | | | | (1224) ~ (all_10_2 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (1145), (1222) imply: % 151.45/22.50 | | | | | | | | (1225) ~ (all_6_1 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.50 | | | | | | | | REDUCE: (1184), (1222) imply: % 151.45/22.50 | | | | | | | | (1226) ~ (e1 = e0) % 151.45/22.50 | | | | | | | | % 151.45/22.51 | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (16), % 151.45/22.51 | | | | | | | | (17), (18), (19), (24), (25), (26), (28), (29), (30), % 151.45/22.51 | | | | | | | | (31), (32), (34), (36), (37), (38), (40), (41), (42), % 151.45/22.51 | | | | | | | | (48), (50), (53), (55), (56), (58), (61), (62), (64), % 151.45/22.51 | | | | | | | | (67), (69), (70), (71), (72), (74), (75), (77), (78), % 151.45/22.51 | | | | | | | | (79), (80), (81), (84), (86), (91), (92), (93), (95), % 151.45/22.51 | | | | | | | | (96), (97), (100), (101), (103), (104), (105), (106), % 151.45/22.51 | | | | | | | | (107), (109), (110), (111), (113), (114), (116), % 151.45/22.51 | | | | | | | | (118), (124), (125), (130), (131), (132), (133), % 151.45/22.51 | | | | | | | | (136), (138), (140), (141), (142), (145), (148), % 151.45/22.51 | | | | | | | | (150), (151), (155), (156), (158), (161), (162), % 151.45/22.51 | | | | | | | | (163), (166), (168), (170), (171), (173), (175), % 151.45/22.51 | | | | | | | | (180), (181), (183), (184), (185), (186), (187), % 151.45/22.51 | | | | | | | | (188), (190), (191), (192), (194), (197), (198), % 151.45/22.51 | | | | | | | | (199), (1129), (1130), (1131), (1132), (1133), % 151.45/22.51 | | | | | | | | (1134), (1142), (1143), (1144), (1145), (1146), % 151.45/22.51 | | | | | | | | (1147), (1148), (1150), (1182), (1183), (1184), % 151.45/22.51 | | | | | | | | (1185), (1186), (1189), (1190), (1191), (1192), % 151.45/22.51 | | | | | | | | (1193), (1194), (1196), (1224) are inconsistent by % 151.45/22.51 | | | | | | | | sub-proof #103. % 151.45/22.51 | | | | | | | | % 151.45/22.51 | | | | | | | Case 2: % 151.45/22.51 | | | | | | | | % 151.45/22.51 | | | | | | | | (1227) all_56_13 = e0 | all_56_14 = e0 % 151.45/22.51 | | | | | | | | % 151.45/22.51 | | | | | | | | REF_CLOSE: (110), (137), (1135), (1216), (1227) are inconsistent % 151.45/22.51 | | | | | | | | by sub-proof #609. % 151.45/22.51 | | | | | | | | % 151.45/22.51 | | | | | | | End of split % 151.45/22.51 | | | | | | | % 151.45/22.51 | | | | | | End of split % 151.45/22.51 | | | | | | % 151.45/22.51 | | | | | End of split % 151.45/22.51 | | | | | % 151.45/22.51 | | | | End of split % 151.45/22.51 | | | | % 151.45/22.51 | | | End of split % 151.45/22.51 | | | % 151.45/22.51 | | End of split % 151.45/22.51 | | % 151.45/22.51 | End of split % 151.45/22.51 | % 151.45/22.51 End of proof % 151.45/22.51 % 151.45/22.51 Sub-proof #85 shows that the following formulas are inconsistent: % 151.45/22.51 ---------------------------------------------------------------- % 151.45/22.51 (1) all_58_31 = all_4_2 % 151.45/22.51 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.45/22.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.45/22.51 (3) all_58_28 = e0 % 151.45/22.51 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.45/22.51 (5) op(e1, e2) = all_52_6 % 151.45/22.51 (6) ~ (e3 = e1) % 151.45/22.51 (7) ~ (all_52_6 = e0) % 151.45/22.51 (8) all_20_2 = all_4_2 % 151.45/22.51 (9) all_58_29 = all_8_2 % 151.45/22.51 (10) all_58_30 = e0 % 151.45/22.51 (11) ~ (e2 = e1) % 151.45/22.51 (12) op(all_8_2, e2) = e0 % 151.45/22.51 (13) ~ (e3 = e0) % 151.45/22.51 (14) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 151.45/22.51 (15) ~ (e2 = e0) % 151.45/22.51 (16) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.45/22.51 (17) ~ (e1 = e0) % 151.45/22.51 (18) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.51 (19) ~ (e3 = e2) % 151.45/22.51 % 151.45/22.51 Begin of proof % 151.45/22.51 | % 151.45/22.51 | BETA: splitting (14) gives: % 151.45/22.51 | % 151.45/22.51 | Case 1: % 151.45/22.51 | | % 151.45/22.51 | | (20) ~ (all_20_2 = e1) % 151.45/22.51 | | % 151.45/22.51 | | REDUCE: (8), (20) imply: % 151.45/22.51 | | (21) ~ (all_4_2 = e1) % 151.45/22.51 | | % 151.45/22.51 | | BETA: splitting (18) gives: % 151.45/22.51 | | % 151.45/22.51 | | Case 1: % 151.45/22.51 | | | % 151.45/22.51 | | | (22) all_58_28 = e1 % 151.45/22.51 | | | % 151.45/22.51 | | | REF_CLOSE: (3), (17), (22) are inconsistent by sub-proof #690. % 151.45/22.51 | | | % 151.45/22.51 | | Case 2: % 151.45/22.51 | | | % 151.45/22.51 | | | (23) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.45/22.51 | | | % 151.45/22.51 | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (12), (17), (21), (23) are % 151.45/22.51 | | | inconsistent by sub-proof #128. % 151.45/22.51 | | | % 151.45/22.51 | | End of split % 151.45/22.51 | | % 151.45/22.51 | Case 2: % 151.45/22.51 | | % 151.45/22.51 | | (24) all_20_2 = e1 % 151.45/22.51 | | % 151.45/22.51 | | COMBINE_EQS: (8), (24) imply: % 151.45/22.51 | | (25) all_4_2 = e1 % 151.45/22.51 | | % 151.45/22.51 | | SIMP: (25) implies: % 151.45/22.51 | | (26) all_4_2 = e1 % 151.45/22.51 | | % 151.45/22.51 | | COMBINE_EQS: (1), (26) imply: % 151.45/22.51 | | (27) all_58_31 = e1 % 151.45/22.51 | | % 151.45/22.51 | | REF_CLOSE: (3), (4), (6), (9), (10), (11), (13), (15), (16), (19), (27) are % 151.45/22.51 | | inconsistent by sub-proof #680. % 151.45/22.51 | | % 151.45/22.51 | End of split % 151.45/22.51 | % 151.45/22.51 End of proof % 151.45/22.51 % 151.45/22.51 Sub-proof #86 shows that the following formulas are inconsistent: % 151.45/22.51 ---------------------------------------------------------------- % 151.45/22.51 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.45/22.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.45/22.51 (2) all_58_31 = e1 % 151.45/22.51 (3) ~ (all_6_2 = e0) % 151.45/22.51 (4) ~ (all_10_2 = e0) % 151.45/22.51 (5) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.45/22.51 (6) all_58_29 = all_8_2 % 151.45/22.51 (7) op(all_8_2, e2) = e0 % 151.45/22.51 (8) all_58_28 = all_10_2 % 151.45/22.51 (9) ~ (all_52_7 = all_8_2) % 151.45/22.51 (10) ~ (e1 = e0) % 151.45/22.51 (11) op(e0, e2) = all_52_7 % 151.45/22.51 (12) all_58_30 = all_6_2 % 151.45/22.51 % 151.45/22.51 Begin of proof % 151.45/22.51 | % 151.45/22.51 | BETA: splitting (5) gives: % 151.45/22.51 | % 151.45/22.51 | Case 1: % 151.45/22.51 | | % 151.45/22.51 | | (13) all_58_28 = e0 % 151.45/22.51 | | % 151.45/22.51 | | COMBINE_EQS: (8), (13) imply: % 151.45/22.51 | | (14) all_10_2 = e0 % 151.45/22.51 | | % 151.45/22.51 | | REDUCE: (4), (14) imply: % 151.45/22.51 | | (15) $false % 151.45/22.51 | | % 151.45/22.51 | | CLOSE: (15) is inconsistent. % 151.45/22.51 | | % 151.45/22.51 | Case 2: % 151.45/22.51 | | % 151.45/22.51 | | (16) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 151.45/22.51 | | % 151.45/22.51 | | BETA: splitting (16) gives: % 151.45/22.51 | | % 151.45/22.51 | | Case 1: % 151.45/22.51 | | | % 151.45/22.51 | | | (17) all_58_29 = e0 % 151.45/22.51 | | | % 151.45/22.51 | | | COMBINE_EQS: (6), (17) imply: % 151.45/22.51 | | | (18) all_8_2 = e0 % 151.45/22.51 | | | % 151.45/22.51 | | | REDUCE: (9), (18) imply: % 151.45/22.51 | | | (19) ~ (all_52_7 = e0) % 151.45/22.51 | | | % 151.45/22.51 | | | REDUCE: (7), (18) imply: % 151.45/22.51 | | | (20) op(e0, e2) = e0 % 151.45/22.51 | | | % 151.45/22.51 | | | REF_CLOSE: (1), (11), (19), (20) are inconsistent by sub-proof #240. % 151.45/22.51 | | | % 151.45/22.51 | | Case 2: % 151.45/22.51 | | | % 151.45/22.51 | | | (21) all_58_30 = e0 | all_58_31 = e0 % 151.45/22.51 | | | % 151.45/22.51 | | | REF_CLOSE: (2), (3), (10), (12), (21) are inconsistent by sub-proof #808. % 151.45/22.51 | | | % 151.45/22.51 | | End of split % 151.45/22.51 | | % 151.45/22.51 | End of split % 151.45/22.51 | % 151.45/22.51 End of proof % 151.45/22.51 % 151.45/22.51 Sub-proof #87 shows that the following formulas are inconsistent: % 151.45/22.51 ---------------------------------------------------------------- % 151.45/22.51 (1) ~ (all_52_8 = all_52_9) % 151.45/22.51 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.45/22.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.45/22.51 (3) all_58_28 = e0 % 151.45/22.51 (4) all_54_2 = all_52_8 % 151.45/22.51 (5) ~ (all_10_1 = e0) % 151.45/22.51 (6) ~ (all_52_13 = e1) % 151.45/22.51 (7) all_58_31 = e1 % 151.45/22.51 (8) op(e3, all_52_4) = all_58_1 % 151.45/22.51 (9) ~ (all_52_11 = all_10_1) % 151.45/22.51 (10) ~ (all_52_8 = all_52_11) % 151.45/22.51 (11) all_56_4 = all_52_8 % 151.45/22.51 (12) ~ (all_52_4 = all_8_2) % 151.45/22.51 (13) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.45/22.51 (14) all_54_1 = all_52_4 % 151.45/22.51 (15) all_56_11 = all_4_1 % 151.45/22.51 (16) op(e2, e2) = all_8_2 % 151.45/22.51 (17) all_56_12 = all_10_1 % 151.45/22.51 (18) ~ (all_52_6 = all_52_7) % 151.45/22.51 (19) op(e3, e2) = all_52_4 % 151.45/22.51 (20) ~ (all_52_8 = all_6_2) % 151.45/22.51 (21) op(e1, all_4_1) = all_4_0 % 151.45/22.51 (22) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 151.45/22.51 (23) all_54_5 = all_8_2 % 151.45/22.51 (24) ~ (all_52_4 = all_52_7) % 151.45/22.51 (25) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 151.45/22.51 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 151.45/22.51 (26) op(e1, e2) = all_52_6 % 151.45/22.51 (27) ~ (e3 = e1) % 151.45/22.51 (28) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.45/22.51 (29) ~ (all_4_0 = e1) % 151.45/22.51 (30) all_56_5 = all_52_9 % 151.45/22.51 (31) all_54_14 = all_52_11 % 151.45/22.51 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.45/22.51 (33) ~ (all_52_12 = e0) % 151.45/22.51 (34) all_56_1 = all_52_4 % 151.45/22.51 (35) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 151.45/22.51 (36) ~ (all_52_9 = all_52_11) % 151.45/22.51 (37) ~ (all_52_1 = all_8_2) % 151.45/22.51 (38) all_56_3 = all_8_2 % 151.45/22.51 (39) ~ (all_52_11 = e1) % 151.45/22.51 (40) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.45/22.51 (41) ~ (all_52_4 = all_52_8) % 151.45/22.51 (42) all_56_9 = all_52_12 % 151.45/22.51 (43) all_58_29 = all_8_2 % 151.45/22.51 (44) ~ (e2 = e1) % 151.45/22.51 (45) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 151.45/22.51 (46) op(all_8_2, e2) = e0 % 151.45/22.51 (47) all_56_13 = all_52_7 % 151.45/22.51 (48) ~ (all_52_9 = all_52_13) % 151.45/22.51 (49) ~ (all_52_11 = all_6_2) % 151.45/22.51 (50) ~ (e3 = e0) % 151.45/22.51 (51) all_56_2 = all_52_1 % 151.45/22.51 (52) ~ (all_52_11 = e0) % 151.45/22.51 (53) all_56_10 = all_52_13 % 151.45/22.51 (54) all_56_14 = all_52_11 % 151.45/22.51 (55) ~ (all_52_7 = all_52_11) % 151.45/22.51 (56) ~ (e2 = e0) % 151.45/22.51 (57) all_56_8 = all_6_2 % 151.45/22.51 (58) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.45/22.51 (59) ~ (all_52_7 = all_8_2) % 151.45/22.51 (60) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.45/22.51 (61) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.45/22.51 (62) ~ (e1 = e0) % 151.45/22.51 (63) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.45/22.51 (64) all_58_30 = all_6_2 % 151.45/22.51 (65) ~ (e3 = e2) % 151.45/22.51 (66) all_56_15 = e1 % 151.45/22.51 (67) op(e2, all_8_2) = all_58_9 % 151.45/22.51 (68) op(e1, e0) = all_4_1 % 151.45/22.51 % 151.45/22.51 Begin of proof % 151.45/22.51 | % 151.45/22.51 | BETA: splitting (25) gives: % 151.45/22.51 | % 151.45/22.51 | Case 1: % 151.45/22.51 | | % 151.45/22.51 | | (69) all_56_15 = e0 % 151.45/22.51 | | % 151.45/22.51 | | REF_CLOSE: (62), (66), (69) are inconsistent by sub-proof #550. % 151.45/22.51 | | % 151.45/22.51 | Case 2: % 151.45/22.51 | | % 151.45/22.51 | | (70) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 = e0 % 151.45/22.51 | | | all_56_13 = e0 | all_56_14 = e0) % 151.45/22.51 | | % 151.45/22.51 | | ALPHA: (70) implies: % 151.45/22.51 | | (71) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 151.45/22.51 | | (72) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 151.45/22.51 | | % 151.45/22.51 | | BETA: splitting (71) gives: % 151.45/22.51 | | % 151.45/22.51 | | Case 1: % 151.45/22.51 | | | % 151.45/22.51 | | | (73) all_56_12 = e0 % 151.45/22.51 | | | % 151.45/22.51 | | | REF_CLOSE: (5), (17), (73) are inconsistent by sub-proof #230. % 151.45/22.51 | | | % 151.45/22.51 | | Case 2: % 151.45/22.51 | | | % 151.45/22.51 | | | (74) all_56_13 = e0 | all_56_14 = e0 % 151.45/22.51 | | | % 151.45/22.51 | | | BETA: splitting (35) gives: % 151.45/22.51 | | | % 151.45/22.51 | | | Case 1: % 151.45/22.51 | | | | % 151.45/22.51 | | | | (75) all_56_5 = e0 % 151.45/22.51 | | | | % 151.45/22.51 | | | | COMBINE_EQS: (30), (75) imply: % 151.45/22.51 | | | | (76) all_52_9 = e0 % 151.45/22.51 | | | | % 151.45/22.51 | | | | REDUCE: (1), (76) imply: % 151.45/22.51 | | | | (77) ~ (all_52_8 = e0) % 151.45/22.51 | | | | % 151.45/22.51 | | | | REDUCE: (36), (76) imply: % 151.45/22.51 | | | | (78) ~ (all_52_11 = e0) % 151.45/22.51 | | | | % 151.45/22.51 | | | | REDUCE: (48), (76) imply: % 151.45/22.51 | | | | (79) ~ (all_52_13 = e0) % 151.45/22.51 | | | | % 151.45/22.51 | | | | SIMP: (79) implies: % 151.45/22.51 | | | | (80) ~ (all_52_13 = e0) % 151.45/22.51 | | | | % 151.45/22.51 | | | | BETA: splitting (72) gives: % 151.45/22.51 | | | | % 151.45/22.51 | | | | Case 1: % 151.45/22.51 | | | | | % 151.45/22.51 | | | | | (81) all_56_9 = e0 % 151.45/22.51 | | | | | % 151.45/22.51 | | | | | REF_CLOSE: (33), (42), (81) are inconsistent by sub-proof #521. % 151.45/22.51 | | | | | % 151.45/22.51 | | | | Case 2: % 151.45/22.51 | | | | | % 151.45/22.51 | | | | | (82) all_56_10 = e0 | all_56_11 = e0 % 151.45/22.51 | | | | | % 151.45/22.51 | | | | | BETA: splitting (82) gives: % 151.45/22.51 | | | | | % 151.45/22.51 | | | | | Case 1: % 151.45/22.51 | | | | | | % 151.45/22.51 | | | | | | (83) all_56_10 = e0 % 151.45/22.51 | | | | | | % 151.45/22.51 | | | | | | REF_CLOSE: (53), (80), (83) are inconsistent by sub-proof #526. % 151.45/22.51 | | | | | | % 151.45/22.51 | | | | | Case 2: % 151.45/22.51 | | | | | | % 151.87/22.55 | | | | | | (84) all_56_11 = e0 % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | | COMBINE_EQS: (15), (84) imply: % 151.87/22.55 | | | | | | (85) all_4_1 = e0 % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | | SIMP: (85) implies: % 151.87/22.55 | | | | | | (86) all_4_1 = e0 % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | | REDUCE: (21), (86) imply: % 151.87/22.55 | | | | | | (87) op(e1, e0) = all_4_0 % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | | REDUCE: (68), (86) imply: % 151.87/22.55 | | | | | | (88) op(e1, e0) = e0 % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | | BETA: splitting (74) gives: % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | | Case 1: % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | (89) all_56_13 = e0 % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | COMBINE_EQS: (47), (89) imply: % 151.87/22.55 | | | | | | | (90) all_52_7 = e0 % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | SIMP: (90) implies: % 151.87/22.55 | | | | | | | (91) all_52_7 = e0 % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | REDUCE: (24), (91) imply: % 151.87/22.55 | | | | | | | (92) ~ (all_52_4 = e0) % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | REDUCE: (18), (91) imply: % 151.87/22.55 | | | | | | | (93) ~ (all_52_6 = e0) % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | REDUCE: (59), (91) imply: % 151.87/22.55 | | | | | | | (94) ~ (all_8_2 = e0) % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | SIMP: (94) implies: % 151.87/22.55 | | | | | | | (95) ~ (all_8_2 = e0) % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | GROUND_INST: instantiating (2) with e0, all_4_0, e0, e1, % 151.87/22.55 | | | | | | | simplifying with (87), (88) gives: % 151.87/22.55 | | | | | | | (96) all_4_0 = e0 % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | REDUCE: (29), (96) imply: % 151.87/22.55 | | | | | | | (97) ~ (e1 = e0) % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | BETA: splitting (32) gives: % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | | (98) all_54_5 = e0 % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | | REF_CLOSE: (23), (95), (98) are inconsistent by sub-proof #158. % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | | (99) ~ (all_54_5 = e0) % 151.87/22.55 | | | | | | | | (100) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | | BETA: splitting (28) gives: % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | (101) all_56_2 = e1 % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | COMBINE_EQS: (51), (101) imply: % 151.87/22.55 | | | | | | | | | (102) all_52_1 = e1 % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | REDUCE: (37), (102) imply: % 151.87/22.55 | | | | | | | | | (103) ~ (all_8_2 = e1) % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | SIMP: (103) implies: % 151.87/22.55 | | | | | | | | | (104) ~ (all_8_2 = e1) % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | BETA: splitting (40) gives: % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | (105) all_56_12 = e3 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | COMBINE_EQS: (17), (105) imply: % 151.87/22.55 | | | | | | | | | | (106) all_10_1 = e3 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | SIMP: (106) implies: % 151.87/22.55 | | | | | | | | | | (107) all_10_1 = e3 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | REDUCE: (9), (107) imply: % 151.87/22.55 | | | | | | | | | | (108) ~ (all_52_11 = e3) % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | BETA: splitting (45) gives: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | (109) all_54_14 = e1 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | COMBINE_EQS: (31), (109) imply: % 151.87/22.55 | | | | | | | | | | | (110) all_52_11 = e1 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | REDUCE: (39), (110) imply: % 151.87/22.55 | | | | | | | | | | | (111) $false % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | CLOSE: (111) is inconsistent. % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | (112) ~ (all_54_14 = e1) % 151.87/22.55 | | | | | | | | | | | (113) all_54_14 = e3 | all_54_14 = e2 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | BETA: splitting (113) gives: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | (114) all_54_14 = e2 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | COMBINE_EQS: (31), (114) imply: % 151.87/22.55 | | | | | | | | | | | | (115) all_52_11 = e2 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | REDUCE: (49), (115) imply: % 151.87/22.55 | | | | | | | | | | | | (116) ~ (all_6_2 = e2) % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | SIMP: (116) implies: % 151.87/22.55 | | | | | | | | | | | | (117) ~ (all_6_2 = e2) % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | BETA: splitting (13) gives: % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | (118) all_58_28 = e2 % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | REF_CLOSE: (3), (56), (118) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | | | #688. % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | (119) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | BETA: splitting (119) gives: % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | (120) all_58_29 = e2 % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | COMBINE_EQS: (43), (120) imply: % 151.87/22.55 | | | | | | | | | | | | | | (121) all_8_2 = e2 % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (46), (56), (67), (121) are % 151.87/22.55 | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | (122) all_58_30 = e2 | all_58_31 = e2 % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | REF_CLOSE: (7), (44), (64), (117), (122) are inconsistent by % 151.87/22.55 | | | | | | | | | | | | | | sub-proof #435. % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | (123) all_54_14 = e3 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | COMBINE_EQS: (31), (123) imply: % 151.87/22.55 | | | | | | | | | | | | (124) all_52_11 = e3 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | REDUCE: (108), (124) imply: % 151.87/22.55 | | | | | | | | | | | | (125) $false % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | CLOSE: (125) is inconsistent. % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | (126) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | BETA: splitting (126) gives: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | (127) all_56_13 = e3 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | COMBINE_EQS: (89), (127) imply: % 151.87/22.55 | | | | | | | | | | | (128) e3 = e0 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | REDUCE: (50), (128) imply: % 151.87/22.55 | | | | | | | | | | | (129) $false % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | CLOSE: (129) is inconsistent. % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | (130) all_56_14 = e3 | all_56_15 = e3 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | BETA: splitting (130) gives: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | (131) all_56_14 = e3 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | COMBINE_EQS: (54), (131) imply: % 151.87/22.55 | | | | | | | | | | | | (132) all_52_11 = e3 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | SIMP: (132) implies: % 151.87/22.55 | | | | | | | | | | | | (133) all_52_11 = e3 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | REDUCE: (10), (133) imply: % 151.87/22.55 | | | | | | | | | | | | (134) ~ (all_52_8 = e3) % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | BETA: splitting (61) gives: % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | (135) all_58_28 = e3 % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | COMBINE_EQS: (3), (135) imply: % 151.87/22.55 | | | | | | | | | | | | | (136) e3 = e0 % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | REF_CLOSE: (27), (50), (66), (130), (131), (136) are % 151.87/22.55 | | | | | | | | | | | | | inconsistent by sub-proof #429. % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | (137) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | BETA: splitting (137) gives: % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | (138) all_58_29 = e3 % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | COMBINE_EQS: (43), (138) imply: % 151.87/22.55 | | | | | | | | | | | | | | (139) all_8_2 = e3 % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | REDUCE: (12), (139) imply: % 151.87/22.55 | | | | | | | | | | | | | | (140) ~ (all_52_4 = e3) % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | REDUCE: (46), (139) imply: % 151.87/22.55 | | | | | | | | | | | | | | (141) op(e3, e2) = e0 % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | BETA: splitting (13) gives: % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | (142) all_58_28 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | REF_CLOSE: (3), (56), (142) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | | | | | #688. % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | (143) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | BETA: splitting (143) gives: % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | (144) all_58_29 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (144) imply: % 151.87/22.55 | | | | | | | | | | | | | | | | (145) e3 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | REDUCE: (65), (145) imply: % 151.87/22.55 | | | | | | | | | | | | | | | | (146) $false % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent. % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | (147) all_58_30 = e2 | all_58_31 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | (148) all_58_30 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (148) imply: % 151.87/22.55 | | | | | | | | | | | | | | | | | (149) all_6_2 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | REDUCE: (20), (149) imply: % 151.87/22.55 | | | | | | | | | | | | | | | | | (150) ~ (all_52_8 = e2) % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | BETA: splitting (63) gives: % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | (151) all_54_2 = e0 % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (77), (151) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | | | | | | | | #860. % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | (152) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | (153) all_54_1 = e0 % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (92), (153) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | | | | | | | | | #798. % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | (154) ~ (all_54_1 = e0) % 151.87/22.55 | | | | | | | | | | | | | | | | | | | (155) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | (156) all_56_1 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (156) imply: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | (157) all_52_4 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | SIMP: (157) implies: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | (158) all_52_4 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (19), (92), (141), (158) are % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #124. % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | (159) ~ (all_56_1 = e2) % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (159) imply: % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | (160) ~ (all_52_4 = e2) % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (14), (22), (41), (134), (140), (150), % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | (152), (155), (160) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | #258. % 151.87/22.55 | | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | (161) all_58_31 = e2 % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (44), (161) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | | | | | | | #697. % 151.87/22.55 | | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | (162) ~ (all_58_29 = e3) % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | REDUCE: (43), (162) imply: % 151.87/22.55 | | | | | | | | | | | | | | (163) ~ (all_8_2 = e3) % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (23), (46), (67), (95), (100), (104), % 151.87/22.55 | | | | | | | | | | | | | | (163) are inconsistent by sub-proof #88. % 151.87/22.55 | | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | (164) all_56_15 = e3 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | COMBINE_EQS: (66), (164) imply: % 151.87/22.55 | | | | | | | | | | | | (165) e3 = e1 % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | REDUCE: (27), (165) imply: % 151.87/22.55 | | | | | | | | | | | | (166) $false % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 151.87/22.55 | | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | (167) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | BETA: splitting (167) gives: % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | (168) all_56_3 = e1 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | COMBINE_EQS: (38), (168) imply: % 151.87/22.55 | | | | | | | | | | (169) all_8_2 = e1 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | REF_CLOSE: (2), (26), (46), (93), (169) are inconsistent by % 151.87/22.55 | | | | | | | | | | sub-proof #129. % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | (170) all_56_5 = e1 | all_56_10 = e1 % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | BETA: splitting (170) gives: % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | Case 1: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | (171) all_56_5 = e1 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | REF_CLOSE: (62), (75), (171) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | #305. % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | Case 2: % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | (172) all_56_10 = e1 % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | | REF_CLOSE: (6), (53), (172) are inconsistent by sub-proof % 151.87/22.55 | | | | | | | | | | | #606. % 151.87/22.55 | | | | | | | | | | | % 151.87/22.55 | | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | | % 151.87/22.55 | | | | | | | | | End of split % 151.87/22.55 | | | | | | | | | % 151.87/22.55 | | | | | | | | End of split % 151.87/22.55 | | | | | | | | % 151.87/22.55 | | | | | | | End of split % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | Case 2: % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | (173) all_56_14 = e0 % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | | REF_CLOSE: (52), (54), (173) are inconsistent by sub-proof #806. % 151.87/22.55 | | | | | | | % 151.87/22.55 | | | | | | End of split % 151.87/22.55 | | | | | | % 151.87/22.55 | | | | | End of split % 151.87/22.55 | | | | | % 151.87/22.55 | | | | End of split % 151.87/22.55 | | | | % 151.87/22.55 | | | Case 2: % 151.87/22.55 | | | | % 151.87/22.55 | | | | (174) all_56_8 = e0 | all_56_14 = e0 % 151.87/22.55 | | | | % 151.87/22.55 | | | | REF_CLOSE: (3), (7), (13), (27), (43), (44), (50), (52), (54), (56), % 151.87/22.55 | | | | (57), (61), (64), (65), (174) are inconsistent by sub-proof % 151.87/22.55 | | | | #401. % 151.87/22.55 | | | | % 151.87/22.55 | | | End of split % 151.87/22.55 | | | % 151.87/22.55 | | End of split % 151.87/22.55 | | % 151.87/22.55 | End of split % 151.87/22.55 | % 151.87/22.55 End of proof % 151.87/22.55 % 151.87/22.55 Sub-proof #88 shows that the following formulas are inconsistent: % 151.87/22.55 ---------------------------------------------------------------- % 151.87/22.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.55 (2) op(e2, e2) = all_8_2 % 151.87/22.55 (3) ~ (all_8_2 = e3) % 151.87/22.55 (4) all_54_5 = all_8_2 % 151.87/22.55 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 151.87/22.55 (6) op(all_8_2, e2) = e0 % 151.87/22.55 (7) ~ (all_8_2 = e0) % 151.87/22.55 (8) ~ (all_8_2 = e1) % 151.87/22.55 (9) op(e2, all_8_2) = all_58_9 % 151.87/22.55 % 151.87/22.55 Begin of proof % 151.87/22.55 | % 151.87/22.55 | BETA: splitting (5) gives: % 151.87/22.55 | % 151.87/22.55 | Case 1: % 151.87/22.55 | | % 151.87/22.55 | | (10) all_54_5 = e1 % 151.87/22.55 | | % 151.87/22.55 | | COMBINE_EQS: (4), (10) imply: % 151.87/22.55 | | (11) all_8_2 = e1 % 151.87/22.55 | | % 151.87/22.55 | | REDUCE: (8), (11) imply: % 151.87/22.55 | | (12) $false % 151.87/22.55 | | % 151.87/22.55 | | CLOSE: (12) is inconsistent. % 151.87/22.55 | | % 151.87/22.55 | Case 2: % 151.87/22.55 | | % 151.87/22.55 | | (13) all_54_5 = e3 | all_54_5 = e2 % 151.87/22.55 | | % 151.87/22.55 | | BETA: splitting (13) gives: % 151.87/22.55 | | % 151.87/22.55 | | Case 1: % 151.87/22.55 | | | % 151.87/22.55 | | | (14) all_54_5 = e2 % 151.87/22.55 | | | % 151.87/22.55 | | | COMBINE_EQS: (4), (14) imply: % 151.87/22.55 | | | (15) all_8_2 = e2 % 151.87/22.55 | | | % 151.87/22.55 | | | REDUCE: (7), (15) imply: % 151.87/22.55 | | | (16) ~ (e2 = e0) % 151.87/22.55 | | | % 151.87/22.55 | | | REF_CLOSE: (1), (2), (6), (9), (15), (16) are inconsistent by sub-proof % 151.87/22.55 | | | #153. % 151.87/22.55 | | | % 151.87/22.55 | | Case 2: % 151.87/22.55 | | | % 151.87/22.55 | | | (17) all_54_5 = e3 % 151.87/22.55 | | | % 151.87/22.55 | | | COMBINE_EQS: (4), (17) imply: % 151.87/22.55 | | | (18) all_8_2 = e3 % 151.87/22.55 | | | % 151.87/22.55 | | | REDUCE: (3), (18) imply: % 151.87/22.55 | | | (19) $false % 151.87/22.55 | | | % 151.87/22.55 | | | CLOSE: (19) is inconsistent. % 151.87/22.55 | | | % 151.87/22.55 | | End of split % 151.87/22.55 | | % 151.87/22.55 | End of split % 151.87/22.55 | % 151.87/22.55 End of proof % 151.87/22.55 % 151.87/22.55 Sub-proof #89 shows that the following formulas are inconsistent: % 151.87/22.55 ---------------------------------------------------------------- % 151.87/22.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.55 (2) all_58_28 = e0 % 151.87/22.55 (3) all_56_14 = e0 % 151.87/22.55 (4) all_54_13 = all_52_7 % 151.87/22.55 (5) all_58_11 = all_52_9 % 151.87/22.55 (6) all_54_2 = all_52_8 % 151.87/22.55 (7) ~ (all_52_2 = e0) % 151.87/22.55 (8) ~ (all_10_1 = e0) % 151.87/22.55 (9) all_54_8 = all_52_2 % 151.87/22.55 (10) ~ (all_52_7 = all_10_1) % 151.87/22.55 (11) all_58_31 = e1 % 151.87/22.56 (12) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 151.87/22.56 (13) all_58_15 = all_52_2 % 151.87/22.56 (14) all_58_6 = all_52_12 % 151.87/22.56 (15) all_56_4 = all_52_8 % 151.87/22.56 (16) all_54_3 = all_52_12 % 151.87/22.56 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.87/22.56 (18) all_54_1 = all_52_4 % 151.87/22.56 (19) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.87/22.56 (20) ~ (all_6_2 = e0) % 151.87/22.56 (21) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 151.87/22.56 (22) ~ (all_52_7 = e1) % 151.87/22.56 (23) all_58_13 = all_52_13 % 151.87/22.56 (24) op(e2, e2) = all_8_2 % 151.87/22.56 (25) all_56_12 = all_10_1 % 151.87/22.56 (26) ~ (all_52_8 = all_6_2) % 151.87/22.56 (27) ~ (all_52_12 = all_52_13) % 151.87/22.56 (28) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 151.87/22.56 (29) ~ (all_52_4 = all_52_7) % 151.87/22.56 (30) ~ (all_52_2 = all_6_2) % 151.87/22.56 (31) ~ (all_52_8 = all_52_12) % 151.87/22.56 (32) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 151.87/22.56 (33) ~ (e3 = e1) % 151.87/22.56 (34) all_56_5 = all_52_9 % 151.87/22.56 (35) ~ (all_52_12 = e0) % 151.87/22.56 (36) all_58_20 = all_4_1 % 151.87/22.56 (37) ~ (all_52_9 = e0) % 151.87/22.56 (38) all_56_3 = all_8_2 % 151.87/22.56 (39) all_58_24 = all_52_7 % 151.87/22.56 (40) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.87/22.56 (41) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.87/22.56 (42) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 151.87/22.56 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 151.87/22.56 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 151.87/22.56 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 151.87/22.56 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 151.87/22.56 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 151.87/22.56 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 151.87/22.56 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 151.87/22.56 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 151.87/22.56 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 151.87/22.56 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.87/22.56 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.87/22.56 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.87/22.56 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.87/22.56 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.87/22.56 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 151.87/22.56 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.87/22.56 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.87/22.56 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.87/22.56 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.87/22.56 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.87/22.56 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 151.87/22.56 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.87/22.56 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.87/22.56 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.87/22.56 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 151.87/22.56 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 151.87/22.56 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 151.87/22.56 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.87/22.56 e0) % 151.87/22.56 (43) ~ (all_52_4 = all_52_8) % 151.87/22.56 (44) all_56_9 = all_52_12 % 151.87/22.56 (45) all_58_29 = all_8_2 % 151.87/22.56 (46) all_58_8 = all_52_1 % 151.87/22.56 (47) ~ (e2 = e1) % 151.87/22.56 (48) ~ (all_52_2 = all_52_6) % 151.87/22.56 (49) op(all_8_2, e2) = e0 % 151.87/22.56 (50) all_56_13 = all_52_7 % 151.87/22.56 (51) all_58_26 = e0 % 151.87/22.56 (52) ~ (all_52_4 = e0) % 151.87/22.56 (53) ~ (e3 = e0) % 151.87/22.56 (54) all_56_2 = all_52_1 % 151.87/22.56 (55) all_58_22 = all_10_1 % 151.87/22.56 (56) all_56_10 = all_52_13 % 151.87/22.56 (57) ~ (all_52_12 = e1) % 151.87/22.56 (58) all_58_17 = all_52_6 % 151.87/22.56 (59) ~ (e2 = e0) % 151.87/22.56 (60) ~ (all_52_9 = all_6_2) % 151.87/22.56 (61) ~ (all_52_1 = e0) % 151.87/22.56 (62) ~ (all_10_1 = e1) % 151.87/22.56 (63) ~ (all_52_7 = all_8_2) % 151.87/22.56 (64) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 151.87/22.56 (65) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.87/22.56 (66) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.87/22.56 (67) ~ (all_52_13 = all_4_1) % 151.87/22.56 (68) ~ (all_52_7 = e0) % 151.87/22.56 (69) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.87/22.56 (70) op(e0, e2) = all_52_7 % 151.87/22.56 (71) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 151.87/22.56 (72) ~ (all_52_8 = e0) % 151.87/22.56 (73) all_58_30 = all_6_2 % 151.87/22.56 (74) ~ (e3 = e2) % 151.87/22.56 (75) all_56_15 = e1 % 151.87/22.56 (76) ~ (all_52_4 = all_52_12) % 151.87/22.56 (77) ~ (all_52_2 = all_10_1) % 151.87/22.56 (78) op(e2, all_8_2) = all_58_9 % 151.87/22.56 % 151.87/22.56 Begin of proof % 151.87/22.56 | % 151.87/22.56 | BETA: splitting (19) gives: % 151.87/22.56 | % 151.87/22.56 | Case 1: % 151.87/22.56 | | % 151.87/22.56 | | (79) all_56_2 = e0 % 151.87/22.56 | | % 151.87/22.56 | | COMBINE_EQS: (54), (79) imply: % 151.87/22.56 | | (80) all_52_1 = e0 % 151.87/22.56 | | % 151.87/22.56 | | REDUCE: (61), (80) imply: % 151.87/22.56 | | (81) $false % 151.87/22.56 | | % 151.87/22.56 | | CLOSE: (81) is inconsistent. % 151.87/22.56 | | % 151.87/22.56 | Case 2: % 151.87/22.56 | | % 151.87/22.56 | | (82) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 151.87/22.56 | | % 151.87/22.56 | | BETA: splitting (64) gives: % 151.87/22.56 | | % 151.87/22.56 | | Case 1: % 151.87/22.56 | | | % 151.87/22.56 | | | (83) all_54_1 = e0 % 151.87/22.56 | | | % 151.87/22.56 | | | REF_CLOSE: (18), (52), (83) are inconsistent by sub-proof #798. % 151.87/22.56 | | | % 151.87/22.56 | | Case 2: % 151.87/22.56 | | | % 151.87/22.56 | | | (84) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.87/22.56 | | | % 151.87/22.56 | | | BETA: splitting (65) gives: % 151.87/22.56 | | | % 151.87/22.56 | | | Case 1: % 151.87/22.56 | | | | % 151.87/22.56 | | | | (85) all_56_12 = e2 % 151.87/22.56 | | | | % 151.87/22.56 | | | | COMBINE_EQS: (25), (85) imply: % 151.87/22.56 | | | | (86) all_10_1 = e2 % 151.87/22.56 | | | | % 151.87/22.56 | | | | SIMP: (86) implies: % 151.87/22.56 | | | | (87) all_10_1 = e2 % 151.87/22.56 | | | | % 151.87/22.56 | | | | REDUCE: (10), (87) imply: % 151.87/22.56 | | | | (88) ~ (all_52_7 = e2) % 151.87/22.56 | | | | % 151.87/22.56 | | | | BETA: splitting (41) gives: % 151.87/22.56 | | | | % 151.87/22.56 | | | | Case 1: % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | (89) all_56_12 = e3 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | COMBINE_EQS: (85), (89) imply: % 151.87/22.56 | | | | | (90) e3 = e2 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | REDUCE: (74), (90) imply: % 151.87/22.56 | | | | | (91) $false % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | CLOSE: (91) is inconsistent. % 151.87/22.56 | | | | | % 151.87/22.56 | | | | Case 2: % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | (92) ~ (all_56_12 = e3) % 151.87/22.56 | | | | | (93) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | REDUCE: (85), (92) imply: % 151.87/22.56 | | | | | (94) ~ (e3 = e2) % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | BETA: splitting (71) gives: % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | Case 1: % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | (95) all_54_13 = e1 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | COMBINE_EQS: (4), (95) imply: % 151.87/22.56 | | | | | | (96) all_52_7 = e1 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | SIMP: (96) implies: % 151.87/22.56 | | | | | | (97) all_52_7 = e1 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | REDUCE: (22), (97) imply: % 151.87/22.56 | | | | | | (98) $false % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | CLOSE: (98) is inconsistent. % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | Case 2: % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | (99) ~ (all_54_13 = e1) % 151.87/22.56 | | | | | | (100) all_54_13 = e3 | all_54_13 = e2 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | BETA: splitting (100) gives: % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | Case 1: % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | (101) all_54_13 = e2 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | COMBINE_EQS: (4), (101) imply: % 151.87/22.56 | | | | | | | (102) all_52_7 = e2 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | SIMP: (102) implies: % 151.87/22.56 | | | | | | | (103) all_52_7 = e2 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | COMBINE_EQS: (50), (103) imply: % 151.87/22.56 | | | | | | | (104) all_56_13 = e2 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | REF_CLOSE: (3), (33), (53), (74), (75), (93), (104) are % 151.87/22.56 | | | | | | | inconsistent by sub-proof #433. % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | Case 2: % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | (105) all_54_13 = e3 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | COMBINE_EQS: (4), (105) imply: % 151.87/22.56 | | | | | | | (106) all_52_7 = e3 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | SIMP: (106) implies: % 151.87/22.56 | | | | | | | (107) all_52_7 = e3 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | COMBINE_EQS: (50), (107) imply: % 151.87/22.56 | | | | | | | (108) all_56_13 = e3 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | REDUCE: (63), (107) imply: % 151.87/22.56 | | | | | | | (109) ~ (all_8_2 = e3) % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | SIMP: (109) implies: % 151.87/22.56 | | | | | | | (110) ~ (all_8_2 = e3) % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | REF_CLOSE: (1), (2), (3), (11), (17), (20), (24), (33), (45), % 151.87/22.56 | | | | | | | (47), (49), (53), (59), (66), (73), (74), (75), (78), % 151.87/22.56 | | | | | | | (93), (108), (110) are inconsistent by sub-proof #94. % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | End of split % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | End of split % 151.87/22.56 | | | | | % 151.87/22.56 | | | | End of split % 151.87/22.56 | | | | % 151.87/22.56 | | | Case 2: % 151.87/22.56 | | | | % 151.87/22.56 | | | | (111) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 151.87/22.56 | | | | % 151.87/22.56 | | | | BETA: splitting (111) gives: % 151.87/22.56 | | | | % 151.87/22.56 | | | | Case 1: % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | (112) all_56_13 = e2 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | COMBINE_EQS: (50), (112) imply: % 151.87/22.56 | | | | | (113) all_52_7 = e2 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | SIMP: (113) implies: % 151.87/22.56 | | | | | (114) all_52_7 = e2 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | COMBINE_EQS: (39), (114) imply: % 151.87/22.56 | | | | | (115) all_58_24 = e2 % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | REDUCE: (29), (114) imply: % 151.87/22.56 | | | | | (116) ~ (all_52_4 = e2) % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | REDUCE: (10), (114) imply: % 151.87/22.56 | | | | | (117) ~ (all_10_1 = e2) % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | SIMP: (117) implies: % 151.87/22.56 | | | | | (118) ~ (all_10_1 = e2) % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | REDUCE: (63), (114) imply: % 151.87/22.56 | | | | | (119) ~ (all_8_2 = e2) % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | SIMP: (119) implies: % 151.87/22.56 | | | | | (120) ~ (all_8_2 = e2) % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | BETA: splitting (41) gives: % 151.87/22.56 | | | | | % 151.87/22.56 | | | | | Case 1: % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | (121) all_56_12 = e3 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | COMBINE_EQS: (25), (121) imply: % 151.87/22.56 | | | | | | (122) all_10_1 = e3 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | SIMP: (122) implies: % 151.87/22.56 | | | | | | (123) all_10_1 = e3 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | COMBINE_EQS: (55), (123) imply: % 151.87/22.56 | | | | | | (124) all_58_22 = e3 % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | REDUCE: (77), (123) imply: % 151.87/22.56 | | | | | | (125) ~ (all_52_2 = e3) % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | BETA: splitting (17) gives: % 151.87/22.56 | | | | | | % 151.87/22.56 | | | | | | Case 1: % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | (126) all_58_28 = e2 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | COMBINE_EQS: (2), (126) imply: % 151.87/22.56 | | | | | | | (127) e2 = e0 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | REDUCE: (59), (127) imply: % 151.87/22.56 | | | | | | | (128) $false % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | CLOSE: (128) is inconsistent. % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | Case 2: % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | (129) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | BETA: splitting (129) gives: % 151.87/22.56 | | | | | | | % 151.87/22.56 | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | % 151.87/22.56 | | | | | | | | (130) all_58_29 = e2 % 151.87/22.56 | | | | | | | | % 151.87/22.56 | | | | | | | | REF_CLOSE: (45), (120), (130) are inconsistent by sub-proof % 151.87/22.56 | | | | | | | | #634. % 151.87/22.56 | | | | | | | | % 151.87/22.56 | | | | | | | Case 2: % 151.87/22.56 | | | | | | | | % 151.87/22.56 | | | | | | | | (131) ~ (all_58_29 = e2) % 151.87/22.56 | | | | | | | | (132) all_58_30 = e2 | all_58_31 = e2 % 151.87/22.56 | | | | | | | | % 151.87/22.56 | | | | | | | | BETA: splitting (132) gives: % 151.87/22.56 | | | | | | | | % 151.87/22.56 | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | (133) all_58_30 = e2 % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | COMBINE_EQS: (73), (133) imply: % 151.87/22.56 | | | | | | | | | (134) all_6_2 = e2 % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | SIMP: (134) implies: % 151.87/22.56 | | | | | | | | | (135) all_6_2 = e2 % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | REDUCE: (30), (135) imply: % 151.87/22.56 | | | | | | | | | (136) ~ (all_52_2 = e2) % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | REDUCE: (26), (135) imply: % 151.87/22.56 | | | | | | | | | (137) ~ (all_52_8 = e2) % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | REDUCE: (60), (135) imply: % 151.87/22.56 | | | | | | | | | (138) ~ (all_52_9 = e2) % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | BETA: splitting (21) gives: % 151.87/22.56 | | | | | | | | | % 151.87/22.56 | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | (139) all_54_8 = e0 % 151.87/22.56 | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | REF_CLOSE: (7), (9), (139) are inconsistent by sub-proof % 151.87/22.56 | | | | | | | | | | #731. % 151.87/22.56 | | | | | | | | | | % 151.87/22.56 | | | | | | | | | Case 2: % 151.87/22.56 | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | (140) ~ (all_54_8 = e0) % 151.87/22.56 | | | | | | | | | | (141) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 151.87/22.56 | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | BETA: splitting (32) gives: % 151.87/22.56 | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | (142) all_56_2 = e2 % 151.87/22.56 | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | COMBINE_EQS: (54), (142) imply: % 151.87/22.56 | | | | | | | | | | | (143) all_52_1 = e2 % 151.87/22.56 | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | SIMP: (143) implies: % 151.87/22.56 | | | | | | | | | | | (144) all_52_1 = e2 % 151.87/22.56 | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | COMBINE_EQS: (46), (144) imply: % 151.87/22.56 | | | | | | | | | | | (145) all_58_8 = e2 % 151.87/22.56 | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | BETA: splitting (12) gives: % 151.87/22.56 | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | (146) all_56_9 = e2 % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | COMBINE_EQS: (44), (146) imply: % 151.87/22.56 | | | | | | | | | | | | (147) all_52_12 = e2 % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | SIMP: (147) implies: % 151.87/22.56 | | | | | | | | | | | | (148) all_52_12 = e2 % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | COMBINE_EQS: (14), (148) imply: % 151.87/22.56 | | | | | | | | | | | | (149) all_58_6 = e2 % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | REDUCE: (27), (148) imply: % 151.87/22.56 | | | | | | | | | | | | (150) ~ (all_52_13 = e2) % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | SIMP: (150) implies: % 151.87/22.56 | | | | | | | | | | | | (151) ~ (all_52_13 = e2) % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | BETA: splitting (141) gives: % 151.87/22.56 | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | (152) all_54_8 = e1 % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | COMBINE_EQS: (9), (152) imply: % 151.87/22.56 | | | | | | | | | | | | | (153) all_52_2 = e1 % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | SIMP: (153) implies: % 151.87/22.56 | | | | | | | | | | | | | (154) all_52_2 = e1 % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | COMBINE_EQS: (13), (154) imply: % 151.87/22.56 | | | | | | | | | | | | | (155) all_58_15 = e1 % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | REDUCE: (48), (154) imply: % 151.87/22.56 | | | | | | | | | | | | | (156) ~ (all_52_6 = e1) % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | SIMP: (156) implies: % 151.87/22.56 | | | | | | | | | | | | | (157) ~ (all_52_6 = e1) % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | REDUCE: (125), (154) imply: % 151.87/22.56 | | | | | | | | | | | | | (158) ~ (e3 = e1) % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | REDUCE: (136), (154) imply: % 151.87/22.56 | | | | | | | | | | | | | (159) ~ (e2 = e1) % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | REDUCE: (7), (154) imply: % 151.87/22.56 | | | | | | | | | | | | | (160) ~ (e1 = e0) % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | BETA: splitting (42) gives: % 151.87/22.56 | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | (161) all_58_31 = e0 % 151.87/22.56 | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | REF_CLOSE: (11), (160), (161) are inconsistent by sub-proof % 151.87/22.56 | | | | | | | | | | | | | | #845. % 151.87/22.56 | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | Case 2: % 151.87/22.56 | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | (162) ~ (all_58_31 = e0) % 151.87/22.56 | | | | | | | | | | | | | | (163) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 151.87/22.56 | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 151.87/22.56 | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 151.87/22.56 | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 151.87/22.56 | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 151.87/22.56 | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 151.87/22.56 | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 151.87/22.56 | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 151.87/22.56 | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 151.87/22.56 | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 151.87/22.56 | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 151.87/22.56 | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 151.87/22.56 | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 151.87/22.56 | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.87/22.56 | | | | | | | | | | | | | | e0) % 151.87/22.56 | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | BETA: splitting (163) gives: % 151.87/22.56 | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | (164) all_58_30 = e1 % 151.87/22.56 | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | REF_CLOSE: (47), (133), (164) are inconsistent by sub-proof % 151.87/22.56 | | | | | | | | | | | | | | | #500. % 151.87/22.56 | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | Case 2: % 151.87/22.56 | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | (165) ~ (all_58_30 = e1) % 151.87/22.56 | | | | | | | | | | | | | | | (166) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 151.87/22.56 | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 151.87/22.56 | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 151.87/22.56 | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 151.87/22.56 | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 151.87/22.56 | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 151.87/22.56 | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 151.87/22.56 | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 151.87/22.56 | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 151.87/22.56 | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 151.87/22.56 | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 151.87/22.56 | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 151.87/22.56 | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 151.87/22.56 | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 151.87/22.56 | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 151.87/22.56 | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | (167) all_58_29 = e2 % 151.87/22.56 | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (120), (167) are inconsistent by sub-proof % 151.87/22.56 | | | | | | | | | | | | | | | | #634. % 151.87/22.56 | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | Case 2: % 151.87/22.56 | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | (168) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 151.87/22.56 | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 151.87/22.56 | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 151.87/22.56 | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 151.87/22.56 | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 151.87/22.56 | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 151.87/22.56 | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 151.87/22.56 | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 151.87/22.56 | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 151.87/22.56 | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 151.87/22.56 | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 151.87/22.56 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 151.87/22.56 | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.87/22.56 | | | | | | | | | | | | | | | | e0) % 151.87/22.56 | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 151.87/22.56 | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | (169) all_58_28 = e3 % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (169) imply: % 151.87/22.56 | | | | | | | | | | | | | | | | | (170) e3 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | REDUCE: (53), (170) imply: % 151.87/22.56 | | | | | | | | | | | | | | | | | (171) $false % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | Case 2: % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | (172) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 151.87/22.56 | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 151.87/22.56 | | | | | | | | | | | | | | | | | e0) % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 151.87/22.56 | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | (173) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 151.87/22.56 | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 151.87/22.56 | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 151.87/22.56 | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.56 | | | | | | | | | | | | | | | | | | = e0) % 151.87/22.56 | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 151.87/22.56 | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | | (174) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 151.87/22.56 | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 151.87/22.56 | | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 151.87/22.56 | | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | (175) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | = e2) % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.56 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (176) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (177) all_58_8 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (177) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (178) e3 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (178) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (179) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (180) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (181) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (182) all_58_22 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (183) all_58_8 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (183) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (184) e3 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (182) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (185) e3 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (186) e3 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (186) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (187) e2 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (187) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (188) all_58_30 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (132), (188) are inconsistent by % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (189) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (190) all_58_8 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (190) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (191) e3 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (191) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (192) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (193) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (194) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (195) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (196) all_58_8 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (196) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (197) e3 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (197) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (198) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (199) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (200) all_58_15 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (155), (200) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #629. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (201) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (202) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (203) all_58_6 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (149), (203) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #93. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (204) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (205) all_58_17 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (205) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (206) all_52_6 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (206) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (207) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (208) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (209) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (210) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (211) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (212) all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (115), (132), (133), (212) are % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (213) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (214) e3 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (214) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (215) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (216) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (217) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (218) all_58_6 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (218) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (219) e2 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (219) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (220) all_58_30 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (132), (220) are inconsistent by % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (221) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (222) all_58_15 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (155), (222) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #629. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (223) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (224) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (225) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (226) all_58_26 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (160), (226) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #343. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (227) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (228) all_58_6 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (149), (228) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #93. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (229) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (230) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (231) all_58_11 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (138), (231) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #626. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (232) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (233) all_58_20 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (233) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (234) all_4_1 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (235) all_4_1 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (235) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_52_13 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (34), (37), (38), (49), (56), (63), (70), % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (82), (236) are inconsistent by sub-proof #126. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (237) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 151.87/22.57 | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (238) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (239) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (240) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (241) e3 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (241) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (242) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (243) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (244) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (245) all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (115), (132), (133), (245) are % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (246) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (247) all_58_6 = e3 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (149), (247) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #93. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (248) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (249) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (250) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (251) all_58_6 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (251) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (252) e2 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (252) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (253) all_58_30 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (132), (253) are inconsistent by % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (254) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (255) all_58_6 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (255) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (256) e2 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (256) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (257) all_58_30 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (132), (257) are inconsistent by % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (258) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (259) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (260) all_58_6 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (260) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (261) e2 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (261) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (262) all_58_30 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (132), (262) are inconsistent by % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (263) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (264) all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (115), (132), (133), (264) are % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (265) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 151.87/22.57 | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (266) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (267) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (268) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (269) all_58_26 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (160), (269) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #343. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (270) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (271) all_58_13 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (151), (271) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #92. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (272) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (273) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (274) all_58_17 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (274) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (275) all_52_6 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (276) all_52_6 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (276) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (277) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (278) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (279) e2 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (279) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (280) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (281) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (282) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (283) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (284) all_58_13 = e2 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (151), (284) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | #92. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (285) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (286) all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (115), (132), (133), (286) are % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (287) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (288) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (289) all_58_24 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (59), (115), (132), (133), (289) are % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (290) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (291) e1 = e0 % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (291) imply: % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | (292) $false % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | (293) all_54_8 = e3 | all_54_8 = e2 % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | BETA: splitting (293) gives: % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | (294) all_54_8 = e2 % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | REF_CLOSE: (9), (136), (294) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | #787. % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | (295) all_54_8 = e3 % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | | REF_CLOSE: (9), (125), (295) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | | #786. % 151.87/22.57 | | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | (296) ~ (all_56_9 = e2) % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | REDUCE: (44), (296) imply: % 151.87/22.57 | | | | | | | | | | | | (297) ~ (all_52_12 = e2) % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | REF_CLOSE: (6), (15), (16), (18), (28), (31), (40), (43), % 151.87/22.57 | | | | | | | | | | | | (57), (69), (72), (76), (84), (116), (137), (297) % 151.87/22.57 | | | | | | | | | | | | are inconsistent by sub-proof #91. % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | (298) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 151.87/22.57 | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | BETA: splitting (298) gives: % 151.87/22.57 | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | (299) all_56_3 = e2 % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | COMBINE_EQS: (38), (299) imply: % 151.87/22.57 | | | | | | | | | | | | (300) all_8_2 = e2 % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | SIMP: (300) implies: % 151.87/22.57 | | | | | | | | | | | | (301) all_8_2 = e2 % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | REDUCE: (120), (301) imply: % 151.87/22.57 | | | | | | | | | | | | (302) $false % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | (303) all_56_5 = e2 | all_56_10 = e2 % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | BETA: splitting (303) gives: % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | Case 1: % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | (304) all_56_5 = e2 % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | REF_CLOSE: (34), (138), (304) are inconsistent by sub-proof % 151.87/22.57 | | | | | | | | | | | | | #90. % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | (305) all_56_10 = e2 % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | COMBINE_EQS: (56), (305) imply: % 151.87/22.57 | | | | | | | | | | | | | (306) all_52_13 = e2 % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | REDUCE: (27), (306) imply: % 151.87/22.57 | | | | | | | | | | | | | (307) ~ (all_52_12 = e2) % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | | REF_CLOSE: (6), (15), (16), (18), (28), (31), (40), (43), % 151.87/22.57 | | | | | | | | | | | | | (57), (69), (72), (76), (84), (116), (137), (307) % 151.87/22.57 | | | | | | | | | | | | | are inconsistent by sub-proof #91. % 151.87/22.57 | | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | | % 151.87/22.57 | | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | | % 151.87/22.57 | | | | | | | | | End of split % 151.87/22.57 | | | | | | | | | % 151.87/22.57 | | | | | | | | Case 2: % 151.87/22.57 | | | | | | | | | % 151.87/22.57 | | | | | | | | | (308) all_58_31 = e2 % 151.87/22.57 | | | | | | | | | % 151.87/22.57 | | | | | | | | | COMBINE_EQS: (11), (308) imply: % 151.87/22.57 | | | | | | | | | (309) e2 = e1 % 151.87/22.57 | | | | | | | | | % 151.87/22.57 | | | | | | | | | REDUCE: (47), (309) imply: % 151.87/22.57 | | | | | | | | | (310) $false % 151.87/22.57 | | | | | | | | | % 151.87/22.57 | | | | | | | | | CLOSE: (310) is inconsistent. % 151.87/22.57 | | | | | | | | | % 151.87/22.57 | | | | | | | | End of split % 151.87/22.57 | | | | | | | | % 151.87/22.57 | | | | | | | End of split % 151.87/22.57 | | | | | | | % 151.87/22.57 | | | | | | End of split % 151.87/22.57 | | | | | | % 151.87/22.57 | | | | | Case 2: % 151.87/22.57 | | | | | | % 151.87/22.57 | | | | | | (311) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.87/22.57 | | | | | | % 151.87/22.57 | | | | | | REF_CLOSE: (3), (33), (53), (74), (75), (112), (311) are % 151.87/22.57 | | | | | | inconsistent by sub-proof #433. % 151.87/22.57 | | | | | | % 151.87/22.57 | | | | | End of split % 151.87/22.57 | | | | | % 151.87/22.57 | | | | Case 2: % 151.87/22.57 | | | | | % 151.87/22.57 | | | | | (312) all_56_14 = e2 | all_56_15 = e2 % 151.87/22.57 | | | | | % 151.87/22.57 | | | | | REF_CLOSE: (3), (47), (59), (75), (312) are inconsistent by sub-proof % 151.87/22.57 | | | | | #256. % 151.87/22.57 | | | | | % 151.87/22.57 | | | | End of split % 151.87/22.57 | | | | % 151.87/22.57 | | | End of split % 151.87/22.57 | | | % 151.87/22.57 | | End of split % 151.87/22.57 | | % 151.87/22.57 | End of split % 151.87/22.57 | % 151.87/22.57 End of proof % 151.87/22.57 % 151.87/22.57 Sub-proof #90 shows that the following formulas are inconsistent: % 151.87/22.57 ---------------------------------------------------------------- % 151.87/22.57 (1) all_56_5 = all_52_9 % 151.87/22.57 (2) all_56_5 = e2 % 151.87/22.57 (3) ~ (all_52_9 = e2) % 151.87/22.57 % 151.87/22.57 Begin of proof % 151.87/22.57 | % 151.87/22.57 | COMBINE_EQS: (1), (2) imply: % 151.87/22.57 | (4) all_52_9 = e2 % 151.87/22.57 | % 151.87/22.57 | SIMP: (4) implies: % 151.87/22.57 | (5) all_52_9 = e2 % 151.87/22.57 | % 151.87/22.57 | REDUCE: (3), (5) imply: % 151.87/22.57 | (6) $false % 151.87/22.57 | % 151.87/22.57 | CLOSE: (6) is inconsistent. % 151.87/22.57 | % 151.87/22.57 End of proof % 151.87/22.57 % 151.87/22.57 Sub-proof #91 shows that the following formulas are inconsistent: % 151.87/22.57 ---------------------------------------------------------------- % 151.87/22.57 (1) ~ (all_52_8 = e2) % 151.87/22.57 (2) all_54_2 = all_52_8 % 151.87/22.57 (3) all_56_4 = all_52_8 % 151.87/22.57 (4) all_54_3 = all_52_12 % 151.87/22.58 (5) all_54_1 = all_52_4 % 151.87/22.58 (6) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.87/22.58 (7) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 151.87/22.58 (8) ~ (all_52_8 = all_52_12) % 151.87/22.58 (9) ~ (all_52_4 = e2) % 151.87/22.58 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 151.87/22.58 (11) ~ (all_52_4 = all_52_8) % 151.87/22.58 (12) ~ (all_52_12 = e1) % 151.87/22.58 (13) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 151.87/22.58 (14) ~ (all_52_8 = e0) % 151.87/22.58 (15) ~ (all_52_12 = e2) % 151.87/22.58 (16) ~ (all_52_4 = all_52_12) % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (10) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (17) all_54_3 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REF_CLOSE: (4), (12), (17) are inconsistent by sub-proof #723. % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (18) all_54_3 = e3 | all_54_3 = e2 % 151.87/22.58 | | % 151.87/22.58 | | BETA: splitting (18) gives: % 151.87/22.58 | | % 151.87/22.58 | | Case 1: % 151.87/22.58 | | | % 151.87/22.58 | | | (19) all_54_3 = e2 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (4), (15), (19) are inconsistent by sub-proof #614. % 151.87/22.58 | | | % 151.87/22.58 | | Case 2: % 151.87/22.58 | | | % 151.87/22.58 | | | (20) all_54_3 = e3 % 151.87/22.58 | | | % 151.87/22.58 | | | COMBINE_EQS: (4), (20) imply: % 151.87/22.58 | | | (21) all_52_12 = e3 % 151.87/22.58 | | | % 151.87/22.58 | | | SIMP: (21) implies: % 151.87/22.58 | | | (22) all_52_12 = e3 % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (16), (22) imply: % 151.87/22.58 | | | (23) ~ (all_52_4 = e3) % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (8), (22) imply: % 151.87/22.58 | | | (24) ~ (all_52_8 = e3) % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (13), (14), (23), (24) % 151.87/22.58 | | | are inconsistent by sub-proof #257. % 151.87/22.58 | | | % 151.87/22.58 | | End of split % 151.87/22.58 | | % 151.87/22.58 | End of split % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #92 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_58_13 = all_52_13 % 151.87/22.58 (2) all_58_13 = e2 % 151.87/22.58 (3) ~ (all_52_13 = e2) % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | COMBINE_EQS: (1), (2) imply: % 151.87/22.58 | (4) all_52_13 = e2 % 151.87/22.58 | % 151.87/22.58 | SIMP: (4) implies: % 151.87/22.58 | (5) all_52_13 = e2 % 151.87/22.58 | % 151.87/22.58 | REDUCE: (3), (5) imply: % 151.87/22.58 | (6) $false % 151.87/22.58 | % 151.87/22.58 | CLOSE: (6) is inconsistent. % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #93 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_58_6 = e3 % 151.87/22.58 (2) all_58_6 = e2 % 151.87/22.58 (3) ~ (e3 = e2) % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | COMBINE_EQS: (1), (2) imply: % 151.87/22.58 | (4) e3 = e2 % 151.87/22.58 | % 151.87/22.58 | SIMP: (4) implies: % 151.87/22.58 | (5) e3 = e2 % 151.87/22.58 | % 151.87/22.58 | REDUCE: (3), (5) imply: % 151.87/22.58 | (6) $false % 151.87/22.58 | % 151.87/22.58 | CLOSE: (6) is inconsistent. % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #94 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.58 (2) all_58_28 = e0 % 151.87/22.58 (3) all_56_14 = e0 % 151.87/22.58 (4) all_58_31 = e1 % 151.87/22.58 (5) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.87/22.58 (6) ~ (all_6_2 = e0) % 151.87/22.58 (7) op(e2, e2) = all_8_2 % 151.87/22.58 (8) ~ (all_8_2 = e3) % 151.87/22.58 (9) ~ (e3 = e1) % 151.87/22.58 (10) all_58_29 = all_8_2 % 151.87/22.58 (11) ~ (e2 = e1) % 151.87/22.58 (12) op(all_8_2, e2) = e0 % 151.87/22.58 (13) ~ (e3 = e0) % 151.87/22.58 (14) all_56_13 = e3 % 151.87/22.58 (15) ~ (e2 = e0) % 151.87/22.58 (16) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.87/22.58 (17) all_58_30 = all_6_2 % 151.87/22.58 (18) ~ (e3 = e2) % 151.87/22.58 (19) all_56_15 = e1 % 151.87/22.58 (20) op(e2, all_8_2) = all_58_9 % 151.87/22.58 (21) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (16) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (22) all_58_28 = e3 % 151.87/22.58 | | % 151.87/22.58 | | COMBINE_EQS: (2), (22) imply: % 151.87/22.58 | | (23) e3 = e0 % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (13), (23) imply: % 151.87/22.58 | | (24) $false % 151.87/22.58 | | % 151.87/22.58 | | CLOSE: (24) is inconsistent. % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (25) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 151.87/22.58 | | % 151.87/22.58 | | BETA: splitting (25) gives: % 151.87/22.58 | | % 151.87/22.58 | | Case 1: % 151.87/22.58 | | | % 151.87/22.58 | | | (26) all_58_29 = e3 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (8), (10), (26) are inconsistent by sub-proof #756. % 151.87/22.58 | | | % 151.87/22.58 | | Case 2: % 151.87/22.58 | | | % 151.87/22.58 | | | (27) all_58_30 = e3 | all_58_31 = e3 % 151.87/22.58 | | | % 151.87/22.58 | | | BETA: splitting (27) gives: % 151.87/22.58 | | | % 151.87/22.58 | | | Case 1: % 151.87/22.58 | | | | % 151.87/22.58 | | | | (28) all_58_30 = e3 % 151.87/22.58 | | | | % 151.87/22.58 | | | | COMBINE_EQS: (17), (28) imply: % 151.87/22.58 | | | | (29) all_6_2 = e3 % 151.87/22.58 | | | | % 151.87/22.58 | | | | SIMP: (29) implies: % 151.87/22.58 | | | | (30) all_6_2 = e3 % 151.87/22.58 | | | | % 151.87/22.58 | | | | BETA: splitting (5) gives: % 151.87/22.58 | | | | % 151.87/22.58 | | | | Case 1: % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | (31) all_58_28 = e2 % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | COMBINE_EQS: (2), (31) imply: % 151.87/22.58 | | | | | (32) e2 = e0 % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | REDUCE: (15), (32) imply: % 151.87/22.58 | | | | | (33) $false % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | CLOSE: (33) is inconsistent. % 151.87/22.58 | | | | | % 151.87/22.58 | | | | Case 2: % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | (34) ~ (all_58_28 = e2) % 151.87/22.58 | | | | | (35) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | REDUCE: (2), (34) imply: % 151.87/22.58 | | | | | (36) ~ (e2 = e0) % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | BETA: splitting (35) gives: % 151.87/22.58 | | | | | % 151.87/22.58 | | | | | Case 1: % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | (37) all_58_29 = e2 % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | COMBINE_EQS: (10), (37) imply: % 151.87/22.58 | | | | | | (38) all_8_2 = e2 % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | SIMP: (38) implies: % 151.87/22.58 | | | | | | (39) all_8_2 = e2 % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | REF_CLOSE: (1), (7), (12), (15), (20), (39) are inconsistent by % 151.87/22.58 | | | | | | sub-proof #153. % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | Case 2: % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | (40) all_58_30 = e2 | all_58_31 = e2 % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | BETA: splitting (40) gives: % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | | Case 1: % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | (41) all_58_30 = e2 % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | COMBINE_EQS: (28), (41) imply: % 151.87/22.58 | | | | | | | (42) e3 = e2 % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | SIMP: (42) implies: % 151.87/22.58 | | | | | | | (43) e3 = e2 % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | COMBINE_EQS: (14), (43) imply: % 151.87/22.58 | | | | | | | (44) all_56_13 = e2 % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | REF_CLOSE: (3), (9), (13), (18), (19), (21), (44) are inconsistent % 151.87/22.58 | | | | | | | by sub-proof #433. % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | Case 2: % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | (45) all_58_31 = e2 % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | COMBINE_EQS: (4), (45) imply: % 151.87/22.58 | | | | | | | (46) e2 = e1 % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | REDUCE: (11), (46) imply: % 151.87/22.58 | | | | | | | (47) $false % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | | CLOSE: (47) is inconsistent. % 151.87/22.58 | | | | | | | % 151.87/22.58 | | | | | | End of split % 151.87/22.58 | | | | | | % 151.87/22.58 | | | | | End of split % 151.87/22.58 | | | | | % 151.87/22.58 | | | | End of split % 151.87/22.58 | | | | % 151.87/22.58 | | | Case 2: % 151.87/22.58 | | | | % 151.87/22.58 | | | | (48) all_58_31 = e3 % 151.87/22.58 | | | | % 151.87/22.58 | | | | COMBINE_EQS: (4), (48) imply: % 151.87/22.58 | | | | (49) e3 = e1 % 151.87/22.58 | | | | % 151.87/22.58 | | | | REDUCE: (9), (49) imply: % 151.87/22.58 | | | | (50) $false % 151.87/22.58 | | | | % 151.87/22.58 | | | | CLOSE: (50) is inconsistent. % 151.87/22.58 | | | | % 151.87/22.58 | | | End of split % 151.87/22.58 | | | % 151.87/22.58 | | End of split % 151.87/22.58 | | % 151.87/22.58 | End of split % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #95 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.87/22.58 (2) all_58_31 = all_4_2 % 151.87/22.58 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.58 (4) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.87/22.58 (5) all_58_28 = e0 % 151.87/22.58 (6) all_56_14 = e0 % 151.87/22.58 (7) all_56_15 = all_4_2 % 151.87/22.58 (8) all_56_7 = all_52_6 % 151.87/22.58 (9) all_54_2 = all_52_8 % 151.87/22.58 (10) ~ (all_52_7 = all_10_1) % 151.87/22.58 (11) all_56_4 = all_52_8 % 151.87/22.58 (12) ~ (all_52_4 = all_8_2) % 151.87/22.58 (13) all_54_1 = all_52_4 % 151.87/22.58 (14) ~ (all_6_2 = e0) % 151.87/22.58 (15) op(e2, e2) = all_8_2 % 151.87/22.58 (16) all_56_12 = all_10_1 % 151.87/22.58 (17) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.87/22.58 (18) ~ (all_52_6 = all_52_7) % 151.87/22.58 (19) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 151.87/22.58 (20) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.87/22.58 (21) all_56_0 = e0 % 151.87/22.58 (22) all_54_5 = all_8_2 % 151.87/22.58 (23) ~ (all_52_4 = all_52_7) % 151.87/22.58 (24) ~ (all_52_2 = all_6_2) % 151.87/22.58 (25) ~ (all_52_8 = all_52_12) % 151.87/22.58 (26) ~ (all_52_1 = all_52_13) % 151.87/22.58 (27) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.87/22.58 (28) all_56_11 = all_52_14 % 151.87/22.58 (29) all_56_1 = all_52_4 % 151.87/22.58 (30) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.87/22.58 (31) ~ (all_52_1 = all_8_2) % 151.87/22.58 (32) all_56_3 = all_8_2 % 151.87/22.58 (33) ~ (all_52_4 = all_52_8) % 151.87/22.58 (34) all_56_9 = all_52_12 % 151.87/22.58 (35) all_58_29 = all_8_2 % 151.87/22.58 (36) op(e3, e0) = all_52_12 % 151.87/22.58 (37) all_56_6 = all_52_2 % 151.87/22.58 (38) op(all_8_2, e2) = e0 % 151.87/22.58 (39) all_56_13 = all_52_7 % 151.87/22.58 (40) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 151.87/22.58 (41) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.87/22.58 (42) ~ (e3 = e0) % 151.87/22.58 (43) all_56_2 = all_52_1 % 151.87/22.58 (44) all_56_10 = all_52_13 % 151.87/22.58 (45) op(all_8_2, e0) = all_8_0 % 151.87/22.58 (46) ~ (e2 = e0) % 151.87/22.58 (47) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.87/22.58 (48) ~ (all_52_7 = all_8_2) % 151.87/22.58 (49) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 151.87/22.58 (50) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 151.87/22.58 (51) ~ (all_52_7 = e0) % 151.87/22.58 (52) ~ (e1 = e0) % 151.87/22.58 (53) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 151.87/22.58 (54) ~ (all_52_7 = all_4_2) % 151.87/22.58 (55) ~ (all_4_2 = e1) % 151.87/22.58 (56) op(e0, e2) = all_52_7 % 151.87/22.58 (57) all_58_30 = all_6_2 % 151.87/22.58 (58) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 (59) ~ (all_52_14 = all_6_2) % 151.87/22.58 (60) ~ (all_52_4 = all_52_12) % 151.87/22.58 (61) op(e2, all_8_2) = all_58_9 % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (4) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (62) all_56_13 = e1 % 151.87/22.58 | | % 151.87/22.58 | | COMBINE_EQS: (39), (62) imply: % 151.87/22.58 | | (63) all_52_7 = e1 % 151.87/22.58 | | % 151.87/22.58 | | SIMP: (63) implies: % 151.87/22.58 | | (64) all_52_7 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (23), (64) imply: % 151.87/22.58 | | (65) ~ (all_52_4 = e1) % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (18), (64) imply: % 151.87/22.58 | | (66) ~ (all_52_6 = e1) % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (10), (64) imply: % 151.87/22.58 | | (67) ~ (all_10_1 = e1) % 151.87/22.58 | | % 151.87/22.58 | | SIMP: (67) implies: % 151.87/22.58 | | (68) ~ (all_10_1 = e1) % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (48), (64) imply: % 151.87/22.58 | | (69) ~ (all_8_2 = e1) % 151.87/22.58 | | % 151.87/22.58 | | SIMP: (69) implies: % 151.87/22.58 | | (70) ~ (all_8_2 = e1) % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (54), (64) imply: % 151.87/22.58 | | (71) ~ (all_4_2 = e1) % 151.87/22.58 | | % 151.87/22.58 | | BETA: splitting (58) gives: % 151.87/22.58 | | % 151.87/22.58 | | Case 1: % 151.87/22.58 | | | % 151.87/22.58 | | | (72) all_58_28 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | COMBINE_EQS: (5), (72) imply: % 151.87/22.58 | | | (73) e1 = e0 % 151.87/22.58 | | | % 151.87/22.58 | | | SIMP: (73) implies: % 151.87/22.58 | | | (74) e1 = e0 % 151.87/22.58 | | | % 151.87/22.58 | | | COMBINE_EQS: (62), (74) imply: % 151.87/22.58 | | | (75) all_56_13 = e0 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (8), (29), (32), (40), (52), (65), (66), (70), (75) are % 151.87/22.58 | | | inconsistent by sub-proof #197. % 151.87/22.58 | | | % 151.87/22.58 | | Case 2: % 151.87/22.58 | | | % 151.87/22.58 | | | (76) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (1), (2), (3), (7), (9), (11), (12), (13), (14), (15), (16), % 151.87/22.58 | | | (17), (19), (20), (21), (22), (24), (25), (26), (27), (28), % 151.87/22.58 | | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), % 151.87/22.58 | | | (41), (42), (43), (44), (45), (46), (47), (49), (50), (51), % 151.87/22.58 | | | (53), (55), (56), (57), (59), (60), (61), (68), (70), (76) are % 151.87/22.58 | | | inconsistent by sub-proof #99. % 151.87/22.58 | | | % 151.87/22.58 | | End of split % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (77) all_56_14 = e1 | all_56_15 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REF_CLOSE: (6), (7), (52), (55), (77) are inconsistent by sub-proof #582. % 151.87/22.58 | | % 151.87/22.58 | End of split % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #96 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_58_31 = all_4_2 % 151.87/22.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.58 (3) all_58_28 = e0 % 151.87/22.58 (4) op(e1, e2) = all_52_6 % 151.87/22.58 (5) ~ (all_52_6 = e0) % 151.87/22.58 (6) all_58_29 = all_8_2 % 151.87/22.58 (7) all_58_30 = e0 % 151.87/22.58 (8) op(all_8_2, e2) = e0 % 151.87/22.58 (9) ~ (e1 = e0) % 151.87/22.58 (10) ~ (all_4_2 = e1) % 151.87/22.58 (11) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (11) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (12) all_58_28 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #690. % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (13) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (13) are % 151.87/22.58 | | inconsistent by sub-proof #128. % 151.87/22.58 | | % 151.87/22.58 | End of split % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #97 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_58_31 = all_4_2 % 151.87/22.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.58 (3) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 151.87/22.58 (4) all_58_28 = e0 % 151.87/22.58 (5) all_56_15 = all_4_2 % 151.87/22.58 (6) ~ (all_52_11 = all_4_2) % 151.87/22.58 (7) all_56_13 = e0 % 151.87/22.58 (8) op(e1, e2) = all_52_6 % 151.87/22.58 (9) ~ (all_52_6 = e0) % 151.87/22.58 (10) all_58_29 = all_8_2 % 151.87/22.58 (11) op(all_8_2, e2) = e0 % 151.87/22.58 (12) ~ (all_52_11 = all_6_2) % 151.87/22.58 (13) ~ (all_52_11 = e0) % 151.87/22.58 (14) all_56_14 = all_52_11 % 151.87/22.58 (15) ~ (e1 = e0) % 151.87/22.58 (16) ~ (all_4_2 = e1) % 151.87/22.58 (17) all_58_30 = all_6_2 % 151.87/22.58 (18) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (3) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (19) all_56_13 = e1 % 151.87/22.58 | | % 151.87/22.58 | | COMBINE_EQS: (7), (19) imply: % 151.87/22.58 | | (20) e1 = e0 % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (15), (20) imply: % 151.87/22.58 | | (21) $false % 151.87/22.58 | | % 151.87/22.58 | | CLOSE: (21) is inconsistent. % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (22) all_56_14 = e1 | all_56_15 = e1 % 151.87/22.58 | | % 151.87/22.58 | | BETA: splitting (22) gives: % 151.87/22.58 | | % 151.87/22.58 | | Case 1: % 151.87/22.58 | | | % 151.87/22.58 | | | (23) all_56_14 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | COMBINE_EQS: (14), (23) imply: % 151.87/22.58 | | | (24) all_52_11 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | SIMP: (24) implies: % 151.87/22.58 | | | (25) all_52_11 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (12), (25) imply: % 151.87/22.58 | | | (26) ~ (all_6_2 = e1) % 151.87/22.58 | | | % 151.87/22.58 | | | SIMP: (26) implies: % 151.87/22.58 | | | (27) ~ (all_6_2 = e1) % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (6), (25) imply: % 151.87/22.58 | | | (28) ~ (all_4_2 = e1) % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (1), (2), (4), (8), (9), (10), (11), (15), (16), (17), (18), % 151.87/22.58 | | | (27) are inconsistent by sub-proof #98. % 151.87/22.58 | | | % 151.87/22.58 | | Case 2: % 151.87/22.58 | | | % 151.87/22.58 | | | (29) all_56_15 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (5), (16), (29) are inconsistent by sub-proof #671. % 151.87/22.58 | | | % 151.87/22.58 | | End of split % 151.87/22.58 | | % 151.87/22.58 | End of split % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #98 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_58_31 = all_4_2 % 151.87/22.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.58 (3) all_58_28 = e0 % 151.87/22.58 (4) op(e1, e2) = all_52_6 % 151.87/22.58 (5) ~ (all_52_6 = e0) % 151.87/22.58 (6) all_58_29 = all_8_2 % 151.87/22.58 (7) op(all_8_2, e2) = e0 % 151.87/22.58 (8) ~ (e1 = e0) % 151.87/22.58 (9) ~ (all_6_2 = e1) % 151.87/22.58 (10) ~ (all_4_2 = e1) % 151.87/22.58 (11) all_58_30 = all_6_2 % 151.87/22.58 (12) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (12) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (13) all_58_28 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #690. % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (14) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 | | % 151.87/22.58 | | BETA: splitting (14) gives: % 151.87/22.58 | | % 151.87/22.58 | | Case 1: % 151.87/22.58 | | | % 151.87/22.58 | | | (15) all_58_29 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | COMBINE_EQS: (6), (15) imply: % 151.87/22.58 | | | (16) all_8_2 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (2), (4), (5), (7), (16) are inconsistent by sub-proof #129. % 151.87/22.58 | | | % 151.87/22.58 | | Case 2: % 151.87/22.58 | | | % 151.87/22.58 | | | (17) all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | REF_CLOSE: (1), (9), (10), (11), (17) are inconsistent by sub-proof #673. % 151.87/22.58 | | | % 151.87/22.58 | | End of split % 151.87/22.58 | | % 151.87/22.58 | End of split % 151.87/22.58 | % 151.87/22.58 End of proof % 151.87/22.58 % 151.87/22.58 Sub-proof #99 shows that the following formulas are inconsistent: % 151.87/22.58 ---------------------------------------------------------------- % 151.87/22.58 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 151.87/22.58 (2) all_58_31 = all_4_2 % 151.87/22.58 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 151.87/22.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 151.87/22.58 (4) all_56_15 = all_4_2 % 151.87/22.58 (5) all_54_2 = all_52_8 % 151.87/22.58 (6) all_56_4 = all_52_8 % 151.87/22.58 (7) ~ (all_52_4 = all_8_2) % 151.87/22.58 (8) all_54_1 = all_52_4 % 151.87/22.58 (9) ~ (all_6_2 = e0) % 151.87/22.58 (10) op(e2, e2) = all_8_2 % 151.87/22.58 (11) all_56_12 = all_10_1 % 151.87/22.58 (12) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.87/22.58 (13) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 151.87/22.58 (14) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 151.87/22.58 (15) all_56_0 = e0 % 151.87/22.58 (16) all_54_5 = all_8_2 % 151.87/22.58 (17) ~ (all_52_2 = all_6_2) % 151.87/22.58 (18) ~ (all_52_8 = all_52_12) % 151.87/22.58 (19) ~ (all_52_1 = all_52_13) % 151.87/22.58 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 151.87/22.58 (21) all_56_11 = all_52_14 % 151.87/22.58 (22) all_56_1 = all_52_4 % 151.87/22.58 (23) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 151.87/22.58 (24) ~ (all_52_1 = all_8_2) % 151.87/22.58 (25) all_56_3 = all_8_2 % 151.87/22.58 (26) ~ (all_52_4 = all_52_8) % 151.87/22.58 (27) all_56_9 = all_52_12 % 151.87/22.58 (28) all_58_29 = all_8_2 % 151.87/22.58 (29) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 (30) op(e3, e0) = all_52_12 % 151.87/22.58 (31) all_56_6 = all_52_2 % 151.87/22.58 (32) op(all_8_2, e2) = e0 % 151.87/22.58 (33) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 151.87/22.58 (34) ~ (e3 = e0) % 151.87/22.58 (35) all_56_2 = all_52_1 % 151.87/22.58 (36) all_56_10 = all_52_13 % 151.87/22.58 (37) op(all_8_2, e0) = all_8_0 % 151.87/22.58 (38) ~ (e2 = e0) % 151.87/22.58 (39) ~ (all_10_1 = e1) % 151.87/22.58 (40) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 151.87/22.58 (41) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 151.87/22.58 (42) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 151.87/22.58 (43) ~ (all_52_7 = e0) % 151.87/22.58 (44) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 151.87/22.58 (45) ~ (all_4_2 = e1) % 151.87/22.58 (46) op(e0, e2) = all_52_7 % 151.87/22.58 (47) all_58_30 = all_6_2 % 151.87/22.58 (48) ~ (all_52_14 = all_6_2) % 151.87/22.58 (49) ~ (all_52_4 = all_52_12) % 151.87/22.58 (50) ~ (all_8_2 = e1) % 151.87/22.58 (51) op(e2, all_8_2) = all_58_9 % 151.87/22.58 % 151.87/22.58 Begin of proof % 151.87/22.58 | % 151.87/22.58 | BETA: splitting (29) gives: % 151.87/22.58 | % 151.87/22.58 | Case 1: % 151.87/22.58 | | % 151.87/22.58 | | (52) all_58_29 = e1 % 151.87/22.58 | | % 151.87/22.58 | | COMBINE_EQS: (28), (52) imply: % 151.87/22.58 | | (53) all_8_2 = e1 % 151.87/22.58 | | % 151.87/22.58 | | REDUCE: (50), (53) imply: % 151.87/22.58 | | (54) $false % 151.87/22.58 | | % 151.87/22.58 | | CLOSE: (54) is inconsistent. % 151.87/22.58 | | % 151.87/22.58 | Case 2: % 151.87/22.58 | | % 151.87/22.58 | | (55) all_58_30 = e1 | all_58_31 = e1 % 151.87/22.58 | | % 151.87/22.58 | | BETA: splitting (55) gives: % 151.87/22.58 | | % 151.87/22.58 | | Case 1: % 151.87/22.58 | | | % 151.87/22.58 | | | (56) all_58_30 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | COMBINE_EQS: (47), (56) imply: % 151.87/22.58 | | | (57) all_6_2 = e1 % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (17), (57) imply: % 151.87/22.58 | | | (58) ~ (all_52_2 = e1) % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (48), (57) imply: % 151.87/22.58 | | | (59) ~ (all_52_14 = e1) % 151.87/22.58 | | | % 151.87/22.58 | | | REDUCE: (9), (57) imply: % 151.87/22.58 | | | (60) ~ (e1 = e0) % 151.87/22.58 | | | % 151.87/22.59 | | | BETA: splitting (12) gives: % 151.87/22.59 | | | % 151.87/22.59 | | | Case 1: % 151.87/22.59 | | | | % 151.87/22.59 | | | | (61) all_56_0 = e1 % 151.87/22.59 | | | | % 151.87/22.59 | | | | COMBINE_EQS: (15), (61) imply: % 151.87/22.59 | | | | (62) e1 = e0 % 151.87/22.59 | | | | % 151.87/22.59 | | | | REF_CLOSE: (2), (45), (55), (56), (60), (62) are inconsistent by % 151.87/22.59 | | | | sub-proof #487. % 151.87/22.59 | | | | % 151.87/22.59 | | | Case 2: % 151.87/22.59 | | | | % 151.87/22.59 | | | | (63) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 151.87/22.59 | | | | % 151.87/22.59 | | | | BETA: splitting (63) gives: % 151.87/22.59 | | | | % 151.87/22.59 | | | | Case 1: % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | (64) all_56_2 = e1 % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | COMBINE_EQS: (35), (64) imply: % 151.87/22.59 | | | | | (65) all_52_1 = e1 % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | REDUCE: (19), (65) imply: % 151.87/22.59 | | | | | (66) ~ (all_52_13 = e1) % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | SIMP: (66) implies: % 151.87/22.59 | | | | | (67) ~ (all_52_13 = e1) % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | REDUCE: (24), (65) imply: % 151.87/22.59 | | | | | (68) ~ (all_8_2 = e1) % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | BETA: splitting (33) gives: % 151.87/22.59 | | | | | % 151.87/22.59 | | | | | Case 1: % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | (69) all_56_9 = e1 % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | COMBINE_EQS: (27), (69) imply: % 151.87/22.59 | | | | | | (70) all_52_12 = e1 % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | REDUCE: (49), (70) imply: % 151.87/22.59 | | | | | | (71) ~ (all_52_4 = e1) % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | REDUCE: (18), (70) imply: % 151.87/22.59 | | | | | | (72) ~ (all_52_8 = e1) % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | REDUCE: (30), (70) imply: % 151.87/22.59 | | | | | | (73) op(e3, e0) = e1 % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | BETA: splitting (20) gives: % 151.87/22.59 | | | | | | % 151.87/22.59 | | | | | | Case 1: % 151.87/22.59 | | | | | | | % 151.87/22.59 | | | | | | | (74) all_54_5 = e0 % 151.87/22.59 | | | | | | | % 151.87/22.59 | | | | | | | COMBINE_EQS: (16), (74) imply: % 151.87/22.59 | | | | | | | (75) all_8_2 = e0 % 151.87/22.59 | | | | | | | % 151.87/22.59 | | | | | | | SIMP: (75) implies: % 151.87/22.59 | | | | | | | (76) all_8_2 = e0 % 151.87/22.59 | | | | | | | % 151.87/22.59 | | | | | | | REDUCE: (32), (76) imply: % 152.16/22.59 | | | | | | | (77) op(e0, e2) = e0 % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | REF_CLOSE: (3), (43), (46), (77) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | #240. % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | Case 2: % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | (78) ~ (all_54_5 = e0) % 152.16/22.59 | | | | | | | (79) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | REDUCE: (16), (78) imply: % 152.16/22.59 | | | | | | | (80) ~ (all_8_2 = e0) % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | BETA: splitting (1) gives: % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | (81) all_56_4 = e3 % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | COMBINE_EQS: (6), (81) imply: % 152.16/22.59 | | | | | | | | (82) all_52_8 = e3 % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | REDUCE: (26), (82) imply: % 152.16/22.59 | | | | | | | | (83) ~ (all_52_4 = e3) % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | REDUCE: (72), (82) imply: % 152.16/22.59 | | | | | | | | (84) ~ (e3 = e1) % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | BETA: splitting (13) gives: % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | (85) all_56_0 = e2 % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | COMBINE_EQS: (15), (85) imply: % 152.16/22.59 | | | | | | | | | (86) e2 = e0 % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | REDUCE: (38), (86) imply: % 152.16/22.59 | | | | | | | | | (87) $false % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | CLOSE: (87) is inconsistent. % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | (88) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | BETA: splitting (42) gives: % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | (89) all_56_2 = e3 % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | REF_CLOSE: (64), (84), (89) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | #206. % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | (90) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | BETA: splitting (14) gives: % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | (91) all_54_1 = e1 % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | REF_CLOSE: (8), (71), (91) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | | #741. % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | (92) all_54_1 = e3 | all_54_1 = e2 % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | BETA: splitting (90) gives: % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | (93) all_56_3 = e3 % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | COMBINE_EQS: (25), (93) imply: % 152.16/22.59 | | | | | | | | | | | | (94) all_8_2 = e3 % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REDUCE: (37), (94) imply: % 152.16/22.59 | | | | | | | | | | | | (95) op(e3, e0) = all_8_0 % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REF_CLOSE: (3), (41), (73), (94), (95) are inconsistent by % 152.16/22.59 | | | | | | | | | | | | sub-proof #156. % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | (96) ~ (all_56_3 = e3) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REDUCE: (25), (96) imply: % 152.16/22.59 | | | | | | | | | | | | (97) ~ (all_8_2 = e3) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | BETA: splitting (79) gives: % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | (98) all_54_5 = e1 % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | REF_CLOSE: (16), (50), (98) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | | | | #534. % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | (99) all_54_5 = e3 | all_54_5 = e2 % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | BETA: splitting (88) gives: % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | (100) all_56_1 = e2 % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | COMBINE_EQS: (22), (100) imply: % 152.16/22.59 | | | | | | | | | | | | | | (101) all_52_4 = e2 % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | SIMP: (101) implies: % 152.16/22.59 | | | | | | | | | | | | | | (102) all_52_4 = e2 % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | REDUCE: (7), (102) imply: % 152.16/22.59 | | | | | | | | | | | | | | (103) ~ (all_8_2 = e2) % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | SIMP: (103) implies: % 152.16/22.59 | | | | | | | | | | | | | | (104) ~ (all_8_2 = e2) % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | REF_CLOSE: (16), (97), (99), (104) are inconsistent by % 152.16/22.59 | | | | | | | | | | | | | | sub-proof #532. % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | (105) ~ (all_56_1 = e2) % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | REDUCE: (22), (105) imply: % 152.16/22.59 | | | | | | | | | | | | | | (106) ~ (all_52_4 = e2) % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | REF_CLOSE: (8), (83), (92), (106) are inconsistent by % 152.16/22.59 | | | | | | | | | | | | | | sub-proof #722. % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | End of split % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | (107) ~ (all_56_4 = e3) % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | REDUCE: (6), (107) imply: % 152.16/22.59 | | | | | | | | (108) ~ (all_52_8 = e3) % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | BETA: splitting (44) gives: % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | (109) all_56_0 = e3 % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | COMBINE_EQS: (15), (109) imply: % 152.16/22.59 | | | | | | | | | (110) e3 = e0 % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | REDUCE: (34), (110) imply: % 152.16/22.59 | | | | | | | | | (111) $false % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | CLOSE: (111) is inconsistent. % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | (112) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | BETA: splitting (23) gives: % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | (113) all_54_2 = e1 % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | REF_CLOSE: (5), (72), (113) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | #819. % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | (114) all_54_2 = e3 | all_54_2 = e2 % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | BETA: splitting (114) gives: % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | (115) all_54_2 = e2 % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | COMBINE_EQS: (5), (115) imply: % 152.16/22.59 | | | | | | | | | | | (116) all_52_8 = e2 % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | SIMP: (116) implies: % 152.16/22.59 | | | | | | | | | | | (117) all_52_8 = e2 % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | REDUCE: (26), (117) imply: % 152.16/22.59 | | | | | | | | | | | (118) ~ (all_52_4 = e2) % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | BETA: splitting (112) gives: % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | (119) all_56_1 = e3 % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | COMBINE_EQS: (22), (119) imply: % 152.16/22.59 | | | | | | | | | | | | (120) all_52_4 = e3 % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | SIMP: (120) implies: % 152.16/22.59 | | | | | | | | | | | | (121) all_52_4 = e3 % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REDUCE: (7), (121) imply: % 152.16/22.59 | | | | | | | | | | | | (122) ~ (all_8_2 = e3) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | SIMP: (122) implies: % 152.16/22.59 | | | | | | | | | | | | (123) ~ (all_8_2 = e3) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REDUCE: (118), (121) imply: % 152.16/22.59 | | | | | | | | | | | | (124) ~ (e3 = e2) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | BETA: splitting (40) gives: % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | (125) all_56_1 = e2 % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | REF_CLOSE: (119), (124), (125) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | | | | #568. % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | (126) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | BETA: splitting (79) gives: % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | (127) all_54_5 = e1 % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | REF_CLOSE: (16), (50), (127) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | | | | | #534. % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | (128) all_54_5 = e3 | all_54_5 = e2 % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | BETA: splitting (126) gives: % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | | (129) all_56_3 = e2 % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | | COMBINE_EQS: (25), (129) imply: % 152.16/22.59 | | | | | | | | | | | | | | | (130) all_8_2 = e2 % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (32), (38), (51), (130) are % 152.16/22.59 | | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | | (131) ~ (all_56_3 = e2) % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | | REDUCE: (25), (131) imply: % 152.16/22.59 | | | | | | | | | | | | | | | (132) ~ (all_8_2 = e2) % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | | REF_CLOSE: (16), (123), (128), (132) are inconsistent by % 152.16/22.59 | | | | | | | | | | | | | | | sub-proof #532. % 152.16/22.59 | | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | (133) ~ (all_56_1 = e3) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REDUCE: (22), (133) imply: % 152.16/22.59 | | | | | | | | | | | | (134) ~ (all_52_4 = e3) % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | | REF_CLOSE: (8), (14), (71), (118), (134) are inconsistent by % 152.16/22.59 | | | | | | | | | | | | sub-proof #738. % 152.16/22.59 | | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | (135) all_54_2 = e3 % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | | REF_CLOSE: (5), (108), (135) are inconsistent by sub-proof % 152.16/22.59 | | | | | | | | | | | #816. % 152.16/22.59 | | | | | | | | | | | % 152.16/22.59 | | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | | % 152.16/22.59 | | | | | | | | | End of split % 152.16/22.59 | | | | | | | | | % 152.16/22.59 | | | | | | | | End of split % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | End of split % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | End of split % 152.16/22.59 | | | | | | % 152.16/22.59 | | | | | Case 2: % 152.16/22.59 | | | | | | % 152.16/22.59 | | | | | | (136) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.16/22.59 | | | | | | % 152.16/22.59 | | | | | | BETA: splitting (136) gives: % 152.16/22.59 | | | | | | % 152.16/22.59 | | | | | | Case 1: % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | (137) all_56_10 = e1 % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | COMBINE_EQS: (36), (137) imply: % 152.16/22.59 | | | | | | | (138) all_52_13 = e1 % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | REDUCE: (67), (138) imply: % 152.16/22.59 | | | | | | | (139) $false % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | CLOSE: (139) is inconsistent. % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | Case 2: % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | (140) all_56_11 = e1 | all_56_15 = e1 % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | BETA: splitting (140) gives: % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | | Case 1: % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | (141) all_56_11 = e1 % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | REF_CLOSE: (21), (59), (141) are inconsistent by sub-proof #580. % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | Case 2: % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | (142) all_56_15 = e1 % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | | REF_CLOSE: (4), (45), (142) are inconsistent by sub-proof #671. % 152.16/22.59 | | | | | | | | % 152.16/22.59 | | | | | | | End of split % 152.16/22.59 | | | | | | | % 152.16/22.59 | | | | | | End of split % 152.16/22.59 | | | | | | % 152.16/22.59 | | | | | End of split % 152.16/22.59 | | | | | % 152.16/22.59 | | | | Case 2: % 152.16/22.59 | | | | | % 152.16/22.59 | | | | | (143) all_56_6 = e1 | all_56_12 = e1 % 152.16/22.59 | | | | | % 152.16/22.59 | | | | | REF_CLOSE: (11), (31), (39), (58), (143) are inconsistent by sub-proof % 152.16/22.59 | | | | | #404. % 152.16/22.59 | | | | | % 152.16/22.59 | | | | End of split % 152.16/22.59 | | | | % 152.16/22.59 | | | End of split % 152.16/22.59 | | | % 152.16/22.59 | | Case 2: % 152.16/22.59 | | | % 152.16/22.59 | | | (144) all_58_31 = e1 % 152.16/22.59 | | | % 152.16/22.59 | | | COMBINE_EQS: (2), (144) imply: % 152.16/22.59 | | | (145) all_4_2 = e1 % 152.16/22.59 | | | % 152.16/22.59 | | | REDUCE: (45), (145) imply: % 152.16/22.59 | | | (146) $false % 152.16/22.59 | | | % 152.16/22.59 | | | CLOSE: (146) is inconsistent. % 152.16/22.59 | | | % 152.16/22.59 | | End of split % 152.16/22.59 | | % 152.16/22.59 | End of split % 152.16/22.59 | % 152.16/22.59 End of proof % 152.16/22.59 % 152.16/22.59 Sub-proof #100 shows that the following formulas are inconsistent: % 152.16/22.59 ---------------------------------------------------------------- % 152.16/22.59 (1) all_54_14 = all_10_0 % 152.16/22.59 (2) all_54_14 = e2 % 152.16/22.59 (3) ~ (all_10_0 = e2) % 152.16/22.59 % 152.16/22.59 Begin of proof % 152.16/22.59 | % 152.16/22.59 | COMBINE_EQS: (1), (2) imply: % 152.16/22.59 | (4) all_10_0 = e2 % 152.16/22.59 | % 152.16/22.59 | SIMP: (4) implies: % 152.16/22.59 | (5) all_10_0 = e2 % 152.16/22.59 | % 152.16/22.59 | REDUCE: (3), (5) imply: % 152.16/22.59 | (6) $false % 152.16/22.59 | % 152.16/22.59 | CLOSE: (6) is inconsistent. % 152.16/22.59 | % 152.16/22.59 End of proof % 152.16/22.59 % 152.16/22.59 Sub-proof #101 shows that the following formulas are inconsistent: % 152.16/22.59 ---------------------------------------------------------------- % 152.16/22.59 (1) all_54_14 = all_10_0 % 152.16/22.59 (2) all_54_14 = e1 % 152.16/22.59 (3) ~ (all_10_0 = e1) % 152.16/22.59 % 152.16/22.59 Begin of proof % 152.16/22.59 | % 152.16/22.59 | COMBINE_EQS: (1), (2) imply: % 152.16/22.59 | (4) all_10_0 = e1 % 152.16/22.59 | % 152.16/22.59 | SIMP: (4) implies: % 152.16/22.59 | (5) all_10_0 = e1 % 152.16/22.59 | % 152.16/22.59 | REDUCE: (3), (5) imply: % 152.16/22.59 | (6) $false % 152.16/22.59 | % 152.16/22.59 | CLOSE: (6) is inconsistent. % 152.16/22.59 | % 152.16/22.59 End of proof % 152.16/22.59 % 152.16/22.59 Sub-proof #102 shows that the following formulas are inconsistent: % 152.16/22.59 ---------------------------------------------------------------- % 152.16/22.59 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 152.16/22.59 (2) all_58_31 = all_4_2 % 152.16/22.59 (3) ~ (all_52_8 = all_52_9) % 152.16/22.59 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.16/22.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.16/22.59 (5) ~ (all_52_2 = all_52_3) % 152.16/22.59 (6) all_58_11 = all_52_9 % 152.16/22.59 (7) all_56_15 = all_4_2 % 152.16/22.59 (8) all_56_7 = all_52_6 % 152.16/22.59 (9) ~ (all_52_6 = all_6_2) % 152.16/22.59 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.16/22.59 (11) all_54_2 = all_52_8 % 152.16/22.59 (12) ~ (all_52_2 = e0) % 152.16/22.59 (13) op(e3, all_52_4) = all_58_1 % 152.16/22.59 (14) ~ (all_6_1 = all_4_2) % 152.16/22.59 (15) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.16/22.59 (16) ~ (all_52_8 = all_10_2) % 152.16/22.59 (17) all_58_15 = all_52_2 % 152.16/22.59 (18) op(e1, all_52_14) = all_58_19 % 152.16/22.59 (19) all_54_7 = all_52_13 % 152.16/22.59 (20) all_58_6 = all_52_12 % 152.16/22.59 (21) ~ (all_52_6 = all_8_2) % 152.16/22.59 (22) all_56_4 = all_52_8 % 152.16/22.59 (23) ~ (all_52_4 = all_8_2) % 152.16/22.59 (24) all_54_3 = all_52_12 % 152.16/22.59 (25) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.16/22.59 (26) all_54_1 = all_52_4 % 152.16/22.59 (27) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.16/22.59 (28) ~ (all_52_4 = all_52_6) % 152.16/22.59 (29) all_58_13 = all_52_13 % 152.16/22.59 (30) op(e2, e2) = all_8_2 % 152.16/22.59 (31) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 152.16/22.59 (32) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.16/22.59 (33) ~ (all_52_6 = all_52_7) % 152.16/22.59 (34) op(e3, e2) = all_52_4 % 152.16/22.59 (35) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 152.16/22.59 (36) all_58_20 = all_52_14 % 152.16/22.59 (37) ~ (all_52_8 = all_6_2) % 152.16/22.59 (38) ~ (all_52_12 = all_52_13) % 152.16/22.59 (39) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.16/22.59 (40) op(e0, all_52_3) = all_58_21 % 152.16/22.59 (41) all_54_5 = all_8_2 % 152.16/22.59 (42) ~ (all_52_6 = all_52_14) % 152.16/22.59 (43) all_54_6 = all_52_9 % 152.16/22.59 (44) all_56_14 = all_6_1 % 152.16/22.59 (45) ~ (all_52_4 = all_52_7) % 152.16/22.59 (46) ~ (all_10_2 = e0) % 152.16/22.59 (47) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 152.16/22.59 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 152.16/22.59 (48) ~ (all_52_8 = all_52_12) % 152.16/22.59 (49) all_54_9 = all_52_6 % 152.16/22.59 (50) ~ (all_52_13 = all_4_2) % 152.16/22.59 (51) op(e1, e2) = all_52_6 % 152.16/22.59 (52) ~ (all_52_13 = all_8_2) % 152.16/22.59 (53) op(e1, all_52_6) = all_58_16 % 152.16/22.59 (54) ~ (e3 = e1) % 152.16/22.59 (55) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.16/22.59 (56) all_56_8 = e0 % 152.16/22.59 (57) ~ (all_52_6 = e0) % 152.16/22.59 (58) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.16/22.59 (59) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.16/22.59 (60) all_54_14 = all_6_1 % 152.16/22.59 (61) ~ (all_52_1 = all_52_13) % 152.16/22.59 (62) all_56_5 = all_52_9 % 152.16/22.59 (63) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.16/22.59 (64) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.16/22.59 (65) all_56_12 = all_52_3 % 152.16/22.59 (66) ~ (all_52_3 = all_52_7) % 152.16/22.59 (67) all_58_2 = all_52_4 % 152.16/22.59 (68) all_20_2 = all_4_2 % 152.16/22.59 (69) all_56_11 = all_52_14 % 152.16/22.59 (70) all_56_1 = all_52_4 % 152.16/22.59 (71) ~ (all_52_7 = all_6_1) % 152.16/22.59 (72) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.16/22.59 (73) ~ (all_52_3 = all_4_2) % 152.16/22.59 (74) op(e1, e3) = all_52_2 % 152.16/22.59 (75) op(e1, e0) = all_52_14 % 152.16/22.59 (76) ~ (all_52_9 = e0) % 152.16/22.59 (77) ~ (all_52_1 = all_8_2) % 152.16/22.59 (78) all_56_3 = all_8_2 % 152.16/22.59 (79) all_58_24 = all_52_7 % 152.16/22.59 (80) ~ (all_52_13 = all_52_14) % 152.16/22.59 (81) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.16/22.59 (82) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 152.16/22.59 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 152.16/22.59 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 152.16/22.59 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 152.16/22.59 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 152.16/22.59 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 152.16/22.59 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 152.16/22.59 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 152.16/22.59 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 152.16/22.59 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 152.16/22.59 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.16/22.59 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.16/22.59 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.59 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.59 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.59 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.59 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.59 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.16/22.59 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.59 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.16/22.59 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.59 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 152.16/22.59 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.16/22.59 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.16/22.59 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.16/22.59 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 152.16/22.59 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 152.16/22.59 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 152.16/22.59 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.59 e0) % 152.16/22.59 (83) ~ (all_52_4 = all_52_8) % 152.16/22.59 (84) all_56_9 = all_52_12 % 152.16/22.59 (85) all_58_29 = all_8_2 % 152.16/22.59 (86) ~ (all_52_12 = all_52_14) % 152.16/22.59 (87) all_58_30 = e0 % 152.16/22.59 (88) all_58_8 = all_52_1 % 152.16/22.59 (89) ~ (e2 = e1) % 152.16/22.59 (90) op(e3, e0) = all_52_12 % 152.16/22.59 (91) all_56_6 = all_52_2 % 152.16/22.59 (92) ~ (all_52_2 = all_52_6) % 152.16/22.59 (93) ~ (all_52_8 = all_6_1) % 152.16/22.59 (94) op(all_8_2, e2) = e0 % 152.16/22.59 (95) all_56_13 = all_52_7 % 152.16/22.59 (96) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.16/22.59 (97) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.16/22.59 (98) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.16/22.59 (99) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.16/22.59 (100) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.16/22.59 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.16/22.59 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.16/22.59 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.16/22.59 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.16/22.59 (all_58_27 = e0)) % 152.16/22.59 (101) ~ (all_52_9 = all_52_13) % 152.16/22.59 (102) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.16/22.59 (103) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.16/22.59 (104) op(e1, e1) = e0 % 152.16/22.59 (105) ~ (e3 = e0) % 152.16/22.59 (106) all_56_2 = all_52_1 % 152.16/22.59 (107) all_58_26 = all_6_1 % 152.16/22.59 (108) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.16/22.59 (109) all_56_10 = all_52_13 % 152.16/22.59 (110) ~ (all_52_12 = all_10_2) % 152.16/22.59 (111) ~ (all_52_1 = all_52_3) % 152.16/22.59 (112) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.16/22.59 (113) ~ (all_52_9 = all_8_2) % 152.16/22.59 (114) all_58_28 = all_10_2 % 152.16/22.59 (115) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.16/22.59 (116) ~ (all_6_1 = e0) % 152.16/22.59 (117) op(all_8_2, e0) = all_8_0 % 152.16/22.59 (118) all_58_17 = all_52_6 % 152.16/22.59 (119) ~ (all_52_1 = all_52_9) % 152.16/22.59 (120) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 152.16/22.59 (121) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 152.16/22.59 (122) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.16/22.59 (123) ~ (e2 = e0) % 152.16/22.59 (124) ~ (all_52_2 = all_10_2) % 152.16/22.59 (125) all_56_0 = all_10_2 % 152.16/22.59 (126) op(e0, e0) = all_4_2 % 152.16/22.59 (127) all_58_22 = all_52_3 % 152.16/22.59 (128) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.16/22.59 (129) ~ (all_52_12 = all_4_2) % 152.16/22.59 (130) ~ (all_52_3 = all_6_1) % 152.16/22.59 (131) ~ (all_52_3 = all_10_2) % 152.16/22.59 (132) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.16/22.59 (133) ~ (all_52_1 = all_52_2) % 152.16/22.59 (134) ~ (all_52_7 = all_8_2) % 152.16/22.59 (135) op(e2, e0) = all_52_13 % 152.16/22.59 (136) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.16/22.59 (137) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.16/22.59 (138) op(e2, all_52_13) = all_58_12 % 152.16/22.59 (139) all_58_4 = all_52_8 % 152.16/22.59 (140) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.16/22.59 (141) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 152.16/22.59 (142) all_54_0 = all_10_2 % 152.16/22.59 (143) ~ (all_52_2 = all_52_14) % 152.16/22.59 (144) ~ (all_52_14 = all_4_2) % 152.16/22.59 (145) ~ (e1 = e0) % 152.16/22.59 (146) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.16/22.59 (147) ~ (all_52_7 = all_4_2) % 152.16/22.59 (148) ~ (all_52_14 = e0) % 152.16/22.59 (149) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.16/22.59 (150) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.16/22.59 (151) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.16/22.59 (152) op(e0, e2) = all_52_7 % 152.16/22.59 (153) ~ (all_52_8 = e0) % 152.16/22.59 (154) ~ (all_52_4 = all_10_2) % 152.16/22.59 (155) ~ (all_52_9 = all_6_1) % 152.16/22.59 (156) all_58_30 = all_6_2 % 152.16/22.59 (157) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.16/22.59 (158) ~ (e3 = e2) % 152.16/22.60 (159) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.16/22.60 (160) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.16/22.60 (161) op(all_4_2, e0) = all_4_1 % 152.16/22.60 (162) op(all_10_2, e3) = all_10_1 % 152.16/22.60 (163) ~ (all_52_4 = all_52_12) % 152.16/22.60 (164) all_54_12 = all_52_3 % 152.16/22.60 (165) op(e2, all_8_2) = all_58_9 % 152.16/22.60 (166) all_54_4 = all_52_1 % 152.16/22.60 (167) ~ (all_52_1 = all_10_2) % 152.16/22.60 % 152.16/22.60 Begin of proof % 152.16/22.60 | % 152.16/22.60 | BETA: splitting (120) gives: % 152.16/22.60 | % 152.16/22.60 | Case 1: % 152.16/22.60 | | % 152.16/22.60 | | (168) ~ (all_20_2 = e1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (68), (168) imply: % 152.16/22.60 | | (169) ~ (all_4_2 = e1) % 152.16/22.60 | | % 152.16/22.60 | | BETA: splitting (47) gives: % 152.16/22.60 | | % 152.16/22.60 | | Case 1: % 152.16/22.60 | | | % 152.16/22.60 | | | (170) all_56_15 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | COMBINE_EQS: (7), (170) imply: % 152.16/22.60 | | | (171) all_4_2 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | SIMP: (171) implies: % 152.16/22.60 | | | (172) all_4_2 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | COMBINE_EQS: (2), (172) imply: % 152.16/22.60 | | | (173) all_58_31 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | REDUCE: (50), (172) imply: % 152.16/22.60 | | | (174) ~ (all_52_13 = e0) % 152.16/22.60 | | | % 152.16/22.60 | | | REDUCE: (169), (172) imply: % 152.16/22.60 | | | (175) ~ (e1 = e0) % 152.16/22.60 | | | % 152.16/22.60 | | | BETA: splitting (128) gives: % 152.16/22.60 | | | % 152.16/22.60 | | | Case 1: % 152.16/22.60 | | | | % 152.16/22.60 | | | | (176) all_56_0 = e0 % 152.16/22.60 | | | | % 152.16/22.60 | | | | COMBINE_EQS: (125), (176) imply: % 152.16/22.60 | | | | (177) all_10_2 = e0 % 152.16/22.60 | | | | % 152.16/22.60 | | | | REDUCE: (46), (177) imply: % 152.16/22.60 | | | | (178) $false % 152.16/22.60 | | | | % 152.16/22.60 | | | | CLOSE: (178) is inconsistent. % 152.16/22.60 | | | | % 152.16/22.60 | | | Case 2: % 152.16/22.60 | | | | % 152.16/22.60 | | | | (179) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.16/22.60 | | | | % 152.16/22.60 | | | | BETA: splitting (179) gives: % 152.16/22.60 | | | | % 152.16/22.60 | | | | Case 1: % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | (180) all_56_2 = e0 % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | REF_CLOSE: (2), (4), (25), (30), (51), (57), (77), (85), (87), (89), % 152.16/22.60 | | | | | (94), (106), (123), (145), (157), (165), (169), (173), % 152.16/22.60 | | | | | (180) are inconsistent by sub-proof #127. % 152.16/22.60 | | | | | % 152.16/22.60 | | | | Case 2: % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | (181) ~ (all_56_2 = e0) % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | REDUCE: (106), (181) imply: % 152.16/22.60 | | | | | (182) ~ (all_52_1 = e0) % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | REF_CLOSE: (4), (27), (62), (76), (78), (94), (106), (109), (134), % 152.16/22.60 | | | | | (152), (174), (182) are inconsistent by sub-proof #125. % 152.16/22.60 | | | | | % 152.16/22.60 | | | | End of split % 152.16/22.60 | | | | % 152.16/22.60 | | | End of split % 152.16/22.60 | | | % 152.16/22.60 | | Case 2: % 152.16/22.60 | | | % 152.16/22.60 | | | (183) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 = % 152.16/22.60 | | | e0 | all_56_13 = e0 | all_56_14 = e0) % 152.16/22.60 | | | % 152.16/22.60 | | | ALPHA: (183) implies: % 152.16/22.60 | | | (184) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 152.16/22.60 | | | (185) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 152.16/22.60 | | | (15), (17), (18), (19), (20), (22), (23), (24), (25), (26), % 152.16/22.60 | | | (27), (29), (30), (34), (35), (36), (38), (40), (42), (43), % 152.16/22.60 | | | (44), (45), (46), (48), (49), (50), (51), (52), (54), (55), % 152.16/22.60 | | | (57), (61), (63), (65), (66), (67), (69), (70), (72), (74), % 152.16/22.60 | | | (76), (77), (78), (79), (80), (81), (82), (84), (85), (86), % 152.16/22.60 | | | (87), (88), (89), (90), (91), (92), (93), (94), (95), (97), % 152.16/22.60 | | | (99), (100), (101), (102), (103), (104), (105), (106), (107), % 152.16/22.60 | | | (109), (110), (113), (114), (115), (118), (119), (122), (123), % 152.16/22.60 | | | (124), (125), (126), (127), (128), (129), (130), (131), (132), % 152.16/22.60 | | | (133), (134), (135), (136), (138), (139), (140), (143), (144), % 152.16/22.60 | | | (145), (147), (148), (149), (150), (151), (152), (153), (154), % 152.16/22.60 | | | (155), (156), (157), (158), (160), (162), (163), (165), (166), % 152.16/22.60 | | | (167), (169), (184), (185) are inconsistent by sub-proof #115. % 152.16/22.60 | | | % 152.16/22.60 | | End of split % 152.16/22.60 | | % 152.16/22.60 | Case 2: % 152.16/22.60 | | % 152.16/22.60 | | (186) all_20_2 = e1 % 152.16/22.60 | | % 152.16/22.60 | | COMBINE_EQS: (68), (186) imply: % 152.16/22.60 | | (187) all_4_2 = e1 % 152.16/22.60 | | % 152.16/22.60 | | COMBINE_EQS: (7), (187) imply: % 152.16/22.60 | | (188) all_56_15 = e1 % 152.16/22.60 | | % 152.16/22.60 | | COMBINE_EQS: (2), (187) imply: % 152.16/22.60 | | (189) all_58_31 = e1 % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (73), (187) imply: % 152.16/22.60 | | (190) ~ (all_52_3 = e1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (147), (187) imply: % 152.16/22.60 | | (191) ~ (all_52_7 = e1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (14), (187) imply: % 152.16/22.60 | | (192) ~ (all_6_1 = e1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (161), (187) imply: % 152.16/22.60 | | (193) op(e1, e0) = all_4_1 % 152.16/22.60 | | % 152.16/22.60 | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, simplifying % 152.16/22.60 | | with (75), (193) gives: % 152.16/22.60 | | (194) all_52_14 = all_4_1 % 152.16/22.60 | | % 152.16/22.60 | | COMBINE_EQS: (69), (194) imply: % 152.16/22.60 | | (195) all_56_11 = all_4_1 % 152.16/22.60 | | % 152.16/22.60 | | COMBINE_EQS: (36), (194) imply: % 152.16/22.60 | | (196) all_58_20 = all_4_1 % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (42), (194) imply: % 152.16/22.60 | | (197) ~ (all_52_6 = all_4_1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (86), (194) imply: % 152.16/22.60 | | (198) ~ (all_52_12 = all_4_1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (80), (194) imply: % 152.16/22.60 | | (199) ~ (all_52_13 = all_4_1) % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (148), (194) imply: % 152.16/22.60 | | (200) ~ (all_4_1 = e0) % 152.16/22.60 | | % 152.16/22.60 | | BETA: splitting (112) gives: % 152.16/22.60 | | % 152.16/22.60 | | Case 1: % 152.16/22.60 | | | % 152.16/22.60 | | | (201) all_54_14 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | REF_CLOSE: (60), (116), (201) are inconsistent by sub-proof #114. % 152.16/22.60 | | | % 152.16/22.60 | | Case 2: % 152.16/22.60 | | | % 152.16/22.60 | | | (202) ~ (all_54_14 = e0) % 152.16/22.60 | | | (203) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 152.16/22.60 | | | % 152.16/22.60 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), % 152.16/22.60 | | | (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 152.16/22.60 | | | (26), (27), (28), (29), (30), (31), (32), (33), (37), (39), % 152.16/22.60 | | | (41), (43), (44), (45), (46), (47), (48), (49), (51), (53), % 152.16/22.60 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), % 152.16/22.60 | | | (64), (65), (66), (67), (70), (71), (72), (76), (77), (78), % 152.16/22.60 | | | (79), (81), (82), (83), (84), (85), (87), (88), (89), (90), % 152.16/22.60 | | | (91), (92), (93), (94), (95), (96), (98), (99), (101), (102), % 152.16/22.60 | | | (105), (106), (107), (108), (109), (110), (111), (113), (114), % 152.16/22.60 | | | (116), (117), (118), (119), (121), (123), (124), (125), (127), % 152.16/22.60 | | | (128), (130), (131), (132), (133), (134), (136), (137), (139), % 152.16/22.60 | | | (140), (141), (142), (145), (146), (149), (150), (151), (152), % 152.16/22.60 | | | (153), (154), (155), (156), (157), (158), (159), (160), (163), % 152.16/22.60 | | | (164), (165), (188), (189), (190), (191), (192), (195), (196), % 152.16/22.60 | | | (197), (198), (199), (200), (203) are inconsistent by sub-proof % 152.16/22.60 | | | #103. % 152.16/22.60 | | | % 152.16/22.60 | | End of split % 152.16/22.60 | | % 152.16/22.60 | End of split % 152.16/22.60 | % 152.16/22.60 End of proof % 152.16/22.60 % 152.16/22.60 Sub-proof #103 shows that the following formulas are inconsistent: % 152.16/22.60 ---------------------------------------------------------------- % 152.16/22.60 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 152.16/22.60 (2) ~ (all_52_8 = all_52_9) % 152.16/22.60 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.16/22.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.16/22.60 (4) ~ (all_52_2 = all_52_3) % 152.16/22.60 (5) all_58_11 = all_52_9 % 152.16/22.60 (6) all_56_7 = all_52_6 % 152.16/22.60 (7) ~ (all_52_6 = all_6_2) % 152.16/22.60 (8) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.16/22.60 (9) all_54_2 = all_52_8 % 152.16/22.60 (10) ~ (all_52_2 = e0) % 152.16/22.60 (11) all_58_31 = e1 % 152.16/22.60 (12) op(e3, all_52_4) = all_58_1 % 152.16/22.60 (13) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.16/22.60 (14) ~ (all_52_8 = all_10_2) % 152.16/22.60 (15) all_58_15 = all_52_2 % 152.16/22.60 (16) all_54_7 = all_52_13 % 152.16/22.60 (17) all_58_6 = all_52_12 % 152.16/22.60 (18) ~ (all_52_6 = all_8_2) % 152.16/22.60 (19) all_56_4 = all_52_8 % 152.16/22.60 (20) ~ (all_6_1 = e1) % 152.16/22.60 (21) ~ (all_52_4 = all_8_2) % 152.16/22.60 (22) all_54_3 = all_52_12 % 152.16/22.60 (23) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.16/22.60 (24) all_54_1 = all_52_4 % 152.16/22.60 (25) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.16/22.60 (26) ~ (all_52_4 = all_52_6) % 152.16/22.60 (27) ~ (all_52_7 = e1) % 152.16/22.60 (28) all_58_13 = all_52_13 % 152.16/22.60 (29) all_56_11 = all_4_1 % 152.16/22.60 (30) op(e2, e2) = all_8_2 % 152.16/22.60 (31) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 152.16/22.60 (32) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.16/22.60 (33) ~ (all_52_6 = all_52_7) % 152.16/22.60 (34) ~ (all_52_8 = all_6_2) % 152.16/22.60 (35) ~ (all_52_3 = e1) % 152.16/22.60 (36) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.16/22.60 (37) all_54_5 = all_8_2 % 152.16/22.60 (38) all_54_6 = all_52_9 % 152.16/22.60 (39) all_56_14 = all_6_1 % 152.16/22.60 (40) ~ (all_52_4 = all_52_7) % 152.16/22.60 (41) ~ (all_10_2 = e0) % 152.16/22.60 (42) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 152.16/22.60 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 152.16/22.60 (43) ~ (all_52_8 = all_52_12) % 152.16/22.60 (44) all_54_9 = all_52_6 % 152.16/22.60 (45) op(e1, e2) = all_52_6 % 152.16/22.60 (46) op(e1, all_52_6) = all_58_16 % 152.16/22.60 (47) ~ (e3 = e1) % 152.16/22.60 (48) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.16/22.60 (49) all_56_8 = e0 % 152.16/22.60 (50) ~ (all_52_6 = e0) % 152.16/22.60 (51) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.16/22.60 (52) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.16/22.60 (53) all_54_14 = all_6_1 % 152.16/22.60 (54) ~ (all_52_1 = all_52_13) % 152.16/22.60 (55) all_56_5 = all_52_9 % 152.16/22.60 (56) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.16/22.60 (57) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.16/22.60 (58) all_56_12 = all_52_3 % 152.16/22.60 (59) ~ (all_52_3 = all_52_7) % 152.16/22.60 (60) all_58_2 = all_52_4 % 152.16/22.60 (61) all_56_1 = all_52_4 % 152.16/22.60 (62) ~ (all_52_7 = all_6_1) % 152.16/22.60 (63) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.16/22.60 (64) all_58_20 = all_4_1 % 152.16/22.60 (65) ~ (all_52_9 = e0) % 152.16/22.60 (66) ~ (all_52_1 = all_8_2) % 152.16/22.60 (67) all_56_3 = all_8_2 % 152.16/22.60 (68) all_58_24 = all_52_7 % 152.16/22.60 (69) ~ (all_52_6 = all_4_1) % 152.16/22.60 (70) ~ (all_52_12 = all_4_1) % 152.16/22.60 (71) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.16/22.60 (72) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 152.16/22.60 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 152.16/22.60 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 152.16/22.60 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 152.16/22.60 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 152.16/22.60 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 152.16/22.60 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 152.16/22.60 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 152.16/22.60 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 152.16/22.60 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 152.16/22.60 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.16/22.60 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.16/22.60 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.60 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.60 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.60 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.60 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.60 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.16/22.60 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.60 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.16/22.60 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.60 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 152.16/22.60 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.16/22.60 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.16/22.60 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.16/22.60 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 152.16/22.60 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 152.16/22.60 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 152.16/22.60 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.60 e0) % 152.16/22.60 (73) ~ (all_52_4 = all_52_8) % 152.16/22.60 (74) all_56_9 = all_52_12 % 152.16/22.60 (75) all_58_29 = all_8_2 % 152.16/22.60 (76) all_58_30 = e0 % 152.16/22.60 (77) all_58_8 = all_52_1 % 152.16/22.60 (78) ~ (e2 = e1) % 152.16/22.60 (79) op(e3, e0) = all_52_12 % 152.16/22.60 (80) all_56_6 = all_52_2 % 152.16/22.60 (81) ~ (all_52_2 = all_52_6) % 152.16/22.60 (82) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 152.16/22.60 (83) ~ (all_52_8 = all_6_1) % 152.16/22.60 (84) op(all_8_2, e2) = e0 % 152.16/22.60 (85) all_56_13 = all_52_7 % 152.16/22.60 (86) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.16/22.60 (87) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.16/22.60 (88) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.16/22.60 (89) ~ (all_52_9 = all_52_13) % 152.16/22.60 (90) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.16/22.60 (91) ~ (e3 = e0) % 152.16/22.60 (92) all_56_2 = all_52_1 % 152.16/22.60 (93) all_58_26 = all_6_1 % 152.16/22.60 (94) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.16/22.60 (95) all_56_10 = all_52_13 % 152.16/22.60 (96) ~ (all_52_12 = all_10_2) % 152.16/22.60 (97) ~ (all_52_1 = all_52_3) % 152.16/22.60 (98) ~ (all_52_9 = all_8_2) % 152.16/22.60 (99) all_58_28 = all_10_2 % 152.16/22.60 (100) ~ (all_6_1 = e0) % 152.16/22.60 (101) op(all_8_2, e0) = all_8_0 % 152.16/22.60 (102) all_58_17 = all_52_6 % 152.16/22.60 (103) ~ (all_52_1 = all_52_9) % 152.16/22.60 (104) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 152.16/22.60 (105) ~ (e2 = e0) % 152.16/22.60 (106) ~ (all_52_2 = all_10_2) % 152.16/22.60 (107) all_56_0 = all_10_2 % 152.16/22.60 (108) all_58_22 = all_52_3 % 152.16/22.60 (109) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.16/22.60 (110) ~ (all_52_3 = all_6_1) % 152.16/22.60 (111) ~ (all_52_3 = all_10_2) % 152.16/22.60 (112) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.16/22.60 (113) ~ (all_52_1 = all_52_2) % 152.16/22.60 (114) ~ (all_52_7 = all_8_2) % 152.16/22.60 (115) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.16/22.60 (116) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.16/22.60 (117) all_58_4 = all_52_8 % 152.16/22.60 (118) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.16/22.60 (119) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 152.16/22.60 (120) ~ (all_52_13 = all_4_1) % 152.16/22.60 (121) all_54_0 = all_10_2 % 152.16/22.60 (122) ~ (e1 = e0) % 152.16/22.60 (123) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.16/22.60 (124) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.16/22.60 (125) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.16/22.60 (126) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.16/22.60 (127) op(e0, e2) = all_52_7 % 152.16/22.60 (128) ~ (all_52_8 = e0) % 152.16/22.60 (129) ~ (all_52_4 = all_10_2) % 152.16/22.60 (130) ~ (all_52_9 = all_6_1) % 152.16/22.60 (131) all_58_30 = all_6_2 % 152.16/22.60 (132) ~ (all_4_1 = e0) % 152.16/22.60 (133) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.16/22.60 (134) ~ (e3 = e2) % 152.16/22.60 (135) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.16/22.60 (136) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.16/22.60 (137) all_56_15 = e1 % 152.16/22.60 (138) ~ (all_52_4 = all_52_12) % 152.16/22.60 (139) all_54_12 = all_52_3 % 152.16/22.60 (140) op(e2, all_8_2) = all_58_9 % 152.16/22.60 % 152.16/22.60 Begin of proof % 152.16/22.60 | % 152.16/22.60 | BETA: splitting (56) gives: % 152.16/22.60 | % 152.16/22.60 | Case 1: % 152.16/22.60 | | % 152.16/22.60 | | (141) all_56_0 = e0 % 152.16/22.60 | | % 152.16/22.60 | | COMBINE_EQS: (107), (141) imply: % 152.16/22.60 | | (142) all_10_2 = e0 % 152.16/22.60 | | % 152.16/22.60 | | REDUCE: (41), (142) imply: % 152.16/22.60 | | (143) $false % 152.16/22.60 | | % 152.16/22.60 | | CLOSE: (143) is inconsistent. % 152.16/22.60 | | % 152.16/22.60 | Case 2: % 152.16/22.60 | | % 152.16/22.60 | | (144) ~ (all_56_0 = e0) % 152.16/22.60 | | (145) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.16/22.60 | | % 152.16/22.60 | | BETA: splitting (109) gives: % 152.16/22.60 | | % 152.16/22.60 | | Case 1: % 152.16/22.60 | | | % 152.16/22.60 | | | (146) all_56_0 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | COMBINE_EQS: (107), (146) imply: % 152.16/22.60 | | | (147) all_10_2 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | REDUCE: (41), (147) imply: % 152.16/22.60 | | | (148) $false % 152.16/22.60 | | | % 152.16/22.60 | | | CLOSE: (148) is inconsistent. % 152.16/22.60 | | | % 152.16/22.60 | | Case 2: % 152.16/22.60 | | | % 152.16/22.60 | | | (149) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.16/22.60 | | | % 152.16/22.60 | | | BETA: splitting (52) gives: % 152.16/22.60 | | | % 152.16/22.60 | | | Case 1: % 152.16/22.60 | | | | % 152.16/22.60 | | | | (150) all_54_0 = e0 % 152.16/22.60 | | | | % 152.16/22.60 | | | | REF_CLOSE: (41), (121), (150) are inconsistent by sub-proof #861. % 152.16/22.60 | | | | % 152.16/22.60 | | | Case 2: % 152.16/22.60 | | | | % 152.16/22.60 | | | | (151) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 152.16/22.60 | | | | % 152.16/22.60 | | | | BETA: splitting (126) gives: % 152.16/22.60 | | | | % 152.16/22.60 | | | | Case 1: % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | (152) all_54_6 = e0 % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | REF_CLOSE: (38), (65), (152) are inconsistent by sub-proof #797. % 152.16/22.60 | | | | | % 152.16/22.60 | | | | Case 2: % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | (153) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | BETA: splitting (124) gives: % 152.16/22.60 | | | | | % 152.16/22.60 | | | | | Case 1: % 152.16/22.60 | | | | | | % 152.16/22.60 | | | | | | (154) all_54_2 = e0 % 152.16/22.60 | | | | | | % 152.16/22.60 | | | | | | REF_CLOSE: (9), (128), (154) are inconsistent by sub-proof #860. % 152.16/22.60 | | | | | | % 152.16/22.60 | | | | | Case 2: % 152.16/22.60 | | | | | | % 152.16/22.60 | | | | | | (155) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.16/22.60 | | | | | | % 152.16/22.60 | | | | | | BETA: splitting (48) gives: % 152.16/22.60 | | | | | | % 152.16/22.60 | | | | | | Case 1: % 152.16/22.60 | | | | | | | % 152.16/22.60 | | | | | | | (156) all_54_9 = e0 % 152.16/22.60 | | | | | | | % 152.16/22.60 | | | | | | | REF_CLOSE: (44), (50), (156) are inconsistent by sub-proof #572. % 152.16/22.60 | | | | | | | % 152.16/22.60 | | | | | | Case 2: % 152.16/22.60 | | | | | | | % 152.16/22.60 | | | | | | | (157) ~ (all_54_9 = e0) % 152.16/22.60 | | | | | | | (158) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.16/22.60 | | | | | | | % 152.16/22.60 | | | | | | | BETA: splitting (136) gives: % 152.16/22.60 | | | | | | | % 152.16/22.60 | | | | | | | Case 1: % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | (159) all_54_7 = e0 % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | COMBINE_EQS: (16), (159) imply: % 152.16/22.60 | | | | | | | | (160) all_52_13 = e0 % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | SIMP: (160) implies: % 152.16/22.60 | | | | | | | | (161) all_52_13 = e0 % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | COMBINE_EQS: (95), (161) imply: % 152.16/22.60 | | | | | | | | (162) all_56_10 = e0 % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | COMBINE_EQS: (28), (161) imply: % 152.16/22.60 | | | | | | | | (163) all_58_13 = e0 % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | REDUCE: (54), (161) imply: % 152.16/22.60 | | | | | | | | (164) ~ (all_52_1 = e0) % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | REDUCE: (120), (161) imply: % 152.16/22.60 | | | | | | | | (165) ~ (all_4_1 = e0) % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | BETA: splitting (145) gives: % 152.16/22.60 | | | | | | | | % 152.16/22.60 | | | | | | | | Case 1: % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | (166) all_56_1 = e0 % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | COMBINE_EQS: (61), (166) imply: % 152.16/22.60 | | | | | | | | | (167) all_52_4 = e0 % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | COMBINE_EQS: (60), (167) imply: % 152.16/22.60 | | | | | | | | | (168) all_58_2 = e0 % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | REDUCE: (26), (167) imply: % 152.16/22.60 | | | | | | | | | (169) ~ (all_52_6 = e0) % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | REDUCE: (73), (167) imply: % 152.16/22.60 | | | | | | | | | (170) ~ (all_52_8 = e0) % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | REDUCE: (138), (167) imply: % 152.16/22.60 | | | | | | | | | (171) ~ (all_52_12 = e0) % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | SIMP: (171) implies: % 152.16/22.60 | | | | | | | | | (172) ~ (all_52_12 = e0) % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | REDUCE: (21), (167) imply: % 152.16/22.60 | | | | | | | | | (173) ~ (all_8_2 = e0) % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | SIMP: (173) implies: % 152.16/22.60 | | | | | | | | | (174) ~ (all_8_2 = e0) % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | REDUCE: (12), (167) imply: % 152.16/22.60 | | | | | | | | | (175) op(e3, e0) = all_58_1 % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | BETA: splitting (149) gives: % 152.16/22.60 | | | | | | | | | % 152.16/22.60 | | | | | | | | | Case 1: % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | (176) all_56_2 = e0 % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | COMBINE_EQS: (92), (176) imply: % 152.16/22.60 | | | | | | | | | | (177) all_52_1 = e0 % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | REDUCE: (164), (177) imply: % 152.16/22.60 | | | | | | | | | | (178) $false % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | CLOSE: (178) is inconsistent. % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | Case 2: % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | (179) all_56_6 = e0 | all_56_12 = e0 % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | BETA: splitting (179) gives: % 152.16/22.60 | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | Case 1: % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | (180) all_56_6 = e0 % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | COMBINE_EQS: (80), (180) imply: % 152.16/22.60 | | | | | | | | | | | (181) all_52_2 = e0 % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | REDUCE: (10), (181) imply: % 152.16/22.60 | | | | | | | | | | | (182) $false % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | CLOSE: (182) is inconsistent. % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | Case 2: % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | (183) all_56_12 = e0 % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | COMBINE_EQS: (58), (183) imply: % 152.16/22.60 | | | | | | | | | | | (184) all_52_3 = e0 % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | SIMP: (184) implies: % 152.16/22.60 | | | | | | | | | | | (185) all_52_3 = e0 % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | COMBINE_EQS: (108), (185) imply: % 152.16/22.60 | | | | | | | | | | | (186) all_58_22 = e0 % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | REDUCE: (59), (185) imply: % 152.16/22.60 | | | | | | | | | | | (187) ~ (all_52_7 = e0) % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | SIMP: (187) implies: % 152.16/22.60 | | | | | | | | | | | (188) ~ (all_52_7 = e0) % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | REDUCE: (111), (185) imply: % 152.16/22.60 | | | | | | | | | | | (189) ~ (all_10_2 = e0) % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | REDUCE: (110), (185) imply: % 152.16/22.60 | | | | | | | | | | | (190) ~ (all_6_1 = e0) % 152.16/22.60 | | | | | | | | | | | % 152.16/22.60 | | | | | | | | | | | REDUCE: (35), (185) imply: % 152.16/22.61 | | | | | | | | | | | (191) ~ (e1 = e0) % 152.16/22.61 | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_12, all_58_1, e0, % 152.16/22.61 | | | | | | | | | | | e3, simplifying with (79), (175) gives: % 152.16/22.61 | | | | | | | | | | | (192) all_58_1 = all_52_12 % 152.16/22.61 | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | BETA: splitting (8) gives: % 152.16/22.61 | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | (193) all_54_3 = e0 % 152.16/22.61 | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | REF_CLOSE: (22), (172), (193) are inconsistent by sub-proof % 152.16/22.61 | | | | | | | | | | | | #733. % 152.16/22.61 | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | (194) ~ (all_54_3 = e0) % 152.16/22.61 | | | | | | | | | | | | (195) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.16/22.61 | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | BETA: splitting (57) gives: % 152.16/22.61 | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | (196) all_54_5 = e0 % 152.16/22.61 | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | REF_CLOSE: (37), (174), (196) are inconsistent by sub-proof % 152.16/22.61 | | | | | | | | | | | | | #158. % 152.16/22.61 | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | (197) ~ (all_54_5 = e0) % 152.16/22.61 | | | | | | | | | | | | | (198) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 152.16/22.61 | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | BETA: splitting (104) gives: % 152.16/22.61 | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | (199) all_56_6 = e1 % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | COMBINE_EQS: (80), (199) imply: % 152.16/22.61 | | | | | | | | | | | | | | (200) all_52_2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | SIMP: (200) implies: % 152.16/22.61 | | | | | | | | | | | | | | (201) all_52_2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | REDUCE: (81), (201) imply: % 152.16/22.61 | | | | | | | | | | | | | | (202) ~ (all_52_6 = e1) % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | SIMP: (202) implies: % 152.16/22.61 | | | | | | | | | | | | | | (203) ~ (all_52_6 = e1) % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (11), (23), (27), (30), (47), (67), % 152.16/22.61 | | | | | | | | | | | | | | (75), (76), (78), (84), (85), (87), (91), (105), % 152.16/22.61 | | | | | | | | | | | | | | (118), (122), (134), (140), (166), (174), (203) % 152.16/22.61 | | | | | | | | | | | | | | are inconsistent by sub-proof #112. % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | (204) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | BETA: splitting (204) gives: % 152.16/22.61 | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | (205) all_56_7 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | COMBINE_EQS: (6), (205) imply: % 152.16/22.61 | | | | | | | | | | | | | | | (206) all_52_6 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | SIMP: (206) implies: % 152.16/22.61 | | | | | | | | | | | | | | | (207) all_52_6 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | COMBINE_EQS: (102), (207) imply: % 152.16/22.61 | | | | | | | | | | | | | | | (208) all_58_17 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | REDUCE: (81), (207) imply: % 152.16/22.61 | | | | | | | | | | | | | | | (209) ~ (all_52_2 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | REDUCE: (33), (207) imply: % 152.16/22.61 | | | | | | | | | | | | | | | (210) ~ (all_52_7 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | REDUCE: (69), (207) imply: % 152.16/22.61 | | | | | | | | | | | | | | | (211) ~ (all_4_1 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | SIMP: (211) implies: % 152.16/22.61 | | | | | | | | | | | | | | | (212) ~ (all_4_1 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 152.16/22.61 | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | (213) all_56_0 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (213) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | (214) all_10_2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (214) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | (215) all_58_28 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | (105), (140), (174), (215) are inconsistent by % 152.16/22.61 | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | (216) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | (217) all_56_2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (217) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | (218) all_52_1 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (218) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | (219) all_58_8 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | REDUCE: (103), (218) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | (220) ~ (all_52_9 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | SIMP: (220) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | (221) ~ (all_52_9 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | REDUCE: (66), (218) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | (222) ~ (all_8_2 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | SIMP: (222) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | (223) ~ (all_8_2 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | (224) all_56_4 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (224) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | (225) all_52_8 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (225) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | (226) all_58_4 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | REDUCE: (43), (225) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | (227) ~ (all_52_12 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | SIMP: (227) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | (228) ~ (all_52_12 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | REDUCE: (83), (225) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | (229) ~ (all_6_1 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | (230) all_56_0 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (230) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | (231) all_10_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (231) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | (232) all_58_28 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | | | | (105), (134), (140), (174), (232) are inconsistent % 152.16/22.61 | | | | | | | | | | | | | | | | | | | by sub-proof #113. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | (233) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (234) all_54_0 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (234) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (235) all_10_2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (235) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (236) all_58_28 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (236) are inconsistent by % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (237) ~ (all_54_0 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (238) all_54_0 = e3 | all_54_0 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (237) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | (239) ~ (all_10_2 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | (240) all_54_0 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (240) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | (241) all_10_2 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (241) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | (242) all_56_0 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (241) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | (243) all_58_28 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (241) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_52_12 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | (245) all_56_9 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (244), (245) are inconsistent by sub-proof % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | #431. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | (246) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | (247) all_56_10 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (247) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | (248) e2 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (248) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | (249) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_56_10 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | (251) all_56_11 = e2 | all_56_15 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (250) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (e2 = e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | (253) all_56_11 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (253) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | (254) all_4_1 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (254) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | (255) all_4_1 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (255) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_20 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_56_6 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (257) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_52_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (258) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_52_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (259) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_58_15 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_56_9 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (261) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_52_12 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (262) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_52_12 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (263) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_58_6 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_28 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (134), (140), (174), (265) are inconsistent % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #113. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) ~ (all_58_28 = e3) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (243), (266) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) ~ (e3 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_31 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (269) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) e1 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (270) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) ~ (all_58_31 = e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_30 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (122), (274) are inconsistent by sub-proof % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #111. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) ~ (all_58_30 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_29 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (277) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_8_2 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (30), (84), (105), (140), (278) are % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_58_29 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (279) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) ~ (all_8_2 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_56_1 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (282) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) e2 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) e2 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (284) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_56_1 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_56_3 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (288) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_8_2 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (281), (289) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_56_7 = e2 | all_56_13 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_56_7 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (292) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) e2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (293) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_28 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (294) are inconsistent by % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_56_13 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (295) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_52_7 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_52_7 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (297) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_58_24 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_56_12 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (299) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) e3 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (300) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_56_4 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (303) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) e2 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (304) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_28 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (305) are inconsistent by % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_56_5 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (307) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_52_9 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_52_9 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (309) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_11 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (309) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) ~ (all_8_2 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (309) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) ~ (all_6_1 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) ~ (all_6_1 = e2) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_56_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (314) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) e3 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (315) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (316) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_56_2 = e3) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (317) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (e3 = e1) % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_56_4 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (320) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) e3 = e1 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (321) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_56_3 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (324) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_8_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_8_2 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (326) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_29 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_56_5 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (328) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) e3 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (329) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) e3 = e2 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (330) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_56_8 = e3 | all_56_14 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_56_8 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (333) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) e3 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (334) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) $false % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (335) is inconsistent. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_56_14 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (336) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_6_1 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (337) implies: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_6_1 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (338) imply: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_58_26 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_58_28 = e3 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (134), (140), (174), (340) are inconsistent % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #113. % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_15 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_58_2 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (347) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (346) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (350) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (351) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (351), (352) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_8 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_58_6 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (356) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (357) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (355) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (358), (359) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_58_8 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_2 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (362) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (363) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (361) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (364), (365) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (366) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_8 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_58_2 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (370) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (371) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (369) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (373) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (373), (374) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_58_4 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_58_2 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (378) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (379) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (377) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (381) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (376) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (383) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (382), (384) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_22 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_58_2 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (389) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (388) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (387) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (391), (392), (393) are inconsistent % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #108. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (394) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_58_11 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_58_2 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (396) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (397) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (310), (395) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (399) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (400) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) $false % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (401) is inconsistent. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (402) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (405) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_58_24 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (407) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (406) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (408), (409) are inconsistent by sub-proof % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) e3 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_58_8 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_58_2 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (413) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (414) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) e2 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (412) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (416) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (415) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (418) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_56_6 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (417) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_58_31 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (18), (19), (22), (34), (43), (44), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (50), (74), (75), (78), (79), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (419), (420) are inconsistent by sub-proof % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #154. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_58_6 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_58_4 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (424) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (425) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (423) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (427) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (426), (428) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (426), (429) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (430) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_58_11 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (310), (431) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (432) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_58_28 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (433) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (434) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_58_20 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (437) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (438) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_58_28 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (439) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (440) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_58_22 = e3 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_58_15 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (442) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (443) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (441) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (444), (445) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_58_17 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (448) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) e2 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (449) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_58_28 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (450) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_58_26 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_58_15 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (453) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (454) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) e3 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (452) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (456) implies: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) e3 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (455), (457) imply: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) e1 = e0 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (455), (458) are inconsistent by % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_15 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (463) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (464) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (465) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_58_29 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (47), (76), (91), (267), (466) are % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (468) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (298), (469) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #413. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (470) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_58_20 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (471) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (472) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) $false % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (475) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (163), (476) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #627. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_58_26 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_58_6 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (479) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (480) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (478) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (482) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (481), (483) are inconsistent by % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #109. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_58_6 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (264), (486) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #107. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_58_17 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (489) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (488) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (491) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (490), (492) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #625. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (494) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_58_20 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (497) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (498) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_28 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (499) are inconsistent by % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_58_13 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_58_11 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (310), (502) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (501) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (503), (504) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #625. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (506) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_58_26 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_58_20 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_58_11 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (310), (509) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (508) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (507) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (512) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (510), (511), (513) are inconsistent % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #108. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (514) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_58_11 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (310), (515) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (516) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_58_28 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (517) are inconsistent by % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (518) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (519) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (520) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_58_20 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (521) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (522) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) $false % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (523) is inconsistent. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (524) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_58_26 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_20 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (527) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (526) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (525) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (530) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (528), (529) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) e1 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (532) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) e1 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (11), (18), (19), (22), (34), (43), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (47), (50), (74), (75), (78), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (84), (86), (88), (91), (101), (105), (116), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (257), (531), (533) are inconsistent by % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (535) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (298), (536) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #413. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) e1 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_58_26 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (539) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (540) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (541) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_56_6 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (538) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_58_31 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (18), (19), (22), (34), (43), (44), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (50), (74), (75), (78), (79), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (86), (88), (91), (101), (105), (116), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (128), (131), (133), (134), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (158), (166), (172), (195), (242), (243), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (542), (543) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #154. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ~ (all_56_3 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (544) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) ~ (all_8_2 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (198), (223), (281), (545) are inconsistent % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #531. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) ~ (all_56_5 = e2) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (546) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) ~ (all_52_9 = e2) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_56_13 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (548) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) e3 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (549) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) $false % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (550) is inconsistent. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_56_14 = e3 | all_56_15 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (551) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_56_14 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (552) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) all_6_1 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (553) implies: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_6_1 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (554) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) ~ (all_52_9 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (153), (221), (547), (555) are inconsistent % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #771. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_56_15 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (556) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) e3 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (557) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) $false % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (558) is inconsistent. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (559) ~ (all_56_9 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (559) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (560) ~ (all_52_12 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (195), (228), (244), (560) are inconsistent % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | (561) ~ (all_56_6 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (561) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | (562) ~ (all_52_2 = e3) % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_56_2 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (217), (563) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | #206. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_56_6 = e3 | all_56_12 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (564) gives: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_56_6 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (562), (565) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | #788. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_56_12 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (566) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) e3 = e0 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (567) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) $false % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (568) is inconsistent. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | (569) all_56_15 = e2 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (569) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | (570) e2 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (570) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | (571) all_58_28 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | (105), (140), (174), (571) are inconsistent by % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #120. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | (572) all_54_0 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (572) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | (573) all_10_2 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (573) imply: % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | (574) all_58_28 = e3 % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (75), (76), (78), (84), % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | (105), (134), (140), (174), (574) are inconsistent % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | by sub-proof #113. % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | (575) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (39), (49), (55), (122), (221), (575) are % 152.16/22.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #179. % 152.16/22.63 | | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | (576) all_56_6 = e1 | all_56_12 = e1 % 152.16/22.63 | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (122), (183), (209), (576) are inconsistent % 152.16/22.63 | | | | | | | | | | | | | | | | | by sub-proof #638. % 152.16/22.63 | | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | (577) ~ (all_56_7 = e1) % 152.16/22.63 | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | REDUCE: (6), (577) imply: % 152.16/22.63 | | | | | | | | | | | | | | | (578) ~ (all_52_6 = e1) % 152.16/22.63 | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (11), (23), (27), (30), (47), (67), % 152.16/22.63 | | | | | | | | | | | | | | | (75), (76), (78), (84), (85), (87), (91), (105), % 152.16/22.63 | | | | | | | | | | | | | | | (118), (122), (134), (140), (166), (174), (578) % 152.16/22.63 | | | | | | | | | | | | | | | are inconsistent by sub-proof #112. % 152.16/22.63 | | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | End of split % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | (579) ~ (all_56_1 = e0) % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | REDUCE: (61), (579) imply: % 152.16/22.63 | | | | | | | | | (580) ~ (all_52_4 = e0) % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | REF_CLOSE: (3), (6), (10), (50), (58), (59), (61), (67), (80), % 152.16/22.63 | | | | | | | | | (84), (85), (90), (92), (114), (127), (149), (164), % 152.16/22.63 | | | | | | | | | (580) are inconsistent by sub-proof #118. % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | End of split % 152.16/22.63 | | | | | | | | % 152.16/22.63 | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | % 152.16/22.63 | | | | | | | | (581) ~ (all_54_7 = e0) % 152.16/22.63 | | | | | | | | % 152.16/22.63 | | | | | | | | REDUCE: (16), (581) imply: % 152.16/22.63 | | | | | | | | (582) ~ (all_52_13 = e0) % 152.16/22.63 | | | | | | | | % 152.16/22.63 | | | | | | | | BETA: splitting (42) gives: % 152.16/22.63 | | | | | | | | % 152.16/22.63 | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | (583) all_56_15 = e0 % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | REF_CLOSE: (122), (137), (583) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | #550. % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | (584) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 152.16/22.63 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | ALPHA: (584) implies: % 152.16/22.63 | | | | | | | | | (585) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 152.16/22.63 | | | | | | | | | (586) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | BETA: splitting (586) gives: % 152.16/22.63 | | | | | | | | | % 152.16/22.63 | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | (587) all_56_9 = e0 % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | COMBINE_EQS: (74), (587) imply: % 152.16/22.63 | | | | | | | | | | (588) all_52_12 = e0 % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | SIMP: (588) implies: % 152.16/22.63 | | | | | | | | | | (589) all_52_12 = e0 % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | COMBINE_EQS: (17), (589) imply: % 152.16/22.63 | | | | | | | | | | (590) all_58_6 = e0 % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | REDUCE: (138), (589) imply: % 152.16/22.63 | | | | | | | | | | (591) ~ (all_52_4 = e0) % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | BETA: splitting (25) gives: % 152.16/22.63 | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | (592) all_56_2 = e0 % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | COMBINE_EQS: (92), (592) imply: % 152.16/22.63 | | | | | | | | | | | (593) all_52_1 = e0 % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | COMBINE_EQS: (77), (593) imply: % 152.16/22.63 | | | | | | | | | | | (594) all_58_8 = e0 % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | REDUCE: (113), (593) imply: % 152.16/22.63 | | | | | | | | | | | (595) ~ (all_52_2 = e0) % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | REDUCE: (97), (593) imply: % 152.16/22.63 | | | | | | | | | | | (596) ~ (all_52_3 = e0) % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | SIMP: (596) implies: % 152.16/22.63 | | | | | | | | | | | (597) ~ (all_52_3 = e0) % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | REDUCE: (103), (593) imply: % 152.16/22.63 | | | | | | | | | | | (598) ~ (all_52_9 = e0) % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | BETA: splitting (585) gives: % 152.16/22.63 | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | (599) all_56_12 = e0 % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | REF_CLOSE: (58), (597), (599) are inconsistent by sub-proof % 152.16/22.63 | | | | | | | | | | | | #607. % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | Case 2: % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | (600) all_56_13 = e0 | all_56_14 = e0 % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | BETA: splitting (600) gives: % 152.16/22.63 | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | Case 1: % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | (601) all_56_13 = e0 % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | COMBINE_EQS: (85), (601) imply: % 152.16/22.63 | | | | | | | | | | | | | (602) all_52_7 = e0 % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | SIMP: (602) implies: % 152.16/22.63 | | | | | | | | | | | | | (603) all_52_7 = e0 % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | COMBINE_EQS: (68), (603) imply: % 152.16/22.63 | | | | | | | | | | | | | (604) all_58_24 = e0 % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | REDUCE: (114), (603) imply: % 152.16/22.63 | | | | | | | | | | | | | (605) ~ (all_8_2 = e0) % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | SIMP: (605) implies: % 152.16/22.63 | | | | | | | | | | | | | (606) ~ (all_8_2 = e0) % 152.16/22.63 | | | | | | | | | | | | | % 152.16/22.63 | | | | | | | | | | | | | REDUCE: (62), (603) imply: % 152.16/22.63 | | | | | | | | | | | | | (607) ~ (all_6_1 = e0) % 152.16/22.64 | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | REDUCE: (27), (603) imply: % 152.16/22.64 | | | | | | | | | | | | | (608) ~ (e1 = e0) % 152.16/22.64 | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | BETA: splitting (94) gives: % 152.16/22.64 | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | (609) all_54_12 = e0 % 152.16/22.64 | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | REF_CLOSE: (139), (597), (609) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | #762. % 152.16/22.64 | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | (610) ~ (all_54_12 = e0) % 152.16/22.64 | | | | | | | | | | | | | | (611) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 152.16/22.64 | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | BETA: splitting (36) gives: % 152.16/22.64 | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | (612) all_56_4 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | COMBINE_EQS: (19), (612) imply: % 152.16/22.64 | | | | | | | | | | | | | | | (613) all_52_8 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | REDUCE: (73), (613) imply: % 152.16/22.64 | | | | | | | | | | | | | | | (614) ~ (all_52_4 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | REDUCE: (14), (613) imply: % 152.16/22.64 | | | | | | | | | | | | | | | (615) ~ (all_10_2 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | SIMP: (615) implies: % 152.16/22.64 | | | | | | | | | | | | | | | (616) ~ (all_10_2 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | (617) all_56_0 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (617) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | (618) all_10_2 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | REDUCE: (616), (618) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | (619) $false % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | CLOSE: (619) is inconsistent. % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | (620) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | (621) all_56_2 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (592), (621) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | #549. % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | (622) ~ (all_56_2 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | (623) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | BETA: splitting (620) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | (624) all_56_2 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (592), (624) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | #549. % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | (625) all_56_6 = e1 | all_56_12 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | BETA: splitting (625) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (626) all_56_6 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (626) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (627) all_52_2 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | REDUCE: (4), (627) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (628) ~ (all_52_3 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | REDUCE: (81), (627) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (629) ~ (all_52_6 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | SIMP: (629) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (630) ~ (all_52_6 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | BETA: splitting (623) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (631) all_56_3 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (631) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (632) all_8_2 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (632) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (633) op(e1, e2) = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (634) all_58_28 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (634) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (635) all_10_2 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | SIMP: (635) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (636) all_10_2 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (636) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (637) ~ (all_52_3 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (35), (75), (76), (84), % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (99), (111), (139), (140), (597), (606), (611), % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (637) are inconsistent by sub-proof #106. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (638) ~ (all_58_28 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (638) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (639) ~ (all_10_2 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (640) all_54_0 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (616), (640) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | #841. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (641) all_54_0 = e3 | all_54_0 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (642) all_54_0 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (642) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (643) all_10_2 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (643) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (644) all_10_2 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (644) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (645) ~ (all_52_4 = e2) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (646) all_54_1 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (591), (646) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | #798. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (647) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_54_1 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (614), (648) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_54_1 = e3 | all_54_1 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (649) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_54_1 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (645), (650) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | #740. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_54_1 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (651) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_52_4 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (652) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_52_4 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (653) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (654) ~ (all_52_6 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (654) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (655) ~ (all_52_6 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_54_9 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (630), (656) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_54_9 = e3 | all_54_9 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (657) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_54_9 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (658) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_52_6 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (659) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_52_6 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (45), (46), (50), (633), (660) are % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_54_9 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (655), (661) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #620. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (662) all_54_0 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (639), (662) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | #827. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (663) ~ (all_56_3 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (663) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (664) ~ (all_8_2 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (61), (67), (87), (122), (601), (614), (630), % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (664) are inconsistent by sub-proof #197. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (665) all_56_12 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (58), (665) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | #577. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | (666) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | BETA: splitting (666) gives: % 152.16/22.64 | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | (667) all_56_5 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (667) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | (668) all_52_9 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (668) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | (669) all_58_11 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | REDUCE: (2), (668) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | (670) ~ (all_52_8 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | REDUCE: (130), (668) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | (671) ~ (all_6_1 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | (672) all_56_12 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (672) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | (673) all_52_3 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | SIMP: (673) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | (674) all_52_3 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (674) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | (675) all_58_22 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | REDUCE: (4), (674) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | (676) ~ (all_52_2 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | REDUCE: (110), (674) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | (677) ~ (all_6_1 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | SIMP: (677) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | (678) ~ (all_6_1 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | (679) all_54_14 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (679) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | (680) all_6_1 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | REDUCE: (20), (680) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | (681) $false % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | CLOSE: (681) is inconsistent. % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | (682) ~ (all_54_14 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | (683) all_54_14 = e3 | all_54_14 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | BETA: splitting (683) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (684) all_54_14 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (684) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (685) all_6_1 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (685) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (686) all_58_26 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | REDUCE: (83), (685) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | (687) ~ (all_52_8 = e2) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (688) all_54_2 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (670), (688) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | #819. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (689) ~ (all_54_2 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | (690) all_54_2 = e3 | all_54_2 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | BETA: splitting (690) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (691) all_54_2 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (687), (691) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | #556. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (692) all_54_2 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (692) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (693) all_52_8 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | SIMP: (693) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (694) all_52_8 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (694) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (695) all_58_4 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (694) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (696) ~ (all_10_2 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | SIMP: (696) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | (697) ~ (all_10_2 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (698) all_58_31 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (698) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (699) e1 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (699) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (700) $false % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (700) is inconsistent. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (701) ~ (all_58_31 = e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (702) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_30 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (122), (703) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | #111. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (704) ~ (all_58_30 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (705) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (705) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (706) all_58_29 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (706) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (707) all_8_2 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (30), (84), (105), (140), (707) are % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (708) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (708) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (709) all_58_28 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (709) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (710) all_10_2 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (697), (710) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (711) $false % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (711) is inconsistent. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | (712) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (712) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (713) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (713) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (715) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (716) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_58_8 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_58_4 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (695), (718) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) e3 = e1 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (594), (717) imply: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) e3 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (719), (720) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #633. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (722) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_58_22 = e0 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (675), (723) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #299. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (724) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) all_58_11 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (669), (725) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (728) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_58_24 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (604), (729) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #413. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (594), (730) are inconsistent by sub-proof % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #598. % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (732) implies: % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_58_8 = e2 % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (594), (733) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) e2 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (734) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (735) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (736) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_58_8 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (594), (737) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #596. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (739) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (594), (740) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #595. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (742) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_58_22 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (675), (743) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #299. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (744) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_58_15 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (745) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_52_2 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (746) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_52_2 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (676), (747) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (748) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (751) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (686), (752) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #105. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_58_6 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_58_4 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (695), (755) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) e3 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (590), (754) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) e3 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (757) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) e3 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (756), (758) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) e1 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (759) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (760) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (761) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (762) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_58_11 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (669), (763) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (764) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (686), (765) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #104. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (766) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (769) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_58_4 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (695), (770) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) e3 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (771) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (772) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (774) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_58_6 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (590), (775) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #107. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (776) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (686), (777) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #104. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (779) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (780) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_58_24 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (604), (781) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) e2 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (782) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (783) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (784) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (686), (785) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #105. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (787) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_58_22 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (675), (788) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #299. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (789) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_58_11 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (669), (790) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (792) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (793) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (794) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (686), (795) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #105. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (604), (796) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #591. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (797) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (798) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (686), (799) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #104. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (800) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) e2 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (801) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (802) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (803) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (804) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (805) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_58_26 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (686), (806) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #104. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_58_26 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (686), (808) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #105. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (809) gives: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (810) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) e2 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (811) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (812) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) e1 = e0 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (814) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (815) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | (816) all_54_14 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (816) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | (817) all_6_1 = e3 % 152.16/22.65 | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | REDUCE: (678), (817) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | | | (818) $false % 152.16/22.65 | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | | CLOSE: (818) is inconsistent. % 152.16/22.65 | | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | (819) ~ (all_56_12 = e3) % 152.16/22.65 | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | REDUCE: (58), (819) imply: % 152.16/22.65 | | | | | | | | | | | | | | | | | (820) ~ (all_52_3 = e3) % 152.16/22.65 | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (23), (30), (35), (75), (76), (84), % 152.16/22.65 | | | | | | | | | | | | | | | | | (99), (111), (139), (140), (597), (606), (611), % 152.16/22.65 | | | | | | | | | | | | | | | | | (820) are inconsistent by sub-proof #106. % 152.16/22.65 | | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | (821) all_56_8 = e1 | all_56_14 = e1 % 152.16/22.65 | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (39), (49), (122), (821) are inconsistent by % 152.16/22.65 | | | | | | | | | | | | | | | | sub-proof #527. % 152.16/22.65 | | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | (822) all_56_14 = e0 % 152.16/22.65 | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | | REF_CLOSE: (39), (100), (822) are inconsistent by sub-proof % 152.16/22.65 | | | | | | | | | | | | | #575. % 152.16/22.65 | | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | (823) ~ (all_56_2 = e0) % 152.16/22.65 | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | REDUCE: (92), (823) imply: % 152.16/22.65 | | | | | | | | | | | (824) ~ (all_52_1 = e0) % 152.16/22.65 | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | | REF_CLOSE: (3), (6), (10), (50), (58), (59), (61), (67), % 152.16/22.65 | | | | | | | | | | | (80), (84), (85), (90), (92), (114), (127), (149), % 152.16/22.65 | | | | | | | | | | | (591), (824) are inconsistent by sub-proof #118. % 152.16/22.65 | | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | | % 152.16/22.65 | | | | | | | | | Case 2: % 152.16/22.65 | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | (825) all_56_10 = e0 | all_56_11 = e0 % 152.16/22.65 | | | | | | | | | | % 152.16/22.65 | | | | | | | | | | REF_CLOSE: (29), (95), (132), (582), (825) are inconsistent % 152.16/22.65 | | | | | | | | | | by sub-proof #524. % 152.16/22.65 | | | | | | | | | | % 152.16/22.65 | | | | | | | | | End of split % 152.16/22.65 | | | | | | | | | % 152.16/22.65 | | | | | | | | End of split % 152.16/22.65 | | | | | | | | % 152.16/22.65 | | | | | | | End of split % 152.16/22.65 | | | | | | | % 152.16/22.65 | | | | | | End of split % 152.16/22.65 | | | | | | % 152.16/22.65 | | | | | End of split % 152.16/22.65 | | | | | % 152.16/22.65 | | | | End of split % 152.16/22.65 | | | | % 152.16/22.65 | | | End of split % 152.16/22.65 | | | % 152.16/22.65 | | End of split % 152.16/22.65 | | % 152.16/22.65 | End of split % 152.16/22.65 | % 152.16/22.65 End of proof % 152.16/22.65 % 152.16/22.65 Sub-proof #104 shows that the following formulas are inconsistent: % 152.16/22.65 ---------------------------------------------------------------- % 152.16/22.65 (1) all_58_26 = e2 % 152.16/22.65 (2) all_58_26 = e0 % 152.16/22.65 (3) ~ (e2 = e0) % 152.16/22.65 % 152.16/22.65 Begin of proof % 152.16/22.65 | % 152.16/22.65 | COMBINE_EQS: (1), (2) imply: % 152.16/22.65 | (4) e2 = e0 % 152.16/22.65 | % 152.16/22.65 | SIMP: (4) implies: % 152.16/22.65 | (5) e2 = e0 % 152.16/22.65 | % 152.16/22.65 | REDUCE: (3), (5) imply: % 152.16/22.65 | (6) $false % 152.16/22.65 | % 152.16/22.65 | CLOSE: (6) is inconsistent. % 152.16/22.65 | % 152.16/22.65 End of proof % 152.16/22.65 % 152.16/22.65 Sub-proof #105 shows that the following formulas are inconsistent: % 152.16/22.65 ---------------------------------------------------------------- % 152.16/22.65 (1) all_58_26 = e2 % 152.16/22.65 (2) all_58_26 = e1 % 152.16/22.65 (3) ~ (e2 = e1) % 152.16/22.65 % 152.16/22.65 Begin of proof % 152.16/22.65 | % 152.16/22.65 | COMBINE_EQS: (1), (2) imply: % 152.16/22.65 | (4) e2 = e1 % 152.16/22.65 | % 152.16/22.65 | SIMP: (4) implies: % 152.16/22.65 | (5) e2 = e1 % 152.16/22.65 | % 152.16/22.65 | REDUCE: (3), (5) imply: % 152.16/22.65 | (6) $false % 152.16/22.65 | % 152.16/22.65 | CLOSE: (6) is inconsistent. % 152.16/22.65 | % 152.16/22.65 End of proof % 152.16/22.65 % 152.16/22.65 Sub-proof #106 shows that the following formulas are inconsistent: % 152.16/22.65 ---------------------------------------------------------------- % 152.16/22.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.16/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.16/22.65 (2) ~ (all_52_3 = e3) % 152.16/22.65 (3) all_58_31 = e1 % 152.16/22.65 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.16/22.65 (5) op(e2, e2) = all_8_2 % 152.16/22.65 (6) ~ (all_52_3 = e1) % 152.16/22.65 (7) ~ (all_52_3 = e0) % 152.16/22.65 (8) all_58_29 = all_8_2 % 152.16/22.65 (9) all_58_30 = e0 % 152.16/22.65 (10) op(all_8_2, e2) = e0 % 152.16/22.65 (11) all_58_28 = all_10_2 % 152.43/22.65 (12) ~ (all_52_3 = all_10_2) % 152.43/22.65 (13) ~ (all_8_2 = e0) % 152.43/22.65 (14) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 152.43/22.65 (15) all_54_12 = all_52_3 % 152.43/22.65 (16) op(e2, all_8_2) = all_58_9 % 152.43/22.65 % 152.43/22.65 Begin of proof % 152.43/22.65 | % 152.43/22.65 | BETA: splitting (14) gives: % 152.43/22.65 | % 152.43/22.65 | Case 1: % 152.43/22.65 | | % 152.43/22.65 | | (17) all_54_12 = e1 % 152.43/22.65 | | % 152.43/22.65 | | COMBINE_EQS: (15), (17) imply: % 152.43/22.65 | | (18) all_52_3 = e1 % 152.43/22.65 | | % 152.43/22.65 | | REDUCE: (6), (18) imply: % 152.43/22.65 | | (19) $false % 152.43/22.65 | | % 152.43/22.65 | | CLOSE: (19) is inconsistent. % 152.43/22.65 | | % 152.43/22.65 | Case 2: % 152.43/22.65 | | % 152.43/22.65 | | (20) ~ (all_54_12 = e1) % 152.43/22.65 | | (21) all_54_12 = e3 | all_54_12 = e2 % 152.43/22.65 | | % 152.43/22.65 | | BETA: splitting (21) gives: % 152.43/22.65 | | % 152.43/22.65 | | Case 1: % 152.43/22.65 | | | % 152.43/22.65 | | | (22) all_54_12 = e2 % 152.43/22.65 | | | % 152.43/22.65 | | | COMBINE_EQS: (15), (22) imply: % 152.43/22.65 | | | (23) all_52_3 = e2 % 152.43/22.65 | | | % 152.43/22.65 | | | REDUCE: (12), (23) imply: % 152.43/22.65 | | | (24) ~ (all_10_2 = e2) % 152.43/22.65 | | | % 152.43/22.65 | | | SIMP: (24) implies: % 152.43/22.65 | | | (25) ~ (all_10_2 = e2) % 152.43/22.65 | | | % 152.43/22.65 | | | REDUCE: (6), (23) imply: % 152.43/22.65 | | | (26) ~ (e2 = e1) % 152.43/22.65 | | | % 152.43/22.65 | | | REDUCE: (7), (23) imply: % 152.43/22.65 | | | (27) ~ (e2 = e0) % 152.43/22.65 | | | % 152.43/22.65 | | | BETA: splitting (4) gives: % 152.43/22.65 | | | % 152.43/22.65 | | | Case 1: % 152.43/22.65 | | | | % 152.43/22.65 | | | | (28) all_58_28 = e2 % 152.43/22.65 | | | | % 152.43/22.65 | | | | COMBINE_EQS: (11), (28) imply: % 152.43/22.65 | | | | (29) all_10_2 = e2 % 152.43/22.65 | | | | % 152.43/22.65 | | | | REDUCE: (25), (29) imply: % 152.43/22.65 | | | | (30) $false % 152.43/22.65 | | | | % 152.43/22.65 | | | | CLOSE: (30) is inconsistent. % 152.43/22.65 | | | | % 152.43/22.65 | | | Case 2: % 152.43/22.65 | | | | % 152.43/22.65 | | | | (31) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.65 | | | | % 152.43/22.65 | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (13), (16), (26), (27), (31) % 152.43/22.65 | | | | are inconsistent by sub-proof #121. % 152.43/22.65 | | | | % 152.43/22.65 | | | End of split % 152.43/22.65 | | | % 152.43/22.65 | | Case 2: % 152.43/22.65 | | | % 152.43/22.65 | | | (32) all_54_12 = e3 % 152.43/22.65 | | | % 152.43/22.65 | | | COMBINE_EQS: (15), (32) imply: % 152.43/22.65 | | | (33) all_52_3 = e3 % 152.43/22.65 | | | % 152.43/22.65 | | | REDUCE: (2), (33) imply: % 152.43/22.65 | | | (34) $false % 152.43/22.65 | | | % 152.43/22.65 | | | CLOSE: (34) is inconsistent. % 152.43/22.65 | | | % 152.43/22.65 | | End of split % 152.43/22.65 | | % 152.43/22.65 | End of split % 152.43/22.65 | % 152.43/22.65 End of proof % 152.43/22.65 % 152.43/22.65 Sub-proof #107 shows that the following formulas are inconsistent: % 152.43/22.65 ---------------------------------------------------------------- % 152.43/22.65 (1) all_58_6 = e3 % 152.43/22.65 (2) all_58_6 = e0 % 152.43/22.65 (3) ~ (e3 = e0) % 152.43/22.65 % 152.43/22.65 Begin of proof % 152.43/22.65 | % 152.43/22.65 | COMBINE_EQS: (1), (2) imply: % 152.43/22.65 | (4) e3 = e0 % 152.43/22.65 | % 152.43/22.65 | SIMP: (4) implies: % 152.43/22.65 | (5) e3 = e0 % 152.43/22.65 | % 152.43/22.65 | REDUCE: (3), (5) imply: % 152.43/22.65 | (6) $false % 152.43/22.65 | % 152.43/22.65 | CLOSE: (6) is inconsistent. % 152.43/22.65 | % 152.43/22.65 End of proof % 152.43/22.65 % 152.43/22.65 Sub-proof #108 shows that the following formulas are inconsistent: % 152.43/22.65 ---------------------------------------------------------------- % 152.43/22.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.65 (2) all_56_7 = all_52_6 % 152.43/22.65 (3) ~ (all_52_6 = all_6_2) % 152.43/22.65 (4) all_58_31 = e1 % 152.43/22.65 (5) ~ (all_52_6 = all_8_2) % 152.43/22.65 (6) all_56_4 = all_52_8 % 152.43/22.65 (7) all_54_3 = all_52_12 % 152.43/22.65 (8) ~ (all_52_8 = all_6_2) % 152.43/22.65 (9) ~ (all_52_8 = all_52_12) % 152.43/22.65 (10) all_54_9 = all_52_6 % 152.43/22.65 (11) op(e1, e2) = all_52_6 % 152.43/22.66 (12) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.66 (13) op(e1, all_52_6) = all_58_16 % 152.43/22.66 (14) ~ (e3 = e1) % 152.43/22.66 (15) ~ (all_52_6 = e0) % 152.43/22.66 (16) ~ (all_52_12 = e0) % 152.43/22.66 (17) all_56_1 = e0 % 152.43/22.66 (18) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.66 (19) all_56_9 = all_52_12 % 152.43/22.66 (20) all_58_29 = all_8_2 % 152.43/22.66 (21) all_56_6 = e3 % 152.43/22.66 (22) ~ (e2 = e1) % 152.43/22.66 (23) e2 = e1 % 152.43/22.66 (24) op(e3, e0) = all_52_12 % 152.43/22.66 (25) op(all_8_2, e2) = e0 % 152.43/22.66 (26) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.66 (27) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.66 (28) all_56_0 = e2 % 152.43/22.66 (29) ~ (e3 = e0) % 152.43/22.66 (30) e3 = e0 % 152.43/22.66 (31) op(all_8_2, e0) = all_8_0 % 152.43/22.66 (32) ~ (e2 = e0) % 152.43/22.66 (33) e2 = e0 % 152.43/22.66 (34) all_58_28 = e2 % 152.43/22.66 (35) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.66 (36) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.66 (37) ~ (e1 = e0) % 152.43/22.66 (38) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.66 (39) ~ (all_52_8 = e0) % 152.43/22.66 (40) all_58_30 = all_6_2 % 152.43/22.66 (41) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.66 (42) ~ (e3 = e2) % 152.43/22.66 (43) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.66 (44) ~ (all_52_12 = e2) % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (23), (33) imply: % 152.43/22.66 | (45) e1 = e0 % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (21), (30) imply: % 152.43/22.66 | (46) all_56_6 = e0 % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (4), (45) imply: % 152.43/22.66 | (47) all_58_31 = e0 % 152.43/22.66 | % 152.43/22.66 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 152.43/22.66 | (14), (15), (16), (17), (18), (19), (20), (22), (24), (25), (26), % 152.43/22.66 | (27), (28), (29), (31), (32), (34), (35), (36), (37), (38), (39), % 152.43/22.66 | (40), (41), (42), (43), (44), (46), (47) are inconsistent by % 152.43/22.66 | sub-proof #154. % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #109 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.66 (2) all_56_7 = all_52_6 % 152.43/22.66 (3) ~ (all_52_6 = all_6_2) % 152.43/22.66 (4) all_58_31 = e1 % 152.43/22.66 (5) ~ (all_52_6 = all_8_2) % 152.43/22.66 (6) all_56_4 = all_52_8 % 152.43/22.66 (7) all_54_3 = all_52_12 % 152.43/22.66 (8) ~ (all_52_8 = all_6_2) % 152.43/22.66 (9) ~ (all_52_8 = all_52_12) % 152.43/22.66 (10) all_54_9 = all_52_6 % 152.43/22.66 (11) op(e1, e2) = all_52_6 % 152.43/22.66 (12) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.66 (13) op(e1, all_52_6) = all_58_16 % 152.43/22.66 (14) ~ (e3 = e1) % 152.43/22.66 (15) e3 = e1 % 152.43/22.66 (16) ~ (all_52_6 = e0) % 152.43/22.66 (17) ~ (all_52_12 = e0) % 152.43/22.66 (18) all_56_1 = e0 % 152.43/22.66 (19) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.66 (20) all_56_9 = all_52_12 % 152.43/22.66 (21) all_58_29 = all_8_2 % 152.43/22.66 (22) all_56_6 = e3 % 152.43/22.66 (23) ~ (e2 = e1) % 152.43/22.66 (24) op(e3, e0) = all_52_12 % 152.43/22.66 (25) op(all_8_2, e2) = e0 % 152.43/22.66 (26) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.66 (27) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.66 (28) all_56_0 = e2 % 152.43/22.66 (29) ~ (e3 = e0) % 152.43/22.66 (30) e3 = e0 % 152.43/22.66 (31) op(all_8_2, e0) = all_8_0 % 152.43/22.66 (32) ~ (e2 = e0) % 152.43/22.66 (33) all_58_28 = e2 % 152.43/22.66 (34) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.66 (35) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.66 (36) ~ (e1 = e0) % 152.43/22.66 (37) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.66 (38) ~ (all_52_8 = e0) % 152.43/22.66 (39) all_58_30 = all_6_2 % 152.43/22.66 (40) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.66 (41) ~ (e3 = e2) % 152.43/22.66 (42) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.66 (43) ~ (all_52_12 = e2) % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (15), (30) imply: % 152.43/22.66 | (44) e1 = e0 % 152.43/22.66 | % 152.43/22.66 | SIMP: (44) implies: % 152.43/22.66 | (45) e1 = e0 % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (22), (30) imply: % 152.43/22.66 | (46) all_56_6 = e0 % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (4), (45) imply: % 152.43/22.66 | (47) all_58_31 = e0 % 152.43/22.66 | % 152.43/22.66 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 152.43/22.66 | (14), (16), (17), (18), (19), (20), (21), (23), (24), (25), (26), % 152.43/22.66 | (27), (28), (29), (31), (32), (33), (34), (35), (36), (37), (38), % 152.43/22.66 | (39), (40), (41), (42), (43), (46), (47) are inconsistent by % 152.43/22.66 | sub-proof #154. % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #110 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.66 (2) all_56_7 = all_52_6 % 152.43/22.66 (3) ~ (all_52_6 = all_6_2) % 152.43/22.66 (4) all_58_31 = e1 % 152.43/22.66 (5) ~ (all_52_6 = all_8_2) % 152.43/22.66 (6) all_56_4 = all_52_8 % 152.43/22.66 (7) all_54_3 = all_52_12 % 152.43/22.66 (8) ~ (all_52_8 = all_6_2) % 152.43/22.66 (9) ~ (all_52_8 = all_52_12) % 152.43/22.66 (10) all_54_9 = all_52_6 % 152.43/22.66 (11) op(e1, e2) = all_52_6 % 152.43/22.66 (12) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.66 (13) op(e1, all_52_6) = all_58_16 % 152.43/22.66 (14) ~ (e3 = e1) % 152.43/22.66 (15) e3 = e1 % 152.43/22.66 (16) ~ (all_52_6 = e0) % 152.43/22.66 (17) ~ (all_52_12 = e0) % 152.43/22.66 (18) all_56_1 = e0 % 152.43/22.66 (19) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.66 (20) all_56_9 = all_52_12 % 152.43/22.66 (21) all_58_29 = all_8_2 % 152.43/22.66 (22) all_56_6 = e3 % 152.43/22.66 (23) ~ (e2 = e1) % 152.43/22.66 (24) op(e3, e0) = all_52_12 % 152.43/22.66 (25) op(all_8_2, e2) = e0 % 152.43/22.66 (26) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.66 (27) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.66 (28) all_56_0 = e2 % 152.43/22.66 (29) ~ (e3 = e0) % 152.43/22.66 (30) op(all_8_2, e0) = all_8_0 % 152.43/22.66 (31) ~ (e2 = e0) % 152.43/22.66 (32) all_58_28 = e2 % 152.43/22.66 (33) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.66 (34) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.66 (35) ~ (e1 = e0) % 152.43/22.66 (36) e1 = e0 % 152.43/22.66 (37) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.66 (38) ~ (all_52_8 = e0) % 152.43/22.66 (39) all_58_30 = all_6_2 % 152.43/22.66 (40) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.66 (41) ~ (e3 = e2) % 152.43/22.66 (42) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.66 (43) ~ (all_52_12 = e2) % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (15), (36) imply: % 152.43/22.66 | (44) e3 = e0 % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (22), (44) imply: % 152.43/22.66 | (45) all_56_6 = e0 % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (4), (36) imply: % 152.43/22.66 | (46) all_58_31 = e0 % 152.43/22.66 | % 152.43/22.66 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 152.43/22.66 | (14), (16), (17), (18), (19), (20), (21), (23), (24), (25), (26), % 152.43/22.66 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (37), (38), % 152.43/22.66 | (39), (40), (41), (42), (43), (45), (46) are inconsistent by % 152.43/22.66 | sub-proof #154. % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #111 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) all_58_30 = e1 % 152.43/22.66 (2) all_58_30 = e0 % 152.43/22.66 (3) ~ (e1 = e0) % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (1), (2) imply: % 152.43/22.66 | (4) e1 = e0 % 152.43/22.66 | % 152.43/22.66 | SIMP: (4) implies: % 152.43/22.66 | (5) e1 = e0 % 152.43/22.66 | % 152.43/22.66 | REDUCE: (3), (5) imply: % 152.43/22.66 | (6) $false % 152.43/22.66 | % 152.43/22.66 | CLOSE: (6) is inconsistent. % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #112 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.66 (2) all_56_7 = all_52_6 % 152.43/22.66 (3) all_58_31 = e1 % 152.43/22.66 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.66 (5) ~ (all_52_7 = e1) % 152.43/22.66 (6) op(e2, e2) = all_8_2 % 152.43/22.66 (7) ~ (all_52_6 = e1) % 152.43/22.66 (8) ~ (e3 = e1) % 152.43/22.66 (9) all_56_1 = e0 % 152.43/22.66 (10) all_56_3 = all_8_2 % 152.43/22.66 (11) all_58_29 = all_8_2 % 152.43/22.66 (12) all_58_30 = e0 % 152.43/22.66 (13) ~ (e2 = e1) % 152.43/22.66 (14) op(all_8_2, e2) = e0 % 152.43/22.66 (15) all_56_13 = all_52_7 % 152.43/22.66 (16) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.66 (17) ~ (e3 = e0) % 152.43/22.66 (18) ~ (e2 = e0) % 152.43/22.66 (19) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.66 (20) ~ (e1 = e0) % 152.43/22.66 (21) ~ (e3 = e2) % 152.43/22.66 (22) ~ (all_8_2 = e0) % 152.43/22.66 (23) op(e2, all_8_2) = all_58_9 % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | BETA: splitting (16) gives: % 152.43/22.66 | % 152.43/22.66 | Case 1: % 152.43/22.66 | | % 152.43/22.66 | | (24) all_56_1 = e1 % 152.43/22.66 | | % 152.43/22.66 | | REF_CLOSE: (9), (20), (24) are inconsistent by sub-proof #213. % 152.43/22.66 | | % 152.43/22.66 | Case 2: % 152.43/22.66 | | % 152.43/22.66 | | (25) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.66 | | % 152.43/22.66 | | BETA: splitting (25) gives: % 152.43/22.66 | | % 152.43/22.66 | | Case 1: % 152.43/22.66 | | | % 152.43/22.66 | | | (26) all_56_3 = e1 % 152.43/22.66 | | | % 152.43/22.66 | | | COMBINE_EQS: (10), (26) imply: % 152.43/22.66 | | | (27) all_8_2 = e1 % 152.43/22.66 | | | % 152.43/22.66 | | | COMBINE_EQS: (11), (27) imply: % 152.43/22.66 | | | (28) all_58_29 = e1 % 152.43/22.66 | | | % 152.43/22.66 | | | BETA: splitting (19) gives: % 152.43/22.66 | | | % 152.43/22.66 | | | Case 1: % 152.43/22.66 | | | | % 152.43/22.66 | | | | (29) all_58_28 = e3 % 152.43/22.66 | | | | % 152.43/22.66 | | | | REF_CLOSE: (1), (3), (4), (6), (11), (12), (13), (14), (18), (21), (22), % 152.43/22.66 | | | | (23), (29) are inconsistent by sub-proof #113. % 152.43/22.66 | | | | % 152.43/22.66 | | | Case 2: % 152.43/22.66 | | | | % 152.43/22.66 | | | | (30) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.66 | | | | % 152.43/22.66 | | | | REF_CLOSE: (3), (8), (12), (17), (28), (30) are inconsistent by % 152.43/22.66 | | | | sub-proof #640. % 152.43/22.66 | | | | % 152.43/22.66 | | | End of split % 152.43/22.66 | | | % 152.43/22.66 | | Case 2: % 152.43/22.66 | | | % 152.43/22.66 | | | (31) all_56_7 = e1 | all_56_13 = e1 % 152.43/22.66 | | | % 152.43/22.66 | | | REF_CLOSE: (2), (5), (7), (15), (31) are inconsistent by sub-proof #546. % 152.43/22.66 | | | % 152.43/22.66 | | End of split % 152.43/22.66 | | % 152.43/22.66 | End of split % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #113 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.66 (2) all_58_31 = e1 % 152.43/22.66 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.66 (4) op(e2, e2) = all_8_2 % 152.43/22.66 (5) all_58_29 = all_8_2 % 152.43/22.66 (6) all_58_30 = e0 % 152.43/22.66 (7) ~ (e2 = e1) % 152.43/22.66 (8) op(all_8_2, e2) = e0 % 152.43/22.66 (9) ~ (e2 = e0) % 152.43/22.66 (10) all_58_28 = e3 % 152.43/22.66 (11) ~ (e3 = e2) % 152.43/22.66 (12) ~ (all_8_2 = e0) % 152.43/22.66 (13) op(e2, all_8_2) = all_58_9 % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | BETA: splitting (3) gives: % 152.43/22.66 | % 152.43/22.66 | Case 1: % 152.43/22.66 | | % 152.43/22.66 | | (14) all_58_28 = e2 % 152.43/22.66 | | % 152.43/22.66 | | REF_CLOSE: (10), (11), (14) are inconsistent by sub-proof #849. % 152.43/22.66 | | % 152.43/22.66 | Case 2: % 152.43/22.66 | | % 152.43/22.66 | | (15) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.66 | | % 152.43/22.66 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (12), (13), (15) are % 152.43/22.66 | | inconsistent by sub-proof #121. % 152.43/22.66 | | % 152.43/22.66 | End of split % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #114 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) all_54_14 = all_6_1 % 152.43/22.66 (2) all_54_14 = e0 % 152.43/22.66 (3) ~ (all_6_1 = e0) % 152.43/22.66 % 152.43/22.66 Begin of proof % 152.43/22.66 | % 152.43/22.66 | COMBINE_EQS: (1), (2) imply: % 152.43/22.66 | (4) all_6_1 = e0 % 152.43/22.66 | % 152.43/22.66 | SIMP: (4) implies: % 152.43/22.66 | (5) all_6_1 = e0 % 152.43/22.66 | % 152.43/22.66 | REDUCE: (3), (5) imply: % 152.43/22.66 | (6) $false % 152.43/22.66 | % 152.43/22.66 | CLOSE: (6) is inconsistent. % 152.43/22.66 | % 152.43/22.66 End of proof % 152.43/22.66 % 152.43/22.66 Sub-proof #115 shows that the following formulas are inconsistent: % 152.43/22.66 ---------------------------------------------------------------- % 152.43/22.66 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 152.43/22.66 (2) all_58_31 = all_4_2 % 152.43/22.66 (3) ~ (all_52_8 = all_52_9) % 152.43/22.66 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.66 (5) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 152.43/22.66 (6) ~ (all_52_2 = all_52_3) % 152.43/22.66 (7) all_58_11 = all_52_9 % 152.43/22.66 (8) all_56_15 = all_4_2 % 152.43/22.66 (9) all_56_7 = all_52_6 % 152.43/22.66 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.43/22.66 (11) all_54_2 = all_52_8 % 152.43/22.66 (12) ~ (all_52_2 = e0) % 152.43/22.66 (13) op(e3, all_52_4) = all_58_1 % 152.43/22.66 (14) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.43/22.66 (15) all_58_15 = all_52_2 % 152.43/22.66 (16) op(e1, all_52_14) = all_58_19 % 152.43/22.66 (17) all_54_7 = all_52_13 % 152.43/22.66 (18) all_58_6 = all_52_12 % 152.43/22.66 (19) all_56_4 = all_52_8 % 152.43/22.66 (20) ~ (all_52_4 = all_8_2) % 152.43/22.66 (21) all_54_3 = all_52_12 % 152.43/22.66 (22) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.66 (23) all_54_1 = all_52_4 % 152.43/22.66 (24) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.66 (25) all_58_13 = all_52_13 % 152.43/22.66 (26) op(e2, e2) = all_8_2 % 152.43/22.66 (27) op(e3, e2) = all_52_4 % 152.43/22.66 (28) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 152.43/22.66 (29) all_58_20 = all_52_14 % 152.43/22.66 (30) ~ (all_52_12 = all_52_13) % 152.43/22.66 (31) op(e0, all_52_3) = all_58_21 % 152.43/22.66 (32) ~ (all_52_6 = all_52_14) % 152.43/22.66 (33) all_54_6 = all_52_9 % 152.43/22.66 (34) all_56_14 = all_6_1 % 152.43/22.66 (35) ~ (all_52_4 = all_52_7) % 152.43/22.66 (36) ~ (all_10_2 = e0) % 152.43/22.66 (37) ~ (all_52_8 = all_52_12) % 152.43/22.66 (38) all_54_9 = all_52_6 % 152.43/22.66 (39) ~ (all_52_13 = all_4_2) % 152.43/22.66 (40) op(e1, e2) = all_52_6 % 152.43/22.66 (41) ~ (all_52_13 = all_8_2) % 152.43/22.66 (42) ~ (e3 = e1) % 152.43/22.66 (43) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.43/22.66 (44) ~ (all_52_6 = e0) % 152.43/22.66 (45) ~ (all_52_1 = all_52_13) % 152.43/22.66 (46) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.66 (47) all_56_12 = all_52_3 % 152.43/22.66 (48) ~ (all_52_3 = all_52_7) % 152.43/22.66 (49) all_58_2 = all_52_4 % 152.43/22.66 (50) all_56_11 = all_52_14 % 152.43/22.66 (51) all_56_1 = all_52_4 % 152.43/22.66 (52) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.66 (53) op(e1, e3) = all_52_2 % 152.43/22.66 (54) ~ (all_52_9 = e0) % 152.43/22.66 (55) ~ (all_52_1 = all_8_2) % 152.43/22.66 (56) all_56_3 = all_8_2 % 152.43/22.66 (57) all_58_24 = all_52_7 % 152.43/22.66 (58) ~ (all_52_13 = all_52_14) % 152.43/22.66 (59) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.43/22.66 (60) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 152.43/22.66 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 152.43/22.66 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 152.43/22.66 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 152.43/22.66 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 152.43/22.66 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 152.43/22.66 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 152.43/22.66 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 152.43/22.66 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 152.43/22.66 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 152.43/22.66 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.43/22.66 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.43/22.66 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.43/22.66 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.43/22.66 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.43/22.66 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 152.43/22.66 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.66 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.43/22.66 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.66 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.43/22.66 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.43/22.66 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 152.43/22.66 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.43/22.66 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.43/22.66 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.43/22.66 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 152.43/22.66 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 152.43/22.66 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 152.43/22.66 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.43/22.66 e0) % 152.43/22.66 (61) all_56_9 = all_52_12 % 152.43/22.66 (62) all_58_29 = all_8_2 % 152.43/22.66 (63) ~ (all_52_12 = all_52_14) % 152.43/22.66 (64) all_58_30 = e0 % 152.43/22.66 (65) all_58_8 = all_52_1 % 152.43/22.66 (66) ~ (e2 = e1) % 152.43/22.66 (67) op(e3, e0) = all_52_12 % 152.43/22.66 (68) all_56_6 = all_52_2 % 152.43/22.66 (69) ~ (all_52_2 = all_52_6) % 152.43/22.66 (70) ~ (all_52_8 = all_6_1) % 152.43/22.66 (71) op(all_8_2, e2) = e0 % 152.43/22.66 (72) all_56_13 = all_52_7 % 152.43/22.66 (73) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.43/22.66 (74) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.66 (75) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.66 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.66 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.66 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.66 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.66 (all_58_27 = e0)) % 152.43/22.66 (76) ~ (all_52_9 = all_52_13) % 152.43/22.66 (77) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.67 (78) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.67 (79) op(e1, e1) = e0 % 152.43/22.67 (80) ~ (e3 = e0) % 152.43/22.67 (81) all_56_2 = all_52_1 % 152.43/22.67 (82) all_58_26 = all_6_1 % 152.43/22.67 (83) all_56_10 = all_52_13 % 152.43/22.67 (84) ~ (all_52_12 = all_10_2) % 152.43/22.67 (85) ~ (all_52_9 = all_8_2) % 152.43/22.67 (86) all_58_28 = all_10_2 % 152.43/22.67 (87) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.67 (88) all_58_17 = all_52_6 % 152.43/22.67 (89) ~ (all_52_1 = all_52_9) % 152.43/22.67 (90) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.67 (91) ~ (e2 = e0) % 152.43/22.67 (92) ~ (all_52_2 = all_10_2) % 152.43/22.67 (93) all_56_0 = all_10_2 % 152.43/22.67 (94) op(e0, e0) = all_4_2 % 152.43/22.67 (95) all_58_22 = all_52_3 % 152.43/22.67 (96) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.43/22.67 (97) ~ (all_52_12 = all_4_2) % 152.43/22.67 (98) ~ (all_52_3 = all_6_1) % 152.43/22.67 (99) ~ (all_52_3 = all_10_2) % 152.43/22.67 (100) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.43/22.67 (101) ~ (all_52_1 = all_52_2) % 152.43/22.67 (102) ~ (all_52_7 = all_8_2) % 152.43/22.67 (103) op(e2, e0) = all_52_13 % 152.43/22.67 (104) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.43/22.67 (105) op(e2, all_52_13) = all_58_12 % 152.43/22.67 (106) all_58_4 = all_52_8 % 152.43/22.67 (107) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.67 (108) ~ (all_52_2 = all_52_14) % 152.43/22.67 (109) ~ (all_52_14 = all_4_2) % 152.43/22.67 (110) ~ (e1 = e0) % 152.43/22.67 (111) ~ (all_52_7 = all_4_2) % 152.43/22.67 (112) ~ (all_52_14 = e0) % 152.43/22.67 (113) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.43/22.67 (114) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.67 (115) ~ (all_4_2 = e1) % 152.43/22.67 (116) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.43/22.67 (117) op(e0, e2) = all_52_7 % 152.43/22.67 (118) ~ (all_52_8 = e0) % 152.43/22.67 (119) ~ (all_52_4 = all_10_2) % 152.43/22.67 (120) ~ (all_52_9 = all_6_1) % 152.43/22.67 (121) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 152.43/22.67 (122) all_58_30 = all_6_2 % 152.43/22.67 (123) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.67 (124) ~ (e3 = e2) % 152.43/22.67 (125) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.43/22.67 (126) op(all_10_2, e3) = all_10_1 % 152.43/22.67 (127) ~ (all_52_4 = all_52_12) % 152.43/22.67 (128) op(e2, all_8_2) = all_58_9 % 152.43/22.67 (129) all_54_4 = all_52_1 % 152.43/22.67 (130) ~ (all_52_1 = all_10_2) % 152.43/22.67 % 152.43/22.67 Begin of proof % 152.43/22.67 | % 152.43/22.67 | BETA: splitting (96) gives: % 152.43/22.67 | % 152.43/22.67 | Case 1: % 152.43/22.67 | | % 152.43/22.67 | | (131) all_56_0 = e0 % 152.43/22.67 | | % 152.43/22.67 | | COMBINE_EQS: (93), (131) imply: % 152.43/22.67 | | (132) all_10_2 = e0 % 152.43/22.67 | | % 152.43/22.67 | | REDUCE: (36), (132) imply: % 152.43/22.67 | | (133) $false % 152.43/22.67 | | % 152.43/22.67 | | CLOSE: (133) is inconsistent. % 152.43/22.67 | | % 152.43/22.67 | Case 2: % 152.43/22.67 | | % 152.43/22.67 | | (134) ~ (all_56_0 = e0) % 152.43/22.67 | | (135) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.43/22.67 | | % 152.43/22.67 | | BETA: splitting (46) gives: % 152.43/22.67 | | % 152.43/22.67 | | Case 1: % 152.43/22.67 | | | % 152.43/22.67 | | | (136) all_56_0 = e0 % 152.43/22.67 | | | % 152.43/22.67 | | | COMBINE_EQS: (93), (136) imply: % 152.43/22.67 | | | (137) all_10_2 = e0 % 152.43/22.67 | | | % 152.43/22.67 | | | REDUCE: (36), (137) imply: % 152.43/22.67 | | | (138) $false % 152.43/22.67 | | | % 152.43/22.67 | | | CLOSE: (138) is inconsistent. % 152.43/22.67 | | | % 152.43/22.67 | | Case 2: % 152.43/22.67 | | | % 152.43/22.67 | | | (139) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.67 | | | % 152.43/22.67 | | | BETA: splitting (116) gives: % 152.43/22.67 | | | % 152.43/22.67 | | | Case 1: % 152.43/22.67 | | | | % 152.43/22.67 | | | | (140) all_54_6 = e0 % 152.43/22.67 | | | | % 152.43/22.67 | | | | REF_CLOSE: (33), (54), (140) are inconsistent by sub-proof #797. % 152.43/22.67 | | | | % 152.43/22.67 | | | Case 2: % 152.43/22.67 | | | | % 152.43/22.67 | | | | (141) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 152.43/22.67 | | | | % 152.43/22.67 | | | | BETA: splitting (113) gives: % 152.43/22.67 | | | | % 152.43/22.67 | | | | Case 1: % 152.43/22.67 | | | | | % 152.43/22.67 | | | | | (142) all_54_2 = e0 % 152.43/22.67 | | | | | % 152.43/22.67 | | | | | REF_CLOSE: (11), (118), (142) are inconsistent by sub-proof #860. % 152.43/22.67 | | | | | % 152.43/22.67 | | | | Case 2: % 152.43/22.67 | | | | | % 152.43/22.67 | | | | | (143) ~ (all_54_2 = e0) % 152.43/22.67 | | | | | (144) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.67 | | | | | % 152.43/22.67 | | | | | BETA: splitting (43) gives: % 152.43/22.67 | | | | | % 152.43/22.67 | | | | | Case 1: % 152.43/22.67 | | | | | | % 152.43/22.67 | | | | | | (145) all_54_9 = e0 % 152.43/22.67 | | | | | | % 152.43/22.67 | | | | | | REF_CLOSE: (38), (44), (145) are inconsistent by sub-proof #572. % 152.43/22.67 | | | | | | % 152.43/22.67 | | | | | Case 2: % 152.43/22.67 | | | | | | % 152.43/22.67 | | | | | | (146) ~ (all_54_9 = e0) % 152.43/22.67 | | | | | | (147) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.67 | | | | | | % 152.43/22.67 | | | | | | BETA: splitting (123) gives: % 152.43/22.67 | | | | | | % 152.43/22.67 | | | | | | Case 1: % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | (148) all_58_28 = e1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | COMBINE_EQS: (86), (148) imply: % 152.43/22.67 | | | | | | | (149) all_10_2 = e1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | COMBINE_EQS: (93), (149) imply: % 152.43/22.67 | | | | | | | (150) all_56_0 = e1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (130), (149) imply: % 152.43/22.67 | | | | | | | (151) ~ (all_52_1 = e1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (92), (149) imply: % 152.43/22.67 | | | | | | | (152) ~ (all_52_2 = e1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (99), (149) imply: % 152.43/22.67 | | | | | | | (153) ~ (all_52_3 = e1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (119), (149) imply: % 152.43/22.67 | | | | | | | (154) ~ (all_52_4 = e1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (84), (149) imply: % 152.43/22.67 | | | | | | | (155) ~ (all_52_12 = e1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (126), (149) imply: % 152.43/22.67 | | | | | | | (156) op(e1, e3) = all_10_1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | GROUND_INST: instantiating (4) with all_52_2, all_10_1, e3, e1, % 152.43/22.67 | | | | | | | simplifying with (53), (156) gives: % 152.43/22.67 | | | | | | | (157) all_52_2 = all_10_1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | COMBINE_EQS: (68), (157) imply: % 152.43/22.67 | | | | | | | (158) all_56_6 = all_10_1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | COMBINE_EQS: (15), (157) imply: % 152.43/22.67 | | | | | | | (159) all_58_15 = all_10_1 % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (101), (157) imply: % 152.43/22.67 | | | | | | | (160) ~ (all_52_1 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (6), (157) imply: % 152.43/22.67 | | | | | | | (161) ~ (all_52_3 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | SIMP: (161) implies: % 152.43/22.67 | | | | | | | (162) ~ (all_52_3 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (69), (157) imply: % 152.43/22.67 | | | | | | | (163) ~ (all_52_6 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | SIMP: (163) implies: % 152.43/22.67 | | | | | | | (164) ~ (all_52_6 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (108), (157) imply: % 152.43/22.67 | | | | | | | (165) ~ (all_52_14 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | SIMP: (165) implies: % 152.43/22.67 | | | | | | | (166) ~ (all_52_14 = all_10_1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (152), (157) imply: % 152.43/22.67 | | | | | | | (167) ~ (all_10_1 = e1) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | REDUCE: (12), (157) imply: % 152.43/22.67 | | | | | | | (168) ~ (all_10_1 = e0) % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | BETA: splitting (10) gives: % 152.43/22.67 | | | | | | | % 152.43/22.67 | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | (169) all_54_3 = e0 % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | COMBINE_EQS: (21), (169) imply: % 152.43/22.67 | | | | | | | | (170) all_52_12 = e0 % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | SIMP: (170) implies: % 152.43/22.67 | | | | | | | | (171) all_52_12 = e0 % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | COMBINE_EQS: (61), (171) imply: % 152.43/22.67 | | | | | | | | (172) all_56_9 = e0 % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | REDUCE: (127), (171) imply: % 152.43/22.67 | | | | | | | | (173) ~ (all_52_4 = e0) % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | BETA: splitting (104) gives: % 152.43/22.67 | | | | | | | | % 152.43/22.67 | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | % 152.43/22.67 | | | | | | | | | (174) all_54_1 = e0 % 152.43/22.67 | | | | | | | | | % 152.43/22.67 | | | | | | | | | REF_CLOSE: (23), (173), (174) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | #798. % 152.43/22.67 | | | | | | | | | % 152.43/22.67 | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | % 152.43/22.67 | | | | | | | | | (175) ~ (all_54_1 = e0) % 152.43/22.67 | | | | | | | | | (176) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 152.43/22.67 | | | | | | | | | % 152.43/22.67 | | | | | | | | | BETA: splitting (77) gives: % 152.43/22.67 | | | | | | | | | % 152.43/22.67 | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | (177) all_56_1 = e0 % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | COMBINE_EQS: (51), (177) imply: % 152.43/22.67 | | | | | | | | | | (178) all_52_4 = e0 % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | REDUCE: (173), (178) imply: % 152.43/22.67 | | | | | | | | | | (179) $false % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | CLOSE: (179) is inconsistent. % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | (180) ~ (all_56_1 = e0) % 152.43/22.67 | | | | | | | | | | (181) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | BETA: splitting (24) gives: % 152.43/22.67 | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | (182) all_56_2 = e0 % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | COMBINE_EQS: (81), (182) imply: % 152.43/22.67 | | | | | | | | | | | (183) all_52_1 = e0 % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | REDUCE: (89), (183) imply: % 152.43/22.67 | | | | | | | | | | | (184) ~ (all_52_9 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | REDUCE: (45), (183) imply: % 152.43/22.67 | | | | | | | | | | | (185) ~ (all_52_13 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | SIMP: (185) implies: % 152.43/22.67 | | | | | | | | | | | (186) ~ (all_52_13 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | REDUCE: (160), (183) imply: % 152.43/22.67 | | | | | | | | | | | (187) ~ (all_10_1 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | REDUCE: (55), (183) imply: % 152.43/22.67 | | | | | | | | | | | (188) ~ (all_8_2 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | SIMP: (188) implies: % 152.43/22.67 | | | | | | | | | | | (189) ~ (all_8_2 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | REDUCE: (151), (183) imply: % 152.43/22.67 | | | | | | | | | | | (190) ~ (e1 = e0) % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | BETA: splitting (181) gives: % 152.43/22.67 | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | (191) all_56_3 = e0 % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | COMBINE_EQS: (56), (191) imply: % 152.43/22.67 | | | | | | | | | | | | (192) all_8_2 = e0 % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | REDUCE: (189), (192) imply: % 152.43/22.67 | | | | | | | | | | | | (193) $false % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | CLOSE: (193) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | (194) all_56_7 = e0 | all_56_13 = e0 % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | BETA: splitting (194) gives: % 152.43/22.67 | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | (195) all_56_7 = e0 % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | COMBINE_EQS: (9), (195) imply: % 152.43/22.67 | | | | | | | | | | | | | (196) all_52_6 = e0 % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | REDUCE: (44), (196) imply: % 152.43/22.67 | | | | | | | | | | | | | (197) $false % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | (198) all_56_13 = e0 % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | COMBINE_EQS: (72), (198) imply: % 152.43/22.67 | | | | | | | | | | | | | (199) all_52_7 = e0 % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | SIMP: (199) implies: % 152.43/22.67 | | | | | | | | | | | | | (200) all_52_7 = e0 % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | REDUCE: (48), (200) imply: % 152.43/22.67 | | | | | | | | | | | | | (201) ~ (all_52_3 = e0) % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | REDUCE: (111), (200) imply: % 152.43/22.67 | | | | | | | | | | | | | (202) ~ (all_4_2 = e0) % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | SIMP: (202) implies: % 152.43/22.67 | | | | | | | | | | | | | (203) ~ (all_4_2 = e0) % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | BETA: splitting (90) gives: % 152.43/22.67 | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | (204) all_56_12 = e1 % 152.43/22.67 | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | REF_CLOSE: (47), (153), (204) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | #577. % 152.43/22.67 | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | (205) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.67 | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | BETA: splitting (205) gives: % 152.43/22.67 | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | (206) all_56_13 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | COMBINE_EQS: (198), (206) imply: % 152.43/22.67 | | | | | | | | | | | | | | | (207) e1 = e0 % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | REDUCE: (110), (207) imply: % 152.43/22.67 | | | | | | | | | | | | | | | (208) $false % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | (209) all_56_14 = e1 | all_56_15 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 152.43/22.67 | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | (210) all_56_14 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (210) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | (211) all_6_1 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | SIMP: (211) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | (212) all_6_1 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | REDUCE: (70), (212) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | (213) ~ (all_52_8 = e1) % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | REDUCE: (120), (212) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | (214) ~ (all_52_9 = e1) % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | (215) all_56_12 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (215) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | (216) all_52_3 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | SIMP: (216) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | (217) all_52_3 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | REDUCE: (162), (217) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | (218) ~ (all_10_1 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | SIMP: (218) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | (219) ~ (all_10_1 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | BETA: splitting (87) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | (220) all_56_0 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (150), (220) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | #796. % 152.43/22.67 | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | (221) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | (222) all_56_2 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (222) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | (223) e2 = e0 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | SIMP: (223) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | (224) e2 = e0 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | REDUCE: (91), (224) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | (225) $false % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | (226) all_56_6 = e2 | all_56_12 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | (227) all_56_6 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (227) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | (228) all_10_1 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | (229) all_10_1 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (229) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | (230) ~ (all_52_14 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (219), (229) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | (231) ~ (e3 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | (232) all_58_28 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (148), (232) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | #857. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | (233) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | (234) all_58_29 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (234) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | (235) all_8_2 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (235) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_52_9 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (235) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_52_13 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (235) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | (238) op(e3, e2) = e0 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | (239) all_56_4 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (239) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | (240) all_52_8 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (240) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | (241) ~ (all_52_9 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | (242) all_54_6 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (214), (242) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | #774. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | (243) all_54_6 = e3 | all_54_6 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_54_6 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (244) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_52_9 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (245) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_52_9 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (246) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | (247) ~ (all_52_13 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (247) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_52_13 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_54_7 = e0 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (186), (249) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | #742. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_54_7 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (251) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_52_13 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_52_13 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (253) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_56_10 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (237), (253) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) ~ (e3 = e1) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (248), (253) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (e2 = e1) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_56_9 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (257) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e2 = e0 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (258) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) $false % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) ~ (all_56_9 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (260) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) ~ (e2 = e0) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_56_0 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (150), (263) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #796. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) ~ (all_56_0 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_56_9 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (266) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) e3 = e0 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (267) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) $false % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_28 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (148), (270) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #856. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) ~ (all_58_28 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_56_1 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (273) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_52_4 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (27), (173), (238), (274) are % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #124. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) ~ (all_56_1 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (275) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) ~ (all_52_4 = e2) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_54_1 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (154), (277) are inconsistent by sub-proof % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_54_1 = e3 | all_54_1 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_56_10 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (279) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) e3 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (280) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) $false % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_56_11 = e3 | all_56_15 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_56_10 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (283) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) e2 = e1 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (284) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) $false % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_56_11 = e2 | all_56_15 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_56_11 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (287) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_52_14 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_52_14 = e3 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (289) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) ~ (all_4_2 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (290) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_4_2 = e3) % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_56_11 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (292) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) e3 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e3 = e2 % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (294) imply: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_56_15 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (296) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_4_2 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (297) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_4_2 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (298) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_31 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_56_1 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (300) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_52_4 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_52_4 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (276), (302) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) $false % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_56_4 = e2 | all_56_9 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_56_4 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (239), (305) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #543. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_56_9 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (306) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) e2 = e0 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (307) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_31 = e0 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (23), (26), (62), (71), (91), (122), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (173), (189), (233), (272), (276), (278), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) are inconsistent by sub-proof #139. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_56_15 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (309) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_4_2 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (310) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_4_2 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (311) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_58_31 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (26), (62), (64), (71), (91), (124), (128), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (272), (312) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #123. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_54_7 = e3 | all_54_7 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (237), (248), (313) are inconsistent by % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #602. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_54_6 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (236), (314) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | #772. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_56_4 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (315) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | (316) ~ (all_52_8 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (317) all_54_6 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (317) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (318) all_52_9 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (318) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (319) $false % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (320) all_54_6 = e3 | all_54_6 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (33), (144), (213), (236), (316), (320) % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #122. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | (321) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | (322) all_58_30 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (80), (322) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | #755. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_31 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_28 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (148), (324) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | #856. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (26), (62), (64), (71), (91), (124), (128), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | (189), (323), (325) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | #123. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | (326) all_56_12 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (215), (326) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | #588. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | (327) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | (328) all_56_13 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (198), (328) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | (329) e3 = e0 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | REDUCE: (80), (329) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | (330) $false % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | (331) all_56_14 = e3 | all_56_15 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (332) all_56_14 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (332) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (333) e3 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | REDUCE: (42), (333) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (334) $false % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (335) all_56_15 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (335) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (336) all_4_2 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (337) all_4_2 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (337) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (338) all_58_31 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | (339) all_58_28 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (148), (339) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | #856. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | (340) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (26), (62), (64), (71), (91), (124), (128), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | (189), (338), (340) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | #123. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | (341) all_56_15 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (22), (26), (62), (64), (66), (71), % 152.43/22.68 | | | | | | | | | | | | | | | | (91), (128), (148), (189), (341) are inconsistent % 152.43/22.68 | | | | | | | | | | | | | | | | by sub-proof #119. % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | (342) ~ (all_56_2 = e0) % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | REDUCE: (81), (342) imply: % 152.43/22.68 | | | | | | | | | | | (343) ~ (all_52_1 = e0) % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (44), (47), (48), (51), (56), % 152.43/22.68 | | | | | | | | | | | (68), (71), (72), (77), (81), (102), (117), (135), % 152.43/22.68 | | | | | | | | | | | (173), (343) are inconsistent by sub-proof #118. % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | End of split % 152.43/22.68 | | | | | | | | % 152.43/22.68 | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | % 152.43/22.68 | | | | | | | | (344) ~ (all_54_3 = e0) % 152.43/22.68 | | | | | | | | (345) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.68 | | | | | | | | % 152.43/22.68 | | | | | | | | REDUCE: (21), (344) imply: % 152.43/22.68 | | | | | | | | (346) ~ (all_52_12 = e0) % 152.43/22.68 | | | | | | | | % 152.43/22.68 | | | | | | | | BETA: splitting (139) gives: % 152.43/22.68 | | | | | | | | % 152.43/22.68 | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | (347) all_56_1 = e0 % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | COMBINE_EQS: (51), (347) imply: % 152.43/22.68 | | | | | | | | | (348) all_52_4 = e0 % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | COMBINE_EQS: (49), (348) imply: % 152.43/22.68 | | | | | | | | | (349) all_58_2 = e0 % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | REDUCE: (127), (348) imply: % 152.43/22.68 | | | | | | | | | (350) ~ (all_52_12 = e0) % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | REDUCE: (13), (348) imply: % 152.43/22.68 | | | | | | | | | (351) op(e3, e0) = all_58_1 % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | BETA: splitting (121) gives: % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | (352) all_56_12 = e0 % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | COMBINE_EQS: (47), (352) imply: % 152.43/22.68 | | | | | | | | | | (353) all_52_3 = e0 % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | SIMP: (353) implies: % 152.43/22.68 | | | | | | | | | | (354) all_52_3 = e0 % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | COMBINE_EQS: (95), (354) imply: % 152.43/22.68 | | | | | | | | | | (355) all_58_22 = e0 % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | REDUCE: (48), (354) imply: % 152.43/22.68 | | | | | | | | | | (356) ~ (all_52_7 = e0) % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | SIMP: (356) implies: % 152.43/22.68 | | | | | | | | | | (357) ~ (all_52_7 = e0) % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | REDUCE: (162), (354) imply: % 152.43/22.68 | | | | | | | | | | (358) ~ (all_10_1 = e0) % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | REDUCE: (153), (354) imply: % 152.43/22.68 | | | | | | | | | | (359) ~ (e1 = e0) % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | REDUCE: (31), (354) imply: % 152.43/22.68 | | | | | | | | | | (360) op(e0, e0) = all_58_21 % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | BETA: splitting (5) gives: % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | (361) all_56_9 = e0 % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | COMBINE_EQS: (61), (361) imply: % 152.43/22.68 | | | | | | | | | | | (362) all_52_12 = e0 % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | REDUCE: (346), (362) imply: % 152.43/22.68 | | | | | | | | | | | (363) $false % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | CLOSE: (363) is inconsistent. % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | (364) all_56_10 = e0 | all_56_11 = e0 % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | BETA: splitting (364) gives: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | (365) all_56_10 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | COMBINE_EQS: (83), (365) imply: % 152.43/22.68 | | | | | | | | | | | | (366) all_52_13 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | SIMP: (366) implies: % 152.43/22.68 | | | | | | | | | | | | (367) all_52_13 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | COMBINE_EQS: (25), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (368) all_58_13 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (45), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (369) ~ (all_52_1 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (58), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (370) ~ (all_52_14 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (41), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (371) ~ (all_8_2 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | SIMP: (371) implies: % 152.43/22.68 | | | | | | | | | | | | (372) ~ (all_8_2 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (39), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (373) ~ (all_4_2 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | SIMP: (373) implies: % 152.43/22.68 | | | | | | | | | | | | (374) ~ (all_4_2 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (105), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (375) op(e2, e0) = all_58_12 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (103), (367) imply: % 152.43/22.68 | | | | | | | | | | | | (376) op(e2, e0) = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | BETA: splitting (78) gives: % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | (377) all_56_9 = e1 % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | REF_CLOSE: (61), (155), (377) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | #486. % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | (378) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | BETA: splitting (378) gives: % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | (379) all_56_10 = e1 % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | COMBINE_EQS: (365), (379) imply: % 152.43/22.68 | | | | | | | | | | | | | | (380) e1 = e0 % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | REDUCE: (110), (380) imply: % 152.43/22.68 | | | | | | | | | | | | | | (381) $false % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | CLOSE: (381) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | (382) all_56_11 = e1 | all_56_15 = e1 % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | BETA: splitting (382) gives: % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | (383) all_56_11 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | COMBINE_EQS: (50), (383) imply: % 152.43/22.68 | | | | | | | | | | | | | | | (384) all_52_14 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | SIMP: (384) implies: % 152.43/22.68 | | | | | | | | | | | | | | | (385) all_52_14 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | COMBINE_EQS: (29), (385) imply: % 152.43/22.68 | | | | | | | | | | | | | | | (386) all_58_20 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | REDUCE: (32), (385) imply: % 152.43/22.68 | | | | | | | | | | | | | | | (387) ~ (all_52_6 = e1) % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | REDUCE: (166), (385) imply: % 152.43/22.68 | | | | | | | | | | | | | | | (388) ~ (all_10_1 = e1) % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | REDUCE: (16), (385) imply: % 152.43/22.68 | | | | | | | | | | | | | | | (389) op(e1, e1) = all_58_19 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_21, e0, e0, % 152.43/22.68 | | | | | | | | | | | | | | | simplifying with (94), (360) gives: % 152.43/22.68 | | | | | | | | | | | | | | | (390) all_58_21 = all_4_2 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_19, e1, e1, % 152.43/22.68 | | | | | | | | | | | | | | | simplifying with (79), (389) gives: % 152.43/22.68 | | | | | | | | | | | | | | | (391) all_58_19 = e0 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e0, e2, % 152.43/22.68 | | | | | | | | | | | | | | | simplifying with (375), (376) gives: % 152.43/22.68 | | | | | | | | | | | | | | | (392) all_58_12 = e0 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_12, all_58_1, e0, % 152.43/22.68 | | | | | | | | | | | | | | | e3, simplifying with (67), (351) gives: % 152.43/22.68 | | | | | | | | | | | | | | | (393) all_58_1 = all_52_12 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | (394) all_54_4 = e0 % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | REF_CLOSE: (129), (369), (394) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | #859. % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | (395) ~ (all_54_4 = e0) % 152.43/22.68 | | | | | | | | | | | | | | | | (396) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | (397) all_56_6 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (397) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | (398) all_10_1 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | SIMP: (398) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | (399) all_10_1 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (399) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | (400) all_58_15 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | REDUCE: (160), (399) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | (401) ~ (all_52_1 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | REDUCE: (164), (399) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | (402) ~ (all_52_6 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | (403) all_54_9 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (387), (403) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | #622. % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | (404) all_54_9 = e3 | all_54_9 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (405) all_54_9 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (405) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (406) all_52_6 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | SIMP: (406) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (407) all_52_6 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (407) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (408) all_58_17 = e2 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (7), (18), (33), (42), (55), (57), (60), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (62), (64), (65), (80), (82), (89), (106), (110), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (120), (129), (141), (148), (151), (346), (349), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (355), (357), (368), (369), (374), (386), (396), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (400), (401), (408) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | #624. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (409) all_54_9 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (402), (409) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | | #620. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | (410) ~ (all_56_6 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | REDUCE: (158), (410) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | (411) ~ (all_10_1 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | BETA: splitting (52) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | (412) all_56_0 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (150), (412) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | | | | | #569. % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | (413) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | BETA: splitting (413) gives: % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (414) all_56_2 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (414) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (415) all_52_1 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | REDUCE: (55), (415) imply: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (416) ~ (all_8_2 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | SIMP: (416) implies: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (417) ~ (all_8_2 = e3) % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (21), (42), (61), (62), (64), (75), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (80), (97), (107), (148), (155), (345), (390), % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (391), (392), (393), (417) are inconsistent by % 152.43/22.68 | | | | | | | | | | | | | | | | | | | sub-proof #183. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | (418) all_56_6 = e3 | all_56_12 = e3 % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (158), (352), (411), (418) are inconsistent % 152.43/22.68 | | | | | | | | | | | | | | | | | | | by sub-proof #116. % 152.43/22.68 | | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | (419) all_56_15 = e1 % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (22), (26), (62), (64), (66), (71), % 152.43/22.68 | | | | | | | | | | | | | | | (91), (128), (148), (372), (419) are inconsistent % 152.43/22.68 | | | | | | | | | | | | | | | by sub-proof #119. % 152.43/22.68 | | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | (420) all_56_11 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REF_CLOSE: (50), (112), (420) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | #220. % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | (421) ~ (all_56_12 = e0) % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | REDUCE: (47), (421) imply: % 152.43/22.68 | | | | | | | | | | (422) ~ (all_52_3 = e0) % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | BETA: splitting (5) gives: % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | (423) all_56_9 = e0 % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | COMBINE_EQS: (61), (423) imply: % 152.43/22.68 | | | | | | | | | | | (424) all_52_12 = e0 % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | REDUCE: (346), (424) imply: % 152.43/22.68 | | | | | | | | | | | (425) $false % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | CLOSE: (425) is inconsistent. % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | (426) all_56_10 = e0 | all_56_11 = e0 % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | BETA: splitting (426) gives: % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | (427) all_56_10 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | COMBINE_EQS: (83), (427) imply: % 152.43/22.68 | | | | | | | | | | | | (428) all_52_13 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | SIMP: (428) implies: % 152.43/22.68 | | | | | | | | | | | | (429) all_52_13 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REDUCE: (45), (429) imply: % 152.43/22.68 | | | | | | | | | | | | (430) ~ (all_52_1 = e0) % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | BETA: splitting (135) gives: % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | (431) all_56_2 = e0 % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | COMBINE_EQS: (81), (431) imply: % 152.43/22.68 | | | | | | | | | | | | | (432) all_52_1 = e0 % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | REDUCE: (430), (432) imply: % 152.43/22.68 | | | | | | | | | | | | | (433) $false % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | CLOSE: (433) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | (434) all_56_6 = e0 | all_56_12 = e0 % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | BETA: splitting (434) gives: % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | Case 1: % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | (435) all_56_6 = e0 % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | COMBINE_EQS: (158), (435) imply: % 152.43/22.68 | | | | | | | | | | | | | | (436) all_10_1 = e0 % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | REDUCE: (168), (436) imply: % 152.43/22.68 | | | | | | | | | | | | | | (437) $false % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | CLOSE: (437) is inconsistent. % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | (438) all_56_12 = e0 % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | | REF_CLOSE: (47), (422), (438) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | | | #607. % 152.43/22.68 | | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | (439) all_56_11 = e0 % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | | REF_CLOSE: (50), (112), (439) are inconsistent by sub-proof % 152.43/22.68 | | | | | | | | | | | | #220. % 152.43/22.68 | | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | | % 152.43/22.68 | | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | | % 152.43/22.68 | | | | | | | | | End of split % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | Case 2: % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | (440) all_56_4 = e0 | all_56_9 = e0 % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | | REF_CLOSE: (19), (61), (118), (346), (440) are inconsistent by % 152.43/22.68 | | | | | | | | | sub-proof #520. % 152.43/22.68 | | | | | | | | | % 152.43/22.68 | | | | | | | | End of split % 152.43/22.68 | | | | | | | | % 152.43/22.68 | | | | | | | End of split % 152.43/22.68 | | | | | | | % 152.43/22.68 | | | | | | Case 2: % 152.43/22.68 | | | | | | | % 152.43/22.68 | | | | | | | (441) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.68 | | | | | | | % 152.43/22.68 | | | | | | | REF_CLOSE: (2), (4), (40), (44), (62), (64), (71), (110), (115), % 152.43/22.68 | | | | | | | (441) are inconsistent by sub-proof #128. % 152.43/22.68 | | | | | | | % 152.43/22.68 | | | | | | End of split % 152.43/22.68 | | | | | | % 152.43/22.68 | | | | | End of split % 152.43/22.68 | | | | | % 152.43/22.68 | | | | End of split % 152.43/22.68 | | | | % 152.43/22.68 | | | End of split % 152.43/22.68 | | | % 152.43/22.68 | | End of split % 152.43/22.68 | | % 152.43/22.68 | End of split % 152.43/22.68 | % 152.43/22.68 End of proof % 152.43/22.68 % 152.43/22.68 Sub-proof #116 shows that the following formulas are inconsistent: % 152.43/22.68 ---------------------------------------------------------------- % 152.43/22.68 (1) all_56_6 = e3 | all_56_12 = e3 % 152.43/22.68 (2) ~ (all_10_1 = e3) % 152.43/22.68 (3) all_56_6 = all_10_1 % 152.43/22.68 (4) ~ (e3 = e0) % 152.43/22.68 (5) all_56_12 = e0 % 152.43/22.68 % 152.43/22.68 Begin of proof % 152.43/22.68 | % 152.43/22.68 | BETA: splitting (1) gives: % 152.43/22.68 | % 152.43/22.68 | Case 1: % 152.43/22.68 | | % 152.43/22.68 | | (6) all_56_6 = e3 % 152.43/22.68 | | % 152.43/22.68 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #117. % 152.43/22.68 | | % 152.43/22.68 | Case 2: % 152.43/22.68 | | % 152.43/22.68 | | (7) all_56_12 = e3 % 152.43/22.68 | | % 152.43/22.68 | | COMBINE_EQS: (5), (7) imply: % 152.43/22.68 | | (8) e3 = e0 % 152.43/22.68 | | % 152.43/22.68 | | REDUCE: (4), (8) imply: % 152.43/22.68 | | (9) $false % 152.43/22.68 | | % 152.43/22.68 | | CLOSE: (9) is inconsistent. % 152.43/22.68 | | % 152.43/22.68 | End of split % 152.43/22.68 | % 152.43/22.68 End of proof % 152.43/22.68 % 152.43/22.68 Sub-proof #117 shows that the following formulas are inconsistent: % 152.43/22.68 ---------------------------------------------------------------- % 152.43/22.68 (1) all_56_6 = all_10_1 % 152.43/22.68 (2) all_56_6 = e3 % 152.43/22.68 (3) ~ (all_10_1 = e3) % 152.43/22.68 % 152.43/22.68 Begin of proof % 152.43/22.68 | % 152.43/22.68 | COMBINE_EQS: (1), (2) imply: % 152.43/22.68 | (4) all_10_1 = e3 % 152.43/22.68 | % 152.43/22.68 | SIMP: (4) implies: % 152.43/22.68 | (5) all_10_1 = e3 % 152.43/22.68 | % 152.43/22.68 | REDUCE: (3), (5) imply: % 152.43/22.68 | (6) $false % 152.43/22.68 | % 152.43/22.68 | CLOSE: (6) is inconsistent. % 152.43/22.68 | % 152.43/22.68 End of proof % 152.43/22.68 % 152.43/22.68 Sub-proof #118 shows that the following formulas are inconsistent: % 152.43/22.68 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) all_56_7 = all_52_6 % 152.43/22.69 (3) ~ (all_52_2 = e0) % 152.43/22.69 (4) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.43/22.69 (5) ~ (all_52_6 = e0) % 152.43/22.69 (6) all_56_12 = all_52_3 % 152.43/22.69 (7) ~ (all_52_3 = all_52_7) % 152.43/22.69 (8) all_56_1 = all_52_4 % 152.43/22.69 (9) all_56_3 = all_8_2 % 152.43/22.69 (10) all_56_6 = all_52_2 % 152.43/22.69 (11) op(all_8_2, e2) = e0 % 152.43/22.69 (12) all_56_13 = all_52_7 % 152.43/22.69 (13) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.69 (14) ~ (all_52_4 = e0) % 152.43/22.69 (15) all_56_2 = all_52_1 % 152.43/22.69 (16) ~ (all_52_1 = e0) % 152.43/22.69 (17) ~ (all_52_7 = all_8_2) % 152.43/22.69 (18) op(e0, e2) = all_52_7 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (4) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (19) all_56_2 = e0 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (15), (19) imply: % 152.43/22.69 | | (20) all_52_1 = e0 % 152.43/22.69 | | % 152.43/22.69 | | REDUCE: (16), (20) imply: % 152.43/22.69 | | (21) $false % 152.43/22.69 | | % 152.43/22.69 | | CLOSE: (21) is inconsistent. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (22) all_56_6 = e0 | all_56_12 = e0 % 152.43/22.69 | | % 152.43/22.69 | | BETA: splitting (22) gives: % 152.43/22.69 | | % 152.43/22.69 | | Case 1: % 152.43/22.69 | | | % 152.43/22.69 | | | (23) all_56_6 = e0 % 152.43/22.69 | | | % 152.43/22.69 | | | COMBINE_EQS: (10), (23) imply: % 152.43/22.69 | | | (24) all_52_2 = e0 % 152.43/22.69 | | | % 152.43/22.69 | | | REDUCE: (3), (24) imply: % 152.43/22.69 | | | (25) $false % 152.43/22.69 | | | % 152.43/22.69 | | | CLOSE: (25) is inconsistent. % 152.43/22.69 | | | % 152.43/22.69 | | Case 2: % 152.43/22.69 | | | % 152.43/22.69 | | | (26) all_56_12 = e0 % 152.43/22.69 | | | % 152.43/22.69 | | | COMBINE_EQS: (6), (26) imply: % 152.43/22.69 | | | (27) all_52_3 = e0 % 152.43/22.69 | | | % 152.43/22.69 | | | SIMP: (27) implies: % 152.43/22.69 | | | (28) all_52_3 = e0 % 152.43/22.69 | | | % 152.43/22.69 | | | REDUCE: (7), (28) imply: % 152.43/22.69 | | | (29) ~ (all_52_7 = e0) % 152.43/22.69 | | | % 152.43/22.69 | | | SIMP: (29) implies: % 152.43/22.69 | | | (30) ~ (all_52_7 = e0) % 152.43/22.69 | | | % 152.43/22.69 | | | REF_CLOSE: (1), (2), (5), (8), (9), (11), (12), (13), (14), (17), (18), % 152.43/22.69 | | | (30) are inconsistent by sub-proof #147. % 152.43/22.69 | | | % 152.43/22.69 | | End of split % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #119 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) all_58_31 = all_4_2 % 152.43/22.69 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (3) all_56_15 = all_4_2 % 152.43/22.69 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 (5) op(e2, e2) = all_8_2 % 152.43/22.69 (6) all_58_28 = e1 % 152.43/22.69 (7) all_58_29 = all_8_2 % 152.43/22.69 (8) all_58_30 = e0 % 152.43/22.69 (9) ~ (e2 = e1) % 152.43/22.69 (10) op(all_8_2, e2) = e0 % 152.43/22.69 (11) ~ (e2 = e0) % 152.43/22.69 (12) all_56_15 = e1 % 152.43/22.69 (13) ~ (all_8_2 = e0) % 152.43/22.69 (14) op(e2, all_8_2) = all_58_9 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | COMBINE_EQS: (3), (12) imply: % 152.43/22.69 | (15) all_4_2 = e1 % 152.43/22.69 | % 152.43/22.69 | SIMP: (15) implies: % 152.43/22.69 | (16) all_4_2 = e1 % 152.43/22.69 | % 152.43/22.69 | COMBINE_EQS: (1), (16) imply: % 152.43/22.69 | (17) all_58_31 = e1 % 152.43/22.69 | % 152.43/22.69 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (17) are % 152.43/22.69 | inconsistent by sub-proof #120. % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #120 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) all_58_31 = e1 % 152.43/22.69 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 (4) op(e2, e2) = all_8_2 % 152.43/22.69 (5) all_58_28 = e1 % 152.43/22.69 (6) all_58_29 = all_8_2 % 152.43/22.69 (7) all_58_30 = e0 % 152.43/22.69 (8) ~ (e2 = e1) % 152.43/22.69 (9) op(all_8_2, e2) = e0 % 152.43/22.69 (10) ~ (e2 = e0) % 152.43/22.69 (11) ~ (all_8_2 = e0) % 152.43/22.69 (12) op(e2, all_8_2) = all_58_9 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (3) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (13) all_58_28 = e2 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #856. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (14) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (14) are % 152.43/22.69 | | inconsistent by sub-proof #121. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #121 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) all_58_31 = e1 % 152.43/22.69 (3) op(e2, e2) = all_8_2 % 152.43/22.69 (4) all_58_29 = all_8_2 % 152.43/22.69 (5) all_58_30 = e0 % 152.43/22.69 (6) ~ (e2 = e1) % 152.43/22.69 (7) op(all_8_2, e2) = e0 % 152.43/22.69 (8) ~ (e2 = e0) % 152.43/22.69 (9) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 (10) ~ (all_8_2 = e0) % 152.43/22.69 (11) op(e2, all_8_2) = all_58_9 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (9) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (12) all_58_29 = e2 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (4), (12) imply: % 152.43/22.69 | | (13) all_8_2 = e2 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (3), (7), (8), (11), (13) are inconsistent by sub-proof % 152.43/22.69 | | #153. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (14) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 | | % 152.43/22.69 | | BETA: splitting (14) gives: % 152.43/22.69 | | % 152.43/22.69 | | Case 1: % 152.43/22.69 | | | % 152.43/22.69 | | | (15) all_58_30 = e2 % 152.43/22.69 | | | % 152.43/22.69 | | | REF_CLOSE: (5), (8), (15) are inconsistent by sub-proof #718. % 152.43/22.69 | | | % 152.43/22.69 | | Case 2: % 152.43/22.69 | | | % 152.43/22.69 | | | (16) all_58_31 = e2 % 152.43/22.69 | | | % 152.43/22.69 | | | REF_CLOSE: (2), (6), (16) are inconsistent by sub-proof #697. % 152.43/22.69 | | | % 152.43/22.69 | | End of split % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #122 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ~ (all_52_8 = all_52_9) % 152.43/22.69 (2) all_54_2 = all_52_8 % 152.43/22.69 (3) all_54_6 = all_52_9 % 152.43/22.69 (4) ~ (all_52_8 = e3) % 152.43/22.69 (5) ~ (all_52_9 = e3) % 152.43/22.69 (6) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.69 (7) ~ (all_52_8 = e1) % 152.43/22.69 (8) all_54_6 = e3 | all_54_6 = e2 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (8) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (9) all_54_6 = e2 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (3), (9) imply: % 152.43/22.69 | | (10) all_52_9 = e2 % 152.43/22.69 | | % 152.43/22.69 | | REDUCE: (1), (10) imply: % 152.43/22.69 | | (11) ~ (all_52_8 = e2) % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (2), (4), (6), (7), (11) are inconsistent by sub-proof #554. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (12) all_54_6 = e3 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (3), (12) imply: % 152.43/22.69 | | (13) all_52_9 = e3 % 152.43/22.69 | | % 152.43/22.69 | | REDUCE: (5), (13) imply: % 152.43/22.69 | | (14) $false % 152.43/22.69 | | % 152.43/22.69 | | CLOSE: (14) is inconsistent. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #123 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) op(e2, e2) = all_8_2 % 152.43/22.69 (3) all_58_29 = all_8_2 % 152.43/22.69 (4) all_58_30 = e0 % 152.43/22.69 (5) op(all_8_2, e2) = e0 % 152.43/22.69 (6) all_58_31 = e3 % 152.43/22.69 (7) ~ (e2 = e0) % 152.43/22.69 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 (9) ~ (e3 = e2) % 152.43/22.69 (10) ~ (all_8_2 = e0) % 152.43/22.69 (11) op(e2, all_8_2) = all_58_9 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (8) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (12) all_58_29 = e2 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (3), (12) imply: % 152.43/22.69 | | (13) all_8_2 = e2 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (2), (5), (7), (11), (13) are inconsistent by sub-proof % 152.43/22.69 | | #153. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (14) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (4), (6), (7), (9), (14) are inconsistent by sub-proof #705. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #124 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) op(e3, e2) = e0 % 152.43/22.69 (3) op(e3, all_52_4) = all_58_1 % 152.43/22.69 (4) op(e3, e2) = all_52_4 % 152.43/22.69 (5) all_52_4 = e2 % 152.43/22.69 (6) ~ (all_52_4 = e0) % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | REDUCE: (5), (6) imply: % 152.43/22.69 | (7) ~ (e2 = e0) % 152.43/22.69 | % 152.43/22.69 | REDUCE: (3), (5) imply: % 152.43/22.69 | (8) op(e3, e2) = all_58_1 % 152.43/22.69 | % 152.43/22.69 | REDUCE: (4), (5) imply: % 152.43/22.69 | (9) op(e3, e2) = e2 % 152.43/22.69 | % 152.43/22.69 | REF_CLOSE: (1), (2), (7), (8), (9) are inconsistent by sub-proof #143. % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #125 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.69 (3) all_56_5 = all_52_9 % 152.43/22.69 (4) ~ (all_52_13 = e0) % 152.43/22.69 (5) ~ (all_52_9 = e0) % 152.43/22.69 (6) all_56_3 = all_8_2 % 152.43/22.69 (7) op(all_8_2, e2) = e0 % 152.43/22.69 (8) all_56_2 = all_52_1 % 152.43/22.69 (9) all_56_10 = all_52_13 % 152.43/22.69 (10) ~ (all_52_1 = e0) % 152.43/22.69 (11) ~ (all_52_7 = all_8_2) % 152.43/22.69 (12) op(e0, e2) = all_52_7 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (2) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (13) all_56_2 = e0 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (8), (13) imply: % 152.43/22.69 | | (14) all_52_1 = e0 % 152.43/22.69 | | % 152.43/22.69 | | REDUCE: (10), (14) imply: % 152.43/22.69 | | (15) $false % 152.43/22.69 | | % 152.43/22.69 | | CLOSE: (15) is inconsistent. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (16) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (12), (16) are % 152.43/22.69 | | inconsistent by sub-proof #126. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #126 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.69 (3) all_56_5 = all_52_9 % 152.43/22.69 (4) ~ (all_52_13 = e0) % 152.43/22.69 (5) ~ (all_52_9 = e0) % 152.43/22.69 (6) all_56_3 = all_8_2 % 152.43/22.69 (7) op(all_8_2, e2) = e0 % 152.43/22.69 (8) all_56_10 = all_52_13 % 152.43/22.69 (9) ~ (all_52_7 = all_8_2) % 152.43/22.69 (10) op(e0, e2) = all_52_7 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (2) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (11) all_56_3 = e0 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (6), (7), (9), (10), (11) are inconsistent by sub-proof % 152.43/22.69 | | #149. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (12) all_56_5 = e0 | all_56_10 = e0 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (3), (4), (5), (8), (12) are inconsistent by sub-proof #574. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #127 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) all_58_31 = all_4_2 % 152.43/22.69 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 (4) op(e2, e2) = all_8_2 % 152.43/22.69 (5) op(e1, e2) = all_52_6 % 152.43/22.69 (6) ~ (all_52_6 = e0) % 152.43/22.69 (7) ~ (all_52_1 = all_8_2) % 152.43/22.69 (8) all_58_29 = all_8_2 % 152.43/22.69 (9) all_58_30 = e0 % 152.43/22.69 (10) ~ (e2 = e1) % 152.43/22.69 (11) op(all_8_2, e2) = e0 % 152.43/22.69 (12) all_56_2 = e0 % 152.43/22.69 (13) all_56_2 = all_52_1 % 152.43/22.69 (14) ~ (e2 = e0) % 152.43/22.69 (15) all_58_31 = e0 % 152.43/22.69 (16) ~ (e1 = e0) % 152.43/22.69 (17) ~ (all_4_2 = e1) % 152.43/22.69 (18) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.69 (19) op(e2, all_8_2) = all_58_9 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | COMBINE_EQS: (12), (13) imply: % 152.43/22.69 | (20) all_52_1 = e0 % 152.43/22.69 | % 152.43/22.69 | REDUCE: (7), (20) imply: % 152.43/22.69 | (21) ~ (all_8_2 = e0) % 152.43/22.69 | % 152.43/22.69 | SIMP: (21) implies: % 152.43/22.69 | (22) ~ (all_8_2 = e0) % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (18) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (23) all_58_28 = e1 % 152.43/22.69 | | % 152.43/22.69 | | BETA: splitting (3) gives: % 152.43/22.69 | | % 152.43/22.69 | | Case 1: % 152.43/22.69 | | | % 152.43/22.69 | | | (24) all_58_28 = e2 % 152.43/22.69 | | | % 152.43/22.69 | | | COMBINE_EQS: (23), (24) imply: % 152.43/22.69 | | | (25) e2 = e1 % 152.43/22.69 | | | % 152.43/22.69 | | | REDUCE: (10), (25) imply: % 152.43/22.69 | | | (26) $false % 152.43/22.69 | | | % 152.43/22.69 | | | CLOSE: (26) is inconsistent. % 152.43/22.69 | | | % 152.43/22.69 | | Case 2: % 152.43/22.69 | | | % 152.43/22.69 | | | (27) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 | | | % 152.43/22.69 | | | BETA: splitting (27) gives: % 152.43/22.69 | | | % 152.43/22.69 | | | Case 1: % 152.43/22.69 | | | | % 152.43/22.69 | | | | (28) all_58_29 = e2 % 152.43/22.69 | | | | % 152.43/22.69 | | | | REF_CLOSE: (2), (4), (8), (11), (19), (22), (28) are inconsistent by % 152.43/22.69 | | | | sub-proof #142. % 152.43/22.69 | | | | % 152.43/22.69 | | | Case 2: % 152.43/22.69 | | | | % 152.43/22.69 | | | | (29) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 | | | | % 152.43/22.69 | | | | BETA: splitting (29) gives: % 152.43/22.69 | | | | % 152.43/22.69 | | | | Case 1: % 152.43/22.69 | | | | | % 152.43/22.69 | | | | | (30) all_58_30 = e2 % 152.43/22.69 | | | | | % 152.43/22.69 | | | | | REF_CLOSE: (9), (14), (30) are inconsistent by sub-proof #718. % 152.43/22.69 | | | | | % 152.43/22.69 | | | | Case 2: % 152.43/22.69 | | | | | % 152.43/22.69 | | | | | (31) all_58_31 = e2 % 152.43/22.69 | | | | | % 152.43/22.69 | | | | | REF_CLOSE: (14), (15), (31) are inconsistent by sub-proof #855. % 152.43/22.69 | | | | | % 152.43/22.69 | | | | End of split % 152.43/22.69 | | | | % 152.43/22.69 | | | End of split % 152.43/22.69 | | | % 152.43/22.69 | | End of split % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (32) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (11), (16), (17), (32) are % 152.43/22.69 | | inconsistent by sub-proof #128. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #128 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) all_58_31 = all_4_2 % 152.43/22.69 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (3) op(e1, e2) = all_52_6 % 152.43/22.69 (4) ~ (all_52_6 = e0) % 152.43/22.69 (5) all_58_29 = all_8_2 % 152.43/22.69 (6) all_58_30 = e0 % 152.43/22.69 (7) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.69 (8) op(all_8_2, e2) = e0 % 152.43/22.69 (9) ~ (e1 = e0) % 152.43/22.69 (10) ~ (all_4_2 = e1) % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | BETA: splitting (7) gives: % 152.43/22.69 | % 152.43/22.69 | Case 1: % 152.43/22.69 | | % 152.43/22.69 | | (11) all_58_29 = e1 % 152.43/22.69 | | % 152.43/22.69 | | COMBINE_EQS: (5), (11) imply: % 152.43/22.69 | | (12) all_8_2 = e1 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (2), (3), (4), (8), (12) are inconsistent by sub-proof #129. % 152.43/22.69 | | % 152.43/22.69 | Case 2: % 152.43/22.69 | | % 152.43/22.69 | | (13) all_58_30 = e1 | all_58_31 = e1 % 152.43/22.69 | | % 152.43/22.69 | | REF_CLOSE: (1), (6), (9), (10), (13) are inconsistent by sub-proof #711. % 152.43/22.69 | | % 152.43/22.69 | End of split % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #129 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (2) op(e1, e2) = all_52_6 % 152.43/22.69 (3) ~ (all_52_6 = e0) % 152.43/22.69 (4) op(all_8_2, e2) = e0 % 152.43/22.69 (5) all_8_2 = e1 % 152.43/22.69 % 152.43/22.69 Begin of proof % 152.43/22.69 | % 152.43/22.69 | REDUCE: (4), (5) imply: % 152.43/22.69 | (6) op(e1, e2) = e0 % 152.43/22.69 | % 152.43/22.69 | GROUND_INST: instantiating (1) with all_52_6, e0, e2, e1, simplifying with % 152.43/22.69 | (2), (6) gives: % 152.43/22.69 | (7) all_52_6 = e0 % 152.43/22.69 | % 152.43/22.69 | REDUCE: (3), (7) imply: % 152.43/22.69 | (8) $false % 152.43/22.69 | % 152.43/22.69 | CLOSE: (8) is inconsistent. % 152.43/22.69 | % 152.43/22.69 End of proof % 152.43/22.69 % 152.43/22.69 Sub-proof #130 shows that the following formulas are inconsistent: % 152.43/22.69 ---------------------------------------------------------------- % 152.43/22.69 (1) ~ (all_52_8 = all_52_9) % 152.43/22.69 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.69 (3) all_56_7 = all_52_6 % 152.43/22.69 (4) ~ (all_52_6 = all_6_2) % 152.43/22.69 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.43/22.69 (6) all_54_2 = all_52_8 % 152.43/22.69 (7) all_22_0 = all_8_0 % 152.43/22.69 (8) op(e1, all_6_2) = all_58_18 % 152.43/22.69 (9) op(e3, all_52_4) = all_58_1 % 152.43/22.69 (10) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.43/22.69 (11) ~ (all_52_8 = all_10_2) % 152.43/22.69 (12) all_54_7 = all_52_13 % 152.43/22.69 (13) ~ (all_52_6 = all_8_2) % 152.43/22.69 (14) all_56_4 = all_52_8 % 152.43/22.69 (15) ~ (all_52_4 = all_8_2) % 152.43/22.69 (16) all_54_3 = all_52_12 % 152.43/22.69 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.69 (18) all_54_1 = all_52_4 % 152.43/22.69 (19) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.69 (20) ~ (all_6_2 = e0) % 152.43/22.69 (21) ~ (all_52_4 = all_52_6) % 152.43/22.69 (22) op(e2, e2) = all_8_2 % 152.43/22.69 (23) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.43/22.69 (24) op(all_10_2, all_10_1) = all_10_0 % 152.43/22.69 (25) op(e3, e2) = all_52_4 % 152.43/22.69 (26) ~ (all_52_8 = all_6_2) % 152.43/22.69 (27) ~ (all_52_12 = all_52_13) % 152.43/22.69 (28) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.43/22.69 (29) all_54_5 = all_8_2 % 152.43/22.69 (30) ~ (all_10_2 = e0) % 152.43/22.69 (31) ~ (all_52_2 = all_6_2) % 152.43/22.69 (32) op(e3, e3) = all_10_2 % 152.43/22.69 (33) ~ (all_52_8 = all_52_12) % 152.43/22.69 (34) all_54_9 = all_52_6 % 152.43/22.69 (35) op(e1, e2) = all_52_6 % 152.43/22.69 (36) op(all_10_2, e0) = all_10_0 % 152.43/22.69 (37) ~ (all_52_13 = all_8_2) % 152.43/22.69 (38) op(e1, all_52_6) = all_58_16 % 152.43/22.69 (39) ~ (e3 = e1) % 152.43/22.69 (40) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.43/22.69 (41) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.69 (42) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.43/22.69 (43) all_56_5 = all_52_9 % 152.43/22.69 (44) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.69 (45) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.43/22.69 (46) all_56_12 = all_52_3 % 152.43/22.69 (47) ~ (all_52_12 = e0) % 152.43/22.69 (48) ~ (all_52_3 = all_52_7) % 152.43/22.69 (49) all_56_11 = all_52_14 % 152.43/22.69 (50) all_56_1 = all_52_4 % 152.43/22.69 (51) ~ (all_52_13 = e0) % 152.43/22.69 (52) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.69 (53) op(e1, e0) = all_52_14 % 152.43/22.69 (54) ~ (all_52_1 = all_8_2) % 152.43/22.69 (55) all_56_3 = all_8_2 % 152.43/22.69 (56) ~ (all_52_4 = all_52_8) % 152.43/22.70 (57) op(e1, all_52_2) = all_58_14 % 152.43/22.70 (58) ~ (all_10_0 = e0) % 152.43/22.70 (59) all_56_9 = all_52_12 % 152.43/22.70 (60) all_58_29 = all_8_2 % 152.43/22.70 (61) ~ (e2 = e1) % 152.43/22.70 (62) op(e3, e0) = all_52_12 % 152.43/22.70 (63) all_56_6 = all_52_2 % 152.43/22.70 (64) ~ (all_52_2 = all_52_6) % 152.43/22.70 (65) op(all_8_2, e2) = e0 % 152.43/22.70 (66) all_56_13 = all_52_7 % 152.43/22.70 (67) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.70 (68) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.43/22.70 (69) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.70 (70) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.70 (71) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.70 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.70 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.70 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.70 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.70 (all_58_27 = e0)) % 152.43/22.70 (72) ~ (all_52_9 = all_52_13) % 152.43/22.70 (73) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.70 (74) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.70 (75) op(e2, all_52_9) = all_58_10 % 152.43/22.70 (76) op(e3, all_10_2) = all_58_0 % 152.43/22.70 (77) ~ (e3 = e0) % 152.43/22.70 (78) all_56_2 = all_52_1 % 152.43/22.70 (79) op(e3, all_52_12) = all_58_5 % 152.43/22.70 (80) all_56_10 = all_52_13 % 152.43/22.70 (81) ~ (all_52_12 = all_10_2) % 152.43/22.70 (82) ~ (all_52_1 = all_52_3) % 152.43/22.70 (83) ~ (all_52_9 = all_8_2) % 152.43/22.70 (84) all_56_14 = all_52_11 % 152.43/22.70 (85) all_58_28 = all_10_2 % 152.43/22.70 (86) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.70 (87) op(all_8_2, e0) = all_8_0 % 152.43/22.70 (88) ~ (all_52_1 = all_52_9) % 152.43/22.70 (89) op(e3, e1) = all_52_8 % 152.43/22.70 (90) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.70 (91) all_56_15 = e0 % 152.43/22.70 (92) ~ (e2 = e0) % 152.43/22.70 (93) ~ (all_52_2 = all_10_2) % 152.43/22.70 (94) all_56_0 = all_10_2 % 152.43/22.70 (95) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 152.43/22.70 (96) all_58_31 = e0 % 152.43/22.70 (97) ~ (all_52_3 = all_52_11) % 152.43/22.70 (98) all_56_8 = all_6_2 % 152.43/22.70 (99) op(e1, e1) = all_6_2 % 152.43/22.70 (100) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.43/22.70 (101) ~ (all_52_1 = all_52_2) % 152.43/22.70 (102) all_58_27 = e0 % 152.43/22.70 (103) ~ (all_52_7 = all_8_2) % 152.43/22.70 (104) op(e2, e0) = all_52_13 % 152.43/22.70 (105) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.43/22.70 (106) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.70 (107) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.70 (108) all_54_0 = all_10_2 % 152.43/22.70 (109) ~ (all_52_2 = all_52_14) % 152.43/22.70 (110) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.43/22.70 (111) ~ (all_52_7 = e0) % 152.43/22.70 (112) all_22_2 = all_8_2 % 152.43/22.70 (113) ~ (e1 = e0) % 152.43/22.70 (114) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.70 (115) ~ (all_52_14 = e0) % 152.43/22.70 (116) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.43/22.70 (117) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.70 (118) op(e0, e2) = all_52_7 % 152.43/22.70 (119) ~ (all_52_4 = all_10_2) % 152.43/22.70 (120) all_58_30 = all_6_2 % 152.43/22.70 (121) op(e2, all_52_1) = all_58_7 % 152.43/22.70 (122) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.70 (123) ~ (e3 = e2) % 152.43/22.70 (124) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.70 (125) ~ (all_52_14 = all_6_2) % 152.43/22.70 (126) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.43/22.70 (127) op(all_10_2, e3) = all_10_1 % 152.43/22.70 (128) ~ (all_52_4 = all_52_12) % 152.43/22.70 (129) op(e2, all_8_2) = all_58_9 % 152.43/22.70 (130) all_54_4 = all_52_1 % 152.43/22.70 (131) ~ (all_52_1 = all_10_2) % 152.43/22.70 % 152.43/22.70 Begin of proof % 152.43/22.70 | % 152.43/22.70 | BETA: splitting (44) gives: % 152.43/22.70 | % 152.43/22.70 | Case 1: % 152.43/22.70 | | % 152.43/22.70 | | (132) all_56_0 = e0 % 152.43/22.70 | | % 152.43/22.70 | | REF_CLOSE: (30), (94), (132) are inconsistent by sub-proof #799. % 152.43/22.70 | | % 152.43/22.70 | Case 2: % 152.43/22.70 | | % 152.43/22.70 | | (133) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.70 | | % 152.43/22.70 | | BETA: splitting (110) gives: % 152.43/22.70 | | % 152.43/22.70 | | Case 1: % 152.43/22.70 | | | % 152.43/22.70 | | | (134) all_56_6 = e0 % 152.43/22.70 | | | % 152.43/22.70 | | | COMBINE_EQS: (63), (134) imply: % 152.43/22.70 | | | (135) all_52_2 = e0 % 152.43/22.70 | | | % 152.43/22.70 | | | SIMP: (135) implies: % 152.43/22.70 | | | (136) all_52_2 = e0 % 152.43/22.70 | | | % 152.43/22.70 | | | REDUCE: (101), (136) imply: % 152.43/22.70 | | | (137) ~ (all_52_1 = e0) % 152.43/22.70 | | | % 152.43/22.70 | | | REDUCE: (64), (136) imply: % 152.43/22.70 | | | (138) ~ (all_52_6 = e0) % 152.43/22.70 | | | % 152.43/22.70 | | | SIMP: (138) implies: % 152.43/22.70 | | | (139) ~ (all_52_6 = e0) % 152.43/22.70 | | | % 152.43/22.70 | | | REDUCE: (57), (136) imply: % 152.43/22.70 | | | (140) op(e1, e0) = all_58_14 % 152.43/22.70 | | | % 152.43/22.70 | | | GROUND_INST: instantiating (2) with all_52_14, all_58_14, e0, e1, % 152.43/22.70 | | | simplifying with (53), (140) gives: % 152.43/22.70 | | | (141) all_58_14 = all_52_14 % 152.43/22.70 | | | % 152.43/22.70 | | | BETA: splitting (133) gives: % 152.43/22.70 | | | % 152.43/22.70 | | | Case 1: % 152.43/22.70 | | | | % 152.43/22.70 | | | | (142) all_56_1 = e0 % 152.43/22.70 | | | | % 152.43/22.70 | | | | COMBINE_EQS: (50), (142) imply: % 152.43/22.70 | | | | (143) all_52_4 = e0 % 152.43/22.70 | | | | % 152.43/22.70 | | | | REDUCE: (128), (143) imply: % 152.43/22.70 | | | | (144) ~ (all_52_12 = e0) % 152.43/22.70 | | | | % 152.43/22.70 | | | | REDUCE: (119), (143) imply: % 152.43/22.70 | | | | (145) ~ (all_10_2 = e0) % 152.43/22.70 | | | | % 152.43/22.70 | | | | REDUCE: (15), (143) imply: % 152.43/22.70 | | | | (146) ~ (all_8_2 = e0) % 152.43/22.70 | | | | % 152.43/22.70 | | | | SIMP: (146) implies: % 152.43/22.70 | | | | (147) ~ (all_8_2 = e0) % 152.43/22.70 | | | | % 152.43/22.70 | | | | REDUCE: (9), (143) imply: % 152.43/22.70 | | | | (148) op(e3, e0) = all_58_1 % 152.43/22.70 | | | | % 152.43/22.70 | | | | BETA: splitting (19) gives: % 152.43/22.70 | | | | % 152.43/22.70 | | | | Case 1: % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | (149) all_56_2 = e0 % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | COMBINE_EQS: (78), (149) imply: % 152.43/22.70 | | | | | (150) all_52_1 = e0 % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | REDUCE: (137), (150) imply: % 152.43/22.70 | | | | | (151) $false % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | CLOSE: (151) is inconsistent. % 152.43/22.70 | | | | | % 152.43/22.70 | | | | Case 2: % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | (152) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | BETA: splitting (152) gives: % 152.43/22.70 | | | | | % 152.43/22.70 | | | | | Case 1: % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | (153) all_56_3 = e0 % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | COMBINE_EQS: (55), (153) imply: % 152.43/22.70 | | | | | | (154) all_8_2 = e0 % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | REDUCE: (147), (154) imply: % 152.43/22.70 | | | | | | (155) $false % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | CLOSE: (155) is inconsistent. % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | Case 2: % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | (156) all_56_5 = e0 | all_56_10 = e0 % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | BETA: splitting (156) gives: % 152.43/22.70 | | | | | | % 152.43/22.70 | | | | | | Case 1: % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | (157) all_56_5 = e0 % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | COMBINE_EQS: (43), (157) imply: % 152.43/22.70 | | | | | | | (158) all_52_9 = e0 % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | SIMP: (158) implies: % 152.43/22.70 | | | | | | | (159) all_52_9 = e0 % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | REDUCE: (1), (159) imply: % 152.43/22.70 | | | | | | | (160) ~ (all_52_8 = e0) % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | REDUCE: (72), (159) imply: % 152.43/22.70 | | | | | | | (161) ~ (all_52_13 = e0) % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | REDUCE: (75), (159) imply: % 152.43/22.70 | | | | | | | (162) op(e2, e0) = all_58_10 % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | GROUND_INST: instantiating (2) with all_52_13, all_58_10, e0, e2, % 152.43/22.70 | | | | | | | simplifying with (104), (162) gives: % 152.43/22.70 | | | | | | | (163) all_58_10 = all_52_13 % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | GROUND_INST: instantiating (2) with all_52_12, all_58_1, e0, e3, % 152.43/22.70 | | | | | | | simplifying with (62), (148) gives: % 152.43/22.70 | | | | | | | (164) all_58_1 = all_52_12 % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | BETA: splitting (126) gives: % 152.43/22.70 | | | | | | | % 152.43/22.70 | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | % 152.43/22.70 | | | | | | | | (165) all_54_7 = e0 % 152.43/22.70 | | | | | | | | % 152.43/22.70 | | | | | | | | REF_CLOSE: (12), (51), (165) are inconsistent by sub-proof #742. % 152.43/22.70 | | | | | | | | % 152.43/22.70 | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | % 152.43/22.70 | | | | | | | | (166) ~ (all_54_7 = e0) % 152.43/22.70 | | | | | | | | (167) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 152.43/22.70 | | | | | | | | % 152.43/22.70 | | | | | | | | BETA: splitting (42) gives: % 152.43/22.70 | | | | | | | | % 152.43/22.70 | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | % 152.43/22.70 | | | | | | | | | (168) all_54_0 = e0 % 152.43/22.70 | | | | | | | | | % 152.43/22.70 | | | | | | | | | REF_CLOSE: (30), (108), (168) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | #861. % 152.43/22.70 | | | | | | | | | % 152.43/22.70 | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | % 152.43/22.70 | | | | | | | | | (169) ~ (all_54_0 = e0) % 152.43/22.70 | | | | | | | | | (170) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 152.43/22.70 | | | | | | | | | % 152.43/22.70 | | | | | | | | | BETA: splitting (5) gives: % 152.43/22.70 | | | | | | | | | % 152.43/22.70 | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | (171) all_54_3 = e0 % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | COMBINE_EQS: (16), (171) imply: % 152.43/22.70 | | | | | | | | | | (172) all_52_12 = e0 % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | REDUCE: (47), (172) imply: % 152.43/22.70 | | | | | | | | | | (173) $false % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | CLOSE: (173) is inconsistent. % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | (174) ~ (all_54_3 = e0) % 152.43/22.70 | | | | | | | | | | (175) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | BETA: splitting (116) gives: % 152.43/22.70 | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | (176) all_54_2 = e0 % 152.43/22.70 | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | REF_CLOSE: (6), (160), (176) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | #860. % 152.43/22.70 | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | (177) ~ (all_54_2 = e0) % 152.43/22.70 | | | | | | | | | | | (178) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.70 | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | BETA: splitting (40) gives: % 152.43/22.70 | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | (179) all_54_9 = e0 % 152.43/22.70 | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | REF_CLOSE: (34), (139), (179) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | #572. % 152.43/22.70 | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | (180) ~ (all_54_9 = e0) % 152.43/22.70 | | | | | | | | | | | | (181) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.70 | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | BETA: splitting (68) gives: % 152.43/22.70 | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | (182) all_54_4 = e0 % 152.43/22.70 | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | REF_CLOSE: (130), (137), (182) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | #859. % 152.43/22.70 | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | (183) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.43/22.70 | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | BETA: splitting (45) gives: % 152.43/22.70 | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | (184) all_54_5 = e0 % 152.43/22.70 | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | REF_CLOSE: (29), (147), (184) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | #158. % 152.43/22.70 | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | (185) ~ (all_54_5 = e0) % 152.43/22.70 | | | | | | | | | | | | | | (186) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 152.43/22.70 | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | BETA: splitting (23) gives: % 152.43/22.70 | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | (187) all_56_0 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | COMBINE_EQS: (94), (187) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (188) all_10_2 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (188) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (189) all_58_28 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | REDUCE: (131), (188) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (190) ~ (all_52_1 = e1) % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | REDUCE: (11), (188) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (191) ~ (all_52_8 = e1) % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | REDUCE: (81), (188) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (192) ~ (all_52_12 = e1) % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | REDUCE: (36), (188) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (193) op(e1, e0) = all_10_0 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_14, all_10_0, e0, % 152.43/22.70 | | | | | | | | | | | | | | | e1, simplifying with (53), (193) gives: % 152.43/22.70 | | | | | | | | | | | | | | | (194) all_52_14 = all_10_0 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | COMBINE_EQS: (49), (194) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (195) all_56_11 = all_10_0 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | COMBINE_EQS: (141), (194) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (196) all_58_14 = all_10_0 % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | (197) all_56_2 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | REF_CLOSE: (78), (190), (197) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | | | #450. % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | (198) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | (199) all_56_0 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (199) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | (200) e3 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | REDUCE: (39), (200) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | (201) $false % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent. % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | (202) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | BETA: splitting (10) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | (203) all_56_9 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (203) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | (204) all_52_12 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | SIMP: (204) implies: % 152.43/22.70 | | | | | | | | | | | | | | | | | | (205) all_52_12 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (205) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | (206) all_58_1 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | REDUCE: (33), (205) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | (207) ~ (all_52_8 = e2) % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | (208) all_56_1 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (208) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | (209) e3 = e0 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | REDUCE: (77), (209) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | (210) $false % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | (211) all_56_4 = e3 | all_56_9 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | (212) all_56_4 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (212) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | (213) all_52_8 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | SIMP: (213) implies: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | (214) all_52_8 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (214) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | (215) ~ (all_6_2 = e3) % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | SIMP: (215) implies: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | (216) ~ (all_6_2 = e3) % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | (217) all_58_28 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (217) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | (218) e3 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (218) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | (219) $false % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_58_28 = e3) % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | (221) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (220) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | (222) ~ (e3 = e1) % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | (223) all_58_29 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (223) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | (224) all_8_2 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | SIMP: (224) implies: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | (225) all_8_2 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (225) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | (226) all_56_3 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (225) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_52_6 = e3) % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | (228) all_56_6 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (134), (228) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | #839. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | (229) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_28 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (230) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | (231) e2 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (231) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | (232) $false % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_56_3 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (226), (234) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | #449. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_56_5 = e1 | all_56_10 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_56_5 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (236) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (237) e1 = e0 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (237) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (238) $false % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_56_10 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (239) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_52_13 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (240) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_58_10 = e1 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_29 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (223), (242) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) ~ (all_58_29 = e2) % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_56_7 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (245) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_52_6 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (227), (246) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) $false % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_56_8 = e3 | all_56_11 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_56_8 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (249) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_6_2 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (250) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_58_30 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (96), (123), (244), (251) are inconsistent % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #854. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_56_11 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (252) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_10_0 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (253) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_14 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (102), (206), (241), (254) are inconsistent % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #778. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | (255) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (96), (120), (216), (255) are inconsistent % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #768. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | (256) all_56_9 = e3 % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (203), (256) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | #415. % 152.43/22.70 | | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | (257) ~ (all_56_9 = e2) % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (16), (17), (22), (26), (33), (59), % 152.43/22.70 | | | | | | | | | | | | | | | | | | (60), (61), (65), (96), (120), (129), (147), % 152.43/22.70 | | | | | | | | | | | | | | | | | | (160), (175), (178), (189), (191), (192), (257) % 152.43/22.70 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #131. % 152.43/22.70 | | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | End of split % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | (258) ~ (all_56_0 = e1) % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | REDUCE: (94), (258) imply: % 152.43/22.70 | | | | | | | | | | | | | | | (259) ~ (all_10_2 = e1) % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | BETA: splitting (86) gives: % 152.43/22.70 | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | (260) all_56_0 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (260) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | (261) all_10_2 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (261) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | (262) all_58_28 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | REDUCE: (81), (261) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | (263) ~ (all_52_12 = e2) % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (13), (14), (16), (26), (33), (34), % 152.43/22.70 | | | | | | | | | | | | | | | | (35), (38), (39), (47), (59), (60), (61), (62), % 152.43/22.70 | | | | | | | | | | | | | | | | (65), (67), (70), (77), (87), (92), (96), (106), % 152.43/22.70 | | | | | | | | | | | | | | | | (107), (113), (114), (120), (122), (123), (124), % 152.43/22.70 | | | | | | | | | | | | | | | | (134), (139), (142), (160), (175), (181), (260), % 152.43/22.70 | | | | | | | | | | | | | | | | (262), (263) are inconsistent by sub-proof #154. % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | (264) ~ (all_56_0 = e2) % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | REDUCE: (94), (264) imply: % 152.43/22.70 | | | | | | | | | | | | | | | | (265) ~ (all_10_2 = e2) % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 152.43/22.70 | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | (266) all_58_28 = e2 % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (265), (266) are inconsistent by sub-proof % 152.43/22.70 | | | | | | | | | | | | | | | | | #388. % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.70 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.70 | | | | | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | | | | | | (267) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.71 | | | | | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (11), (12), (13), (16), % 152.43/22.71 | | | | | | | | | | | | | | | | | (22), (24), (26), (27), (29), (32), (33), (34), % 152.43/22.71 | | | | | | | | | | | | | | | | | (35), (37), (41), (47), (49), (51), (54), (55), % 152.43/22.71 | | | | | | | | | | | | | | | | | (58), (59), (60), (65), (70), (71), (74), (76), % 152.43/22.71 | | | | | | | | | | | | | | | | | (78), (80), (81), (91), (92), (96), (102), (108), % 152.43/22.71 | | | | | | | | | | | | | | | | | (117), (120), (127), (129), (130), (134), (139), % 152.43/22.71 | | | | | | | | | | | | | | | | | (141), (147), (160), (163), (167), (170), (175), % 152.43/22.71 | | | | | | | | | | | | | | | | | (178), (181), (183), (186), (259), (265), (267) % 152.43/22.71 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #150. % 152.43/22.71 | | | | | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | | % 152.43/22.71 | | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | | % 152.43/22.71 | | | | | | | | | End of split % 152.43/22.71 | | | | | | | | | % 152.43/22.71 | | | | | | | | End of split % 152.43/22.71 | | | | | | | | % 152.43/22.71 | | | | | | | End of split % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | Case 2: % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | (268) all_56_10 = e0 % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | COMBINE_EQS: (80), (268) imply: % 152.43/22.71 | | | | | | | (269) all_52_13 = e0 % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | REDUCE: (51), (269) imply: % 152.43/22.71 | | | | | | | (270) $false % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | CLOSE: (270) is inconsistent. % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | End of split % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | End of split % 152.43/22.71 | | | | | % 152.43/22.71 | | | | End of split % 152.43/22.71 | | | | % 152.43/22.71 | | | Case 2: % 152.43/22.71 | | | | % 152.43/22.71 | | | | (271) ~ (all_56_1 = e0) % 152.43/22.71 | | | | % 152.43/22.71 | | | | REDUCE: (50), (271) imply: % 152.43/22.71 | | | | (272) ~ (all_52_4 = e0) % 152.43/22.71 | | | | % 152.43/22.71 | | | | REF_CLOSE: (2), (3), (50), (55), (65), (66), (73), (103), (111), (118), % 152.43/22.71 | | | | (139), (272) are inconsistent by sub-proof #147. % 152.43/22.71 | | | | % 152.43/22.71 | | | End of split % 152.43/22.71 | | | % 152.43/22.71 | | Case 2: % 152.43/22.71 | | | % 152.43/22.71 | | | (273) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.43/22.71 | | | % 152.43/22.71 | | | REF_CLOSE: (1), (2), (3), (7), (9), (13), (14), (15), (17), (18), (19), % 152.43/22.71 | | | (20), (21), (22), (23), (25), (26), (28), (31), (37), (38), % 152.43/22.71 | | | (39), (43), (46), (47), (48), (49), (50), (51), (52), (53), % 152.43/22.71 | | | (54), (55), (56), (57), (59), (60), (61), (63), (65), (66), % 152.43/22.71 | | | (69), (70), (71), (74), (76), (77), (78), (79), (80), (82), % 152.43/22.71 | | | (83), (84), (85), (86), (87), (89), (90), (91), (92), (93), % 152.43/22.71 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (104), % 152.43/22.71 | | | (105), (107), (109), (112), (113), (115), (117), (119), (120), % 152.43/22.71 | | | (121), (122), (123), (125), (129), (131), (133), (273) are % 152.43/22.71 | | | inconsistent by sub-proof #135. % 152.43/22.71 | | | % 152.43/22.71 | | End of split % 152.43/22.71 | | % 152.43/22.71 | End of split % 152.43/22.71 | % 152.43/22.71 End of proof % 152.43/22.71 % 152.43/22.71 Sub-proof #131 shows that the following formulas are inconsistent: % 152.43/22.71 ---------------------------------------------------------------- % 152.43/22.71 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.71 (2) all_54_2 = all_52_8 % 152.43/22.71 (3) all_54_3 = all_52_12 % 152.43/22.71 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.71 (5) op(e2, e2) = all_8_2 % 152.43/22.71 (6) ~ (all_52_8 = all_6_2) % 152.43/22.71 (7) ~ (all_52_8 = all_52_12) % 152.43/22.71 (8) all_58_28 = e1 % 152.43/22.71 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.71 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.71 (11) all_56_9 = all_52_12 % 152.43/22.71 (12) all_58_29 = all_8_2 % 152.43/22.71 (13) ~ (e2 = e1) % 152.43/22.71 (14) op(all_8_2, e2) = e0 % 152.43/22.71 (15) ~ (all_52_12 = e1) % 152.43/22.71 (16) ~ (all_52_8 = e1) % 152.43/22.71 (17) all_58_31 = e0 % 152.43/22.71 (18) ~ (all_52_8 = e0) % 152.43/22.71 (19) all_58_30 = all_6_2 % 152.43/22.71 (20) ~ (all_56_9 = e2) % 152.43/22.71 (21) ~ (all_8_2 = e0) % 152.43/22.71 (22) op(e2, all_8_2) = all_58_9 % 152.43/22.71 % 152.43/22.71 Begin of proof % 152.43/22.71 | % 152.43/22.71 | REDUCE: (11), (20) imply: % 152.43/22.71 | (23) ~ (all_52_12 = e2) % 152.43/22.71 | % 152.43/22.71 | BETA: splitting (10) gives: % 152.43/22.71 | % 152.43/22.71 | Case 1: % 152.43/22.71 | | % 152.43/22.71 | | (24) all_54_3 = e1 % 152.43/22.71 | | % 152.43/22.71 | | REF_CLOSE: (3), (15), (24) are inconsistent by sub-proof #723. % 152.43/22.71 | | % 152.43/22.71 | Case 2: % 152.43/22.71 | | % 152.43/22.71 | | (25) all_54_3 = e3 | all_54_3 = e2 % 152.43/22.71 | | % 152.43/22.71 | | BETA: splitting (25) gives: % 152.43/22.71 | | % 152.43/22.71 | | Case 1: % 152.43/22.71 | | | % 152.43/22.71 | | | (26) all_54_3 = e2 % 152.43/22.71 | | | % 152.43/22.71 | | | REF_CLOSE: (3), (23), (26) are inconsistent by sub-proof #614. % 152.43/22.71 | | | % 152.43/22.71 | | Case 2: % 152.43/22.71 | | | % 152.43/22.71 | | | (27) all_54_3 = e3 % 152.43/22.71 | | | % 152.43/22.71 | | | COMBINE_EQS: (3), (27) imply: % 152.43/22.71 | | | (28) all_52_12 = e3 % 152.43/22.71 | | | % 152.43/22.71 | | | SIMP: (28) implies: % 152.43/22.71 | | | (29) all_52_12 = e3 % 152.43/22.71 | | | % 152.43/22.71 | | | REDUCE: (7), (29) imply: % 152.43/22.71 | | | (30) ~ (all_52_8 = e3) % 152.43/22.71 | | | % 152.43/22.71 | | | BETA: splitting (4) gives: % 152.43/22.71 | | | % 152.43/22.71 | | | Case 1: % 152.43/22.71 | | | | % 152.43/22.71 | | | | (31) all_58_28 = e2 % 152.43/22.71 | | | | % 152.43/22.71 | | | | COMBINE_EQS: (8), (31) imply: % 152.43/22.71 | | | | (32) e2 = e1 % 152.43/22.71 | | | | % 152.43/22.71 | | | | REDUCE: (13), (32) imply: % 152.43/22.71 | | | | (33) $false % 152.43/22.71 | | | | % 152.43/22.71 | | | | CLOSE: (33) is inconsistent. % 152.43/22.71 | | | | % 152.43/22.71 | | | Case 2: % 152.43/22.71 | | | | % 152.43/22.71 | | | | (34) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.71 | | | | % 152.43/22.71 | | | | REF_CLOSE: (1), (2), (5), (6), (9), (12), (14), (16), (17), (18), (19), % 152.43/22.71 | | | | (21), (22), (30), (34) are inconsistent by sub-proof #152. % 152.43/22.71 | | | | % 152.43/22.71 | | | End of split % 152.43/22.71 | | | % 152.43/22.71 | | End of split % 152.43/22.71 | | % 152.43/22.71 | End of split % 152.43/22.71 | % 152.43/22.71 End of proof % 152.43/22.71 % 152.43/22.71 Sub-proof #132 shows that the following formulas are inconsistent: % 152.43/22.71 ---------------------------------------------------------------- % 152.43/22.71 (1) all_58_31 = all_4_2 % 152.43/22.71 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.71 (3) all_56_15 = all_4_2 % 152.43/22.71 (4) ~ (all_6_2 = e0) % 152.43/22.71 (5) ~ (all_10_2 = e0) % 152.43/22.71 (6) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 152.43/22.71 (7) all_58_29 = all_8_2 % 152.43/22.71 (8) op(all_8_2, e2) = e0 % 152.43/22.71 (9) all_58_28 = all_10_2 % 152.43/22.71 (10) ~ (all_56_15 = e0) % 152.43/22.71 (11) ~ (all_52_7 = all_8_2) % 152.43/22.71 (12) op(e0, e2) = all_52_7 % 152.43/22.71 (13) all_58_30 = all_6_2 % 152.43/22.71 % 152.43/22.71 Begin of proof % 152.43/22.71 | % 152.43/22.71 | REDUCE: (3), (10) imply: % 152.43/22.71 | (14) ~ (all_4_2 = e0) % 152.43/22.71 | % 152.43/22.71 | BETA: splitting (6) gives: % 152.43/22.71 | % 152.43/22.71 | Case 1: % 152.43/22.71 | | % 152.43/22.71 | | (15) all_58_28 = e0 % 152.43/22.71 | | % 152.43/22.71 | | COMBINE_EQS: (9), (15) imply: % 152.43/22.71 | | (16) all_10_2 = e0 % 152.43/22.71 | | % 152.43/22.71 | | REDUCE: (5), (16) imply: % 152.43/22.71 | | (17) $false % 152.43/22.71 | | % 152.43/22.71 | | CLOSE: (17) is inconsistent. % 152.43/22.71 | | % 152.43/22.71 | Case 2: % 152.43/22.71 | | % 152.43/22.71 | | (18) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 152.43/22.71 | | % 152.43/22.71 | | REF_CLOSE: (1), (2), (4), (7), (8), (11), (12), (13), (14), (18) are % 152.43/22.71 | | inconsistent by sub-proof #133. % 152.43/22.71 | | % 152.43/22.71 | End of split % 152.43/22.71 | % 152.43/22.71 End of proof % 152.43/22.71 % 152.43/22.71 Sub-proof #133 shows that the following formulas are inconsistent: % 152.43/22.71 ---------------------------------------------------------------- % 152.43/22.71 (1) all_58_31 = all_4_2 % 152.43/22.71 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.71 (3) ~ (all_6_2 = e0) % 152.43/22.71 (4) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 152.43/22.71 (5) all_58_29 = all_8_2 % 152.43/22.71 (6) op(all_8_2, e2) = e0 % 152.43/22.71 (7) ~ (all_4_2 = e0) % 152.43/22.71 (8) ~ (all_52_7 = all_8_2) % 152.43/22.71 (9) op(e0, e2) = all_52_7 % 152.43/22.71 (10) all_58_30 = all_6_2 % 152.43/22.71 % 152.43/22.71 Begin of proof % 152.43/22.71 | % 152.43/22.71 | BETA: splitting (4) gives: % 152.43/22.71 | % 152.43/22.71 | Case 1: % 152.43/22.71 | | % 152.43/22.71 | | (11) all_58_29 = e0 % 152.43/22.71 | | % 152.43/22.71 | | COMBINE_EQS: (5), (11) imply: % 152.43/22.71 | | (12) all_8_2 = e0 % 152.43/22.71 | | % 152.43/22.71 | | SIMP: (12) implies: % 152.43/22.71 | | (13) all_8_2 = e0 % 152.43/22.71 | | % 152.43/22.71 | | REDUCE: (8), (13) imply: % 152.43/22.71 | | (14) ~ (all_52_7 = e0) % 152.43/22.71 | | % 152.43/22.71 | | REDUCE: (6), (13) imply: % 152.43/22.71 | | (15) op(e0, e2) = e0 % 152.43/22.71 | | % 152.43/22.71 | | GROUND_INST: instantiating (2) with all_52_7, e0, e2, e0, simplifying with % 152.43/22.71 | | (9), (15) gives: % 152.43/22.71 | | (16) all_52_7 = e0 % 152.43/22.71 | | % 152.43/22.71 | | REDUCE: (14), (16) imply: % 152.43/22.71 | | (17) $false % 152.43/22.71 | | % 152.43/22.71 | | CLOSE: (17) is inconsistent. % 152.43/22.71 | | % 152.43/22.71 | Case 2: % 152.43/22.71 | | % 152.43/22.71 | | (18) all_58_30 = e0 | all_58_31 = e0 % 152.43/22.71 | | % 152.43/22.71 | | REF_CLOSE: (1), (3), (7), (10), (18) are inconsistent by sub-proof #217. % 152.43/22.71 | | % 152.43/22.71 | End of split % 152.43/22.71 | % 152.43/22.71 End of proof % 152.43/22.71 % 152.43/22.71 Sub-proof #134 shows that the following formulas are inconsistent: % 152.43/22.71 ---------------------------------------------------------------- % 152.43/22.71 (1) ~ (all_52_8 = all_52_9) % 152.43/22.71 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.71 (3) all_56_7 = all_52_6 % 152.43/22.71 (4) ~ (all_52_6 = all_6_2) % 152.43/22.71 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.43/22.71 (6) all_54_2 = all_52_8 % 152.43/22.71 (7) ~ (all_10_1 = e0) % 152.43/22.71 (8) all_22_0 = all_8_0 % 152.43/22.71 (9) op(e1, all_6_2) = all_58_18 % 152.43/22.71 (10) op(e3, all_52_4) = all_58_1 % 152.43/22.71 (11) ~ (all_52_8 = all_10_2) % 152.43/22.71 (12) all_54_7 = all_52_13 % 152.43/22.71 (13) ~ (all_52_6 = all_8_2) % 152.43/22.71 (14) all_56_4 = all_52_8 % 152.43/22.71 (15) ~ (all_52_4 = all_8_2) % 152.43/22.71 (16) all_54_3 = all_52_12 % 152.43/22.71 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.71 (18) all_54_1 = all_52_4 % 152.43/22.71 (19) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.71 (20) ~ (all_6_2 = e0) % 152.43/22.71 (21) ~ (all_52_4 = all_52_6) % 152.43/22.71 (22) op(e2, e2) = all_8_2 % 152.43/22.71 (23) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.43/22.71 (24) op(all_10_2, all_10_1) = all_10_0 % 152.43/22.71 (25) op(e3, e2) = all_52_4 % 152.43/22.71 (26) ~ (all_52_8 = all_6_2) % 152.43/22.71 (27) ~ (all_52_12 = all_52_13) % 152.43/22.71 (28) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.43/22.71 (29) all_54_5 = all_8_2 % 152.43/22.71 (30) ~ (all_10_2 = e0) % 152.43/22.71 (31) ~ (all_52_2 = all_6_2) % 152.43/22.71 (32) op(e3, e3) = all_10_2 % 152.43/22.71 (33) ~ (all_52_8 = all_52_12) % 152.43/22.71 (34) all_54_9 = all_52_6 % 152.43/22.71 (35) op(e1, e2) = all_52_6 % 152.43/22.71 (36) ~ (all_52_13 = all_8_2) % 152.43/22.71 (37) op(e1, all_52_6) = all_58_16 % 152.43/22.71 (38) ~ (e3 = e1) % 152.43/22.71 (39) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.43/22.71 (40) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.71 (41) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.43/22.71 (42) all_56_5 = all_52_9 % 152.43/22.71 (43) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.71 (44) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 152.43/22.71 (45) all_56_12 = all_52_3 % 152.43/22.71 (46) ~ (all_52_12 = e0) % 152.43/22.71 (47) ~ (all_52_3 = all_52_7) % 152.43/22.71 (48) all_56_11 = all_52_14 % 152.43/22.71 (49) all_56_1 = all_52_4 % 152.43/22.71 (50) ~ (all_52_13 = e0) % 152.43/22.71 (51) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.71 (52) op(e1, e3) = all_52_2 % 152.43/22.71 (53) op(e1, e0) = all_52_14 % 152.43/22.71 (54) ~ (all_52_1 = all_8_2) % 152.43/22.71 (55) all_56_3 = all_8_2 % 152.43/22.71 (56) ~ (all_52_4 = all_52_8) % 152.43/22.71 (57) op(e1, all_52_2) = all_58_14 % 152.43/22.71 (58) ~ (all_10_0 = e0) % 152.43/22.71 (59) all_56_9 = all_52_12 % 152.43/22.71 (60) all_58_29 = all_8_2 % 152.43/22.71 (61) ~ (e2 = e1) % 152.43/22.71 (62) op(e3, e0) = all_52_12 % 152.43/22.71 (63) all_56_6 = all_52_2 % 152.43/22.71 (64) ~ (all_52_2 = all_52_6) % 152.43/22.71 (65) op(all_8_2, e2) = e0 % 152.43/22.71 (66) all_56_13 = all_52_7 % 152.43/22.71 (67) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.71 (68) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.43/22.71 (69) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.71 (70) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.71 (71) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.71 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.71 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.71 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.71 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.71 (all_58_27 = e0)) % 152.43/22.71 (72) ~ (all_52_9 = all_52_13) % 152.43/22.71 (73) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.71 (74) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.71 (75) op(e2, all_52_9) = all_58_10 % 152.43/22.71 (76) op(e3, all_10_2) = all_58_0 % 152.43/22.71 (77) ~ (e3 = e0) % 152.43/22.71 (78) all_56_2 = all_52_1 % 152.43/22.71 (79) op(e3, all_52_12) = all_58_5 % 152.43/22.71 (80) all_56_10 = all_52_13 % 152.43/22.71 (81) ~ (all_52_12 = all_10_2) % 152.43/22.71 (82) ~ (all_52_1 = all_52_3) % 152.43/22.71 (83) ~ (all_52_9 = all_8_2) % 152.43/22.71 (84) all_56_14 = all_52_11 % 152.43/22.71 (85) all_58_28 = all_10_2 % 152.43/22.71 (86) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.71 (87) op(all_8_2, e0) = all_8_0 % 152.43/22.71 (88) ~ (all_52_1 = all_52_9) % 152.43/22.71 (89) op(e3, e1) = all_52_8 % 152.43/22.71 (90) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.71 (91) all_56_15 = e0 % 152.43/22.71 (92) ~ (e2 = e0) % 152.43/22.71 (93) ~ (all_52_2 = all_10_2) % 152.43/22.71 (94) all_56_0 = all_10_2 % 152.43/22.71 (95) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 152.43/22.71 (96) all_58_31 = e0 % 152.43/22.71 (97) ~ (all_52_3 = all_52_11) % 152.43/22.71 (98) all_56_8 = all_6_2 % 152.43/22.71 (99) op(e1, e1) = all_6_2 % 152.43/22.71 (100) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.43/22.71 (101) ~ (all_52_1 = all_52_2) % 152.43/22.71 (102) all_58_27 = e0 % 152.43/22.71 (103) ~ (all_52_7 = all_8_2) % 152.43/22.71 (104) op(e2, e0) = all_52_13 % 152.43/22.71 (105) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.43/22.71 (106) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.71 (107) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.71 (108) all_54_0 = all_10_2 % 152.43/22.71 (109) ~ (all_52_2 = all_52_14) % 152.43/22.71 (110) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.43/22.71 (111) ~ (all_52_7 = e0) % 152.43/22.71 (112) all_22_2 = all_8_2 % 152.43/22.71 (113) ~ (e1 = e0) % 152.43/22.71 (114) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.71 (115) ~ (all_52_14 = e0) % 152.43/22.71 (116) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.43/22.71 (117) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.71 (118) op(e0, e2) = all_52_7 % 152.43/22.71 (119) ~ (all_52_4 = all_10_2) % 152.43/22.71 (120) all_58_30 = all_6_2 % 152.43/22.71 (121) op(e2, all_52_1) = all_58_7 % 152.43/22.71 (122) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.71 (123) ~ (e3 = e2) % 152.43/22.71 (124) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.71 (125) ~ (all_52_14 = all_6_2) % 152.43/22.71 (126) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.43/22.71 (127) op(all_10_2, e3) = all_10_1 % 152.43/22.71 (128) ~ (all_52_4 = all_52_12) % 152.43/22.71 (129) op(e2, all_8_2) = all_58_9 % 152.43/22.71 (130) all_54_4 = all_52_1 % 152.43/22.71 (131) ~ (all_52_1 = all_10_2) % 152.43/22.71 % 152.43/22.71 Begin of proof % 152.43/22.71 | % 152.43/22.71 | BETA: splitting (43) gives: % 152.43/22.71 | % 152.43/22.71 | Case 1: % 152.43/22.71 | | % 152.43/22.71 | | (132) all_56_0 = e0 % 152.43/22.71 | | % 152.43/22.71 | | REF_CLOSE: (30), (94), (132) are inconsistent by sub-proof #799. % 152.43/22.71 | | % 152.43/22.71 | Case 2: % 152.43/22.71 | | % 152.43/22.71 | | (133) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.71 | | % 152.43/22.71 | | BETA: splitting (110) gives: % 152.43/22.71 | | % 152.43/22.71 | | Case 1: % 152.43/22.71 | | | % 152.43/22.71 | | | (134) all_56_6 = e0 % 152.43/22.71 | | | % 152.43/22.71 | | | COMBINE_EQS: (63), (134) imply: % 152.43/22.71 | | | (135) all_52_2 = e0 % 152.43/22.71 | | | % 152.43/22.71 | | | SIMP: (135) implies: % 152.43/22.71 | | | (136) all_52_2 = e0 % 152.43/22.71 | | | % 152.43/22.71 | | | REDUCE: (101), (136) imply: % 152.43/22.71 | | | (137) ~ (all_52_1 = e0) % 152.43/22.71 | | | % 152.43/22.71 | | | REDUCE: (64), (136) imply: % 152.43/22.71 | | | (138) ~ (all_52_6 = e0) % 152.43/22.71 | | | % 152.43/22.71 | | | SIMP: (138) implies: % 152.43/22.71 | | | (139) ~ (all_52_6 = e0) % 152.43/22.71 | | | % 152.43/22.71 | | | REDUCE: (57), (136) imply: % 152.43/22.71 | | | (140) op(e1, e0) = all_58_14 % 152.43/22.71 | | | % 152.43/22.71 | | | REDUCE: (52), (136) imply: % 152.43/22.71 | | | (141) op(e1, e3) = e0 % 152.43/22.71 | | | % 152.43/22.71 | | | GROUND_INST: instantiating (2) with all_52_14, all_58_14, e0, e1, % 152.43/22.71 | | | simplifying with (53), (140) gives: % 152.43/22.71 | | | (142) all_58_14 = all_52_14 % 152.43/22.71 | | | % 152.43/22.71 | | | BETA: splitting (133) gives: % 152.43/22.71 | | | % 152.43/22.71 | | | Case 1: % 152.43/22.71 | | | | % 152.43/22.71 | | | | (143) all_56_1 = e0 % 152.43/22.71 | | | | % 152.43/22.71 | | | | COMBINE_EQS: (49), (143) imply: % 152.43/22.71 | | | | (144) all_52_4 = e0 % 152.43/22.71 | | | | % 152.43/22.71 | | | | REDUCE: (128), (144) imply: % 152.43/22.71 | | | | (145) ~ (all_52_12 = e0) % 152.43/22.71 | | | | % 152.43/22.71 | | | | REDUCE: (119), (144) imply: % 152.43/22.71 | | | | (146) ~ (all_10_2 = e0) % 152.43/22.71 | | | | % 152.43/22.71 | | | | REDUCE: (15), (144) imply: % 152.43/22.71 | | | | (147) ~ (all_8_2 = e0) % 152.43/22.71 | | | | % 152.43/22.71 | | | | SIMP: (147) implies: % 152.43/22.71 | | | | (148) ~ (all_8_2 = e0) % 152.43/22.71 | | | | % 152.43/22.71 | | | | REDUCE: (10), (144) imply: % 152.43/22.71 | | | | (149) op(e3, e0) = all_58_1 % 152.43/22.71 | | | | % 152.43/22.71 | | | | BETA: splitting (19) gives: % 152.43/22.71 | | | | % 152.43/22.71 | | | | Case 1: % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | (150) all_56_2 = e0 % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | COMBINE_EQS: (78), (150) imply: % 152.43/22.71 | | | | | (151) all_52_1 = e0 % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | REDUCE: (137), (151) imply: % 152.43/22.71 | | | | | (152) $false % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | CLOSE: (152) is inconsistent. % 152.43/22.71 | | | | | % 152.43/22.71 | | | | Case 2: % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | (153) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | BETA: splitting (153) gives: % 152.43/22.71 | | | | | % 152.43/22.71 | | | | | Case 1: % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | (154) all_56_3 = e0 % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | COMBINE_EQS: (55), (154) imply: % 152.43/22.71 | | | | | | (155) all_8_2 = e0 % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | REDUCE: (148), (155) imply: % 152.43/22.71 | | | | | | (156) $false % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | CLOSE: (156) is inconsistent. % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | Case 2: % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | (157) all_56_5 = e0 | all_56_10 = e0 % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | BETA: splitting (157) gives: % 152.43/22.71 | | | | | | % 152.43/22.71 | | | | | | Case 1: % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | (158) all_56_5 = e0 % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | COMBINE_EQS: (42), (158) imply: % 152.43/22.71 | | | | | | | (159) all_52_9 = e0 % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | SIMP: (159) implies: % 152.43/22.71 | | | | | | | (160) all_52_9 = e0 % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | REDUCE: (1), (160) imply: % 152.43/22.71 | | | | | | | (161) ~ (all_52_8 = e0) % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | REDUCE: (72), (160) imply: % 152.43/22.71 | | | | | | | (162) ~ (all_52_13 = e0) % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | REDUCE: (75), (160) imply: % 152.43/22.71 | | | | | | | (163) op(e2, e0) = all_58_10 % 152.43/22.71 | | | | | | | % 152.43/22.71 | | | | | | | GROUND_INST: instantiating (2) with all_52_13, all_58_10, e0, e2, % 152.43/22.71 | | | | | | | simplifying with (104), (163) gives: % 152.43/22.72 | | | | | | | (164) all_58_10 = all_52_13 % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | GROUND_INST: instantiating (2) with all_52_12, all_58_1, e0, e3, % 152.43/22.72 | | | | | | | simplifying with (62), (149) gives: % 152.43/22.72 | | | | | | | (165) all_58_1 = all_52_12 % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | BETA: splitting (126) gives: % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | (166) all_54_7 = e0 % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | COMBINE_EQS: (12), (166) imply: % 152.43/22.72 | | | | | | | | (167) all_52_13 = e0 % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | REDUCE: (50), (167) imply: % 152.43/22.72 | | | | | | | | (168) $false % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | CLOSE: (168) is inconsistent. % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | (169) ~ (all_54_7 = e0) % 152.43/22.72 | | | | | | | | (170) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | BETA: splitting (41) gives: % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | | (171) all_54_0 = e0 % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | | REF_CLOSE: (30), (108), (171) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | #861. % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | | (172) ~ (all_54_0 = e0) % 152.43/22.72 | | | | | | | | | (173) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | | BETA: splitting (39) gives: % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | (174) all_54_9 = e0 % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | REF_CLOSE: (34), (139), (174) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | | #572. % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | (175) ~ (all_54_9 = e0) % 152.43/22.72 | | | | | | | | | | (176) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | BETA: splitting (68) gives: % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | (177) all_54_4 = e0 % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | REF_CLOSE: (130), (137), (177) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | | | #859. % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | (178) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | BETA: splitting (5) gives: % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | (179) all_54_3 = e0 % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | REF_CLOSE: (16), (46), (179) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | | | | #733. % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | (180) ~ (all_54_3 = e0) % 152.43/22.72 | | | | | | | | | | | | (181) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | BETA: splitting (44) gives: % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | (182) all_54_5 = e0 % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | REF_CLOSE: (29), (148), (182) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | | | | | #158. % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | (183) ~ (all_54_5 = e0) % 152.43/22.72 | | | | | | | | | | | | | (184) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | BETA: splitting (116) gives: % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | (185) all_54_2 = e0 % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (185) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | | | | | | #860. % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | (186) ~ (all_54_2 = e0) % 152.43/22.72 | | | | | | | | | | | | | | (187) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | BETA: splitting (86) gives: % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | (188) all_56_0 = e2 % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | COMBINE_EQS: (94), (188) imply: % 152.43/22.72 | | | | | | | | | | | | | | | (189) all_10_2 = e2 % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (189) imply: % 152.43/22.72 | | | | | | | | | | | | | | | (190) all_58_28 = e2 % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | REDUCE: (81), (189) imply: % 152.43/22.72 | | | | | | | | | | | | | | | (191) ~ (all_52_12 = e2) % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (13), (14), (16), (26), (33), (34), % 152.43/22.72 | | | | | | | | | | | | | | | (35), (37), (38), (46), (59), (60), (61), (62), % 152.43/22.72 | | | | | | | | | | | | | | | (65), (67), (70), (77), (87), (92), (96), (106), % 152.43/22.72 | | | | | | | | | | | | | | | (107), (113), (114), (120), (122), (123), (124), % 152.43/22.72 | | | | | | | | | | | | | | | (134), (139), (143), (161), (176), (181), (188), % 152.43/22.72 | | | | | | | | | | | | | | | (190), (191) are inconsistent by sub-proof #154. % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | (192) ~ (all_56_0 = e2) % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | REDUCE: (94), (192) imply: % 152.43/22.72 | | | | | | | | | | | | | | | (193) ~ (all_10_2 = e2) % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | (194) all_58_28 = e2 % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | REF_CLOSE: (85), (193), (194) are inconsistent by sub-proof % 152.43/22.72 | | | | | | | | | | | | | | | | #388. % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | (195) ~ (all_58_28 = e2) % 152.43/22.72 | | | | | | | | | | | | | | | | (196) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | (197) all_56_0 = e1 % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (197) imply: % 152.43/22.72 | | | | | | | | | | | | | | | | | (198) all_10_2 = e1 % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | REDUCE: (127), (198) imply: % 152.43/22.72 | | | | | | | | | | | | | | | | | (199) op(e1, e3) = all_10_1 % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_10_1, e3, e1, % 152.43/22.72 | | | | | | | | | | | | | | | | | simplifying with (141), (199) gives: % 152.43/22.72 | | | | | | | | | | | | | | | | | (200) all_10_1 = e0 % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | REDUCE: (7), (200) imply: % 152.43/22.72 | | | | | | | | | | | | | | | | | (201) $false % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent. % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | (202) ~ (all_56_0 = e1) % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | REDUCE: (94), (202) imply: % 152.43/22.72 | | | | | | | | | | | | | | | | | (203) ~ (all_10_2 = e1) % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (9), (11), (12), (13), (16), % 152.43/22.72 | | | | | | | | | | | | | | | | | (22), (24), (26), (27), (29), (32), (33), (34), % 152.43/22.72 | | | | | | | | | | | | | | | | | (35), (36), (40), (46), (48), (50), (54), (55), % 152.43/22.72 | | | | | | | | | | | | | | | | | (58), (59), (60), (65), (70), (71), (74), (76), % 152.43/22.72 | | | | | | | | | | | | | | | | | (78), (80), (81), (91), (92), (96), (102), (108), % 152.43/22.72 | | | | | | | | | | | | | | | | | (117), (120), (127), (129), (130), (134), (139), % 152.43/22.72 | | | | | | | | | | | | | | | | | (142), (148), (161), (164), (170), (173), (176), % 152.43/22.72 | | | | | | | | | | | | | | | | | (178), (181), (184), (187), (193), (196), (203) % 152.43/22.72 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #150. % 152.43/22.72 | | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | | % 152.43/22.72 | | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | | % 152.43/22.72 | | | | | | | | | End of split % 152.43/22.72 | | | | | | | | | % 152.43/22.72 | | | | | | | | End of split % 152.43/22.72 | | | | | | | | % 152.43/22.72 | | | | | | | End of split % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | Case 2: % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | (204) all_56_10 = e0 % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | COMBINE_EQS: (80), (204) imply: % 152.43/22.72 | | | | | | | (205) all_52_13 = e0 % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | REDUCE: (50), (205) imply: % 152.43/22.72 | | | | | | | (206) $false % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | | CLOSE: (206) is inconsistent. % 152.43/22.72 | | | | | | | % 152.43/22.72 | | | | | | End of split % 152.43/22.72 | | | | | | % 152.43/22.72 | | | | | End of split % 152.43/22.72 | | | | | % 152.43/22.72 | | | | End of split % 152.43/22.72 | | | | % 152.43/22.72 | | | Case 2: % 152.43/22.72 | | | | % 152.43/22.72 | | | | (207) ~ (all_56_1 = e0) % 152.43/22.72 | | | | % 152.43/22.72 | | | | REDUCE: (49), (207) imply: % 152.43/22.72 | | | | (208) ~ (all_52_4 = e0) % 152.43/22.72 | | | | % 152.43/22.72 | | | | REF_CLOSE: (2), (3), (49), (55), (65), (66), (73), (103), (111), (118), % 152.43/22.72 | | | | (139), (208) are inconsistent by sub-proof #147. % 152.43/22.72 | | | | % 152.43/22.72 | | | End of split % 152.43/22.72 | | | % 152.43/22.72 | | Case 2: % 152.43/22.72 | | | % 152.43/22.72 | | | (209) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.43/22.72 | | | % 152.43/22.72 | | | REF_CLOSE: (1), (2), (3), (8), (10), (13), (14), (15), (17), (18), (19), % 152.43/22.72 | | | (20), (21), (22), (23), (25), (26), (28), (31), (36), (37), % 152.43/22.72 | | | (38), (42), (45), (46), (47), (48), (49), (50), (51), (53), % 152.43/22.72 | | | (54), (55), (56), (57), (59), (60), (61), (63), (65), (66), % 152.43/22.72 | | | (69), (70), (71), (74), (76), (77), (78), (79), (80), (82), % 152.43/22.72 | | | (83), (84), (85), (86), (87), (89), (90), (91), (92), (93), % 152.43/22.72 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (104), % 152.43/22.72 | | | (105), (107), (109), (112), (113), (115), (117), (119), (120), % 152.43/22.72 | | | (121), (122), (123), (125), (129), (131), (133), (209) are % 152.43/22.72 | | | inconsistent by sub-proof #135. % 152.43/22.72 | | | % 152.43/22.72 | | End of split % 152.43/22.72 | | % 152.43/22.72 | End of split % 152.43/22.72 | % 152.43/22.72 End of proof % 152.43/22.72 % 152.43/22.72 Sub-proof #135 shows that the following formulas are inconsistent: % 152.43/22.72 ---------------------------------------------------------------- % 152.43/22.72 (1) ~ (all_52_8 = all_52_9) % 152.43/22.72 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.72 (3) all_56_7 = all_52_6 % 152.43/22.72 (4) all_22_0 = all_8_0 % 152.43/22.72 (5) op(e3, all_52_4) = all_58_1 % 152.43/22.72 (6) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.72 (7) ~ (all_52_6 = all_8_2) % 152.43/22.72 (8) all_56_4 = all_52_8 % 152.43/22.72 (9) ~ (all_52_4 = all_8_2) % 152.43/22.72 (10) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.72 (11) all_54_1 = all_52_4 % 152.43/22.72 (12) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.72 (13) ~ (all_6_2 = e0) % 152.43/22.72 (14) ~ (all_52_4 = all_52_6) % 152.43/22.72 (15) op(e2, e2) = all_8_2 % 152.43/22.72 (16) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.43/22.72 (17) op(e3, e2) = all_52_4 % 152.43/22.72 (18) ~ (all_52_8 = all_6_2) % 152.43/22.72 (19) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.43/22.72 (20) ~ (all_52_2 = all_6_2) % 152.43/22.72 (21) ~ (all_52_13 = all_8_2) % 152.43/22.72 (22) op(e1, all_52_6) = all_58_16 % 152.43/22.72 (23) ~ (e3 = e1) % 152.43/22.72 (24) all_56_5 = all_52_9 % 152.43/22.72 (25) all_56_12 = all_52_3 % 152.43/22.72 (26) ~ (all_52_12 = e0) % 152.43/22.72 (27) ~ (all_52_3 = all_52_7) % 152.43/22.72 (28) all_56_11 = all_52_14 % 152.43/22.72 (29) all_56_1 = all_52_4 % 152.43/22.72 (30) ~ (all_52_13 = e0) % 152.43/22.72 (31) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.72 (32) op(e1, e0) = all_52_14 % 152.43/22.72 (33) ~ (all_52_1 = all_8_2) % 152.43/22.72 (34) all_56_3 = all_8_2 % 152.43/22.72 (35) ~ (all_52_4 = all_52_8) % 152.43/22.72 (36) op(e1, all_52_2) = all_58_14 % 152.43/22.72 (37) all_56_9 = all_52_12 % 152.43/22.72 (38) all_58_29 = all_8_2 % 152.43/22.72 (39) ~ (e2 = e1) % 152.43/22.72 (40) all_56_6 = all_52_2 % 152.43/22.72 (41) op(all_8_2, e2) = e0 % 152.43/22.72 (42) all_56_13 = all_52_7 % 152.43/22.72 (43) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.72 (44) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.72 (45) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.72 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.72 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.72 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.72 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.72 (all_58_27 = e0)) % 152.43/22.72 (46) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.72 (47) op(e3, all_10_2) = all_58_0 % 152.43/22.72 (48) ~ (e3 = e0) % 152.43/22.72 (49) all_56_2 = all_52_1 % 152.43/22.72 (50) op(e3, all_52_12) = all_58_5 % 152.43/22.72 (51) all_56_10 = all_52_13 % 152.43/22.72 (52) ~ (all_52_1 = all_52_3) % 152.43/22.72 (53) ~ (all_52_9 = all_8_2) % 152.43/22.72 (54) all_56_14 = all_52_11 % 152.43/22.72 (55) all_58_28 = all_10_2 % 152.43/22.72 (56) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.43/22.72 (57) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.72 (58) op(all_8_2, e0) = all_8_0 % 152.43/22.72 (59) op(e3, e1) = all_52_8 % 152.43/22.72 (60) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.72 (61) all_56_15 = e0 % 152.43/22.72 (62) ~ (e2 = e0) % 152.43/22.72 (63) ~ (all_52_2 = all_10_2) % 152.43/22.72 (64) all_56_0 = all_10_2 % 152.43/22.72 (65) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 152.43/22.72 (66) all_58_31 = e0 % 152.43/22.72 (67) ~ (all_52_3 = all_52_11) % 152.43/22.72 (68) all_56_8 = all_6_2 % 152.43/22.72 (69) op(e1, e1) = all_6_2 % 152.43/22.72 (70) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.43/22.72 (71) ~ (all_52_1 = all_52_2) % 152.43/22.72 (72) all_58_27 = e0 % 152.43/22.72 (73) op(e2, e0) = all_52_13 % 152.43/22.72 (74) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.43/22.72 (75) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.72 (76) ~ (all_52_2 = all_52_14) % 152.43/22.72 (77) all_22_2 = all_8_2 % 152.43/22.72 (78) ~ (e1 = e0) % 152.43/22.72 (79) ~ (all_52_14 = e0) % 152.43/22.72 (80) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.72 (81) ~ (all_52_4 = all_10_2) % 152.43/22.72 (82) all_58_30 = all_6_2 % 152.43/22.72 (83) op(e2, all_52_1) = all_58_7 % 152.43/22.72 (84) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.72 (85) ~ (e3 = e2) % 152.43/22.72 (86) ~ (all_52_14 = all_6_2) % 152.43/22.72 (87) op(e2, all_8_2) = all_58_9 % 152.43/22.72 (88) ~ (all_52_1 = all_10_2) % 152.43/22.72 % 152.43/22.72 Begin of proof % 152.43/22.72 | % 152.43/22.72 | BETA: splitting (56) gives: % 152.43/22.72 | % 152.43/22.72 | Case 1: % 152.43/22.72 | | % 152.43/22.72 | | (89) all_56_7 = e0 % 152.43/22.72 | | % 152.43/22.72 | | COMBINE_EQS: (3), (89) imply: % 152.43/22.72 | | (90) all_52_6 = e0 % 152.43/22.72 | | % 152.43/22.72 | | SIMP: (90) implies: % 152.43/22.72 | | (91) all_52_6 = e0 % 152.43/22.72 | | % 152.43/22.72 | | REDUCE: (14), (91) imply: % 152.43/22.72 | | (92) ~ (all_52_4 = e0) % 152.43/22.72 | | % 152.43/22.72 | | REDUCE: (7), (91) imply: % 152.43/22.72 | | (93) ~ (all_8_2 = e0) % 152.43/22.72 | | % 152.43/22.72 | | SIMP: (93) implies: % 152.43/22.72 | | (94) ~ (all_8_2 = e0) % 152.43/22.72 | | % 152.43/22.72 | | REDUCE: (22), (91) imply: % 152.43/22.72 | | (95) op(e1, e0) = all_58_16 % 152.43/22.72 | | % 152.43/22.72 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (15), (16), % 152.43/22.72 | | (17), (18), (19), (20), (21), (23), (24), (25), (26), (27), (28), % 152.43/22.72 | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 152.43/22.72 | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), % 152.43/22.72 | | (51), (52), (53), (54), (55), (57), (58), (59), (60), (61), (62), % 152.43/22.72 | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 152.43/22.72 | | (74), (75), (76), (77), (78), (80), (81), (82), (83), (84), (85), % 152.43/22.72 | | (86), (87), (88), (89), (92), (94), (95) are inconsistent by % 152.43/22.72 | | sub-proof #136. % 152.43/22.72 | | % 152.43/22.72 | Case 2: % 152.43/22.72 | | % 152.43/22.72 | | (96) all_56_8 = e0 | all_56_11 = e0 % 152.43/22.72 | | % 152.43/22.72 | | REF_CLOSE: (13), (28), (68), (79), (96) are inconsistent by sub-proof #763. % 152.43/22.72 | | % 152.43/22.72 | End of split % 152.43/22.72 | % 152.43/22.72 End of proof % 152.43/22.72 % 152.43/22.72 Sub-proof #136 shows that the following formulas are inconsistent: % 152.43/22.72 ---------------------------------------------------------------- % 152.43/22.72 (1) ~ (all_52_8 = all_52_9) % 152.43/22.72 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.72 (3) all_22_0 = all_8_0 % 152.43/22.72 (4) op(e3, all_52_4) = all_58_1 % 152.43/22.72 (5) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.72 (6) all_56_4 = all_52_8 % 152.43/22.72 (7) ~ (all_52_4 = all_8_2) % 152.43/22.72 (8) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.72 (9) all_54_1 = all_52_4 % 152.43/22.72 (10) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.72 (11) op(e2, e2) = all_8_2 % 152.43/22.72 (12) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.43/22.72 (13) all_56_7 = e0 % 152.43/22.72 (14) op(e3, e2) = all_52_4 % 152.43/22.72 (15) ~ (all_52_8 = all_6_2) % 152.43/22.72 (16) op(e1, e0) = all_58_16 % 152.43/22.72 (17) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.43/22.72 (18) ~ (all_52_2 = all_6_2) % 152.43/22.72 (19) ~ (all_52_13 = all_8_2) % 152.43/22.72 (20) ~ (e3 = e1) % 152.43/22.72 (21) all_56_5 = all_52_9 % 152.43/22.72 (22) all_56_12 = all_52_3 % 152.43/22.72 (23) ~ (all_52_12 = e0) % 152.43/22.72 (24) ~ (all_52_3 = all_52_7) % 152.43/22.72 (25) all_56_11 = all_52_14 % 152.43/22.72 (26) all_56_1 = all_52_4 % 152.43/22.72 (27) ~ (all_52_13 = e0) % 152.43/22.72 (28) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.72 (29) op(e1, e0) = all_52_14 % 152.43/22.72 (30) ~ (all_52_1 = all_8_2) % 152.43/22.72 (31) all_56_3 = all_8_2 % 152.43/22.72 (32) ~ (all_52_4 = all_52_8) % 152.43/22.72 (33) op(e1, all_52_2) = all_58_14 % 152.43/22.72 (34) all_56_9 = all_52_12 % 152.43/22.72 (35) all_58_29 = all_8_2 % 152.43/22.72 (36) ~ (e2 = e1) % 152.43/22.72 (37) all_56_6 = all_52_2 % 152.43/22.72 (38) op(all_8_2, e2) = e0 % 152.43/22.72 (39) all_56_13 = all_52_7 % 152.43/22.72 (40) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.72 (41) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.72 (42) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.72 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.72 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.72 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.72 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.72 (all_58_27 = e0)) % 152.43/22.72 (43) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.72 (44) ~ (all_52_4 = e0) % 152.43/22.72 (45) op(e3, all_10_2) = all_58_0 % 152.43/22.72 (46) ~ (e3 = e0) % 152.43/22.72 (47) all_56_2 = all_52_1 % 152.43/22.72 (48) op(e3, all_52_12) = all_58_5 % 152.43/22.72 (49) all_56_10 = all_52_13 % 152.43/22.72 (50) ~ (all_52_1 = all_52_3) % 152.43/22.72 (51) ~ (all_52_9 = all_8_2) % 152.43/22.72 (52) all_56_14 = all_52_11 % 152.43/22.72 (53) all_58_28 = all_10_2 % 152.43/22.72 (54) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.72 (55) op(all_8_2, e0) = all_8_0 % 152.43/22.72 (56) op(e3, e1) = all_52_8 % 152.43/22.72 (57) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.72 (58) all_56_15 = e0 % 152.43/22.72 (59) ~ (e2 = e0) % 152.43/22.72 (60) ~ (all_52_2 = all_10_2) % 152.43/22.72 (61) all_56_0 = all_10_2 % 152.43/22.72 (62) ~ (all_22_0 = e3) | ~ (all_22_2 = e1) % 152.43/22.72 (63) all_58_31 = e0 % 152.43/22.72 (64) ~ (all_52_3 = all_52_11) % 152.43/22.72 (65) all_56_8 = all_6_2 % 152.43/22.72 (66) op(e1, e1) = all_6_2 % 152.43/22.72 (67) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.43/22.72 (68) ~ (all_52_1 = all_52_2) % 152.43/22.72 (69) all_58_27 = e0 % 152.43/22.72 (70) op(e2, e0) = all_52_13 % 152.43/22.72 (71) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.43/22.72 (72) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.72 (73) ~ (all_52_2 = all_52_14) % 152.43/22.72 (74) all_22_2 = all_8_2 % 152.43/22.72 (75) ~ (e1 = e0) % 152.43/22.72 (76) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.72 (77) ~ (all_52_4 = all_10_2) % 152.43/22.72 (78) all_58_30 = all_6_2 % 152.43/22.72 (79) op(e2, all_52_1) = all_58_7 % 152.43/22.72 (80) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.72 (81) ~ (e3 = e2) % 152.43/22.72 (82) ~ (all_52_14 = all_6_2) % 152.43/22.72 (83) ~ (all_8_2 = e0) % 152.43/22.72 (84) op(e2, all_8_2) = all_58_9 % 152.43/22.72 (85) ~ (all_52_1 = all_10_2) % 152.43/22.72 % 152.43/22.72 Begin of proof % 152.43/22.72 | % 152.43/22.72 | BETA: splitting (5) gives: % 152.43/22.72 | % 152.43/22.72 | Case 1: % 152.43/22.72 | | % 152.43/22.72 | | (86) all_56_1 = e0 % 152.43/22.72 | | % 152.43/22.72 | | REF_CLOSE: (26), (44), (86) are inconsistent by sub-proof #244. % 152.43/22.72 | | % 152.43/22.72 | Case 2: % 152.43/22.72 | | % 152.43/22.72 | | (87) all_56_4 = e0 | all_56_9 = e0 % 152.43/22.72 | | % 152.43/22.72 | | BETA: splitting (87) gives: % 152.43/22.72 | | % 152.43/22.72 | | Case 1: % 152.43/22.72 | | | % 152.43/22.72 | | | (88) all_56_4 = e0 % 152.43/22.72 | | | % 152.43/22.72 | | | COMBINE_EQS: (6), (88) imply: % 152.43/22.72 | | | (89) all_52_8 = e0 % 152.43/22.72 | | | % 152.43/22.72 | | | REDUCE: (1), (89) imply: % 152.43/22.72 | | | (90) ~ (all_52_9 = e0) % 152.43/22.72 | | | % 152.43/22.72 | | | SIMP: (90) implies: % 152.43/22.73 | | | (91) ~ (all_52_9 = e0) % 152.43/22.73 | | | % 152.43/22.73 | | | REDUCE: (15), (89) imply: % 152.43/22.73 | | | (92) ~ (all_6_2 = e0) % 152.43/22.73 | | | % 152.43/22.73 | | | SIMP: (92) implies: % 152.43/22.73 | | | (93) ~ (all_6_2 = e0) % 152.43/22.73 | | | % 152.43/22.73 | | | REDUCE: (56), (89) imply: % 152.43/22.73 | | | (94) op(e3, e1) = e0 % 152.43/22.73 | | | % 152.43/22.73 | | | BETA: splitting (10) gives: % 152.43/22.73 | | | % 152.43/22.73 | | | Case 1: % 152.43/22.73 | | | | % 152.43/22.73 | | | | (95) all_56_2 = e0 % 152.43/22.73 | | | | % 152.43/22.73 | | | | COMBINE_EQS: (47), (95) imply: % 152.43/22.73 | | | | (96) all_52_1 = e0 % 152.43/22.73 | | | | % 152.43/22.73 | | | | REDUCE: (68), (96) imply: % 152.43/22.73 | | | | (97) ~ (all_52_2 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | SIMP: (97) implies: % 152.43/22.73 | | | | (98) ~ (all_52_2 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | REDUCE: (50), (96) imply: % 152.43/22.73 | | | | (99) ~ (all_52_3 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | SIMP: (99) implies: % 152.43/22.73 | | | | (100) ~ (all_52_3 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | REDUCE: (85), (96) imply: % 152.43/22.73 | | | | (101) ~ (all_10_2 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | SIMP: (101) implies: % 152.43/22.73 | | | | (102) ~ (all_10_2 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | REDUCE: (30), (96) imply: % 152.43/22.73 | | | | (103) ~ (all_8_2 = e0) % 152.43/22.73 | | | | % 152.43/22.73 | | | | REDUCE: (79), (96) imply: % 152.43/22.73 | | | | (104) op(e2, e0) = all_58_7 % 152.43/22.73 | | | | % 152.43/22.73 | | | | GROUND_INST: instantiating (2) with all_52_14, all_58_16, e0, e1, % 152.43/22.73 | | | | simplifying with (16), (29) gives: % 152.43/22.73 | | | | (105) all_58_16 = all_52_14 % 152.43/22.73 | | | | % 152.43/22.73 | | | | GROUND_INST: instantiating (2) with all_52_13, all_58_7, e0, e2, % 152.43/22.73 | | | | simplifying with (70), (104) gives: % 152.43/22.73 | | | | (106) all_58_7 = all_52_13 % 152.43/22.73 | | | | % 152.43/22.73 | | | | BETA: splitting (71) gives: % 152.43/22.73 | | | | % 152.43/22.73 | | | | Case 1: % 152.43/22.73 | | | | | % 152.43/22.73 | | | | | (107) all_54_1 = e0 % 152.43/22.73 | | | | | % 152.43/22.73 | | | | | REF_CLOSE: (9), (44), (107) are inconsistent by sub-proof #798. % 152.43/22.73 | | | | | % 152.43/22.73 | | | | Case 2: % 152.43/22.73 | | | | | % 152.43/22.73 | | | | | (108) ~ (all_54_1 = e0) % 152.43/22.73 | | | | | (109) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 152.43/22.73 | | | | | % 152.43/22.73 | | | | | BETA: splitting (57) gives: % 152.43/22.73 | | | | | % 152.43/22.73 | | | | | Case 1: % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | (110) all_56_12 = e1 % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | COMBINE_EQS: (22), (110) imply: % 152.43/22.73 | | | | | | (111) all_52_3 = e1 % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | SIMP: (111) implies: % 152.43/22.73 | | | | | | (112) all_52_3 = e1 % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | REDUCE: (24), (112) imply: % 152.43/22.73 | | | | | | (113) ~ (all_52_7 = e1) % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | SIMP: (113) implies: % 152.43/22.73 | | | | | | (114) ~ (all_52_7 = e1) % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | REDUCE: (64), (112) imply: % 152.43/22.73 | | | | | | (115) ~ (all_52_11 = e1) % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | SIMP: (115) implies: % 152.43/22.73 | | | | | | (116) ~ (all_52_11 = e1) % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | BETA: splitting (40) gives: % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | Case 1: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | (117) all_56_1 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | COMBINE_EQS: (26), (117) imply: % 152.43/22.73 | | | | | | | (118) all_52_4 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | SIMP: (118) implies: % 152.43/22.73 | | | | | | | (119) all_52_4 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | REDUCE: (77), (119) imply: % 152.43/22.73 | | | | | | | (120) ~ (all_10_2 = e1) % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | SIMP: (120) implies: % 152.43/22.73 | | | | | | | (121) ~ (all_10_2 = e1) % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | REDUCE: (7), (119) imply: % 152.43/22.73 | | | | | | | (122) ~ (all_8_2 = e1) % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | SIMP: (122) implies: % 152.43/22.73 | | | | | | | (123) ~ (all_8_2 = e1) % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | REDUCE: (14), (119) imply: % 152.43/22.73 | | | | | | | (124) op(e3, e2) = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | BETA: splitting (80) gives: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (125) all_58_28 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | REF_CLOSE: (53), (121), (125) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | #858. % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (126) ~ (all_58_28 = e1) % 152.43/22.73 | | | | | | | | (127) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | BETA: splitting (127) gives: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (128) all_58_29 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REF_CLOSE: (35), (123), (128) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | #809. % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (129) all_58_30 = e1 | all_58_31 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | BETA: splitting (129) gives: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | (130) all_58_30 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | COMBINE_EQS: (78), (130) imply: % 152.43/22.73 | | | | | | | | | | (131) all_6_2 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | REDUCE: (18), (131) imply: % 152.43/22.73 | | | | | | | | | | (132) ~ (all_52_2 = e1) % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | BETA: splitting (76) gives: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | (133) all_56_6 = e3 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | COMBINE_EQS: (37), (133) imply: % 152.43/22.73 | | | | | | | | | | | (134) all_52_2 = e3 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | SIMP: (134) implies: % 152.43/22.73 | | | | | | | | | | | (135) all_52_2 = e3 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | REDUCE: (60), (135) imply: % 152.43/22.73 | | | | | | | | | | | (136) ~ (all_10_2 = e3) % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | SIMP: (136) implies: % 152.43/22.73 | | | | | | | | | | | (137) ~ (all_10_2 = e3) % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | BETA: splitting (54) gives: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (138) all_56_0 = e2 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | COMBINE_EQS: (61), (138) imply: % 152.43/22.73 | | | | | | | | | | | | (139) all_10_2 = e2 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | SIMP: (139) implies: % 152.43/22.73 | | | | | | | | | | | | (140) all_10_2 = e2 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REDUCE: (137), (140) imply: % 152.43/22.73 | | | | | | | | | | | | (141) ~ (e3 = e2) % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REDUCE: (45), (140) imply: % 152.43/22.73 | | | | | | | | | | | | (142) op(e3, e2) = all_58_0 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | BETA: splitting (72) gives: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (143) all_58_28 = e3 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REF_CLOSE: (2), (8), (11), (35), (36), (38), (59), (63), % 152.43/22.73 | | | | | | | | | | | | | (81), (83), (84), (130), (143) are inconsistent by % 152.43/22.73 | | | | | | | | | | | | | sub-proof #145. % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (144) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | BETA: splitting (144) gives: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | (145) all_58_29 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | COMBINE_EQS: (35), (145) imply: % 152.43/22.73 | | | | | | | | | | | | | | (146) all_8_2 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | REDUCE: (38), (146) imply: % 152.43/22.73 | | | | | | | | | | | | | | (147) op(e3, e2) = e0 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e1, all_58_0, e2, e3, % 152.43/22.73 | | | | | | | | | | | | | | simplifying with (124), (142) gives: % 152.43/22.73 | | | | | | | | | | | | | | (148) all_58_0 = e1 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_58_0, e2, e3, % 152.43/22.73 | | | | | | | | | | | | | | simplifying with (142), (147) gives: % 152.43/22.73 | | | | | | | | | | | | | | (149) all_58_0 = e0 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | COMBINE_EQS: (148), (149) imply: % 152.43/22.73 | | | | | | | | | | | | | | (150) e1 = e0 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | SIMP: (150) implies: % 152.43/22.73 | | | | | | | | | | | | | | (151) e1 = e0 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | REDUCE: (75), (151) imply: % 152.43/22.73 | | | | | | | | | | | | | | (152) $false % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | CLOSE: (152) is inconsistent. % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | (153) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | REF_CLOSE: (20), (46), (63), (130), (153) are inconsistent by % 152.43/22.73 | | | | | | | | | | | | | | sub-proof #848. % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (154) ~ (all_56_0 = e2) % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REDUCE: (61), (154) imply: % 152.43/22.73 | | | | | | | | | | | | (155) ~ (all_10_2 = e2) % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REF_CLOSE: (2), (8), (11), (35), (36), (38), (53), (59), % 152.43/22.73 | | | | | | | | | | | | (63), (83), (84), (130), (155) are inconsistent by % 152.43/22.73 | | | | | | | | | | | | sub-proof #144. % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | (156) ~ (all_56_6 = e3) % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | REDUCE: (37), (156) imply: % 152.43/22.73 | | | | | | | | | | | (157) ~ (all_52_2 = e3) % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | BETA: splitting (28) gives: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (158) all_56_0 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | COMBINE_EQS: (61), (158) imply: % 152.43/22.73 | | | | | | | | | | | | (159) all_10_2 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | SIMP: (159) implies: % 152.43/22.73 | | | | | | | | | | | | (160) all_10_2 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | COMBINE_EQS: (53), (160) imply: % 152.43/22.73 | | | | | | | | | | | | (161) all_58_28 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REF_CLOSE: (2), (8), (11), (35), (36), (38), (59), (63), % 152.43/22.73 | | | | | | | | | | | | (81), (83), (84), (130), (161) are inconsistent by % 152.43/22.73 | | | | | | | | | | | | sub-proof #145. % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (162) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | BETA: splitting (162) gives: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (163) all_56_2 = e3 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | COMBINE_EQS: (95), (163) imply: % 152.43/22.73 | | | | | | | | | | | | | (164) e3 = e0 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REDUCE: (46), (164) imply: % 152.43/22.73 | | | | | | | | | | | | | (165) $false % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | CLOSE: (165) is inconsistent. % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (166) all_56_6 = e3 | all_56_12 = e3 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | BETA: splitting (166) gives: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | (167) all_56_6 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | REF_CLOSE: (37), (157), (167) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | | | | | | #788. % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | (168) all_56_12 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | COMBINE_EQS: (110), (168) imply: % 152.43/22.73 | | | | | | | | | | | | | | (169) e3 = e1 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | REDUCE: (20), (169) imply: % 152.43/22.73 | | | | | | | | | | | | | | (170) $false % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | (171) all_58_31 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | REF_CLOSE: (63), (75), (171) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | | #845. % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | End of split % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | End of split % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | Case 2: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | (172) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | BETA: splitting (172) gives: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (173) all_56_3 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | COMBINE_EQS: (31), (173) imply: % 152.43/22.73 | | | | | | | | (174) all_8_2 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | SIMP: (174) implies: % 152.43/22.73 | | | | | | | | (175) all_8_2 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | COMBINE_EQS: (35), (175) imply: % 152.43/22.73 | | | | | | | | (176) all_58_29 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | REDUCE: (51), (175) imply: % 152.43/22.73 | | | | | | | | (177) ~ (all_52_9 = e1) % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | BETA: splitting (17) gives: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (178) all_56_4 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | COMBINE_EQS: (88), (178) imply: % 152.43/22.73 | | | | | | | | | (179) e1 = e0 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REDUCE: (75), (179) imply: % 152.43/22.73 | | | | | | | | | (180) $false % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | CLOSE: (180) is inconsistent. % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (181) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | BETA: splitting (181) gives: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | (182) all_56_5 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | REF_CLOSE: (21), (177), (182) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | | #285. % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | (183) all_56_8 = e1 | all_56_14 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | BETA: splitting (183) gives: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | (184) all_56_8 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | COMBINE_EQS: (65), (184) imply: % 152.43/22.73 | | | | | | | | | | | (185) all_6_2 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | COMBINE_EQS: (78), (185) imply: % 152.43/22.73 | | | | | | | | | | | (186) all_58_30 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | BETA: splitting (72) gives: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (187) all_58_28 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REF_CLOSE: (2), (8), (11), (35), (36), (38), (59), (63), % 152.43/22.73 | | | | | | | | | | | | (81), (83), (84), (186), (187) are inconsistent by % 152.43/22.73 | | | | | | | | | | | | sub-proof #145. % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (188) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | BETA: splitting (188) gives: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (189) all_58_29 = e3 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | COMBINE_EQS: (176), (189) imply: % 152.43/22.73 | | | | | | | | | | | | | (190) e3 = e1 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REDUCE: (20), (190) imply: % 152.43/22.73 | | | | | | | | | | | | | (191) $false % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (192) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REF_CLOSE: (20), (46), (63), (186), (192) are inconsistent by % 152.43/22.73 | | | | | | | | | | | | | sub-proof #848. % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | (193) all_56_14 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | REF_CLOSE: (52), (116), (193) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | | | #811. % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | End of split % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | End of split % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (194) all_56_7 = e1 | all_56_13 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | REF_CLOSE: (13), (39), (75), (114), (194) are inconsistent by % 152.43/22.73 | | | | | | | | sub-proof #419. % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | End of split % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | End of split % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | Case 2: % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | (195) ~ (all_56_12 = e1) % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | REDUCE: (22), (195) imply: % 152.43/22.73 | | | | | | (196) ~ (all_52_3 = e1) % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | BETA: splitting (12) gives: % 152.43/22.73 | | | | | | % 152.43/22.73 | | | | | | Case 1: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | (197) all_56_0 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | COMBINE_EQS: (61), (197) imply: % 152.43/22.73 | | | | | | | (198) all_10_2 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | COMBINE_EQS: (53), (198) imply: % 152.43/22.73 | | | | | | | (199) all_58_28 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | REDUCE: (77), (198) imply: % 152.43/22.73 | | | | | | | (200) ~ (all_52_4 = e1) % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | BETA: splitting (72) gives: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (201) all_58_28 = e3 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | COMBINE_EQS: (199), (201) imply: % 152.43/22.73 | | | | | | | | (202) e3 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | REDUCE: (20), (202) imply: % 152.43/22.73 | | | | | | | | (203) $false % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | CLOSE: (203) is inconsistent. % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (204) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | BETA: splitting (8) gives: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (205) all_58_28 = e2 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | COMBINE_EQS: (199), (205) imply: % 152.43/22.73 | | | | | | | | | (206) e2 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REDUCE: (36), (206) imply: % 152.43/22.73 | | | | | | | | | (207) $false % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | CLOSE: (207) is inconsistent. % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (208) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (11), (14), (26), (35), (38), % 152.43/22.73 | | | | | | | | | (44), (46), (59), (63), (67), (78), (81), (83), % 152.43/22.73 | | | | | | | | | (84), (109), (200), (204), (208) are inconsistent % 152.43/22.73 | | | | | | | | | by sub-proof #138. % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | End of split % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | End of split % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | Case 2: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | (209) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | BETA: splitting (209) gives: % 152.43/22.73 | | | | | | | % 152.43/22.73 | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (210) all_56_2 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | COMBINE_EQS: (95), (210) imply: % 152.43/22.73 | | | | | | | | (211) e1 = e0 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | REDUCE: (75), (211) imply: % 152.43/22.73 | | | | | | | | (212) $false % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | CLOSE: (212) is inconsistent. % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | (213) all_56_6 = e1 | all_56_12 = e1 % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | BETA: splitting (213) gives: % 152.43/22.73 | | | | | | | | % 152.43/22.73 | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | (214) all_56_6 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | COMBINE_EQS: (37), (214) imply: % 152.43/22.73 | | | | | | | | | (215) all_52_2 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | SIMP: (215) implies: % 152.43/22.73 | | | | | | | | | (216) all_52_2 = e1 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REDUCE: (73), (216) imply: % 152.43/22.73 | | | | | | | | | (217) ~ (all_52_14 = e1) % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | SIMP: (217) implies: % 152.43/22.73 | | | | | | | | | (218) ~ (all_52_14 = e1) % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REDUCE: (60), (216) imply: % 152.43/22.73 | | | | | | | | | (219) ~ (all_10_2 = e1) % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | SIMP: (219) implies: % 152.43/22.73 | | | | | | | | | (220) ~ (all_10_2 = e1) % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REDUCE: (18), (216) imply: % 152.43/22.73 | | | | | | | | | (221) ~ (all_6_2 = e1) % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | SIMP: (221) implies: % 152.43/22.73 | | | | | | | | | (222) ~ (all_6_2 = e1) % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | REDUCE: (33), (216) imply: % 152.43/22.73 | | | | | | | | | (223) op(e1, e1) = all_58_14 % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | BETA: splitting (80) gives: % 152.43/22.73 | | | | | | | | | % 152.43/22.73 | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | (224) all_58_28 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | COMBINE_EQS: (53), (224) imply: % 152.43/22.73 | | | | | | | | | | (225) all_10_2 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | REDUCE: (220), (225) imply: % 152.43/22.73 | | | | | | | | | | (226) $false % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | CLOSE: (226) is inconsistent. % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | (227) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | BETA: splitting (227) gives: % 152.43/22.73 | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | (228) all_58_29 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | COMBINE_EQS: (35), (228) imply: % 152.43/22.73 | | | | | | | | | | | (229) all_8_2 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | SIMP: (229) implies: % 152.43/22.73 | | | | | | | | | | | (230) all_8_2 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | COMBINE_EQS: (74), (230) imply: % 152.43/22.73 | | | | | | | | | | | (231) all_22_2 = e1 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | REDUCE: (19), (230) imply: % 152.43/22.73 | | | | | | | | | | | (232) ~ (all_52_13 = e1) % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | REDUCE: (55), (230) imply: % 152.43/22.73 | | | | | | | | | | | (233) op(e1, e0) = all_8_0 % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | BETA: splitting (43) gives: % 152.43/22.73 | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | (234) all_56_9 = e1 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | COMBINE_EQS: (34), (234) imply: % 152.43/22.73 | | | | | | | | | | | | (235) all_52_12 = e1 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | REDUCE: (48), (235) imply: % 152.43/22.73 | | | | | | | | | | | | (236) op(e3, e1) = all_58_5 % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | BETA: splitting (62) gives: % 152.43/22.73 | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (237) ~ (all_22_2 = e1) % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REDUCE: (231), (237) imply: % 152.43/22.73 | | | | | | | | | | | | | (238) $false % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | CLOSE: (238) is inconsistent. % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | (239) ~ (all_22_0 = e3) % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REDUCE: (3), (239) imply: % 152.43/22.73 | | | | | | | | | | | | | (240) ~ (all_8_0 = e3) % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_52_14, all_8_0, e0, e1, % 152.43/22.73 | | | | | | | | | | | | | simplifying with (29), (233) gives: % 152.43/22.73 | | | | | | | | | | | | | (241) all_52_14 = all_8_0 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_6_2, all_58_14, e1, e1, % 152.43/22.73 | | | | | | | | | | | | | simplifying with (66), (223) gives: % 152.43/22.73 | | | | | | | | | | | | | (242) all_58_14 = all_6_2 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_58_5, e1, e3, % 152.43/22.73 | | | | | | | | | | | | | simplifying with (94), (236) gives: % 152.43/22.73 | | | | | | | | | | | | | (243) all_58_5 = e0 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | COMBINE_EQS: (25), (241) imply: % 152.43/22.73 | | | | | | | | | | | | | (244) all_56_11 = all_8_0 % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | REDUCE: (82), (241) imply: % 152.43/22.73 | | | | | | | | | | | | | (245) ~ (all_8_0 = all_6_2) % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | BETA: splitting (76) gives: % 152.43/22.73 | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | (246) all_56_6 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | REF_CLOSE: (20), (214), (246) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | | | | | | #137. % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | (247) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | BETA: splitting (247) gives: % 152.43/22.73 | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | (248) all_56_7 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | COMBINE_EQS: (13), (248) imply: % 152.43/22.73 | | | | | | | | | | | | | | | (249) e3 = e0 % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | SIMP: (249) implies: % 152.43/22.73 | | | | | | | | | | | | | | | (250) e3 = e0 % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | REDUCE: (46), (250) imply: % 152.43/22.73 | | | | | | | | | | | | | | | (251) $false % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | (252) all_56_8 = e3 | all_56_11 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 152.43/22.73 | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | (253) all_56_8 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (253) imply: % 152.43/22.73 | | | | | | | | | | | | | | | | (254) all_6_2 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (254) imply: % 152.43/22.73 | | | | | | | | | | | | | | | | (255) all_58_14 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 152.43/22.73 | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.73 | | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | | (256) all_56_9 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (234), (256) are inconsistent by sub-proof % 152.43/22.73 | | | | | | | | | | | | | | | | | #155. % 152.43/22.73 | | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.73 | | | | | | | | | | | | | | | | | % 152.43/22.73 | | | | | | | | | | | | | | | | | (257) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.73 | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 152.43/22.74 | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | (258) all_56_10 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (258) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | | | (259) all_52_13 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (259) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | | | (260) all_58_7 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (261) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (260), (261) are inconsistent by sub-proof % 152.43/22.74 | | | | | | | | | | | | | | | | | | | #393. % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (262) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (255), (262) are inconsistent by sub-proof % 152.43/22.74 | | | | | | | | | | | | | | | | | | | #779. % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | (263) all_56_11 = e3 | all_56_15 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (264) all_56_11 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (264) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (265) all_8_0 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | REDUCE: (240), (265) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (266) $false % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent. % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (267) all_56_15 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (267) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (268) e3 = e0 % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | REDUCE: (46), (268) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | | | | (269) $false % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent. % 152.43/22.74 | | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | (270) all_56_11 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (270) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | (271) all_8_0 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | SIMP: (271) implies: % 152.43/22.74 | | | | | | | | | | | | | | | | (272) all_8_0 = e3 % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | REDUCE: (240), (272) imply: % 152.43/22.74 | | | | | | | | | | | | | | | | (273) $false % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent. % 152.43/22.74 | | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | (274) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.74 | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | BETA: splitting (274) gives: % 152.43/22.74 | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | Case 1: % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | (275) all_56_10 = e1 % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | COMBINE_EQS: (49), (275) imply: % 152.43/22.74 | | | | | | | | | | | | | (276) all_52_13 = e1 % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | REDUCE: (232), (276) imply: % 152.43/22.74 | | | | | | | | | | | | | (277) $false % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | CLOSE: (277) is inconsistent. % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | (278) all_56_11 = e1 | all_56_15 = e1 % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | BETA: splitting (278) gives: % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | Case 1: % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | (279) all_56_11 = e1 % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | COMBINE_EQS: (25), (279) imply: % 152.43/22.74 | | | | | | | | | | | | | | (280) all_52_14 = e1 % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | REDUCE: (218), (280) imply: % 152.43/22.74 | | | | | | | | | | | | | | (281) $false % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | (282) all_56_15 = e1 % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | COMBINE_EQS: (58), (282) imply: % 152.43/22.74 | | | | | | | | | | | | | | (283) e1 = e0 % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | REDUCE: (75), (283) imply: % 152.43/22.74 | | | | | | | | | | | | | | (284) $false % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | | CLOSE: (284) is inconsistent. % 152.43/22.74 | | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | (285) all_58_30 = e1 | all_58_31 = e1 % 152.43/22.74 | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | | REF_CLOSE: (63), (75), (78), (222), (285) are inconsistent by % 152.43/22.74 | | | | | | | | | | | sub-proof #824. % 152.43/22.74 | | | | | | | | | | | % 152.43/22.74 | | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | | % 152.43/22.74 | | | | | | | | | End of split % 152.43/22.74 | | | | | | | | | % 152.43/22.74 | | | | | | | | Case 2: % 152.43/22.74 | | | | | | | | | % 152.43/22.74 | | | | | | | | | (286) all_56_12 = e1 % 152.43/22.74 | | | | | | | | | % 152.43/22.74 | | | | | | | | | REF_CLOSE: (22), (196), (286) are inconsistent by sub-proof % 152.43/22.74 | | | | | | | | | #577. % 152.43/22.74 | | | | | | | | | % 152.43/22.74 | | | | | | | | End of split % 152.43/22.74 | | | | | | | | % 152.43/22.74 | | | | | | | End of split % 152.43/22.74 | | | | | | | % 152.43/22.74 | | | | | | End of split % 152.43/22.74 | | | | | | % 152.43/22.74 | | | | | End of split % 152.43/22.74 | | | | | % 152.43/22.74 | | | | End of split % 152.43/22.74 | | | | % 152.43/22.74 | | | Case 2: % 152.43/22.74 | | | | % 152.43/22.74 | | | | (287) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 152.43/22.74 | | | | % 152.43/22.74 | | | | REF_CLOSE: (21), (27), (31), (49), (83), (91), (287) are inconsistent by % 152.43/22.74 | | | | sub-proof #573. % 152.43/22.74 | | | | % 152.43/22.74 | | | End of split % 152.43/22.74 | | | % 152.43/22.74 | | Case 2: % 152.43/22.74 | | | % 152.43/22.74 | | | (288) all_56_9 = e0 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (23), (34), (288) are inconsistent by sub-proof #521. % 152.43/22.74 | | | % 152.43/22.74 | | End of split % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #137 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) all_56_6 = e3 % 152.43/22.74 (2) all_56_6 = e1 % 152.43/22.74 (3) ~ (e3 = e1) % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | COMBINE_EQS: (1), (2) imply: % 152.43/22.74 | (4) e3 = e1 % 152.43/22.74 | % 152.43/22.74 | SIMP: (4) implies: % 152.43/22.74 | (5) e3 = e1 % 152.43/22.74 | % 152.43/22.74 | REDUCE: (3), (5) imply: % 152.43/22.74 | (6) $false % 152.43/22.74 | % 152.43/22.74 | CLOSE: (6) is inconsistent. % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #138 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) op(e3, all_52_4) = all_58_1 % 152.43/22.74 (3) ~ (all_52_4 = all_8_2) % 152.43/22.74 (4) all_54_1 = all_52_4 % 152.43/22.74 (5) op(e2, e2) = all_8_2 % 152.43/22.74 (6) op(e3, e2) = all_52_4 % 152.43/22.74 (7) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 152.43/22.74 (8) all_56_1 = all_52_4 % 152.43/22.74 (9) all_58_29 = all_8_2 % 152.43/22.74 (10) ~ (all_52_4 = e1) % 152.43/22.74 (11) op(all_8_2, e2) = e0 % 152.43/22.74 (12) ~ (all_52_4 = e0) % 152.43/22.74 (13) ~ (e3 = e0) % 152.43/22.74 (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.74 (15) ~ (e2 = e0) % 152.43/22.74 (16) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (17) all_58_31 = e0 % 152.43/22.74 (18) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 152.43/22.74 (19) all_58_30 = all_6_2 % 152.43/22.74 (20) ~ (e3 = e2) % 152.43/22.74 (21) ~ (all_8_2 = e0) % 152.43/22.74 (22) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (18) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (23) all_56_1 = e2 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (8), (23) imply: % 152.43/22.74 | | (24) all_52_4 = e2 % 152.43/22.74 | | % 152.43/22.74 | | SIMP: (24) implies: % 152.43/22.74 | | (25) all_52_4 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (2), (25) imply: % 152.43/22.74 | | (26) op(e3, e2) = all_58_1 % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (6), (25) imply: % 152.43/22.74 | | (27) op(e3, e2) = e2 % 152.43/22.74 | | % 152.43/22.74 | | BETA: splitting (14) gives: % 152.43/22.74 | | % 152.43/22.74 | | Case 1: % 152.43/22.74 | | | % 152.43/22.74 | | | (28) all_58_29 = e3 % 152.43/22.74 | | | % 152.43/22.74 | | | COMBINE_EQS: (9), (28) imply: % 152.43/22.74 | | | (29) all_8_2 = e3 % 152.43/22.74 | | | % 152.43/22.74 | | | SIMP: (29) implies: % 152.43/22.74 | | | (30) all_8_2 = e3 % 152.43/22.74 | | | % 152.43/22.74 | | | REDUCE: (11), (30) imply: % 152.43/22.74 | | | (31) op(e3, e2) = e0 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (1), (15), (26), (27), (31) are inconsistent by sub-proof #143. % 152.43/22.74 | | | % 152.43/22.74 | | Case 2: % 152.43/22.74 | | | % 152.43/22.74 | | | (32) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (1), (5), (9), (11), (13), (15), (16), (17), (19), (20), (21), % 152.43/22.74 | | | (22), (32) are inconsistent by sub-proof #140. % 152.43/22.74 | | | % 152.43/22.74 | | End of split % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (33) ~ (all_56_1 = e2) % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (8), (33) imply: % 152.43/22.74 | | (34) ~ (all_52_4 = e2) % 152.43/22.74 | | % 152.43/22.74 | | BETA: splitting (7) gives: % 152.43/22.74 | | % 152.43/22.74 | | Case 1: % 152.43/22.74 | | | % 152.43/22.74 | | | (35) all_54_1 = e1 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (4), (10), (35) are inconsistent by sub-proof #741. % 152.43/22.74 | | | % 152.43/22.74 | | Case 2: % 152.43/22.74 | | | % 152.43/22.74 | | | (36) all_54_1 = e3 | all_54_1 = e2 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (1), (3), (4), (5), (9), (11), (12), (14), (15), (16), (17), % 152.43/22.74 | | | (19), (21), (22), (34), (36) are inconsistent by sub-proof % 152.43/22.74 | | | #139. % 152.43/22.74 | | | % 152.43/22.74 | | End of split % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #139 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) all_54_1 = e3 | all_54_1 = e2 % 152.43/22.74 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (3) ~ (all_52_4 = all_8_2) % 152.43/22.74 (4) all_54_1 = all_52_4 % 152.43/22.74 (5) op(e2, e2) = all_8_2 % 152.43/22.74 (6) ~ (all_52_4 = e2) % 152.43/22.74 (7) all_58_29 = all_8_2 % 152.43/22.74 (8) op(all_8_2, e2) = e0 % 152.43/22.74 (9) ~ (all_52_4 = e0) % 152.43/22.74 (10) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.74 (11) ~ (e2 = e0) % 152.43/22.74 (12) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (13) all_58_31 = e0 % 152.43/22.74 (14) all_58_30 = all_6_2 % 152.43/22.74 (15) ~ (all_8_2 = e0) % 152.43/22.74 (16) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (1) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (17) all_54_1 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #740. % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (18) all_54_1 = e3 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (4), (18) imply: % 152.43/22.74 | | (19) all_52_4 = e3 % 152.43/22.74 | | % 152.43/22.74 | | SIMP: (19) implies: % 152.43/22.74 | | (20) all_52_4 = e3 % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (3), (20) imply: % 152.43/22.74 | | (21) ~ (all_8_2 = e3) % 152.43/22.74 | | % 152.43/22.74 | | SIMP: (21) implies: % 152.43/22.74 | | (22) ~ (all_8_2 = e3) % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (6), (20) imply: % 152.43/22.74 | | (23) ~ (e3 = e2) % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (9), (20) imply: % 152.43/22.74 | | (24) ~ (e3 = e0) % 152.43/22.74 | | % 152.43/22.74 | | BETA: splitting (10) gives: % 152.43/22.74 | | % 152.43/22.74 | | Case 1: % 152.43/22.74 | | | % 152.43/22.74 | | | (25) all_58_29 = e3 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (7), (22), (25) are inconsistent by sub-proof #756. % 152.43/22.74 | | | % 152.43/22.74 | | Case 2: % 152.43/22.74 | | | % 152.43/22.74 | | | (26) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.74 | | | % 152.43/22.74 | | | REF_CLOSE: (2), (5), (7), (8), (11), (12), (13), (14), (15), (16), (23), % 152.43/22.74 | | | (24), (26) are inconsistent by sub-proof #140. % 152.43/22.74 | | | % 152.43/22.74 | | End of split % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #140 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) op(e2, e2) = all_8_2 % 152.43/22.74 (3) all_58_29 = all_8_2 % 152.43/22.74 (4) op(all_8_2, e2) = e0 % 152.43/22.74 (5) ~ (e3 = e0) % 152.43/22.74 (6) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.74 (7) ~ (e2 = e0) % 152.43/22.74 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (9) all_58_31 = e0 % 152.43/22.74 (10) all_58_30 = all_6_2 % 152.43/22.74 (11) ~ (e3 = e2) % 152.43/22.74 (12) ~ (all_8_2 = e0) % 152.43/22.74 (13) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (6) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (14) all_58_30 = e3 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (10), (14) imply: % 152.43/22.74 | | (15) all_6_2 = e3 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (13), (14) are % 152.43/22.74 | | inconsistent by sub-proof #141. % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (16) all_58_31 = e3 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (5), (9), (16) are inconsistent by sub-proof #853. % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #141 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) all_58_30 = e3 % 152.43/22.74 (3) op(e2, e2) = all_8_2 % 152.43/22.74 (4) all_58_29 = all_8_2 % 152.43/22.74 (5) op(all_8_2, e2) = e0 % 152.43/22.74 (6) ~ (e2 = e0) % 152.43/22.74 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (8) all_58_31 = e0 % 152.43/22.74 (9) ~ (e3 = e2) % 152.43/22.74 (10) ~ (all_8_2 = e0) % 152.43/22.74 (11) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (7) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (12) all_58_29 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (1), (3), (4), (5), (10), (11), (12) are inconsistent by % 152.43/22.74 | | sub-proof #142. % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (13) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (2), (6), (8), (9), (13) are inconsistent by sub-proof #854. % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #142 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) op(e2, e2) = all_8_2 % 152.43/22.74 (3) all_58_29 = all_8_2 % 152.43/22.74 (4) op(all_8_2, e2) = e0 % 152.43/22.74 (5) all_58_29 = e2 % 152.43/22.74 (6) ~ (all_8_2 = e0) % 152.43/22.74 (7) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | COMBINE_EQS: (3), (5) imply: % 152.43/22.74 | (8) all_8_2 = e2 % 152.43/22.74 | % 152.43/22.74 | SIMP: (8) implies: % 152.43/22.74 | (9) all_8_2 = e2 % 152.43/22.74 | % 152.43/22.74 | REDUCE: (6), (9) imply: % 152.43/22.74 | (10) ~ (e2 = e0) % 152.43/22.74 | % 152.43/22.74 | REF_CLOSE: (1), (2), (4), (7), (9), (10) are inconsistent by sub-proof #153. % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #143 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) op(e3, e2) = e0 % 152.43/22.74 (3) op(e3, e2) = e2 % 152.43/22.74 (4) op(e3, e2) = all_58_1 % 152.43/22.74 (5) ~ (e2 = e0) % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | GROUND_INST: instantiating (1) with e2, all_58_1, e2, e3, simplifying with % 152.43/22.74 | (3), (4) gives: % 152.43/22.74 | (6) all_58_1 = e2 % 152.43/22.74 | % 152.43/22.74 | GROUND_INST: instantiating (1) with e0, all_58_1, e2, e3, simplifying with % 152.43/22.74 | (2), (4) gives: % 152.43/22.74 | (7) all_58_1 = e0 % 152.43/22.74 | % 152.43/22.74 | COMBINE_EQS: (6), (7) imply: % 152.43/22.74 | (8) e2 = e0 % 152.43/22.74 | % 152.43/22.74 | REDUCE: (5), (8) imply: % 152.43/22.74 | (9) $false % 152.43/22.74 | % 152.43/22.74 | CLOSE: (9) is inconsistent. % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #144 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (3) op(e2, e2) = all_8_2 % 152.43/22.74 (4) all_58_29 = all_8_2 % 152.43/22.74 (5) ~ (e2 = e1) % 152.43/22.74 (6) op(all_8_2, e2) = e0 % 152.43/22.74 (7) ~ (all_10_2 = e2) % 152.43/22.74 (8) all_58_28 = all_10_2 % 152.43/22.74 (9) all_58_30 = e1 % 152.43/22.74 (10) ~ (e2 = e0) % 152.43/22.74 (11) all_58_31 = e0 % 152.43/22.74 (12) ~ (all_8_2 = e0) % 152.43/22.74 (13) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (2) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (14) all_58_28 = e2 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (8), (14) imply: % 152.43/22.74 | | (15) all_10_2 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (7), (15) imply: % 152.43/22.74 | | (16) $false % 152.43/22.74 | | % 152.43/22.74 | | CLOSE: (16) is inconsistent. % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (17) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (13), (17) are % 152.43/22.74 | | inconsistent by sub-proof #146. % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #145 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (3) op(e2, e2) = all_8_2 % 152.43/22.74 (4) all_58_29 = all_8_2 % 152.43/22.74 (5) ~ (e2 = e1) % 152.43/22.74 (6) op(all_8_2, e2) = e0 % 152.43/22.74 (7) all_58_30 = e1 % 152.43/22.74 (8) ~ (e2 = e0) % 152.43/22.74 (9) all_58_31 = e0 % 152.43/22.74 (10) all_58_28 = e3 % 152.43/22.74 (11) ~ (e3 = e2) % 152.43/22.74 (12) ~ (all_8_2 = e0) % 152.43/22.74 (13) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (2) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (14) all_58_28 = e2 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (10), (14) imply: % 152.43/22.74 | | (15) e3 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (11), (15) imply: % 152.43/22.74 | | (16) $false % 152.43/22.74 | | % 152.43/22.74 | | CLOSE: (16) is inconsistent. % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (17) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (12), (13), (17) are % 152.43/22.74 | | inconsistent by sub-proof #146. % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #146 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) op(e2, e2) = all_8_2 % 152.43/22.74 (3) all_58_29 = all_8_2 % 152.43/22.74 (4) ~ (e2 = e1) % 152.43/22.74 (5) op(all_8_2, e2) = e0 % 152.43/22.74 (6) all_58_30 = e1 % 152.43/22.74 (7) ~ (e2 = e0) % 152.43/22.74 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 (9) all_58_31 = e0 % 152.43/22.74 (10) ~ (all_8_2 = e0) % 152.43/22.74 (11) op(e2, all_8_2) = all_58_9 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (8) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (12) all_58_29 = e2 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (3), (12) imply: % 152.43/22.74 | | (13) all_8_2 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (1), (2), (5), (7), (11), (13) are inconsistent by sub-proof % 152.43/22.74 | | #153. % 152.43/22.74 | | % 152.43/22.74 | Case 2: % 152.43/22.74 | | % 152.43/22.74 | | (14) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.74 | | % 152.43/22.74 | | REF_CLOSE: (4), (6), (7), (9), (14) are inconsistent by sub-proof #846. % 152.43/22.74 | | % 152.43/22.74 | End of split % 152.43/22.74 | % 152.43/22.74 End of proof % 152.43/22.74 % 152.43/22.74 Sub-proof #147 shows that the following formulas are inconsistent: % 152.43/22.74 ---------------------------------------------------------------- % 152.43/22.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.74 (2) all_56_7 = all_52_6 % 152.43/22.74 (3) ~ (all_52_6 = e0) % 152.43/22.74 (4) all_56_1 = all_52_4 % 152.43/22.74 (5) all_56_3 = all_8_2 % 152.43/22.74 (6) op(all_8_2, e2) = e0 % 152.43/22.74 (7) all_56_13 = all_52_7 % 152.43/22.74 (8) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.74 (9) ~ (all_52_4 = e0) % 152.43/22.74 (10) ~ (all_52_7 = all_8_2) % 152.43/22.74 (11) ~ (all_52_7 = e0) % 152.43/22.74 (12) op(e0, e2) = all_52_7 % 152.43/22.74 % 152.43/22.74 Begin of proof % 152.43/22.74 | % 152.43/22.74 | BETA: splitting (8) gives: % 152.43/22.74 | % 152.43/22.74 | Case 1: % 152.43/22.74 | | % 152.43/22.74 | | (13) all_56_1 = e0 % 152.43/22.74 | | % 152.43/22.74 | | COMBINE_EQS: (4), (13) imply: % 152.43/22.74 | | (14) all_52_4 = e0 % 152.43/22.74 | | % 152.43/22.74 | | REDUCE: (9), (14) imply: % 152.43/22.74 | | (15) $false % 152.43/22.74 | | % 152.43/22.74 | | CLOSE: (15) is inconsistent. % 152.43/22.75 | | % 152.43/22.75 | Case 2: % 152.43/22.75 | | % 152.43/22.75 | | (16) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.75 | | % 152.43/22.75 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (11), (12), (16) are % 152.43/22.75 | | inconsistent by sub-proof #148. % 152.43/22.75 | | % 152.43/22.75 | End of split % 152.43/22.75 | % 152.43/22.75 End of proof % 152.43/22.75 % 152.43/22.75 Sub-proof #148 shows that the following formulas are inconsistent: % 152.43/22.75 ---------------------------------------------------------------- % 152.43/22.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.75 (2) all_56_7 = all_52_6 % 152.43/22.75 (3) ~ (all_52_6 = e0) % 152.43/22.75 (4) all_56_3 = all_8_2 % 152.43/22.75 (5) op(all_8_2, e2) = e0 % 152.43/22.75 (6) all_56_13 = all_52_7 % 152.43/22.75 (7) ~ (all_52_7 = all_8_2) % 152.43/22.75 (8) ~ (all_52_7 = e0) % 152.43/22.75 (9) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 152.43/22.75 (10) op(e0, e2) = all_52_7 % 152.43/22.75 % 152.43/22.75 Begin of proof % 152.43/22.75 | % 152.43/22.75 | BETA: splitting (9) gives: % 152.43/22.75 | % 152.43/22.75 | Case 1: % 152.43/22.75 | | % 152.43/22.75 | | (11) all_56_3 = e0 % 152.43/22.75 | | % 152.43/22.75 | | REF_CLOSE: (1), (4), (5), (7), (10), (11) are inconsistent by sub-proof % 152.43/22.75 | | #149. % 152.43/22.75 | | % 152.43/22.75 | Case 2: % 152.43/22.75 | | % 152.43/22.75 | | (12) all_56_7 = e0 | all_56_13 = e0 % 152.43/22.75 | | % 152.43/22.75 | | BETA: splitting (12) gives: % 152.43/22.75 | | % 152.43/22.75 | | Case 1: % 152.43/22.75 | | | % 152.43/22.75 | | | (13) all_56_7 = e0 % 152.43/22.75 | | | % 152.43/22.75 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #803. % 152.43/22.75 | | | % 152.43/22.75 | | Case 2: % 152.43/22.75 | | | % 152.43/22.75 | | | (14) all_56_13 = e0 % 152.43/22.75 | | | % 152.43/22.75 | | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #802. % 152.43/22.75 | | | % 152.43/22.75 | | End of split % 152.43/22.75 | | % 152.43/22.75 | End of split % 152.43/22.75 | % 152.43/22.75 End of proof % 152.43/22.75 % 152.43/22.75 Sub-proof #149 shows that the following formulas are inconsistent: % 152.43/22.75 ---------------------------------------------------------------- % 152.43/22.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.75 (2) all_56_3 = e0 % 152.43/22.75 (3) all_56_3 = all_8_2 % 152.43/22.75 (4) op(all_8_2, e2) = e0 % 152.43/22.75 (5) ~ (all_52_7 = all_8_2) % 152.43/22.75 (6) op(e0, e2) = all_52_7 % 152.43/22.75 % 152.43/22.75 Begin of proof % 152.43/22.75 | % 152.43/22.75 | COMBINE_EQS: (2), (3) imply: % 152.43/22.75 | (7) all_8_2 = e0 % 152.43/22.75 | % 152.43/22.75 | REDUCE: (5), (7) imply: % 152.43/22.75 | (8) ~ (all_52_7 = e0) % 152.43/22.75 | % 152.43/22.75 | REDUCE: (4), (7) imply: % 152.43/22.75 | (9) op(e0, e2) = e0 % 152.43/22.75 | % 152.43/22.75 | REF_CLOSE: (1), (6), (8), (9) are inconsistent by sub-proof #240. % 152.43/22.75 | % 152.43/22.75 End of proof % 152.43/22.75 % 152.43/22.75 Sub-proof #150 shows that the following formulas are inconsistent: % 152.43/22.75 ---------------------------------------------------------------- % 152.43/22.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.75 (2) all_56_7 = all_52_6 % 152.43/22.75 (3) ~ (all_52_6 = all_6_2) % 152.43/22.75 (4) all_54_2 = all_52_8 % 152.43/22.75 (5) op(e1, all_6_2) = all_58_18 % 152.43/22.75 (6) ~ (all_52_8 = all_10_2) % 152.43/22.75 (7) all_54_7 = all_52_13 % 152.43/22.75 (8) ~ (all_52_6 = all_8_2) % 152.43/22.75 (9) all_56_6 = e0 % 152.43/22.75 (10) all_54_3 = all_52_12 % 152.43/22.75 (11) op(e2, e2) = all_8_2 % 152.43/22.75 (12) op(all_10_2, all_10_1) = all_10_0 % 152.43/22.75 (13) ~ (all_52_8 = all_6_2) % 152.43/22.75 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 152.43/22.75 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.43/22.75 (16) ~ (all_52_12 = all_52_13) % 152.43/22.75 (17) all_54_5 = all_8_2 % 152.43/22.75 (18) op(e3, e3) = all_10_2 % 152.43/22.75 (19) ~ (all_52_8 = all_52_12) % 152.43/22.75 (20) all_54_9 = all_52_6 % 152.43/22.75 (21) op(e1, e2) = all_52_6 % 152.43/22.75 (22) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.75 (23) ~ (all_52_13 = all_8_2) % 152.43/22.75 (24) ~ (all_52_6 = e0) % 152.43/22.75 (25) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.75 (26) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 152.43/22.75 (27) ~ (all_52_12 = e0) % 152.43/22.75 (28) all_56_11 = all_52_14 % 152.43/22.75 (29) ~ (all_52_13 = e0) % 152.43/22.75 (30) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.75 (31) ~ (all_10_2 = e1) % 152.43/22.75 (32) ~ (all_52_1 = all_8_2) % 152.43/22.75 (33) all_56_3 = all_8_2 % 152.43/22.75 (34) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.75 (35) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 152.43/22.75 (36) ~ (all_10_0 = e0) % 152.43/22.75 (37) all_56_9 = all_52_12 % 152.43/22.75 (38) all_58_29 = all_8_2 % 152.43/22.75 (39) all_58_14 = all_52_14 % 152.43/22.75 (40) op(all_8_2, e2) = e0 % 152.43/22.75 (41) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.75 (42) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.75 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.75 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.75 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.75 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.75 (all_58_27 = e0)) % 152.43/22.75 (43) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.75 (44) ~ (all_10_2 = e2) % 152.43/22.75 (45) op(e3, all_10_2) = all_58_0 % 152.43/22.75 (46) all_56_2 = all_52_1 % 152.43/22.75 (47) all_56_10 = all_52_13 % 152.43/22.75 (48) ~ (all_52_12 = all_10_2) % 152.43/22.75 (49) all_56_15 = e0 % 152.43/22.75 (50) ~ (e2 = e0) % 152.43/22.75 (51) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.75 (52) all_58_31 = e0 % 152.43/22.75 (53) all_58_27 = e0 % 152.43/22.75 (54) all_54_0 = all_10_2 % 152.43/22.75 (55) all_58_10 = all_52_13 % 152.43/22.75 (56) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.75 (57) ~ (all_52_8 = e0) % 152.43/22.75 (58) all_58_30 = all_6_2 % 152.43/22.75 (59) op(all_10_2, e3) = all_10_1 % 152.43/22.75 (60) ~ (all_8_2 = e0) % 152.43/22.75 (61) op(e2, all_8_2) = all_58_9 % 152.43/22.75 (62) all_54_4 = all_52_1 % 152.43/22.75 % 152.43/22.75 Begin of proof % 152.43/22.75 | % 152.43/22.75 | BETA: splitting (14) gives: % 152.43/22.75 | % 152.43/22.75 | Case 1: % 152.43/22.75 | | % 152.43/22.75 | | (63) all_54_0 = e1 % 152.43/22.75 | | % 152.43/22.75 | | REF_CLOSE: (31), (54), (63) are inconsistent by sub-proof #841. % 152.43/22.75 | | % 152.43/22.75 | Case 2: % 152.43/22.75 | | % 152.43/22.75 | | (64) all_54_0 = e3 | all_54_0 = e2 % 152.43/22.75 | | % 152.43/22.75 | | BETA: splitting (64) gives: % 152.43/22.75 | | % 152.43/22.75 | | Case 1: % 152.43/22.75 | | | % 152.43/22.75 | | | (65) all_54_0 = e2 % 152.43/22.75 | | | % 152.43/22.75 | | | REF_CLOSE: (44), (54), (65) are inconsistent by sub-proof #822. % 152.43/22.75 | | | % 152.43/22.75 | | Case 2: % 152.43/22.75 | | | % 152.43/22.75 | | | (66) all_54_0 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | COMBINE_EQS: (54), (66) imply: % 152.43/22.75 | | | (67) all_10_2 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | SIMP: (67) implies: % 152.43/22.75 | | | (68) all_10_2 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (6), (68) imply: % 152.43/22.75 | | | (69) ~ (all_52_8 = e3) % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (48), (68) imply: % 152.43/22.75 | | | (70) ~ (all_52_12 = e3) % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (12), (68) imply: % 152.43/22.75 | | | (71) op(e3, all_10_1) = all_10_0 % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (59), (68) imply: % 152.43/22.75 | | | (72) op(e3, e3) = all_10_1 % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (45), (68) imply: % 152.43/22.75 | | | (73) op(e3, e3) = all_58_0 % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (18), (68) imply: % 152.43/22.75 | | | (74) op(e3, e3) = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | GROUND_INST: instantiating (1) with all_10_1, all_58_0, e3, e3, % 152.43/22.75 | | | simplifying with (72), (73) gives: % 152.43/22.75 | | | (75) all_58_0 = all_10_1 % 152.43/22.75 | | | % 152.43/22.75 | | | GROUND_INST: instantiating (1) with e3, all_58_0, e3, e3, simplifying with % 152.43/22.75 | | | (73), (74) gives: % 152.43/22.75 | | | (76) all_58_0 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | COMBINE_EQS: (75), (76) imply: % 152.43/22.75 | | | (77) all_10_1 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | SIMP: (77) implies: % 152.43/22.75 | | | (78) all_10_1 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (71), (78) imply: % 152.43/22.75 | | | (79) op(e3, e3) = all_10_0 % 152.43/22.75 | | | % 152.43/22.75 | | | GROUND_INST: instantiating (1) with e3, all_10_0, e3, e3, simplifying with % 152.43/22.75 | | | (74), (79) gives: % 152.43/22.75 | | | (80) all_10_0 = e3 % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (36), (80) imply: % 152.43/22.75 | | | (81) ~ (e3 = e0) % 152.43/22.75 | | | % 152.43/22.75 | | | BETA: splitting (41) gives: % 152.43/22.75 | | | % 152.43/22.75 | | | Case 1: % 152.43/22.75 | | | | % 152.43/22.75 | | | | (82) all_56_9 = e3 % 152.43/22.75 | | | | % 152.43/22.75 | | | | COMBINE_EQS: (37), (82) imply: % 152.43/22.75 | | | | (83) all_52_12 = e3 % 152.43/22.75 | | | | % 152.43/22.75 | | | | REDUCE: (70), (83) imply: % 152.43/22.75 | | | | (84) $false % 152.43/22.75 | | | | % 152.43/22.75 | | | | CLOSE: (84) is inconsistent. % 152.43/22.75 | | | | % 152.43/22.75 | | | Case 2: % 152.43/22.75 | | | | % 152.43/22.75 | | | | (85) ~ (all_56_9 = e3) % 152.43/22.75 | | | | (86) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.75 | | | | % 152.43/22.75 | | | | BETA: splitting (42) gives: % 152.43/22.75 | | | | % 152.43/22.75 | | | | Case 1: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | (87) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) % 152.43/22.75 | | | | | & ~ (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = % 152.43/22.75 | | | | | e2) & ~ (all_58_10 = e1) & ~ (all_58_12 = e0)) % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | BETA: splitting (87) gives: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | Case 1: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | (88) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) % 152.43/22.75 | | | | | | & ~ (all_58_5 = e0) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | ALPHA: (88) implies: % 152.43/22.75 | | | | | | (89) ~ (all_58_0 = e3) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (76), (89) imply: % 152.43/22.75 | | | | | | (90) $false % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | CLOSE: (90) is inconsistent. % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | Case 2: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | (91) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = % 152.43/22.75 | | | | | | e1) & ~ (all_58_12 = e0) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | ALPHA: (91) implies: % 152.43/22.75 | | | | | | (92) ~ (all_58_10 = e1) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (55), (92) imply: % 152.43/22.75 | | | | | | (93) ~ (all_52_13 = e1) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | BETA: splitting (43) gives: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | Case 1: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | (94) all_56_9 = e1 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | COMBINE_EQS: (37), (94) imply: % 152.43/22.75 | | | | | | | (95) all_52_12 = e1 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | SIMP: (95) implies: % 152.43/22.75 | | | | | | | (96) all_52_12 = e1 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REDUCE: (19), (96) imply: % 152.43/22.75 | | | | | | | (97) ~ (all_52_8 = e1) % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REF_CLOSE: (1), (4), (11), (13), (30), (38), (40), (51), (52), % 152.43/22.75 | | | | | | | (57), (58), (60), (61), (69), (97) are inconsistent by % 152.43/22.75 | | | | | | | sub-proof #152. % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | Case 2: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | (98) ~ (all_56_9 = e1) % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REDUCE: (37), (98) imply: % 152.43/22.75 | | | | | | | (99) ~ (all_52_12 = e1) % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | BETA: splitting (34) gives: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | Case 1: % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | (100) all_54_3 = e1 % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | REF_CLOSE: (10), (99), (100) are inconsistent by sub-proof #723. % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | Case 2: % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | (101) all_54_3 = e3 | all_54_3 = e2 % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | BETA: splitting (101) gives: % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | Case 1: % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | (102) all_54_3 = e2 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | COMBINE_EQS: (10), (102) imply: % 152.43/22.75 | | | | | | | | | (103) all_52_12 = e2 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | SIMP: (103) implies: % 152.43/22.75 | | | | | | | | | (104) all_52_12 = e2 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | REDUCE: (16), (104) imply: % 152.43/22.75 | | | | | | | | | (105) ~ (all_52_13 = e2) % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | SIMP: (105) implies: % 152.43/22.75 | | | | | | | | | (106) ~ (all_52_13 = e2) % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | BETA: splitting (26) gives: % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | Case 1: % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | (107) all_54_7 = e1 % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | REF_CLOSE: (7), (93), (107) are inconsistent by sub-proof % 152.43/22.75 | | | | | | | | | | #605. % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | Case 2: % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | (108) all_54_7 = e3 | all_54_7 = e2 % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | BETA: splitting (108) gives: % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | Case 1: % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | (109) all_54_7 = e2 % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | REF_CLOSE: (7), (106), (109) are inconsistent by sub-proof % 152.43/22.75 | | | | | | | | | | | #604. % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | Case 2: % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | (110) all_54_7 = e3 % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | COMBINE_EQS: (7), (110) imply: % 152.43/22.75 | | | | | | | | | | | (111) all_52_13 = e3 % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | SIMP: (111) implies: % 152.43/22.75 | | | | | | | | | | | (112) all_52_13 = e3 % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | REDUCE: (23), (112) imply: % 152.43/22.75 | | | | | | | | | | | (113) ~ (all_8_2 = e3) % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | SIMP: (113) implies: % 152.43/22.75 | | | | | | | | | | | (114) ~ (all_8_2 = e3) % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (11), (15), (17), % 152.43/22.75 | | | | | | | | | | | (20), (21), (22), (24), (25), (32), (33), (35), % 152.43/22.75 | | | | | | | | | | | (38), (40), (46), (50), (51), (52), (56), (58), % 152.43/22.75 | | | | | | | | | | | (60), (61), (62), (81), (114) are inconsistent by % 152.43/22.75 | | | | | | | | | | | sub-proof #151. % 152.43/22.75 | | | | | | | | | | | % 152.43/22.75 | | | | | | | | | | End of split % 152.43/22.75 | | | | | | | | | | % 152.43/22.75 | | | | | | | | | End of split % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | Case 2: % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | (115) all_54_3 = e3 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | REF_CLOSE: (10), (70), (115) are inconsistent by sub-proof % 152.43/22.75 | | | | | | | | | #721. % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | End of split % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | End of split % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | End of split % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | End of split % 152.43/22.75 | | | | | % 152.43/22.75 | | | | Case 2: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | (116) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = % 152.43/22.75 | | | | | e1) & ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ % 152.43/22.75 | | | | | (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ (all_58_27 = % 152.43/22.75 | | | | | e0)) % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | BETA: splitting (116) gives: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | Case 1: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | (117) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = % 152.43/22.75 | | | | | | e1) & ~ (all_58_19 = e0) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | ALPHA: (117) implies: % 152.43/22.75 | | | | | | (118) ~ (all_58_14 = e3) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (39), (118) imply: % 152.43/22.75 | | | | | | (119) ~ (all_52_14 = e3) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | BETA: splitting (86) gives: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | Case 1: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | (120) all_56_10 = e3 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | COMBINE_EQS: (47), (120) imply: % 152.43/22.75 | | | | | | | (121) all_52_13 = e3 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | SIMP: (121) implies: % 152.43/22.75 | | | | | | | (122) all_52_13 = e3 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REDUCE: (23), (122) imply: % 152.43/22.75 | | | | | | | (123) ~ (all_8_2 = e3) % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | SIMP: (123) implies: % 152.43/22.75 | | | | | | | (124) ~ (all_8_2 = e3) % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (11), (15), (17), (20), % 152.43/22.75 | | | | | | | (21), (22), (24), (25), (32), (33), (35), (38), (40), % 152.43/22.75 | | | | | | | (46), (50), (51), (52), (56), (58), (60), (61), (62), % 152.43/22.75 | | | | | | | (81), (124) are inconsistent by sub-proof #151. % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | Case 2: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | (125) all_56_11 = e3 | all_56_15 = e3 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REF_CLOSE: (28), (49), (81), (119), (125) are inconsistent by % 152.43/22.75 | | | | | | | sub-proof #770. % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | End of split % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | Case 2: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | (126) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = % 152.43/22.75 | | | | | | e1) & ~ (all_58_27 = e0) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | ALPHA: (126) implies: % 152.43/22.75 | | | | | | (127) ~ (all_58_27 = e0) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (53), (127) imply: % 152.43/22.75 | | | | | | (128) $false % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | CLOSE: (128) is inconsistent. % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | End of split % 152.43/22.75 | | | | | % 152.43/22.75 | | | | End of split % 152.43/22.75 | | | | % 152.43/22.75 | | | End of split % 152.43/22.75 | | | % 152.43/22.75 | | End of split % 152.43/22.75 | | % 152.43/22.75 | End of split % 152.43/22.75 | % 152.43/22.75 End of proof % 152.43/22.75 % 152.43/22.75 Sub-proof #151 shows that the following formulas are inconsistent: % 152.43/22.75 ---------------------------------------------------------------- % 152.43/22.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.75 (2) all_56_7 = all_52_6 % 152.43/22.75 (3) ~ (all_52_6 = all_6_2) % 152.43/22.75 (4) op(e1, all_6_2) = all_58_18 % 152.43/22.75 (5) ~ (all_52_6 = all_8_2) % 152.43/22.75 (6) all_56_6 = e0 % 152.43/22.75 (7) op(e2, e2) = all_8_2 % 152.43/22.75 (8) ~ (all_8_2 = e3) % 152.43/22.75 (9) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.43/22.75 (10) all_54_5 = all_8_2 % 152.43/22.75 (11) all_54_9 = all_52_6 % 152.43/22.75 (12) op(e1, e2) = all_52_6 % 152.43/22.75 (13) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.75 (14) ~ (all_52_6 = e0) % 152.43/22.75 (15) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.75 (16) ~ (all_52_1 = all_8_2) % 152.43/22.75 (17) all_56_3 = all_8_2 % 152.43/22.75 (18) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 152.43/22.75 (19) all_58_29 = all_8_2 % 152.43/22.75 (20) op(all_8_2, e2) = e0 % 152.43/22.75 (21) ~ (e3 = e0) % 152.43/22.75 (22) all_56_2 = all_52_1 % 152.43/22.75 (23) ~ (e2 = e0) % 152.43/22.75 (24) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.75 (25) all_58_31 = e0 % 152.43/22.75 (26) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.75 (27) all_58_30 = all_6_2 % 152.43/22.75 (28) ~ (all_8_2 = e0) % 152.43/22.75 (29) op(e2, all_8_2) = all_58_9 % 152.43/22.75 (30) all_54_4 = all_52_1 % 152.43/22.75 % 152.43/22.75 Begin of proof % 152.43/22.75 | % 152.43/22.75 | BETA: splitting (26) gives: % 152.43/22.75 | % 152.43/22.75 | Case 1: % 152.43/22.75 | | % 152.43/22.75 | | (31) all_56_6 = e3 % 152.43/22.75 | | % 152.43/22.75 | | COMBINE_EQS: (6), (31) imply: % 152.43/22.75 | | (32) e3 = e0 % 152.43/22.75 | | % 152.43/22.75 | | REDUCE: (21), (32) imply: % 152.43/22.75 | | (33) $false % 152.43/22.75 | | % 152.43/22.75 | | CLOSE: (33) is inconsistent. % 152.43/22.75 | | % 152.43/22.75 | Case 2: % 152.43/22.75 | | % 152.43/22.75 | | (34) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.75 | | % 152.43/22.75 | | BETA: splitting (24) gives: % 152.43/22.75 | | % 152.43/22.75 | | Case 1: % 152.43/22.75 | | | % 152.43/22.75 | | | (35) all_58_29 = e2 % 152.43/22.75 | | | % 152.43/22.75 | | | COMBINE_EQS: (19), (35) imply: % 152.43/22.75 | | | (36) all_8_2 = e2 % 152.43/22.75 | | | % 152.43/22.75 | | | REF_CLOSE: (1), (7), (20), (23), (29), (36) are inconsistent by sub-proof % 152.43/22.75 | | | #153. % 152.43/22.75 | | | % 152.43/22.75 | | Case 2: % 152.43/22.75 | | | % 152.43/22.75 | | | (37) ~ (all_58_29 = e2) % 152.43/22.75 | | | % 152.43/22.75 | | | REDUCE: (19), (37) imply: % 152.43/22.75 | | | (38) ~ (all_8_2 = e2) % 152.43/22.75 | | | % 152.43/22.75 | | | BETA: splitting (9) gives: % 152.43/22.75 | | | % 152.43/22.75 | | | Case 1: % 152.43/22.75 | | | | % 152.43/22.75 | | | | (39) all_54_4 = e1 % 152.43/22.75 | | | | % 152.43/22.75 | | | | COMBINE_EQS: (30), (39) imply: % 152.43/22.75 | | | | (40) all_52_1 = e1 % 152.43/22.75 | | | | % 152.43/22.75 | | | | SIMP: (40) implies: % 152.43/22.75 | | | | (41) all_52_1 = e1 % 152.43/22.75 | | | | % 152.43/22.75 | | | | REDUCE: (16), (41) imply: % 152.43/22.75 | | | | (42) ~ (all_8_2 = e1) % 152.43/22.75 | | | | % 152.43/22.75 | | | | SIMP: (42) implies: % 152.43/22.75 | | | | (43) ~ (all_8_2 = e1) % 152.43/22.75 | | | | % 152.43/22.75 | | | | REF_CLOSE: (8), (10), (18), (38), (43) are inconsistent by sub-proof % 152.43/22.75 | | | | #531. % 152.43/22.75 | | | | % 152.43/22.75 | | | Case 2: % 152.43/22.75 | | | | % 152.43/22.75 | | | | (44) ~ (all_54_4 = e1) % 152.43/22.75 | | | | % 152.43/22.75 | | | | REDUCE: (30), (44) imply: % 152.43/22.75 | | | | (45) ~ (all_52_1 = e1) % 152.43/22.75 | | | | % 152.43/22.75 | | | | BETA: splitting (15) gives: % 152.43/22.75 | | | | % 152.43/22.75 | | | | Case 1: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | (46) all_56_2 = e1 % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | REF_CLOSE: (22), (45), (46) are inconsistent by sub-proof #450. % 152.43/22.75 | | | | | % 152.43/22.75 | | | | Case 2: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | (47) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | BETA: splitting (47) gives: % 152.43/22.75 | | | | | % 152.43/22.75 | | | | | Case 1: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | (48) all_56_3 = e1 % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | COMBINE_EQS: (17), (48) imply: % 152.43/22.75 | | | | | | (49) all_8_2 = e1 % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | SIMP: (49) implies: % 152.43/22.75 | | | | | | (50) all_8_2 = e1 % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | COMBINE_EQS: (19), (50) imply: % 152.43/22.75 | | | | | | (51) all_58_29 = e1 % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (5), (50) imply: % 152.43/22.75 | | | | | | (52) ~ (all_52_6 = e1) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (38), (50) imply: % 152.43/22.75 | | | | | | (53) ~ (e2 = e1) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | SIMP: (53) implies: % 152.43/22.75 | | | | | | (54) ~ (e2 = e1) % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | REDUCE: (20), (50) imply: % 152.43/22.75 | | | | | | (55) op(e1, e2) = e0 % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | BETA: splitting (24) gives: % 152.43/22.75 | | | | | | % 152.43/22.75 | | | | | | Case 1: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | (56) all_58_29 = e2 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | REF_CLOSE: (51), (54), (56) are inconsistent by sub-proof #687. % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | Case 2: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | (57) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | BETA: splitting (57) gives: % 152.43/22.75 | | | | | | | % 152.43/22.75 | | | | | | | Case 1: % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | (58) all_58_30 = e2 % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | COMBINE_EQS: (27), (58) imply: % 152.43/22.75 | | | | | | | | (59) all_6_2 = e2 % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | SIMP: (59) implies: % 152.43/22.75 | | | | | | | | (60) all_6_2 = e2 % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | REDUCE: (3), (60) imply: % 152.43/22.75 | | | | | | | | (61) ~ (all_52_6 = e2) % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | REDUCE: (4), (60) imply: % 152.43/22.75 | | | | | | | | (62) op(e1, e2) = all_58_18 % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | BETA: splitting (34) gives: % 152.43/22.75 | | | | | | | | % 152.43/22.75 | | | | | | | | Case 1: % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | (63) all_56_7 = e3 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | COMBINE_EQS: (2), (63) imply: % 152.43/22.75 | | | | | | | | | (64) all_52_6 = e3 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | SIMP: (64) implies: % 152.43/22.75 | | | | | | | | | (65) all_52_6 = e3 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | REDUCE: (12), (65) imply: % 152.43/22.75 | | | | | | | | | (66) op(e1, e2) = e3 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | GROUND_INST: instantiating (1) with e3, all_58_18, e2, e1, % 152.43/22.75 | | | | | | | | | simplifying with (62), (66) gives: % 152.43/22.75 | | | | | | | | | (67) all_58_18 = e3 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | GROUND_INST: instantiating (1) with e0, all_58_18, e2, e1, % 152.43/22.75 | | | | | | | | | simplifying with (55), (62) gives: % 152.43/22.75 | | | | | | | | | (68) all_58_18 = e0 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | COMBINE_EQS: (67), (68) imply: % 152.43/22.75 | | | | | | | | | (69) e3 = e0 % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | REDUCE: (21), (69) imply: % 152.43/22.75 | | | | | | | | | (70) $false % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | | CLOSE: (70) is inconsistent. % 152.43/22.75 | | | | | | | | | % 152.43/22.75 | | | | | | | | Case 2: % 152.43/22.75 | | | | | | | | | % 152.43/22.76 | | | | | | | | | (71) ~ (all_56_7 = e3) % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REDUCE: (2), (71) imply: % 152.43/22.76 | | | | | | | | | (72) ~ (all_52_6 = e3) % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REF_CLOSE: (11), (13), (52), (61), (72) are inconsistent by % 152.43/22.76 | | | | | | | | | sub-proof #619. % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | End of split % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | (73) all_58_31 = e2 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | REF_CLOSE: (23), (25), (73) are inconsistent by sub-proof #855. % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | End of split % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | End of split % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | Case 2: % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | (74) ~ (all_56_3 = e1) % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | REDUCE: (17), (74) imply: % 152.43/22.76 | | | | | | (75) ~ (all_8_2 = e1) % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | REF_CLOSE: (8), (10), (18), (38), (75) are inconsistent by sub-proof % 152.43/22.76 | | | | | | #531. % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | End of split % 152.43/22.76 | | | | | % 152.43/22.76 | | | | End of split % 152.43/22.76 | | | | % 152.43/22.76 | | | End of split % 152.43/22.76 | | | % 152.43/22.76 | | End of split % 152.43/22.76 | | % 152.43/22.76 | End of split % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #152 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.76 (2) all_54_2 = all_52_8 % 152.43/22.76 (3) op(e2, e2) = all_8_2 % 152.43/22.76 (4) ~ (all_52_8 = all_6_2) % 152.43/22.76 (5) ~ (all_52_8 = e3) % 152.43/22.76 (6) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.43/22.76 (7) all_58_29 = all_8_2 % 152.43/22.76 (8) op(all_8_2, e2) = e0 % 152.43/22.76 (9) ~ (all_52_8 = e1) % 152.43/22.76 (10) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.76 (11) all_58_31 = e0 % 152.43/22.76 (12) ~ (all_52_8 = e0) % 152.43/22.76 (13) all_58_30 = all_6_2 % 152.43/22.76 (14) ~ (all_8_2 = e0) % 152.43/22.76 (15) op(e2, all_8_2) = all_58_9 % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | BETA: splitting (6) gives: % 152.43/22.76 | % 152.43/22.76 | Case 1: % 152.43/22.76 | | % 152.43/22.76 | | (16) all_54_2 = e1 % 152.43/22.76 | | % 152.43/22.76 | | REF_CLOSE: (2), (9), (16) are inconsistent by sub-proof #819. % 152.43/22.76 | | % 152.43/22.76 | Case 2: % 152.43/22.76 | | % 152.43/22.76 | | (17) all_54_2 = e3 | all_54_2 = e2 % 152.43/22.76 | | % 152.43/22.76 | | BETA: splitting (17) gives: % 152.43/22.76 | | % 152.43/22.76 | | Case 1: % 152.43/22.76 | | | % 152.43/22.76 | | | (18) all_54_2 = e2 % 152.43/22.76 | | | % 152.43/22.76 | | | COMBINE_EQS: (2), (18) imply: % 152.43/22.76 | | | (19) all_52_8 = e2 % 152.43/22.76 | | | % 152.43/22.76 | | | SIMP: (19) implies: % 152.43/22.76 | | | (20) all_52_8 = e2 % 152.43/22.76 | | | % 152.43/22.76 | | | REDUCE: (4), (20) imply: % 152.43/22.76 | | | (21) ~ (all_6_2 = e2) % 152.43/22.76 | | | % 152.43/22.76 | | | SIMP: (21) implies: % 152.43/22.76 | | | (22) ~ (all_6_2 = e2) % 152.43/22.76 | | | % 152.43/22.76 | | | REDUCE: (12), (20) imply: % 152.43/22.76 | | | (23) ~ (e2 = e0) % 152.43/22.76 | | | % 152.43/22.76 | | | BETA: splitting (10) gives: % 152.43/22.76 | | | % 152.43/22.76 | | | Case 1: % 152.43/22.76 | | | | % 152.43/22.76 | | | | (24) all_58_29 = e2 % 152.43/22.76 | | | | % 152.43/22.76 | | | | COMBINE_EQS: (7), (24) imply: % 152.43/22.76 | | | | (25) all_8_2 = e2 % 152.43/22.76 | | | | % 152.43/22.76 | | | | REF_CLOSE: (1), (3), (8), (15), (23), (25) are inconsistent by sub-proof % 152.43/22.76 | | | | #153. % 152.43/22.76 | | | | % 152.43/22.76 | | | Case 2: % 152.43/22.76 | | | | % 152.43/22.76 | | | | (26) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.76 | | | | % 152.43/22.76 | | | | REF_CLOSE: (11), (13), (22), (23), (26) are inconsistent by sub-proof % 152.43/22.76 | | | | #817. % 152.43/22.76 | | | | % 152.43/22.76 | | | End of split % 152.43/22.76 | | | % 152.43/22.76 | | Case 2: % 152.43/22.76 | | | % 152.43/22.76 | | | (27) all_54_2 = e3 % 152.43/22.76 | | | % 152.43/22.76 | | | REF_CLOSE: (2), (5), (27) are inconsistent by sub-proof #816. % 152.43/22.76 | | | % 152.43/22.76 | | End of split % 152.43/22.76 | | % 152.43/22.76 | End of split % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #153 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.76 (2) op(e2, e2) = all_8_2 % 152.43/22.76 (3) all_8_2 = e2 % 152.43/22.76 (4) op(all_8_2, e2) = e0 % 152.43/22.76 (5) ~ (e2 = e0) % 152.43/22.76 (6) op(e2, all_8_2) = all_58_9 % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | REDUCE: (3), (4) imply: % 152.43/22.76 | (7) op(e2, e2) = e0 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (3), (6) imply: % 152.43/22.76 | (8) op(e2, e2) = all_58_9 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (2), (3) imply: % 152.43/22.76 | (9) op(e2, e2) = e2 % 152.43/22.76 | % 152.43/22.76 | GROUND_INST: instantiating (1) with e2, all_58_9, e2, e2, simplifying with % 152.43/22.76 | (8), (9) gives: % 152.43/22.76 | (10) all_58_9 = e2 % 152.43/22.76 | % 152.43/22.76 | GROUND_INST: instantiating (1) with e0, all_58_9, e2, e2, simplifying with % 152.43/22.76 | (7), (8) gives: % 152.43/22.76 | (11) all_58_9 = e0 % 152.43/22.76 | % 152.43/22.76 | COMBINE_EQS: (10), (11) imply: % 152.43/22.76 | (12) e2 = e0 % 152.43/22.76 | % 152.43/22.76 | SIMP: (12) implies: % 152.43/22.76 | (13) e2 = e0 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (5), (13) imply: % 152.43/22.76 | (14) $false % 152.43/22.76 | % 152.43/22.76 | CLOSE: (14) is inconsistent. % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #154 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.76 (2) all_56_7 = all_52_6 % 152.43/22.76 (3) ~ (all_52_6 = all_6_2) % 152.43/22.76 (4) ~ (all_52_6 = all_8_2) % 152.43/22.76 (5) all_56_4 = all_52_8 % 152.43/22.76 (6) all_56_6 = e0 % 152.43/22.76 (7) all_54_3 = all_52_12 % 152.43/22.76 (8) ~ (all_52_8 = all_6_2) % 152.43/22.76 (9) ~ (all_52_8 = all_52_12) % 152.43/22.76 (10) all_54_9 = all_52_6 % 152.43/22.76 (11) op(e1, e2) = all_52_6 % 152.43/22.76 (12) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.76 (13) op(e1, all_52_6) = all_58_16 % 152.43/22.76 (14) ~ (e3 = e1) % 152.43/22.76 (15) ~ (all_52_6 = e0) % 152.43/22.76 (16) ~ (all_52_12 = e0) % 152.43/22.76 (17) all_56_1 = e0 % 152.43/22.76 (18) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.76 (19) all_56_9 = all_52_12 % 152.43/22.76 (20) all_58_29 = all_8_2 % 152.43/22.76 (21) ~ (e2 = e1) % 152.43/22.76 (22) op(e3, e0) = all_52_12 % 152.43/22.76 (23) op(all_8_2, e2) = e0 % 152.43/22.76 (24) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.76 (25) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.76 (26) all_56_0 = e2 % 152.43/22.76 (27) ~ (e3 = e0) % 152.43/22.76 (28) op(all_8_2, e0) = all_8_0 % 152.43/22.76 (29) ~ (e2 = e0) % 152.43/22.76 (30) all_58_31 = e0 % 152.43/22.76 (31) all_58_28 = e2 % 152.43/22.76 (32) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.76 (33) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.76 (34) ~ (e1 = e0) % 152.43/22.76 (35) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.76 (36) ~ (all_52_8 = e0) % 152.43/22.76 (37) all_58_30 = all_6_2 % 152.43/22.76 (38) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.76 (39) ~ (e3 = e2) % 152.43/22.76 (40) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.76 (41) ~ (all_52_12 = e2) % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | BETA: splitting (24) gives: % 152.43/22.76 | % 152.43/22.76 | Case 1: % 152.43/22.76 | | % 152.43/22.76 | | (42) all_56_0 = e1 % 152.43/22.76 | | % 152.43/22.76 | | REF_CLOSE: (21), (26), (42) are inconsistent by sub-proof #796. % 152.43/22.76 | | % 152.43/22.76 | Case 2: % 152.43/22.76 | | % 152.43/22.76 | | (43) ~ (all_56_0 = e1) % 152.43/22.76 | | (44) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.76 | | % 152.43/22.76 | | BETA: splitting (35) gives: % 152.43/22.76 | | % 152.43/22.76 | | Case 1: % 152.43/22.76 | | | % 152.43/22.76 | | | (45) all_56_0 = e3 % 152.43/22.76 | | | % 152.43/22.76 | | | COMBINE_EQS: (26), (45) imply: % 152.43/22.76 | | | (46) e3 = e2 % 152.43/22.76 | | | % 152.43/22.76 | | | REDUCE: (39), (46) imply: % 152.43/22.76 | | | (47) $false % 152.43/22.76 | | | % 152.43/22.76 | | | CLOSE: (47) is inconsistent. % 152.43/22.76 | | | % 152.43/22.76 | | Case 2: % 152.43/22.76 | | | % 152.43/22.76 | | | (48) ~ (all_56_0 = e3) % 152.43/22.76 | | | (49) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.76 | | | % 152.43/22.76 | | | REDUCE: (26), (48) imply: % 152.43/22.76 | | | (50) ~ (e3 = e2) % 152.43/22.76 | | | % 152.43/22.76 | | | BETA: splitting (33) gives: % 152.43/22.76 | | | % 152.43/22.76 | | | Case 1: % 152.43/22.76 | | | | % 152.43/22.76 | | | | (51) all_58_28 = e3 % 152.43/22.76 | | | | % 152.43/22.76 | | | | COMBINE_EQS: (31), (51) imply: % 152.43/22.76 | | | | (52) e3 = e2 % 152.43/22.76 | | | | % 152.43/22.76 | | | | REDUCE: (39), (52) imply: % 152.43/22.76 | | | | (53) $false % 152.43/22.76 | | | | % 152.43/22.76 | | | | CLOSE: (53) is inconsistent. % 152.43/22.76 | | | | % 152.43/22.76 | | | Case 2: % 152.43/22.76 | | | | % 152.43/22.76 | | | | (54) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.76 | | | | % 152.43/22.76 | | | | BETA: splitting (38) gives: % 152.43/22.76 | | | | % 152.43/22.76 | | | | Case 1: % 152.43/22.76 | | | | | % 152.43/22.76 | | | | | (55) all_58_28 = e1 % 152.43/22.76 | | | | | % 152.43/22.76 | | | | | REF_CLOSE: (21), (31), (55) are inconsistent by sub-proof #856. % 152.43/22.76 | | | | | % 152.43/22.76 | | | | Case 2: % 152.43/22.76 | | | | | % 152.43/22.76 | | | | | (56) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.76 | | | | | % 152.43/22.76 | | | | | BETA: splitting (25) gives: % 152.43/22.76 | | | | | % 152.43/22.76 | | | | | Case 1: % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | (57) all_56_9 = e3 % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | COMBINE_EQS: (19), (57) imply: % 152.43/22.76 | | | | | | (58) all_52_12 = e3 % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | REDUCE: (9), (58) imply: % 152.43/22.76 | | | | | | (59) ~ (all_52_8 = e3) % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | BETA: splitting (44) gives: % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | Case 1: % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | (60) all_56_1 = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | COMBINE_EQS: (17), (60) imply: % 152.43/22.76 | | | | | | | (61) e1 = e0 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | REDUCE: (34), (61) imply: % 152.43/22.76 | | | | | | | (62) $false % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | CLOSE: (62) is inconsistent. % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | Case 2: % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | (63) all_56_4 = e1 | all_56_9 = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | BETA: splitting (63) gives: % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | (64) all_56_4 = e1 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | COMBINE_EQS: (5), (64) imply: % 152.43/22.76 | | | | | | | | (65) all_52_8 = e1 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | SIMP: (65) implies: % 152.43/22.76 | | | | | | | | (66) all_52_8 = e1 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | REDUCE: (8), (66) imply: % 152.43/22.76 | | | | | | | | (67) ~ (all_6_2 = e1) % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | SIMP: (67) implies: % 152.43/22.76 | | | | | | | | (68) ~ (all_6_2 = e1) % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | REDUCE: (59), (66) imply: % 152.43/22.76 | | | | | | | | (69) ~ (e3 = e1) % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | BETA: splitting (56) gives: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | (70) all_58_29 = e1 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | COMBINE_EQS: (20), (70) imply: % 152.43/22.76 | | | | | | | | | (71) all_8_2 = e1 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | SIMP: (71) implies: % 152.43/22.76 | | | | | | | | | (72) all_8_2 = e1 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REDUCE: (4), (72) imply: % 152.43/22.76 | | | | | | | | | (73) ~ (all_52_6 = e1) % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REDUCE: (23), (72) imply: % 152.43/22.76 | | | | | | | | | (74) op(e1, e2) = e0 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | BETA: splitting (54) gives: % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | (75) all_58_29 = e3 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | COMBINE_EQS: (70), (75) imply: % 152.43/22.76 | | | | | | | | | | (76) e3 = e1 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | REDUCE: (14), (76) imply: % 152.43/22.76 | | | | | | | | | | (77) $false % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | CLOSE: (77) is inconsistent. % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | (78) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | BETA: splitting (78) gives: % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | (79) all_58_30 = e3 % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | COMBINE_EQS: (37), (79) imply: % 152.43/22.76 | | | | | | | | | | | (80) all_6_2 = e3 % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | REDUCE: (3), (80) imply: % 152.43/22.76 | | | | | | | | | | | (81) ~ (all_52_6 = e3) % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | BETA: splitting (40) gives: % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | (82) all_56_6 = e2 % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | COMBINE_EQS: (6), (82) imply: % 152.43/22.76 | | | | | | | | | | | | (83) e2 = e0 % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | REDUCE: (29), (83) imply: % 152.43/22.76 | | | | | | | | | | | | (84) $false % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | CLOSE: (84) is inconsistent. % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | (85) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | BETA: splitting (85) gives: % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | | (86) all_56_7 = e2 % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | | COMBINE_EQS: (2), (86) imply: % 152.43/22.76 | | | | | | | | | | | | | (87) all_52_6 = e2 % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | | REF_CLOSE: (1), (11), (13), (15), (74), (87) are inconsistent % 152.43/22.76 | | | | | | | | | | | | | by sub-proof #157. % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | | (88) ~ (all_56_7 = e2) % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | | REDUCE: (2), (88) imply: % 152.43/22.76 | | | | | | | | | | | | | (89) ~ (all_52_6 = e2) % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | | REF_CLOSE: (10), (12), (73), (81), (89) are inconsistent by % 152.43/22.76 | | | | | | | | | | | | | sub-proof #619. % 152.43/22.76 | | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | | End of split % 152.43/22.76 | | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | End of split % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | (90) all_58_31 = e3 % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | | REF_CLOSE: (27), (30), (90) are inconsistent by sub-proof % 152.43/22.76 | | | | | | | | | | | #853. % 152.43/22.76 | | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | End of split % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | End of split % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | (91) all_58_30 = e1 | all_58_31 = e1 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REF_CLOSE: (30), (34), (37), (68), (91) are inconsistent by % 152.43/22.76 | | | | | | | | | sub-proof #824. % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | End of split % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | (92) all_56_9 = e1 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | COMBINE_EQS: (57), (92) imply: % 152.43/22.76 | | | | | | | | (93) e3 = e1 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | REDUCE: (14), (93) imply: % 152.43/22.76 | | | | | | | | (94) $false % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | CLOSE: (94) is inconsistent. % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | End of split % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | End of split % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | Case 2: % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | (95) ~ (all_56_9 = e3) % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | REDUCE: (19), (95) imply: % 152.43/22.76 | | | | | | (96) ~ (all_52_12 = e3) % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | BETA: splitting (18) gives: % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | | Case 1: % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | (97) all_54_3 = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | COMBINE_EQS: (7), (97) imply: % 152.43/22.76 | | | | | | | (98) all_52_12 = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | SIMP: (98) implies: % 152.43/22.76 | | | | | | | (99) all_52_12 = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | COMBINE_EQS: (19), (99) imply: % 152.43/22.76 | | | | | | | (100) all_56_9 = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | REDUCE: (96), (99) imply: % 152.43/22.76 | | | | | | | (101) ~ (e3 = e1) % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | REDUCE: (22), (99) imply: % 152.43/22.76 | | | | | | | (102) op(e3, e0) = e1 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | BETA: splitting (49) gives: % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | (103) all_56_1 = e3 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | COMBINE_EQS: (17), (103) imply: % 152.43/22.76 | | | | | | | | (104) e3 = e0 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | REDUCE: (27), (104) imply: % 152.43/22.76 | | | | | | | | (105) $false % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | CLOSE: (105) is inconsistent. % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | (106) all_56_4 = e3 | all_56_9 = e3 % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | BETA: splitting (106) gives: % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | (107) all_56_4 = e3 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | COMBINE_EQS: (5), (107) imply: % 152.43/22.76 | | | | | | | | | (108) all_52_8 = e3 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | SIMP: (108) implies: % 152.43/22.76 | | | | | | | | | (109) all_52_8 = e3 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REDUCE: (8), (109) imply: % 152.43/22.76 | | | | | | | | | (110) ~ (all_6_2 = e3) % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | SIMP: (110) implies: % 152.43/22.76 | | | | | | | | | (111) ~ (all_6_2 = e3) % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | BETA: splitting (54) gives: % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | Case 1: % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | (112) all_58_29 = e3 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | COMBINE_EQS: (20), (112) imply: % 152.43/22.76 | | | | | | | | | | (113) all_8_2 = e3 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | SIMP: (113) implies: % 152.43/22.76 | | | | | | | | | | (114) all_8_2 = e3 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | REDUCE: (28), (114) imply: % 152.43/22.76 | | | | | | | | | | (115) op(e3, e0) = all_8_0 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | REF_CLOSE: (1), (32), (102), (114), (115) are inconsistent by % 152.43/22.76 | | | | | | | | | | sub-proof #156. % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | (116) all_58_30 = e3 | all_58_31 = e3 % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | | REF_CLOSE: (27), (30), (37), (111), (116) are inconsistent by % 152.43/22.76 | | | | | | | | | | sub-proof #768. % 152.43/22.76 | | | | | | | | | | % 152.43/22.76 | | | | | | | | | End of split % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | Case 2: % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | (117) all_56_9 = e3 % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | | REF_CLOSE: (14), (100), (117) are inconsistent by sub-proof % 152.43/22.76 | | | | | | | | | #155. % 152.43/22.76 | | | | | | | | | % 152.43/22.76 | | | | | | | | End of split % 152.43/22.76 | | | | | | | | % 152.43/22.76 | | | | | | | End of split % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | Case 2: % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | (118) all_54_3 = e3 | all_54_3 = e2 % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | | REF_CLOSE: (7), (41), (96), (118) are inconsistent by sub-proof % 152.43/22.76 | | | | | | | #613. % 152.43/22.76 | | | | | | | % 152.43/22.76 | | | | | | End of split % 152.43/22.76 | | | | | | % 152.43/22.76 | | | | | End of split % 152.43/22.76 | | | | | % 152.43/22.76 | | | | End of split % 152.43/22.76 | | | | % 152.43/22.76 | | | End of split % 152.43/22.76 | | | % 152.43/22.76 | | End of split % 152.43/22.76 | | % 152.43/22.76 | End of split % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #155 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) all_56_9 = e3 % 152.43/22.76 (2) all_56_9 = e1 % 152.43/22.76 (3) ~ (e3 = e1) % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | COMBINE_EQS: (1), (2) imply: % 152.43/22.76 | (4) e3 = e1 % 152.43/22.76 | % 152.43/22.76 | SIMP: (4) implies: % 152.43/22.76 | (5) e3 = e1 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (3), (5) imply: % 152.43/22.76 | (6) $false % 152.43/22.76 | % 152.43/22.76 | CLOSE: (6) is inconsistent. % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #156 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.76 (2) all_8_2 = e3 % 152.43/22.76 (3) op(e3, e0) = e1 % 152.43/22.76 (4) ~ (all_8_0 = e1) | ~ (all_8_2 = e3) % 152.43/22.76 (5) op(e3, e0) = all_8_0 % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | BETA: splitting (4) gives: % 152.43/22.76 | % 152.43/22.76 | Case 1: % 152.43/22.76 | | % 152.43/22.76 | | (6) ~ (all_8_0 = e1) % 152.43/22.76 | | % 152.43/22.76 | | GROUND_INST: instantiating (1) with e1, all_8_0, e0, e3, simplifying with % 152.43/22.76 | | (3), (5) gives: % 152.43/22.76 | | (7) all_8_0 = e1 % 152.43/22.76 | | % 152.43/22.76 | | REDUCE: (6), (7) imply: % 152.43/22.76 | | (8) $false % 152.43/22.76 | | % 152.43/22.76 | | CLOSE: (8) is inconsistent. % 152.43/22.76 | | % 152.43/22.76 | Case 2: % 152.43/22.76 | | % 152.43/22.76 | | (9) ~ (all_8_2 = e3) % 152.43/22.76 | | % 152.43/22.76 | | REDUCE: (2), (9) imply: % 152.43/22.76 | | (10) $false % 152.43/22.76 | | % 152.43/22.76 | | CLOSE: (10) is inconsistent. % 152.43/22.76 | | % 152.43/22.76 | End of split % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #157 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.76 (2) all_52_6 = e2 % 152.43/22.76 (3) op(e1, e2) = all_52_6 % 152.43/22.76 (4) op(e1, all_52_6) = all_58_16 % 152.43/22.76 (5) ~ (all_52_6 = e0) % 152.43/22.76 (6) op(e1, e2) = e0 % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | REDUCE: (2), (5) imply: % 152.43/22.76 | (7) ~ (e2 = e0) % 152.43/22.76 | % 152.43/22.76 | REDUCE: (2), (4) imply: % 152.43/22.76 | (8) op(e1, e2) = all_58_16 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (2), (3) imply: % 152.43/22.76 | (9) op(e1, e2) = e2 % 152.43/22.76 | % 152.43/22.76 | GROUND_INST: instantiating (1) with e2, all_58_16, e2, e1, simplifying with % 152.43/22.76 | (8), (9) gives: % 152.43/22.76 | (10) all_58_16 = e2 % 152.43/22.76 | % 152.43/22.76 | GROUND_INST: instantiating (1) with e0, all_58_16, e2, e1, simplifying with % 152.43/22.76 | (6), (8) gives: % 152.43/22.76 | (11) all_58_16 = e0 % 152.43/22.76 | % 152.43/22.76 | COMBINE_EQS: (10), (11) imply: % 152.43/22.76 | (12) e2 = e0 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (7), (12) imply: % 152.43/22.76 | (13) $false % 152.43/22.76 | % 152.43/22.76 | CLOSE: (13) is inconsistent. % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #158 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) all_54_5 = all_8_2 % 152.43/22.76 (2) all_54_5 = e0 % 152.43/22.76 (3) ~ (all_8_2 = e0) % 152.43/22.76 % 152.43/22.76 Begin of proof % 152.43/22.76 | % 152.43/22.76 | COMBINE_EQS: (1), (2) imply: % 152.43/22.76 | (4) all_8_2 = e0 % 152.43/22.76 | % 152.43/22.76 | SIMP: (4) implies: % 152.43/22.76 | (5) all_8_2 = e0 % 152.43/22.76 | % 152.43/22.76 | REDUCE: (3), (5) imply: % 152.43/22.76 | (6) $false % 152.43/22.76 | % 152.43/22.76 | CLOSE: (6) is inconsistent. % 152.43/22.76 | % 152.43/22.76 End of proof % 152.43/22.76 % 152.43/22.76 Sub-proof #159 shows that the following formulas are inconsistent: % 152.43/22.76 ---------------------------------------------------------------- % 152.43/22.76 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 152.43/22.76 (2) all_58_31 = all_4_2 % 152.43/22.76 (3) ~ (all_52_8 = all_52_9) % 152.43/22.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.43/22.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 152.43/22.76 (5) all_54_13 = all_52_7 % 152.43/22.76 (6) ~ (all_52_2 = all_52_3) % 152.43/22.76 (7) all_58_11 = all_52_9 % 152.43/22.76 (8) all_56_15 = all_4_2 % 152.43/22.76 (9) all_56_7 = all_52_6 % 152.43/22.76 (10) ~ (all_52_6 = all_6_2) % 152.43/22.76 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 152.43/22.76 (12) all_54_2 = all_52_8 % 152.43/22.76 (13) op(e2, e0) = all_58_9 % 152.43/22.76 (14) all_54_8 = all_52_2 % 152.43/22.76 (15) op(e1, all_6_2) = all_58_18 % 152.43/22.76 (16) op(all_10_2, all_10_1) = e0 % 152.43/22.76 (17) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.43/22.76 (18) ~ (all_52_8 = all_10_2) % 152.43/22.76 (19) all_58_15 = all_52_2 % 152.43/22.76 (20) all_58_26 = all_52_11 % 152.43/22.76 (21) op(e1, all_52_14) = all_58_19 % 152.43/22.76 (22) all_56_3 = e0 % 152.43/22.76 (23) ~ (all_52_8 = all_52_11) % 152.43/22.76 (24) ~ (all_52_11 = all_4_2) % 152.43/22.76 (25) all_54_7 = all_52_13 % 152.43/22.76 (26) all_58_6 = all_52_12 % 152.43/22.76 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 152.43/22.76 (28) all_56_4 = all_52_8 % 152.43/22.76 (29) all_54_3 = all_52_12 % 152.43/22.76 (30) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.76 (31) all_54_1 = all_52_4 % 152.43/22.76 (32) op(e0, all_4_2) = all_58_27 % 152.43/22.77 (33) op(e0, e2) = all_8_1 % 152.43/22.77 (34) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 152.43/22.77 (35) ~ (all_52_4 = all_52_6) % 152.43/22.77 (36) all_58_13 = all_52_13 % 152.43/22.77 (37) op(e0, e1) = all_52_11 % 152.43/22.77 (38) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 152.43/22.77 (39) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.43/22.77 (40) ~ (all_52_6 = all_52_7) % 152.43/22.77 (41) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 152.43/22.77 (42) all_54_11 = all_52_14 % 152.43/22.77 (43) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 152.43/22.77 (44) all_58_20 = all_52_14 % 152.43/22.77 (45) ~ (all_52_8 = all_6_2) % 152.43/22.77 (46) op(e2, e3) = all_52_1 % 152.43/22.77 (47) ~ (all_52_12 = all_52_13) % 152.43/22.77 (48) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.43/22.77 (49) all_54_10 = all_6_2 % 152.43/22.77 (50) op(e0, all_52_7) = all_58_23 % 152.43/22.77 (51) ~ (all_52_6 = all_52_14) % 152.43/22.77 (52) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 152.43/22.77 (53) all_54_6 = all_52_9 % 152.43/22.77 (54) all_54_15 = all_4_2 % 152.43/22.77 (55) ~ (all_52_4 = all_52_7) % 152.43/22.77 (56) ~ (all_52_2 = all_6_2) % 152.43/22.77 (57) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 152.43/22.77 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 152.43/22.77 (58) op(e3, e3) = all_10_2 % 152.43/22.77 (59) ~ (all_52_8 = all_52_12) % 152.43/22.77 (60) all_54_9 = all_52_6 % 152.43/22.77 (61) ~ (all_52_13 = all_4_2) % 152.43/22.77 (62) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 152.43/22.77 (63) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 152.43/22.77 (64) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 152.43/22.77 (65) ~ (e3 = e1) % 152.43/22.77 (66) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 152.43/22.77 (67) ~ (all_52_6 = e0) % 152.43/22.77 (68) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.43/22.77 (69) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 152.43/22.77 (70) ~ (all_52_1 = all_52_13) % 152.43/22.77 (71) all_56_5 = all_52_9 % 152.43/22.77 (72) all_54_14 = all_52_11 % 152.43/22.77 (73) op(e0, all_8_1) = all_8_0 % 152.43/22.77 (74) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.43/22.77 (75) all_56_12 = all_52_3 % 152.43/22.77 (76) ~ (all_52_3 = all_52_7) % 152.43/22.77 (77) all_58_2 = all_52_4 % 152.43/22.77 (78) all_20_2 = all_4_2 % 152.43/22.77 (79) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 152.43/22.77 (80) all_56_11 = all_52_14 % 152.43/22.77 (81) all_56_1 = all_52_4 % 152.43/22.77 (82) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 152.43/22.77 (83) ~ (all_52_13 = e0) % 152.43/22.77 (84) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.43/22.77 (85) ~ (all_52_3 = all_4_2) % 152.43/22.77 (86) op(e1, e0) = all_52_14 % 152.43/22.77 (87) ~ (all_52_9 = all_52_11) % 152.43/22.77 (88) ~ (all_52_9 = e0) % 152.43/22.77 (89) all_58_24 = all_52_7 % 152.43/22.77 (90) ~ (all_52_13 = all_52_14) % 152.43/22.77 (91) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.43/22.77 (92) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 152.43/22.77 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 152.43/22.77 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 152.43/22.77 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 152.43/22.77 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 152.43/22.77 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 152.43/22.77 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 152.43/22.77 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 152.43/22.77 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 152.43/22.77 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 152.43/22.77 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.43/22.77 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.43/22.77 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.43/22.77 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.43/22.77 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.43/22.77 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 152.43/22.77 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.77 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.43/22.77 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.77 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.43/22.77 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.43/22.77 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 152.43/22.77 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.43/22.77 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.43/22.77 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.43/22.77 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 152.43/22.77 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 152.43/22.77 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 152.43/22.77 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.43/22.77 e0) % 152.43/22.77 (93) ~ (all_52_4 = all_52_8) % 152.43/22.77 (94) op(e1, all_52_2) = all_58_14 % 152.43/22.77 (95) all_58_29 = e0 % 152.43/22.77 (96) op(e2, e1) = all_52_9 % 152.43/22.77 (97) all_56_9 = all_52_12 % 152.43/22.77 (98) all_58_29 = all_8_2 % 152.43/22.77 (99) ~ (all_52_12 = all_52_14) % 152.43/22.77 (100) all_58_8 = all_52_1 % 152.43/22.77 (101) ~ (e2 = e1) % 152.43/22.77 (102) op(e3, e0) = all_52_12 % 152.43/22.77 (103) all_56_6 = all_52_2 % 152.43/22.77 (104) ~ (all_52_2 = all_52_6) % 152.43/22.77 (105) all_18_2 = all_6_2 % 152.43/22.77 (106) all_56_13 = all_52_7 % 152.43/22.77 (107) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.43/22.77 (108) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 152.43/22.77 (109) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 152.43/22.77 (110) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.43/22.77 (111) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 152.43/22.77 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 152.43/22.77 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 152.43/22.77 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 152.43/22.77 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 152.43/22.77 (all_58_27 = e0)) % 152.43/22.77 (112) ~ (all_52_9 = all_52_13) % 152.43/22.77 (113) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.77 (114) ~ (all_52_4 = e0) % 152.43/22.77 (115) ~ (all_52_11 = all_6_2) % 152.43/22.77 (116) op(e3, all_10_2) = all_58_0 % 152.43/22.77 (117) ~ (e3 = e0) % 152.43/22.77 (118) all_56_2 = all_52_1 % 152.43/22.77 (119) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 152.43/22.77 (120) op(e3, all_52_12) = all_58_5 % 152.43/22.77 (121) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 152.43/22.77 (122) all_56_10 = all_52_13 % 152.43/22.77 (123) ~ (all_52_12 = all_10_2) % 152.43/22.77 (124) ~ (all_52_1 = all_52_3) % 152.43/22.77 (125) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 152.43/22.77 (126) all_56_14 = all_52_11 % 152.43/22.77 (127) all_58_28 = all_10_2 % 152.43/22.77 (128) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 152.43/22.77 (129) all_58_17 = all_52_6 % 152.43/22.77 (130) ~ (all_52_1 = all_52_9) % 152.43/22.77 (131) op(e3, e1) = all_52_8 % 152.43/22.77 (132) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 152.43/22.77 (133) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 152.43/22.77 (134) ~ (all_52_7 = all_52_11) % 152.43/22.77 (135) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.43/22.77 (136) all_14_0 = all_8_0 % 152.43/22.77 (137) ~ (e2 = e0) % 152.43/22.77 (138) ~ (all_52_9 = all_6_2) % 152.43/22.77 (139) ~ (all_52_2 = all_10_2) % 152.43/22.77 (140) all_56_0 = all_10_2 % 152.43/22.77 (141) ~ (all_52_1 = e0) % 152.43/22.77 (142) ~ (all_52_3 = all_52_11) % 152.43/22.77 (143) all_58_22 = all_52_3 % 152.43/22.77 (144) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.43/22.77 (145) ~ (all_52_12 = all_4_2) % 152.43/22.77 (146) ~ (all_52_3 = all_10_2) % 152.43/22.77 (147) all_56_8 = all_6_2 % 152.43/22.77 (148) op(e1, e1) = all_6_2 % 152.43/22.77 (149) ~ (all_52_1 = all_52_2) % 152.43/22.77 (150) op(e2, e0) = all_52_13 % 152.43/22.77 (151) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 152.43/22.77 (152) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 152.43/22.77 (153) all_58_4 = all_52_8 % 152.43/22.77 (154) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.43/22.77 (155) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 152.43/22.77 (156) all_54_0 = all_10_2 % 152.43/22.77 (157) ~ (all_52_2 = all_52_14) % 152.43/22.77 (158) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.43/22.77 (159) all_14_1 = all_8_1 % 152.43/22.77 (160) ~ (all_52_7 = e0) % 152.43/22.77 (161) ~ (all_52_14 = all_4_2) % 152.43/22.77 (162) ~ (e1 = e0) % 152.43/22.77 (163) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.43/22.77 (164) ~ (all_52_7 = all_4_2) % 152.43/22.77 (165) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 152.43/22.77 (166) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.43/22.77 (167) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 152.43/22.77 (168) op(e0, e2) = all_52_7 % 152.43/22.77 (169) ~ (all_52_4 = all_10_2) % 152.43/22.77 (170) all_58_30 = all_6_2 % 152.43/22.77 (171) op(e2, all_52_1) = all_58_7 % 152.43/22.77 (172) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.43/22.77 (173) ~ (e3 = e2) % 152.43/22.77 (174) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.43/22.77 (175) ~ (all_52_14 = all_6_2) % 152.43/22.77 (176) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 152.43/22.77 (177) op(all_4_2, e0) = all_4_1 % 152.43/22.77 (178) op(all_10_2, e3) = all_10_1 % 152.43/22.77 (179) ~ (all_52_4 = all_52_12) % 152.43/22.77 (180) all_54_12 = all_52_3 % 152.43/22.77 (181) all_54_4 = all_52_1 % 152.43/22.77 (182) ~ (all_52_1 = all_10_2) % 152.43/22.77 % 152.43/22.77 Begin of proof % 152.43/22.77 | % 152.43/22.77 | GROUND_INST: instantiating (4) with all_52_7, all_8_1, e2, e0, simplifying % 152.43/22.77 | with (33), (168) gives: % 152.43/22.77 | (183) all_52_7 = all_8_1 % 152.43/22.77 | % 152.43/22.77 | GROUND_INST: instantiating (4) with all_52_13, all_58_9, e0, e2, simplifying % 152.43/22.77 | with (13), (150) gives: % 152.43/22.77 | (184) all_58_9 = all_52_13 % 152.43/22.77 | % 152.43/22.77 | COMBINE_EQS: (5), (183) imply: % 152.43/22.77 | (185) all_54_13 = all_8_1 % 152.43/22.77 | % 152.43/22.77 | COMBINE_EQS: (106), (183) imply: % 152.43/22.77 | (186) all_56_13 = all_8_1 % 152.43/22.77 | % 152.43/22.77 | COMBINE_EQS: (89), (183) imply: % 152.43/22.77 | (187) all_58_24 = all_8_1 % 152.43/22.77 | % 152.43/22.77 | REDUCE: (76), (183) imply: % 152.43/22.77 | (188) ~ (all_52_3 = all_8_1) % 152.43/22.77 | % 152.43/22.77 | REDUCE: (55), (183) imply: % 152.43/22.77 | (189) ~ (all_52_4 = all_8_1) % 152.43/22.77 | % 152.43/22.77 | REDUCE: (40), (183) imply: % 152.43/22.77 | (190) ~ (all_52_6 = all_8_1) % 152.43/22.77 | % 152.43/22.77 | REDUCE: (134), (183) imply: % 152.43/22.77 | (191) ~ (all_52_11 = all_8_1) % 152.43/22.77 | % 152.43/22.77 | SIMP: (191) implies: % 152.43/22.77 | (192) ~ (all_52_11 = all_8_1) % 152.43/22.77 | % 152.43/22.77 | REDUCE: (164), (183) imply: % 152.43/22.77 | (193) ~ (all_8_1 = all_4_2) % 152.43/22.77 | % 152.43/22.77 | REDUCE: (160), (183) imply: % 152.43/22.77 | (194) ~ (all_8_1 = e0) % 152.43/22.77 | % 152.43/22.77 | REDUCE: (50), (183) imply: % 152.43/22.77 | (195) op(e0, all_8_1) = all_58_23 % 152.43/22.77 | % 152.43/22.77 | GROUND_INST: instantiating (4) with all_8_0, all_58_23, all_8_1, e0, % 152.43/22.77 | simplifying with (73), (195) gives: % 152.43/22.77 | (196) all_58_23 = all_8_0 % 152.43/22.77 | % 152.43/22.77 | BETA: splitting (64) gives: % 152.43/22.77 | % 152.43/22.77 | Case 1: % 152.43/22.77 | | % 152.43/22.77 | | (197) ~ (all_18_2 = e0) % 152.43/22.77 | | % 152.43/22.77 | | REDUCE: (105), (197) imply: % 152.43/22.77 | | (198) ~ (all_6_2 = e0) % 152.43/22.77 | | % 152.43/22.77 | | BETA: splitting (132) gives: % 152.43/22.77 | | % 152.43/22.77 | | Case 1: % 152.43/22.77 | | | % 152.43/22.77 | | | (199) ~ (all_20_2 = e1) % 152.43/22.77 | | | % 152.43/22.77 | | | REDUCE: (78), (199) imply: % 152.43/22.77 | | | (200) ~ (all_4_2 = e1) % 152.43/22.77 | | | % 152.43/22.77 | | | BETA: splitting (57) gives: % 152.43/22.77 | | | % 152.43/22.77 | | | Case 1: % 152.43/22.77 | | | | % 152.43/22.77 | | | | (201) all_56_15 = e0 % 152.43/22.77 | | | | % 152.43/22.77 | | | | COMBINE_EQS: (8), (201) imply: % 152.43/22.77 | | | | (202) all_4_2 = e0 % 152.43/22.77 | | | | % 152.43/22.77 | | | | SIMP: (202) implies: % 152.43/22.77 | | | | (203) all_4_2 = e0 % 152.43/22.77 | | | | % 152.43/22.77 | | | | COMBINE_EQS: (2), (203) imply: % 152.43/22.77 | | | | (204) all_58_31 = e0 % 152.43/22.77 | | | | % 152.43/22.77 | | | | REDUCE: (161), (203) imply: % 152.43/22.77 | | | | (205) ~ (all_52_14 = e0) % 152.43/22.77 | | | | % 152.43/22.77 | | | | REDUCE: (200), (203) imply: % 152.43/22.77 | | | | (206) ~ (e1 = e0) % 152.43/22.77 | | | | % 152.43/22.77 | | | | REF_CLOSE: (4), (9), (16), (30), (58), (65), (67), (80), (95), (101), % 152.43/22.77 | | | | (103), (116), (117), (127), (137), (139), (140), (147), % 152.43/22.77 | | | | (154), (158), (162), (163), (170), (172), (173), (178), % 152.43/22.77 | | | | (198), (204), (205) are inconsistent by sub-proof #173. % 152.43/22.77 | | | | % 152.43/22.77 | | | Case 2: % 152.43/22.77 | | | | % 152.43/22.77 | | | | (207) ~ (all_56_15 = e0) % 152.43/22.77 | | | | (208) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 % 152.43/22.77 | | | | = e0 | all_56_13 = e0 | all_56_14 = e0) % 152.43/22.77 | | | | % 152.43/22.77 | | | | ALPHA: (208) implies: % 152.43/22.77 | | | | (209) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 152.43/22.77 | | | | (210) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 152.43/22.77 | | | | % 152.43/22.77 | | | | REDUCE: (8), (207) imply: % 152.43/22.77 | | | | (211) ~ (all_4_2 = e0) % 152.43/22.77 | | | | % 152.43/22.77 | | | | BETA: splitting (27) gives: % 152.43/22.77 | | | | % 152.43/22.77 | | | | Case 1: % 152.43/22.77 | | | | | % 152.43/22.77 | | | | | (212) all_54_15 = e0 % 152.43/22.77 | | | | | % 152.43/22.77 | | | | | REF_CLOSE: (54), (211), (212) are inconsistent by sub-proof #493. % 152.43/22.77 | | | | | % 152.43/22.77 | | | | Case 2: % 152.43/22.77 | | | | | % 152.43/22.77 | | | | | (213) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 152.43/22.77 | | | | | % 152.43/22.77 | | | | | BETA: splitting (82) gives: % 152.43/22.77 | | | | | % 152.43/22.77 | | | | | Case 1: % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | (214) all_56_4 = e0 % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | COMBINE_EQS: (28), (214) imply: % 152.43/22.77 | | | | | | (215) all_52_8 = e0 % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | COMBINE_EQS: (153), (215) imply: % 152.43/22.77 | | | | | | (216) all_58_4 = e0 % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | REDUCE: (3), (215) imply: % 152.43/22.77 | | | | | | (217) ~ (all_52_9 = e0) % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | REDUCE: (23), (215) imply: % 152.43/22.77 | | | | | | (218) ~ (all_52_11 = e0) % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | SIMP: (218) implies: % 152.43/22.77 | | | | | | (219) ~ (all_52_11 = e0) % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | REDUCE: (59), (215) imply: % 152.43/22.77 | | | | | | (220) ~ (all_52_12 = e0) % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | SIMP: (220) implies: % 152.43/22.77 | | | | | | (221) ~ (all_52_12 = e0) % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | REDUCE: (131), (215) imply: % 152.43/22.77 | | | | | | (222) op(e3, e1) = e0 % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | BETA: splitting (209) gives: % 152.43/22.77 | | | | | | % 152.43/22.77 | | | | | | Case 1: % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | (223) all_56_12 = e0 % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | COMBINE_EQS: (75), (223) imply: % 152.43/22.77 | | | | | | | (224) all_52_3 = e0 % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | SIMP: (224) implies: % 152.43/22.77 | | | | | | | (225) all_52_3 = e0 % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | COMBINE_EQS: (143), (225) imply: % 152.43/22.77 | | | | | | | (226) all_58_22 = e0 % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | REDUCE: (146), (225) imply: % 152.43/22.77 | | | | | | | (227) ~ (all_10_2 = e0) % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | SIMP: (227) implies: % 152.43/22.77 | | | | | | | (228) ~ (all_10_2 = e0) % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | REDUCE: (188), (225) imply: % 152.43/22.77 | | | | | | | (229) ~ (all_8_1 = e0) % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | BETA: splitting (210) gives: % 152.43/22.77 | | | | | | | % 152.43/22.77 | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | % 152.43/22.77 | | | | | | | | (230) all_56_9 = e0 % 152.43/22.77 | | | | | | | | % 152.43/22.77 | | | | | | | | REF_CLOSE: (97), (221), (230) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | #521. % 152.43/22.77 | | | | | | | | % 152.43/22.77 | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | % 152.43/22.77 | | | | | | | | (231) all_56_10 = e0 | all_56_11 = e0 % 152.43/22.77 | | | | | | | | % 152.43/22.77 | | | | | | | | BETA: splitting (231) gives: % 152.43/22.77 | | | | | | | | % 152.43/22.77 | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | (232) all_56_10 = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | REF_CLOSE: (83), (122), (232) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | | #526. % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | (233) all_56_11 = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | COMBINE_EQS: (80), (233) imply: % 152.43/22.77 | | | | | | | | | (234) all_52_14 = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | SIMP: (234) implies: % 152.43/22.77 | | | | | | | | | (235) all_52_14 = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | COMBINE_EQS: (44), (235) imply: % 152.43/22.77 | | | | | | | | | (236) all_58_20 = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | REDUCE: (157), (235) imply: % 152.43/22.77 | | | | | | | | | (237) ~ (all_52_2 = e0) % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | REDUCE: (175), (235) imply: % 152.43/22.77 | | | | | | | | | (238) ~ (all_6_2 = e0) % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | REDUCE: (161), (235) imply: % 152.43/22.77 | | | | | | | | | (239) ~ (all_4_2 = e0) % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | REDUCE: (21), (235) imply: % 152.43/22.77 | | | | | | | | | (240) op(e1, e0) = all_58_19 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | REDUCE: (86), (235) imply: % 152.43/22.77 | | | | | | | | | (241) op(e1, e0) = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_19, e0, e1, % 152.43/22.77 | | | | | | | | | simplifying with (240), (241) gives: % 152.43/22.77 | | | | | | | | | (242) all_58_19 = e0 % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | BETA: splitting (34) gives: % 152.43/22.77 | | | | | | | | | % 152.43/22.77 | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | (243) all_54_8 = e0 % 152.43/22.77 | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | REF_CLOSE: (14), (237), (243) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | | | #731. % 152.43/22.77 | | | | | | | | | | % 152.43/22.77 | | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | (244) ~ (all_54_8 = e0) % 152.43/22.77 | | | | | | | | | | (245) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 152.43/22.77 | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | BETA: splitting (113) gives: % 152.43/22.77 | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | (246) all_56_9 = e1 % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | COMBINE_EQS: (97), (246) imply: % 152.43/22.77 | | | | | | | | | | | (247) all_52_12 = e1 % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | SIMP: (247) implies: % 152.43/22.77 | | | | | | | | | | | (248) all_52_12 = e1 % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | REDUCE: (179), (248) imply: % 152.43/22.77 | | | | | | | | | | | (249) ~ (all_52_4 = e1) % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | REDUCE: (123), (248) imply: % 152.43/22.77 | | | | | | | | | | | (250) ~ (all_10_2 = e1) % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | SIMP: (250) implies: % 152.43/22.77 | | | | | | | | | | | (251) ~ (all_10_2 = e1) % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | REDUCE: (145), (248) imply: % 152.43/22.77 | | | | | | | | | | | (252) ~ (all_4_2 = e1) % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | REDUCE: (120), (248) imply: % 152.43/22.77 | | | | | | | | | | | (253) op(e3, e1) = all_58_5 % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (22), (37), (39), (56), % 152.43/22.77 | | | | | | | | | | | (61), (65), (68), (71), (72), (73), (79), (81), % 152.43/22.77 | | | | | | | | | | | (91), (95), (96), (103), (109), (111), (117), % 152.43/22.77 | | | | | | | | | | | (118), (122), (125), (126), (127), (136), (140), % 152.43/22.77 | | | | | | | | | | | (141), (155), (159), (162), (170), (171), (172), % 152.43/22.77 | | | | | | | | | | | (186), (192), (196), (198), (200), (219), (222), % 152.43/22.77 | | | | | | | | | | | (223), (242), (249), (251), (253) are inconsistent % 152.43/22.77 | | | | | | | | | | | by sub-proof #390. % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | (254) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | BETA: splitting (254) gives: % 152.43/22.77 | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | (255) all_56_10 = e1 % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | COMBINE_EQS: (122), (255) imply: % 152.43/22.77 | | | | | | | | | | | | (256) all_52_13 = e1 % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | SIMP: (256) implies: % 152.43/22.77 | | | | | | | | | | | | (257) all_52_13 = e1 % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | COMBINE_EQS: (36), (257) imply: % 152.43/22.77 | | | | | | | | | | | | (258) all_58_13 = e1 % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | REDUCE: (70), (257) imply: % 152.43/22.77 | | | | | | | | | | | | (259) ~ (all_52_1 = e1) % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | REDUCE: (112), (257) imply: % 152.43/22.77 | | | | | | | | | | | | (260) ~ (all_52_9 = e1) % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | REDUCE: (47), (257) imply: % 152.43/22.77 | | | | | | | | | | | | (261) ~ (all_52_12 = e1) % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | REDUCE: (61), (257) imply: % 152.43/22.77 | | | | | | | | | | | | (262) ~ (all_4_2 = e1) % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | BETA: splitting (108) gives: % 152.43/22.77 | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | (263) all_54_4 = e0 % 152.43/22.77 | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | REF_CLOSE: (141), (181), (263) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | | | | | | #859. % 152.43/22.77 | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | (264) ~ (all_54_4 = e0) % 152.43/22.77 | | | | | | | | | | | | | (265) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.43/22.77 | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | BETA: splitting (167) gives: % 152.43/22.77 | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | (266) all_54_6 = e0 % 152.43/22.77 | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | REF_CLOSE: (53), (88), (266) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | | | | | | | #797. % 152.43/22.77 | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | (267) ~ (all_54_6 = e0) % 152.43/22.77 | | | | | | | | | | | | | | (268) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 152.43/22.77 | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | BETA: splitting (11) gives: % 152.43/22.77 | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | (269) all_54_3 = e0 % 152.43/22.77 | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | REF_CLOSE: (29), (221), (269) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | | | | | | | | #733. % 152.43/22.77 | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | (270) ~ (all_54_3 = e0) % 152.43/22.77 | | | | | | | | | | | | | | | (271) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 152.43/22.77 | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 152.43/22.77 | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | (272) all_54_13 = e0 % 152.43/22.77 | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | REF_CLOSE: (185), (194), (272) are inconsistent by sub-proof % 152.43/22.77 | | | | | | | | | | | | | | | | #397. % 152.43/22.77 | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | Case 2: % 152.43/22.77 | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | (273) ~ (all_54_13 = e0) % 152.43/22.77 | | | | | | | | | | | | | | | | (274) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 152.43/22.77 | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 152.43/22.77 | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | Case 1: % 152.43/22.77 | | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | | (275) all_56_2 = e3 % 152.43/22.77 | | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (275) imply: % 152.43/22.77 | | | | | | | | | | | | | | | | | (276) all_52_1 = e3 % 152.43/22.77 | | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | | SIMP: (276) implies: % 152.43/22.77 | | | | | | | | | | | | | | | | | (277) all_52_1 = e3 % 152.43/22.77 | | | | | | | | | | | | | | | | | % 152.43/22.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (277) imply: % 152.43/22.77 | | | | | | | | | | | | | | | | | (278) all_58_8 = e3 % 152.43/22.77 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | REDUCE: (149), (277) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | (279) ~ (all_52_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | SIMP: (279) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | (280) ~ (all_52_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | REDUCE: (130), (277) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | (281) ~ (all_52_9 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | SIMP: (281) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | (282) ~ (all_52_9 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | REDUCE: (182), (277) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | (283) ~ (all_10_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | SIMP: (283) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | (284) ~ (all_10_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | (285) all_54_6 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (260), (285) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | #774. % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | (286) ~ (all_54_6 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | (287) all_54_6 = e3 | all_54_6 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (288) all_54_6 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (288) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (289) all_52_9 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | SIMP: (289) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (290) all_52_9 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (290) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (291) all_56_5 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (290) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (292) all_58_11 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | REDUCE: (138), (290) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (293) ~ (all_6_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (294) ~ (all_6_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (295) all_54_0 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (228), (295) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | #861. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (296) ~ (all_54_0 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (297) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (10), (14), (19), (20), (22), (24), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (26), (29), (30), (31), (35), (39), (43), (48), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (49), (56), (67), (77), (81), (91), (92), (95), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (97), (101), (103), (104), (109), (110), (114), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (115), (119), (123), (126), (127), (129), (137), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (139), (140), (145), (147), (151), (154), (156), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (169), (170), (172), (174), (179), (185), (186), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (187), (189), (192), (194), (198), (200), (211), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (214), (216), (219), (221), (223), (226), (228), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (233), (236), (237), (245), (258), (271), (274), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (278), (280), (284), (291), (292), (294), (297) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #336. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (298) all_54_6 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (282), (298) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | #772. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | End of split % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | End of split % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | (299) ~ (all_56_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | REDUCE: (118), (299) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | (300) ~ (all_52_1 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | (301) all_54_4 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (181), (259), (301) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | #832. % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | (302) ~ (all_54_4 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | (303) all_54_4 = e3 | all_54_4 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (304) all_54_4 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (304) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (305) all_52_1 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | SIMP: (305) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (306) all_52_1 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (306) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (307) all_58_8 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | REDUCE: (130), (306) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_9 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | SIMP: (308) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | (309) ~ (all_52_9 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (310) all_54_6 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (260), (310) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | #774. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (311) ~ (all_54_6 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | (312) all_54_6 = e3 | all_54_6 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (313) all_54_6 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (309), (313) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | #773. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (314) all_54_6 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (314) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (315) all_52_9 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (316) all_52_9 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (316) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (317) all_58_11 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (316) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_6_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_6_2 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | (320) all_54_10 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (320) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | (321) all_6_2 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | (322) all_6_2 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (322) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | (323) $false % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (323) is inconsistent. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | (324) ~ (all_54_10 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | (325) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | (326) all_54_14 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (219), (326) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | #517. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | (327) ~ (all_54_14 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | (328) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | (329) all_54_9 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (67), (329) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | #572. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | (330) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_56_9 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (331) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_52_12 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_52_12 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (333) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_6 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (333) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_52_4 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (333) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_10_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_10_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (333) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (338) ~ (all_4_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (all_4_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_54_15 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (200), (340) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | #587. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (341) ~ (all_54_15 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_54_15 = e3 | all_54_15 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_54_15 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (343) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_4_2 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (49), (58), (65), (95), (116), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (127), (154), (170), (173), (178), (228), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (319), (325), (344) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | #171. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_54_15 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (345) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_4_2 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (346) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_4_2 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (347) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_56_15 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (347) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_58_31 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (347) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_52_11 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_28 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (351) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_10_2 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (352) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) $false % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (353) is inconsistent. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_29 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (355) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) e2 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (356) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) $false % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_30 = e2 | all_58_31 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (358) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_30 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (359) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_6_2 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_6_2 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (361) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) ~ (all_52_2 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (361) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_52_6 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (361) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_52_11 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (319), (361) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (e3 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_28 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (366) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_10_2 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (367) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_52_2 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (367) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_52_4 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_54_1 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (114), (370) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #798. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) ~ (all_54_1 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_56_12 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (223), (349), (358), (359), (373) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #293. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_31 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (375) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) e3 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (376) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) $false % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_54_8 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (368), (379) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_54_8 = e3 | all_54_8 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_54_1 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (369), (381) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_54_1 = e3 | all_54_1 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_54_8 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (362), (383) are inconsistent by sub-proof % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #787. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_54_8 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (384) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_52_2 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (385) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_52_2 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (386) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_15 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_56_1 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (388) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_52_4 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (389) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_58_2 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (389) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_52_6 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (391) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) ~ (all_52_6 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (389) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) ~ (all_8_1 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (393) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_8_1 = e3) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_54_9 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (395) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_52_6 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (396) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_52_6 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (397) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_58_17 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (397) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) ~ (all_8_1 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (399) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) ~ (all_8_1 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (397) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) ~ (e3 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_56_13 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (402) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_8_1 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (403) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_8_1 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (404) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_58_24 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_58_30 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (406) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) e2 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (407) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) $false % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (408) is inconsistent. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_58_29 = e2 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (410) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) e2 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (411) are % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) ~ (all_58_29 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (412) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (e2 = e0) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_54_14 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (415) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_52_11 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (416) implies: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_52_11 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (417) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_58_26 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (417) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) ~ (e2 = e1) % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (413) gives: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_58_28 = e3 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (420) imply: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) e3 = e1 % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (173), (349), (366), (421) are inconsistent % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #382. % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) ~ (all_58_28 = e3) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (423) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (424) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (425) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_58_15 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_58_8 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_58_4 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (430) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) e1 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (431) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) e1 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (429) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (433) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (387), (428), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432), (434) are inconsistent by sub-proof #168. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (334), (349), (358), (359), (437) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #167. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (101), (137), (317), (349), (354), (359), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (438) are inconsistent by sub-proof #377. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (439) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (101), (137), (258), (307), (349), (354), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359), (441) are inconsistent by sub-proof #376. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_58_4 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_58_2 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (390), (444) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (443) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (446) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (445), (447) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #166. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (449) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_58_22 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_58_6 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (451) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (452) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (450) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (453), (454) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #166. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (101), (137), (317), (349), (354), (359), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390), (455) are inconsistent by sub-proof #373. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (456) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_58_24 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (460) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) e2 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (461) are % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_2 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (390), (463) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (464) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_58_31 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (49), (58), (65), (95), (116), (117), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (154), (170), (173), (178), (228), (319), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (465) are inconsistent by sub-proof #172. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (467) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (334), (349), (358), (359), (468) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #167. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_58_11 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_58_4 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (471) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (472) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (470) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) e3 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (473), (474) are inconsistent by sub-proof % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #633. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (475) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (476) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_58_20 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (236), (478) are inconsistent by sub-proof % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_58_22 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_58_15 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_58_6 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (482) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (483) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (481) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) e3 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (485) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) e3 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (480) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (484), (486) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) e2 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (484), (487) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) e2 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (488), (489) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) e1 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (488), (490) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #169. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_58_15 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_11 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_58_4 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (495) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) e1 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (496) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) e1 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (494) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (387), (493), % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497), (498) are inconsistent by sub-proof #168. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_58_26 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (418), (500) are inconsistent by sub-proof % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #343. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (501) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (504) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_58_4 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (216), (505) are inconsistent by sub-proof % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #165. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (506) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (507) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_58_22 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_58_6 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (509) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (510) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (508) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (512) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (511), (513) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) e2 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (514) are % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (515) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_58_22 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_58_6 = e3 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (517) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (518) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) e3 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (516) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (520) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (519), (521) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #166. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (524) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (334), (349), (358), (359), (525) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #167. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (526) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (334), (349), (358), (359), (527) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #167. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (528) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_6 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (334), (349), (358), (359), (530) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #167. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (531) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_58_24 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (405), (532) imply: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) e2 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (533) are % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (536) gives: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies: % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_58_20 = e1 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_58_17 = e2 % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.43/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (398), (539) imply: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) e2 = e1 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (540) implies: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) e2 = e1 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (538) imply: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) e1 = e0 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (542) implies: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) e1 = e0 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (541), (543) % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #169. % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (101), (137), (258), (317), (349), (354), % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359), (544) are inconsistent by sub-proof #364. % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (546) implies: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_58_26 = e0 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (418), (547) are inconsistent by sub-proof % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #343. % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) e2 = e1 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_58_11 = e1 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (550) imply: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) e3 = e1 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (101), (137), (349), (354), (359), (549), % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) are inconsistent by sub-proof #378. % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (552) gives: % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_58_26 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_58_13 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (556) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) e2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (557) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) e2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (418), (555) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) e1 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (559) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) e1 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (558), (560) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #169. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (561) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_58_24 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (405), (562) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #164. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (563) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (564) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_58_24 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (349), (358), (359), (405), (565) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #164. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (566) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_58_26 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (418), (567) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) e1 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (568) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (569) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_54_14 = e3 | all_54_14 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (350), (364), (570) are inconsistent by % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #358. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_56_14 = e2 | all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (571) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_56_14 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (364), (572) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #422. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (573) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) e3 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (574) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) e3 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (575) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_58_31 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (49), (58), (65), (95), (116), (117), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (154), (170), (173), (178), (228), (319), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (576) are inconsistent by sub-proof #172. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_54_9 = e3 | all_54_9 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (363), (392), (577) are inconsistent by % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #559. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) ~ (all_56_1 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (578) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) ~ (all_52_4 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (335), (382), (579) are inconsistent by % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #722. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (95), (101), (162), (349), (359), (580) are % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #357. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_58_31 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (49), (58), (65), (95), (116), (117), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (154), (170), (173), (178), (228), (319), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325), (581) are inconsistent by sub-proof #172. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | (582) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (582) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_56_10 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (583) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (584) e2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (584) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (585) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (585) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_56_11 = e2 | all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_56_11 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (587) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) e2 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (588) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (589) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (590) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_4_2 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (49), (58), (65), (95), (116), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (127), (154), (170), (173), (178), (228), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (319), (325), (591) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | #171. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | (592) all_54_4 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (181), (300), (592) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | | | | | | | | | #830. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | (593) all_56_11 = e1 | all_56_15 = e1 % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | REF_CLOSE: (8), (162), (200), (233), (593) are inconsistent % 152.97/22.80 | | | | | | | | | | | | by sub-proof #334. % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | End of split % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | End of split % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | Case 2: % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | (594) all_56_13 = e0 | all_56_14 = e0 % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | REF_CLOSE: (106), (126), (160), (219), (594) are inconsistent by % 152.97/22.80 | | | | | | | sub-proof #609. % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | End of split % 152.97/22.80 | | | | | | % 152.97/22.80 | | | | | Case 2: % 152.97/22.80 | | | | | | % 152.97/22.80 | | | | | | (595) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 152.97/22.80 | | | | | | % 152.97/22.80 | | | | | | BETA: splitting (595) gives: % 152.97/22.80 | | | | | | % 152.97/22.80 | | | | | | Case 1: % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | (596) all_56_5 = e0 % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | COMBINE_EQS: (71), (596) imply: % 152.97/22.80 | | | | | | | (597) all_52_9 = e0 % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | REDUCE: (88), (597) imply: % 152.97/22.80 | | | | | | | (598) $false % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | CLOSE: (598) is inconsistent. % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | Case 2: % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | (599) all_56_8 = e0 | all_56_14 = e0 % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | BETA: splitting (599) gives: % 152.97/22.80 | | | | | | | % 152.97/22.80 | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | (600) all_56_8 = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | COMBINE_EQS: (147), (600) imply: % 152.97/22.80 | | | | | | | | (601) all_6_2 = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | REDUCE: (198), (601) imply: % 152.97/22.80 | | | | | | | | (602) $false % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | CLOSE: (602) is inconsistent. % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | (603) all_56_14 = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | COMBINE_EQS: (126), (603) imply: % 152.97/22.80 | | | | | | | | (604) all_52_11 = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | SIMP: (604) implies: % 152.97/22.80 | | | | | | | | (605) all_52_11 = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | COMBINE_EQS: (20), (605) imply: % 152.97/22.80 | | | | | | | | (606) all_58_26 = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | REDUCE: (23), (605) imply: % 152.97/22.80 | | | | | | | | (607) ~ (all_52_8 = e0) % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | REDUCE: (192), (605) imply: % 152.97/22.80 | | | | | | | | (608) ~ (all_8_1 = e0) % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | REDUCE: (115), (605) imply: % 152.97/22.80 | | | | | | | | (609) ~ (all_6_2 = e0) % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | REDUCE: (37), (605) imply: % 152.97/22.80 | | | | | | | | (610) op(e0, e1) = e0 % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | BETA: splitting (158) gives: % 152.97/22.80 | | | | | | | | % 152.97/22.80 | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | (611) all_56_6 = e0 % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | COMBINE_EQS: (103), (611) imply: % 152.97/22.80 | | | | | | | | | (612) all_52_2 = e0 % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | COMBINE_EQS: (19), (612) imply: % 152.97/22.80 | | | | | | | | | (613) all_58_15 = e0 % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | REDUCE: (6), (612) imply: % 152.97/22.80 | | | | | | | | | (614) ~ (all_52_3 = e0) % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | SIMP: (614) implies: % 152.97/22.80 | | | | | | | | | (615) ~ (all_52_3 = e0) % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | REDUCE: (104), (612) imply: % 152.97/22.80 | | | | | | | | | (616) ~ (all_52_6 = e0) % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | REDUCE: (157), (612) imply: % 152.97/22.80 | | | | | | | | | (617) ~ (all_52_14 = e0) % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | SIMP: (617) implies: % 152.97/22.80 | | | | | | | | | (618) ~ (all_52_14 = e0) % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | BETA: splitting (210) gives: % 152.97/22.80 | | | | | | | | | % 152.97/22.80 | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | (619) all_56_9 = e0 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | COMBINE_EQS: (97), (619) imply: % 152.97/22.80 | | | | | | | | | | (620) all_52_12 = e0 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | SIMP: (620) implies: % 152.97/22.80 | | | | | | | | | | (621) all_52_12 = e0 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | COMBINE_EQS: (26), (621) imply: % 152.97/22.80 | | | | | | | | | | (622) all_58_6 = e0 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | REDUCE: (47), (621) imply: % 152.97/22.80 | | | | | | | | | | (623) ~ (all_52_13 = e0) % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | REDUCE: (145), (621) imply: % 152.97/22.80 | | | | | | | | | | (624) ~ (all_4_2 = e0) % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | REDUCE: (120), (621) imply: % 152.97/22.80 | | | | | | | | | | (625) op(e3, e0) = all_58_5 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | REDUCE: (102), (621) imply: % 152.97/22.80 | | | | | | | | | | (626) op(e3, e0) = e0 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_5, e0, e3, % 152.97/22.80 | | | | | | | | | | simplifying with (625), (626) gives: % 152.97/22.80 | | | | | | | | | | (627) all_58_5 = e0 % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | BETA: splitting (121) gives: % 152.97/22.80 | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | (628) all_54_12 = e0 % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | REF_CLOSE: (180), (615), (628) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | #762. % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | (629) ~ (all_54_12 = e0) % 152.97/22.80 | | | | | | | | | | | (630) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | BETA: splitting (69) gives: % 152.97/22.80 | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | (631) all_54_0 = e0 % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (127), (137), % 152.97/22.80 | | | | | | | | | | | | (154), (156), (162), (170), (172), (173), (631) % 152.97/22.80 | | | | | | | | | | | | are inconsistent by sub-proof #395. % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | (632) ~ (all_54_0 = e0) % 152.97/22.80 | | | | | | | | | | | | (633) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | REDUCE: (156), (632) imply: % 152.97/22.80 | | | | | | | | | | | | (634) ~ (all_10_2 = e0) % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | BETA: splitting (108) gives: % 152.97/22.80 | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | (635) all_54_4 = e0 % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | REF_CLOSE: (141), (181), (635) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | | | #859. % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | (636) ~ (all_54_4 = e0) % 152.97/22.80 | | | | | | | | | | | | | (637) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | BETA: splitting (135) gives: % 152.97/22.80 | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | (638) all_56_12 = e1 % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | COMBINE_EQS: (75), (638) imply: % 152.97/22.80 | | | | | | | | | | | | | | (639) all_52_3 = e1 % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | SIMP: (639) implies: % 152.97/22.80 | | | | | | | | | | | | | | (640) all_52_3 = e1 % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | REDUCE: (124), (640) imply: % 152.97/22.80 | | | | | | | | | | | | | | (641) ~ (all_52_1 = e1) % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | REDUCE: (146), (640) imply: % 152.97/22.80 | | | | | | | | | | | | | | (642) ~ (all_10_2 = e1) % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | SIMP: (642) implies: % 152.97/22.80 | | | | | | | | | | | | | | (643) ~ (all_10_2 = e1) % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | REDUCE: (188), (640) imply: % 152.97/22.80 | | | | | | | | | | | | | | (644) ~ (all_8_1 = e1) % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | SIMP: (644) implies: % 152.97/22.80 | | | | | | | | | | | | | | (645) ~ (all_8_1 = e1) % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | REDUCE: (85), (640) imply: % 152.97/22.80 | | | | | | | | | | | | | | (646) ~ (all_4_2 = e1) % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | BETA: splitting (172) gives: % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | (647) all_58_28 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | COMBINE_EQS: (127), (647) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (648) all_10_2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | REDUCE: (643), (648) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (649) $false % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | CLOSE: (649) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | (650) ~ (all_58_28 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | (651) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | BETA: splitting (651) gives: % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | (652) all_58_29 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | REF_CLOSE: (95), (162), (652) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | | | | | | #700. % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | (653) all_58_30 = e1 | all_58_31 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | BETA: splitting (653) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | (654) all_58_30 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (654) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (655) all_6_2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | REDUCE: (138), (655) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (656) ~ (all_52_9 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | REDUCE: (15), (655) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (657) op(e1, e1) = all_58_18 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | REDUCE: (148), (655) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (658) op(e1, e1) = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | BETA: splitting (68) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | (659) all_56_2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (659) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (660) all_52_1 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | REDUCE: (641), (660) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (661) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | CLOSE: (661) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | (662) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | BETA: splitting (662) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | (663) all_56_3 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (663) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | (664) e1 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (162), (200), (653), (654), (664) are % 152.97/22.80 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #487. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | (665) all_56_5 = e1 | all_56_10 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (665) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (666) all_56_5 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (666) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (667) all_52_9 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (667) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (668) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | CLOSE: (668) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (669) all_56_10 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (669) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (670) all_52_13 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | SIMP: (670) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (671) all_52_13 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_58_18, e1, e1, % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | simplifying with (657), (658) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (672) all_58_18 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | (673) all_54_13 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (673) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | (674) all_8_1 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | REDUCE: (194), (674) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | (675) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | CLOSE: (675) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | (676) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (677) all_56_2 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (677) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (678) all_52_1 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | (679) all_56_0 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (679) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | (680) all_10_2 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (680) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | (681) all_10_2 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (116), (178), (634), (681) are % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | (682) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (117), (173), (611), (638), (677), (682) are % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #837. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (683) ~ (all_56_2 = e2) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (683) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (684) ~ (all_52_1 = e2) % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (33), (46), (73), (95), (101), (111), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (118), (127), (128), (137), (140), (141), (152), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (154), (155), (171), (181), (182), (185), (186), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (193), (196), (611), (627), (637), (638), (641), % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | (643), (645), (654), (672), (676), (684) are % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | (685) all_58_31 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (685) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (686) all_4_2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | REDUCE: (200), (686) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (687) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | CLOSE: (687) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | End of split % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | (688) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | BETA: splitting (688) gives: % 152.97/22.80 | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | (689) all_56_13 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | COMBINE_EQS: (186), (689) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (690) all_8_1 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | SIMP: (690) implies: % 152.97/22.80 | | | | | | | | | | | | | | | (691) all_8_1 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | COMBINE_EQS: (159), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (692) all_14_1 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | COMBINE_EQS: (187), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (693) all_58_24 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | REDUCE: (188), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (694) ~ (all_52_3 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | REDUCE: (189), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (695) ~ (all_52_4 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | REDUCE: (190), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (696) ~ (all_52_6 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | REDUCE: (193), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (697) ~ (all_4_2 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | REDUCE: (73), (691) imply: % 152.97/22.80 | | | | | | | | | | | | | | | (698) op(e0, e1) = all_8_0 % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 152.97/22.80 | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | (699) ~ (all_14_1 = e1) % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | REDUCE: (692), (699) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | (700) $false % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | CLOSE: (700) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | (701) ~ (all_14_0 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | REDUCE: (136), (701) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | (702) ~ (all_8_0 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_8_0, e1, e0, % 152.97/22.80 | | | | | | | | | | | | | | | | simplifying with (610), (698) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | (703) all_8_0 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | REDUCE: (702), (703) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | (704) ~ (e3 = e0) % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | (705) all_54_9 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (705) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (706) all_52_6 = e0 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | REDUCE: (67), (706) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | (707) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | CLOSE: (707) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | (708) ~ (all_54_9 = e0) % 152.97/22.80 | | | | | | | | | | | | | | | | | (709) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | (710) all_56_12 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (710) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (711) all_52_3 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | SIMP: (711) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (712) all_52_3 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (712) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (713) all_58_22 = e3 % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | REDUCE: (124), (712) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (714) ~ (all_52_1 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | REDUCE: (146), (712) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (715) ~ (all_10_2 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | SIMP: (715) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (716) ~ (all_10_2 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | REDUCE: (85), (712) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (717) ~ (all_4_2 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | SIMP: (717) implies: % 152.97/22.80 | | | | | | | | | | | | | | | | | | (718) ~ (all_4_2 = e3) % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | (719) all_56_12 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (710), (719) are inconsistent by sub-proof % 152.97/22.80 | | | | | | | | | | | | | | | | | | | #588. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | (720) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (720) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (721) all_56_13 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (689), (721) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (722) e2 = e1 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (722) imply: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (723) $false % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | CLOSE: (723) is inconsistent. % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | (724) all_56_14 = e2 | all_56_15 = e2 % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.80 | | | | | | | | | | | | | | | | | | | | | (725) all_58_28 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (725) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (726) all_10_2 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (716), (726) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (727) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | CLOSE: (727) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (728) ~ (all_58_28 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (729) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (730) all_58_29 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (117), (730) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | #707. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (731) all_58_30 = e3 | all_58_31 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (724) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (732) all_56_14 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (603), (732) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (733) e2 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (733) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (734) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (734) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (735) all_56_15 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (735) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (736) all_4_2 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (736) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (737) all_4_2 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (737) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (738) all_58_31 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (718), (737) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (739) ~ (e3 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (740) all_58_30 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (740) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (741) all_6_2 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (741) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (742) all_56_8 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (741) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (743) ~ (all_52_6 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (741) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (744) ~ (all_52_8 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (741) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (745) ~ (all_52_14 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (746) all_56_0 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (746) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_10_2 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (716), (747) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (748) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (748) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (750) all_56_9 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (619), (750) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (751) e3 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (751) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (752) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (752) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (753) ~ (all_56_9 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_56_6 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (755) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) e1 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (756) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (757) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) ~ (all_56_6 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (758) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) ~ (e1 = e0) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_56_7 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (696), (761) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #547. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) ~ (all_56_7 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_56_8 = e1 | all_56_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_56_6 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (764) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) e2 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (738), (765) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_58_31 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (16), (30), (58), (65), (67), (80), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (95), (101), (103), (116), (117), (127), (137), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (140), (147), (154), (158), (162), (163), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (172), (173), (178), (198), (618), (766) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #173. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) all_56_7 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (768) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_52_6 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (769) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_52_6 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (770) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_58_17 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (770) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) ~ (all_52_4 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_56_1 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (773) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_52_4 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (774) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_58_2 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (774) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) ~ (all_52_8 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_56_8 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (742), (777) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) e3 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (778) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) e3 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (740), (779) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_30 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (173), (731), (738), (780) are inconsistent % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #664. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_56_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (781) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_52_14 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (782) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_52_14 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (783) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_20 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (783) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) ~ (all_52_13 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (745), (783) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) ~ (e3 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (12), (18), (22), (25), (28), (30), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (36), (38), (62), (65), (68), (70), (71), (83), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (92), (95), (100), (112), (117), (118), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (127), (137), (153), (154), (156), (162), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (170), (172), (173), (176), (181), (182), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606), (607), (613), (622), (633), (634), (637), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693), (713), (714), (716), (731), (738), (740), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744), (754), (771), (775), (784), (785) are % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #296. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_56_4 = e3 | all_56_9 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (117), (619), (744), (787) are inconsistent % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #751. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ (all_56_7 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (788) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ~ (all_52_6 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (696), (709), (743), (789) are inconsistent % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #619. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (790) all_58_31 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (738), (790) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | #585. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | End of split % 152.97/22.81 | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | (791) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | (792) all_56_13 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (689), (792) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | #341. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | (793) all_56_14 = e3 | all_56_15 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (793) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (794) all_56_14 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (603), (794) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (795) e3 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | SIMP: (795) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (796) e3 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (796) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (797) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | CLOSE: (797) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (798) all_56_15 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (798) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (799) all_4_2 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (799) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (800) all_58_31 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (799) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | (801) ~ (all_52_3 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (630) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (802) all_54_12 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (180), (694), (802) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | #558. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (803) ~ (all_54_12 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | (804) all_54_12 = e3 | all_54_12 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (804) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (805) all_54_12 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (805) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (806) all_52_3 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | SIMP: (806) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (807) all_52_3 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (807) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (808) all_58_22 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (807) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (809) ~ (all_10_2 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | SIMP: (809) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (810) ~ (all_10_2 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (801), (807) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | (811) ~ (e3 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (812) all_58_28 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (812) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (813) all_10_2 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (810), (813) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (814) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (814) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (815) ~ (all_58_28 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | (816) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (816) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (817) all_58_29 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (137), (817) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | #706. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | (818) all_58_30 = e2 | all_58_31 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (818) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_58_30 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (819) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_6_2 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (820) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (821) all_56_8 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (820) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (822) ~ (all_52_6 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (820) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (823) ~ (all_52_8 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (820) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | (824) ~ (all_52_14 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_56_6 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (611), (825) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | #839. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (826) ~ (all_56_6 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_58_28 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (828) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_10_2 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (829) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) all_56_0 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (829) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) ~ (all_52_1 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (829) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) ~ (all_52_8 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (810), (829) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) ~ (e2 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_56_6 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (834) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) e1 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (835) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) e1 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (828), (836) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) all_58_28 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (837) are inconsistent % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #483. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_54_2 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (607), (839) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #860. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) ~ (all_54_2 = e0) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_56_0 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (830), (842) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) e3 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (173), (800), (828), (843) are inconsistent % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #382. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) all_56_9 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (619), (845) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) e2 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (846) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_58_30 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (800), (818), (847) are inconsistent % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #705. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (848) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_56_10 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (849) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_52_13 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (850) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_52_13 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (851) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_58_13 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (851) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) ~ (all_52_1 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (851) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) ~ (all_52_9 = e2) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (827) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_56_7 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (855) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_52_6 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (856) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_58_17 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (838) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) all_56_7 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (855), (858) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) e3 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (859) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) all_58_31 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (173), (828), (860) are inconsistent by % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #383. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) ~ (all_56_7 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) all_56_8 = e1 | all_56_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (862) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) all_56_8 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (821), (863) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) e2 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (864) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_58_30 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (816), (865) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_56_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (866) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_52_14 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (867) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_52_14 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (868) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_58_20 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_58_31 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (870) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) e3 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (871) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) $false % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (872) is inconsistent. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (637) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_54_4 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (181), (831), (874) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #832. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_54_4 = e3 | all_54_4 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (844) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_56_2 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (876) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_52_1 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (877) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_58_8 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_54_6 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (88), (879) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #797. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) ~ (all_54_6 = e0) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_56_4 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (882) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_52_8 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (883) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_52_8 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (884) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_58_4 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (884) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) ~ (all_52_9 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (886) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) ~ (all_52_9 = e3) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (881) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_54_6 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (888) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_52_9 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (889) implies: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_52_9 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (890) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_58_11 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (887), (890) imply: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) ~ (e3 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (873) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_58_30 = e1 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (816), (893) are inconsistent by sub-proof % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250. % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) ~ (all_58_30 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (895) gives: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_58_29 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (896) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (897) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) all_58_30 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (800), (818), (898) are inconsistent % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #705. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) ~ (all_58_29 = e2) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (899) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) ~ (e2 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (900) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_58_28 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (828), (902) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) e3 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (903) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) all_58_31 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (173), (828), (904) are inconsistent by % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #383. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) ~ (all_58_28 = e3) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (906) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (907) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (908) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (909) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (613), (828), (910) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #321. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (912) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) all_58_22 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (808), (913) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (800), (818), (819), (914) are % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (915) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_58_11 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (891), (916) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) e2 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (917) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_58_30 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (816), (918) are inconsistent by sub-proof % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (919) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (920) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (921) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (693), (816), (819), (922) are inconsistent % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #163. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (923) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) all_58_15 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (878), (925) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) e3 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (926) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) e3 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (613), (924) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) e3 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (927), (928) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (800), (818), (819), (929) are % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (930) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (622), (800), (808), (818), (819), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) are inconsistent by sub-proof #162. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (932) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) all_58_17 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (878), (934) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) e3 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (935) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) e3 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (857), (933) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) e3 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (937) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) e3 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (936), (938) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) e2 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (939) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) all_58_30 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (816), (940) are inconsistent by sub-proof % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (941) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (942) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (943) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (944) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_58_24 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (693), (828), (945) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #317. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (946) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_58_8 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (878), (947) are inconsistent by sub-proof % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #347. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (948) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (949) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_58_22 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (808), (950) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (800), (818), (819), (951) are % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (613), (828), (857), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) are inconsistent by sub-proof #316. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (953) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (954) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (606), (828), (955) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #315. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (956) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_58_6 = e3 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) all_58_4 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (885), (958) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) e3 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (957) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) e3 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (960) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) e3 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (959), (961) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) e1 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (828), (962) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_58_28 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (963) are inconsistent % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #483. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (613), (828), (869), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) are inconsistent by sub-proof #313. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (965) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (966) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (613), (693), (828), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869), (967) are inconsistent by sub-proof #311. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (968) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (969) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_58_22 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (808), (972) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (973) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (971) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) e2 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (828), (974), (975) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #366. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (606), (828), (976) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #310. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (977) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (978) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_58_22 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (808), (979) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (173), (800), (818), (819), (980) are % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (981) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_58_13 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_58_11 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (891), (983) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) e2 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (852), (982) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) e2 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (828), (984), (985) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #366. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (986) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (987) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (988) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (989) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_58_26 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (606), (828), (990) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #309. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (693), (816), (819), (992) are inconsistent % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #163. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (993) gives: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (994) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_58_20 = e0 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (828), (869), (995) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #369. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (996) implies: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) e2 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (997) imply: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_58_30 = e1 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (101), (116), (117), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (137), (140), (154), (163), (173), (178), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634), (816), (998) are inconsistent by sub-proof % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (170), (172), (173), (606), (693), (828), % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869), (999) are inconsistent by sub-proof #308. % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_54_6 = e3 | all_54_6 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (854), (887), (1000) are inconsistent by % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #729. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) ~ (all_56_4 = e3) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (1001) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) ~ (all_52_8 = e3) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (823), (832), (841), (1002) are inconsistent % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #554. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) ~ (all_56_2 = e3) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1003) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) ~ (all_52_1 = e3) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (181), (853), (875), (1004) are inconsistent by % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #329. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) ~ (all_56_7 = e3) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1005) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) ~ (all_52_6 = e3) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (696), (709), (822), (1006) are inconsistent % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #619. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) all_56_11 = e2 | all_56_15 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (173), (798), (824), (1007) are inconsistent % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #161. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (95), (101), (162), (800), (819), (1008) are % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #357. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_58_31 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (1009) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | (1010) e3 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1010) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | (1011) $false % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1011) is inconsistent. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | (1012) all_54_12 = e3 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (180), (801), (1012) are inconsistent by sub-proof % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | #748. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | (1013) all_56_14 = e1 | all_56_15 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (200), (603), (1013) are inconsistent % 152.97/22.83 | | | | | | | | | | | | | | | by sub-proof #582. % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | (1014) all_56_10 = e0 | all_56_11 = e0 % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | REF_CLOSE: (80), (83), (122), (618), (1014) are inconsistent % 152.97/22.83 | | | | | | | | | | by sub-proof #294. % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | (1015) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | REF_CLOSE: (9), (28), (30), (65), (67), (74), (80), (81), % 152.97/22.83 | | | | | | | | | (95), (97), (99), (101), (114), (117), (127), % 152.97/22.83 | | | | | | | | | (137), (140), (147), (154), (162), (170), (172), % 152.97/22.83 | | | | | | | | | (173), (198), (607), (1015) are inconsistent by % 152.97/22.83 | | | | | | | | | sub-proof #481. % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | End of split % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | End of split % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | End of split % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | End of split % 152.97/22.83 | | | | | % 152.97/22.83 | | | | End of split % 152.97/22.83 | | | | % 152.97/22.83 | | | End of split % 152.97/22.83 | | | % 152.97/22.83 | | Case 2: % 152.97/22.83 | | | % 152.97/22.83 | | | (1016) all_20_2 = e1 % 152.97/22.83 | | | % 152.97/22.83 | | | COMBINE_EQS: (78), (1016) imply: % 152.97/22.83 | | | (1017) all_4_2 = e1 % 152.97/22.83 | | | % 152.97/22.83 | | | SIMP: (1017) implies: % 152.97/22.83 | | | (1018) all_4_2 = e1 % 152.97/22.83 | | | % 152.97/22.83 | | | COMBINE_EQS: (8), (1018) imply: % 152.97/22.83 | | | (1019) all_56_15 = e1 % 152.97/22.83 | | | % 152.97/22.83 | | | COMBINE_EQS: (2), (1018) imply: % 152.97/22.83 | | | (1020) all_58_31 = e1 % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (85), (1018) imply: % 152.97/22.83 | | | (1021) ~ (all_52_3 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (24), (1018) imply: % 152.97/22.83 | | | (1022) ~ (all_52_11 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (145), (1018) imply: % 152.97/22.83 | | | (1023) ~ (all_52_12 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (61), (1018) imply: % 152.97/22.83 | | | (1024) ~ (all_52_13 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (161), (1018) imply: % 152.97/22.83 | | | (1025) ~ (all_52_14 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (193), (1018) imply: % 152.97/22.83 | | | (1026) ~ (all_8_1 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (177), (1018) imply: % 152.97/22.83 | | | (1027) op(e1, e0) = all_4_1 % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (32), (1018) imply: % 152.97/22.83 | | | (1028) op(e0, e1) = all_58_27 % 152.97/22.83 | | | % 152.97/22.83 | | | GROUND_INST: instantiating (4) with all_52_11, all_58_27, e1, e0, % 152.97/22.83 | | | simplifying with (37), (1028) gives: % 152.97/22.83 | | | (1029) all_58_27 = all_52_11 % 152.97/22.83 | | | % 152.97/22.83 | | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, % 152.97/22.83 | | | simplifying with (86), (1027) gives: % 152.97/22.83 | | | (1030) all_52_14 = all_4_1 % 152.97/22.83 | | | % 152.97/22.83 | | | COMBINE_EQS: (42), (1030) imply: % 152.97/22.83 | | | (1031) all_54_11 = all_4_1 % 152.97/22.83 | | | % 152.97/22.83 | | | COMBINE_EQS: (80), (1030) imply: % 152.97/22.83 | | | (1032) all_56_11 = all_4_1 % 152.97/22.83 | | | % 152.97/22.83 | | | COMBINE_EQS: (44), (1030) imply: % 152.97/22.83 | | | (1033) all_58_20 = all_4_1 % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (157), (1030) imply: % 152.97/22.83 | | | (1034) ~ (all_52_2 = all_4_1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (51), (1030) imply: % 152.97/22.83 | | | (1035) ~ (all_52_6 = all_4_1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (99), (1030) imply: % 152.97/22.83 | | | (1036) ~ (all_52_12 = all_4_1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (90), (1030) imply: % 152.97/22.83 | | | (1037) ~ (all_52_13 = all_4_1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (175), (1030) imply: % 152.97/22.83 | | | (1038) ~ (all_6_2 = all_4_1) % 152.97/22.83 | | | % 152.97/22.83 | | | SIMP: (1038) implies: % 152.97/22.83 | | | (1039) ~ (all_6_2 = all_4_1) % 152.97/22.83 | | | % 152.97/22.83 | | | REDUCE: (1025), (1030) imply: % 152.97/22.83 | | | (1040) ~ (all_4_1 = e1) % 152.97/22.83 | | | % 152.97/22.83 | | | BETA: splitting (176) gives: % 152.97/22.83 | | | % 152.97/22.83 | | | Case 1: % 152.97/22.83 | | | | % 152.97/22.83 | | | | (1041) all_54_7 = e0 % 152.97/22.83 | | | | % 152.97/22.83 | | | | REF_CLOSE: (25), (83), (1041) are inconsistent by sub-proof #742. % 152.97/22.83 | | | | % 152.97/22.83 | | | Case 2: % 152.97/22.83 | | | | % 152.97/22.83 | | | | (1042) ~ (all_54_7 = e0) % 152.97/22.83 | | | | (1043) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 152.97/22.83 | | | | % 152.97/22.83 | | | | BETA: splitting (158) gives: % 152.97/22.83 | | | | % 152.97/22.83 | | | | Case 1: % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | (1044) all_56_6 = e0 % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | COMBINE_EQS: (103), (1044) imply: % 152.97/22.83 | | | | | (1045) all_52_2 = e0 % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | COMBINE_EQS: (19), (1045) imply: % 152.97/22.83 | | | | | (1046) all_58_15 = e0 % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | REDUCE: (6), (1045) imply: % 152.97/22.83 | | | | | (1047) ~ (all_52_3 = e0) % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | SIMP: (1047) implies: % 152.97/22.83 | | | | | (1048) ~ (all_52_3 = e0) % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | REDUCE: (104), (1045) imply: % 152.97/22.83 | | | | | (1049) ~ (all_52_6 = e0) % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | REDUCE: (1034), (1045) imply: % 152.97/22.83 | | | | | (1050) ~ (all_4_1 = e0) % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | SIMP: (1050) implies: % 152.97/22.83 | | | | | (1051) ~ (all_4_1 = e0) % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | REDUCE: (94), (1045) imply: % 152.97/22.83 | | | | | (1052) op(e1, e0) = all_58_14 % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | REF_CLOSE: (4), (7), (12), (17), (18), (20), (22), (25), (26), (28), % 152.97/22.83 | | | | | (30), (31), (35), (36), (38), (45), (47), (48), (52), (53), % 152.97/22.83 | | | | | (57), (59), (60), (63), (66), (67), (68), (70), (71), (75), % 152.97/22.83 | | | | | (77), (81), (83), (87), (92), (93), (95), (97), (98), % 152.97/22.83 | | | | | (100), (101), (102), (108), (111), (112), (115), (118), % 152.97/22.83 | | | | | (120), (121), (122), (124), (126), (127), (129), (130), % 152.97/22.83 | | | | | (137), (138), (141), (142), (143), (146), (151), (152), % 152.97/22.83 | | | | | (153), (154), (155), (162), (165), (167), (169), (170), % 152.97/22.83 | | | | | (179), (180), (181), (182), (184), (186), (187), (188), % 152.97/22.83 | | | | | (190), (192), (194), (1019), (1020), (1021), (1023), % 152.97/22.83 | | | | | (1024), (1026), (1027), (1029), (1031), (1032), (1033), % 152.97/22.83 | | | | | (1035), (1036), (1037), (1039), (1040), (1043), (1046), % 152.97/22.83 | | | | | (1048), (1051), (1052) are inconsistent by sub-proof #255. % 152.97/22.83 | | | | | % 152.97/22.83 | | | | Case 2: % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | (1053) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | BETA: splitting (1053) gives: % 152.97/22.83 | | | | | % 152.97/22.83 | | | | | Case 1: % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | (1054) all_56_7 = e0 % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | COMBINE_EQS: (9), (1054) imply: % 152.97/22.83 | | | | | | (1055) all_52_6 = e0 % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | REDUCE: (67), (1055) imply: % 152.97/22.83 | | | | | | (1056) $false % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | CLOSE: (1056) is inconsistent. % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | Case 2: % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | (1057) all_56_8 = e0 | all_56_11 = e0 % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | BETA: splitting (1057) gives: % 152.97/22.83 | | | | | | % 152.97/22.83 | | | | | | Case 1: % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | (1058) all_56_8 = e0 % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | COMBINE_EQS: (147), (1058) imply: % 152.97/22.83 | | | | | | | (1059) all_6_2 = e0 % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | REDUCE: (198), (1059) imply: % 152.97/22.83 | | | | | | | (1060) $false % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | CLOSE: (1060) is inconsistent. % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | Case 2: % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | (1061) all_56_11 = e0 % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | COMBINE_EQS: (1032), (1061) imply: % 152.97/22.83 | | | | | | | (1062) all_4_1 = e0 % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | SIMP: (1062) implies: % 152.97/22.83 | | | | | | | (1063) all_4_1 = e0 % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | COMBINE_EQS: (1033), (1063) imply: % 152.97/22.83 | | | | | | | (1064) all_58_20 = e0 % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | REDUCE: (1034), (1063) imply: % 152.97/22.83 | | | | | | | (1065) ~ (all_52_2 = e0) % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | REDUCE: (1036), (1063) imply: % 152.97/22.83 | | | | | | | (1066) ~ (all_52_12 = e0) % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | BETA: splitting (74) gives: % 152.97/22.83 | | | | | | | % 152.97/22.83 | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | (1067) all_56_0 = e0 % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | COMBINE_EQS: (140), (1067) imply: % 152.97/22.83 | | | | | | | | (1068) all_10_2 = e0 % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | COMBINE_EQS: (127), (1068) imply: % 152.97/22.83 | | | | | | | | (1069) all_58_28 = e0 % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), (170), % 152.97/22.83 | | | | | | | | (173), (1020), (1069) are inconsistent by sub-proof % 152.97/22.83 | | | | | | | | #653. % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | (1070) ~ (all_56_0 = e0) % 152.97/22.83 | | | | | | | | (1071) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | REDUCE: (140), (1070) imply: % 152.97/22.83 | | | | | | | | (1072) ~ (all_10_2 = e0) % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | BETA: splitting (144) gives: % 152.97/22.83 | | | | | | | | % 152.97/22.83 | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | (1073) all_56_0 = e0 % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | COMBINE_EQS: (140), (1073) imply: % 152.97/22.83 | | | | | | | | | (1074) all_10_2 = e0 % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | REDUCE: (1072), (1074) imply: % 152.97/22.83 | | | | | | | | | (1075) $false % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | CLOSE: (1075) is inconsistent. % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | (1076) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | BETA: splitting (1076) gives: % 152.97/22.83 | | | | | | | | | % 152.97/22.83 | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | (1077) all_56_2 = e0 % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | COMBINE_EQS: (118), (1077) imply: % 152.97/22.83 | | | | | | | | | | (1078) all_52_1 = e0 % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | REDUCE: (141), (1078) imply: % 152.97/22.83 | | | | | | | | | | (1079) $false % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | CLOSE: (1079) is inconsistent. % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | (1080) all_56_6 = e0 | all_56_12 = e0 % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | BETA: splitting (1080) gives: % 152.97/22.83 | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | (1081) all_56_6 = e0 % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | COMBINE_EQS: (103), (1081) imply: % 152.97/22.83 | | | | | | | | | | | (1082) all_52_2 = e0 % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | REDUCE: (1065), (1082) imply: % 152.97/22.83 | | | | | | | | | | | (1083) $false % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | CLOSE: (1083) is inconsistent. % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | (1084) all_56_12 = e0 % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | COMBINE_EQS: (75), (1084) imply: % 152.97/22.83 | | | | | | | | | | | (1085) all_52_3 = e0 % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | SIMP: (1085) implies: % 152.97/22.83 | | | | | | | | | | | (1086) all_52_3 = e0 % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | COMBINE_EQS: (143), (1086) imply: % 152.97/22.83 | | | | | | | | | | | (1087) all_58_22 = e0 % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | REDUCE: (1021), (1086) imply: % 152.97/22.83 | | | | | | | | | | | (1088) ~ (e1 = e0) % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | BETA: splitting (82) gives: % 152.97/22.83 | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | (1089) all_56_4 = e0 % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | COMBINE_EQS: (28), (1089) imply: % 152.97/22.83 | | | | | | | | | | | | (1090) all_52_8 = e0 % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | COMBINE_EQS: (153), (1090) imply: % 152.97/22.83 | | | | | | | | | | | | (1091) all_58_4 = e0 % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | REDUCE: (3), (1090) imply: % 152.97/22.83 | | | | | | | | | | | | (1092) ~ (all_52_9 = e0) % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | REDUCE: (23), (1090) imply: % 152.97/22.83 | | | | | | | | | | | | (1093) ~ (all_52_11 = e0) % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | SIMP: (1093) implies: % 152.97/22.83 | | | | | | | | | | | | (1094) ~ (all_52_11 = e0) % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | REDUCE: (59), (1090) imply: % 152.97/22.83 | | | | | | | | | | | | (1095) ~ (all_52_12 = e0) % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | REDUCE: (18), (1090) imply: % 152.97/22.83 | | | | | | | | | | | | (1096) ~ (all_10_2 = e0) % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | BETA: splitting (68) gives: % 152.97/22.83 | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | (1097) all_56_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | COMBINE_EQS: (118), (1097) imply: % 152.97/22.83 | | | | | | | | | | | | | (1098) all_52_1 = e1 % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | REDUCE: (130), (1098) imply: % 152.97/22.83 | | | | | | | | | | | | | (1099) ~ (all_52_9 = e1) % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | SIMP: (1099) implies: % 152.97/22.83 | | | | | | | | | | | | | (1100) ~ (all_52_9 = e1) % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | BETA: splitting (48) gives: % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | (1101) all_56_4 = e1 % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | REF_CLOSE: (162), (1089), (1101) are inconsistent by % 152.97/22.83 | | | | | | | | | | | | | | sub-proof #782. % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | (1102) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | BETA: splitting (1102) gives: % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | (1103) all_56_5 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (1103) imply: % 152.97/22.83 | | | | | | | | | | | | | | | (1104) all_52_9 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | REDUCE: (1100), (1104) imply: % 152.97/22.83 | | | | | | | | | | | | | | | (1105) $false % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | CLOSE: (1105) is inconsistent. % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | (1106) all_56_8 = e1 | all_56_14 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | BETA: splitting (1106) gives: % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | (1107) all_56_8 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (1107) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | (1108) all_6_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | SIMP: (1108) implies: % 152.97/22.83 | | | | | | | | | | | | | | | | (1109) all_6_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (1109) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | (1110) all_58_30 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (116), (117), (127), % 152.97/22.83 | | | | | | | | | | | | | | | | (154), (178), (1020), (1072), (1110) are % 152.97/22.83 | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | (1111) all_56_14 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | REF_CLOSE: (126), (1022), (1111) are inconsistent by % 152.97/22.83 | | | | | | | | | | | | | | | | sub-proof #811. % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | End of split % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | (1112) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | BETA: splitting (1112) gives: % 152.97/22.83 | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | (1113) all_56_3 = e1 % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | REF_CLOSE: (22), (162), (1113) are inconsistent by sub-proof % 152.97/22.83 | | | | | | | | | | | | | | #306. % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | (1114) all_56_5 = e1 | all_56_10 = e1 % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | BETA: splitting (1114) gives: % 152.97/22.83 | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | (1115) all_56_5 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (1115) imply: % 152.97/22.83 | | | | | | | | | | | | | | | (1116) all_52_9 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | COMBINE_EQS: (7), (1116) imply: % 152.97/22.83 | | | | | | | | | | | | | | | (1117) all_58_11 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | REDUCE: (130), (1116) imply: % 152.97/22.83 | | | | | | | | | | | | | | | (1118) ~ (all_52_1 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | REDUCE: (112), (1116) imply: % 152.97/22.83 | | | | | | | | | | | | | | | (1119) ~ (all_52_13 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 152.97/22.83 | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | (1120) all_56_0 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (1120) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | (1121) all_10_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (1121) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | (1122) all_58_28 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (65), (95), (101), (117), (137), (154), % 152.97/22.83 | | | | | | | | | | | | | | | | (170), (173), (1020), (1122) are inconsistent by % 152.97/22.83 | | | | | | | | | | | | | | | | sub-proof #383. % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | (1123) ~ (all_56_0 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | | (1124) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | REDUCE: (140), (1123) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | (1125) ~ (all_10_2 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | BETA: splitting (1124) gives: % 152.97/22.83 | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | (1126) all_56_1 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (1126) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | (1127) all_52_4 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (1127) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | (1128) all_58_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 152.97/22.83 | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | (1129) all_56_0 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (1129) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | (1130) all_10_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | REDUCE: (1125), (1130) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | (1131) $false % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | CLOSE: (1131) is inconsistent. % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | (1132) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 152.97/22.83 | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | (1133) all_56_6 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (1133) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | (1134) all_52_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | SIMP: (1134) implies: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | (1135) all_52_2 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (1135) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | (1136) all_58_15 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | REDUCE: (104), (1135) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | (1137) ~ (all_52_6 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | SIMP: (1137) implies: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | (1138) ~ (all_52_6 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | (1139) all_58_31 = e0 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1020), (1139) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | (1140) e1 = e0 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1115), (1140) imply: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | (1141) all_56_5 = e0 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (162), (1024), (1114), (1141) are % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #304. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | (1142) ~ (all_58_31 = e0) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | (1143) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | e0) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1143) gives: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | (1144) all_58_30 = e1 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (116), (117), (127), % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | (154), (178), (1020), (1072), (1144) are % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | (1145) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1145) gives: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | (1146) all_58_29 = e2 % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (137), (1146) are inconsistent by sub-proof % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | #706. % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.83 | | | | | | | | | | | | | | | | | | | | | | (1147) ~ (all_58_29 = e2) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | (1148) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | e0) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (1147) imply: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | (1149) ~ (e2 = e0) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1148) gives: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (1150) all_58_28 = e3 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (1150) imply: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (1151) all_10_2 = e3 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (58), (116), (178), (1072), (1151) are % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (1152) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | e0) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (26), (65), (101), (117), (122), (129), % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (137), (162), (1024), (1064), (1066), (1087), % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (1091), (1094), (1114), (1115), (1117), (1128), % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | (1136), (1138), (1152) are inconsistent by % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #272. % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | (1153) ~ (all_56_6 = e1) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | REDUCE: (103), (1153) imply: % 152.97/22.84 | | | | | | | | | | | | | | | | | | | (1154) ~ (all_52_2 = e1) % 152.97/22.84 | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (118), (162), (1084), (1118), (1132), % 152.97/22.84 | | | | | | | | | | | | | | | | | | | (1154) are inconsistent by sub-proof #637. % 152.97/22.84 | | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | Case 2: % 152.97/22.84 | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | (1155) all_56_4 = e1 | all_56_9 = e1 % 152.97/22.84 | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives: % 152.97/22.84 | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | Case 1: % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | (1156) all_56_4 = e1 % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1089), (1156) imply: % 152.97/22.84 | | | | | | | | | | | | | | | | | | (1157) e1 = e0 % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | SIMP: (1157) implies: % 152.97/22.84 | | | | | | | | | | | | | | | | | | (1158) e1 = e0 % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1115), (1158) imply: % 152.97/22.84 | | | | | | | | | | | | | | | | | | (1159) all_56_5 = e0 % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (162), (1024), (1114), (1159) are % 152.97/22.84 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #304. % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | Case 2: % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | (1160) all_56_9 = e1 % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (1023), (1160) are inconsistent by sub-proof % 152.97/22.84 | | | | | | | | | | | | | | | | | | #486. % 152.97/22.84 | | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | Case 2: % 152.97/22.84 | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | (1161) all_56_10 = e1 % 152.97/22.84 | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | | REF_CLOSE: (122), (1024), (1161) are inconsistent by % 152.97/22.84 | | | | | | | | | | | | | | | sub-proof #606. % 152.97/22.84 | | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | Case 2: % 152.97/22.84 | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | (1162) ~ (all_56_4 = e0) % 152.97/22.84 | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | REDUCE: (28), (1162) imply: % 152.97/22.84 | | | | | | | | | | | | (1163) ~ (all_52_8 = e0) % 152.97/22.84 | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | | REF_CLOSE: (28), (81), (97), (114), (1066), (1071), (1163) % 152.97/22.84 | | | | | | | | | | | | are inconsistent by sub-proof #519. % 152.97/22.84 | | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | | % 152.97/22.84 | | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | | % 152.97/22.84 | | | | | | | | | End of split % 152.97/22.84 | | | | | | | | | % 152.97/22.84 | | | | | | | | End of split % 152.97/22.84 | | | | | | | | % 152.97/22.84 | | | | | | | End of split % 152.97/22.84 | | | | | | | % 152.97/22.84 | | | | | | End of split % 152.97/22.84 | | | | | | % 152.97/22.84 | | | | | End of split % 152.97/22.84 | | | | | % 152.97/22.84 | | | | End of split % 152.97/22.84 | | | | % 152.97/22.84 | | | End of split % 152.97/22.84 | | | % 152.97/22.84 | | End of split % 152.97/22.84 | | % 152.97/22.84 | Case 2: % 152.97/22.84 | | % 152.97/22.84 | | (1164) all_18_2 = e0 % 152.97/22.84 | | % 152.97/22.84 | | COMBINE_EQS: (105), (1164) imply: % 152.97/22.84 | | (1165) all_6_2 = e0 % 152.97/22.84 | | % 152.97/22.84 | | COMBINE_EQS: (170), (1165) imply: % 152.97/22.84 | | (1166) all_58_30 = e0 % 152.97/22.84 | | % 152.97/22.84 | | REDUCE: (115), (1165) imply: % 152.97/22.84 | | (1167) ~ (all_52_11 = e0) % 152.97/22.84 | | % 152.97/22.84 | | BETA: splitting (132) gives: % 152.97/22.84 | | % 152.97/22.84 | | Case 1: % 152.97/22.84 | | | % 152.97/22.84 | | | (1168) ~ (all_20_2 = e1) % 152.97/22.84 | | | % 152.97/22.84 | | | REDUCE: (78), (1168) imply: % 152.97/22.84 | | | (1169) ~ (all_4_2 = e1) % 152.97/22.84 | | | % 152.97/22.84 | | | REF_CLOSE: (2), (30), (65), (95), (101), (117), (127), (137), (154), % 152.97/22.84 | | | (162), (172), (173), (1166), (1169) are inconsistent by % 152.97/22.84 | | | sub-proof #698. % 152.97/22.84 | | | % 152.97/22.84 | | Case 2: % 152.97/22.84 | | | % 152.97/22.84 | | | (1170) all_20_2 = e1 % 152.97/22.84 | | | % 152.97/22.84 | | | COMBINE_EQS: (78), (1170) imply: % 152.97/22.84 | | | (1171) all_4_2 = e1 % 152.97/22.84 | | | % 152.97/22.84 | | | COMBINE_EQS: (8), (1171) imply: % 152.97/22.84 | | | (1172) all_56_15 = e1 % 152.97/22.84 | | | % 152.97/22.84 | | | COMBINE_EQS: (2), (1171) imply: % 152.97/22.84 | | | (1173) all_58_31 = e1 % 152.97/22.84 | | | % 152.97/22.84 | | | BETA: splitting (57) gives: % 152.97/22.84 | | | % 152.97/22.84 | | | Case 1: % 152.97/22.84 | | | | % 152.97/22.84 | | | | (1174) all_56_15 = e0 % 152.97/22.84 | | | | % 152.97/22.84 | | | | COMBINE_EQS: (1172), (1174) imply: % 152.97/22.84 | | | | (1175) e1 = e0 % 152.97/22.84 | | | | % 152.97/22.84 | | | | REDUCE: (162), (1175) imply: % 152.97/22.84 | | | | (1176) $false % 152.97/22.84 | | | | % 152.97/22.84 | | | | CLOSE: (1176) is inconsistent. % 152.97/22.84 | | | | % 152.97/22.84 | | | Case 2: % 152.97/22.84 | | | | % 152.97/22.84 | | | | (1177) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 % 152.97/22.84 | | | | = e0 | all_56_13 = e0 | all_56_14 = e0) % 152.97/22.84 | | | | % 152.97/22.84 | | | | ALPHA: (1177) implies: % 152.97/22.84 | | | | (1178) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 152.97/22.84 | | | | % 152.97/22.84 | | | | BETA: splitting (1178) gives: % 152.97/22.84 | | | | % 152.97/22.84 | | | | Case 1: % 152.97/22.84 | | | | | % 152.97/22.84 | | | | | (1179) all_56_12 = e0 % 152.97/22.84 | | | | | % 152.97/22.84 | | | | | COMBINE_EQS: (75), (1179) imply: % 152.97/22.84 | | | | | (1180) all_52_3 = e0 % 152.97/22.84 | | | | | % 152.97/22.84 | | | | | REDUCE: (146), (1180) imply: % 153.19/22.84 | | | | | (1181) ~ (all_10_2 = e0) % 153.19/22.84 | | | | | % 153.19/22.84 | | | | | SIMP: (1181) implies: % 153.19/22.84 | | | | | (1182) ~ (all_10_2 = e0) % 153.19/22.84 | | | | | % 153.19/22.84 | | | | | REF_CLOSE: (4), (16), (58), (65), (95), (116), (117), (127), (154), % 153.19/22.84 | | | | | (178), (1166), (1173), (1182) are inconsistent by sub-proof % 153.19/22.84 | | | | | #178. % 153.19/22.84 | | | | | % 153.19/22.84 | | | | Case 2: % 153.19/22.84 | | | | | % 153.19/22.84 | | | | | (1183) all_56_13 = e0 | all_56_14 = e0 % 153.19/22.84 | | | | | % 153.19/22.84 | | | | | REF_CLOSE: (106), (126), (160), (1167), (1183) are inconsistent by % 153.19/22.84 | | | | | sub-proof #609. % 153.19/22.84 | | | | | % 153.19/22.84 | | | | End of split % 153.19/22.84 | | | | % 153.19/22.84 | | | End of split % 153.19/22.84 | | | % 153.19/22.84 | | End of split % 153.19/22.84 | | % 153.19/22.84 | End of split % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #160 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.19/22.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.19/22.84 (2) all_58_31 = e1 % 153.19/22.84 (3) op(all_10_2, all_10_1) = e0 % 153.19/22.84 (4) ~ (all_10_2 = e0) % 153.19/22.84 (5) op(e3, e3) = all_10_2 % 153.19/22.84 (6) ~ (e3 = e1) % 153.19/22.84 (7) all_58_29 = e0 % 153.19/22.84 (8) op(e3, all_10_2) = all_58_0 % 153.19/22.84 (9) ~ (e3 = e0) % 153.19/22.84 (10) all_58_28 = all_10_2 % 153.19/22.84 (11) all_58_30 = e1 % 153.19/22.84 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.84 (13) op(all_10_2, e3) = all_10_1 % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | BETA: splitting (12) gives: % 153.19/22.84 | % 153.19/22.84 | Case 1: % 153.19/22.84 | | % 153.19/22.84 | | (14) all_58_28 = e3 % 153.19/22.84 | | % 153.19/22.84 | | COMBINE_EQS: (10), (14) imply: % 153.19/22.84 | | (15) all_10_2 = e3 % 153.19/22.84 | | % 153.19/22.84 | | REF_CLOSE: (1), (3), (4), (5), (8), (13), (15) are inconsistent by sub-proof % 153.19/22.84 | | #251. % 153.19/22.84 | | % 153.19/22.84 | Case 2: % 153.19/22.84 | | % 153.19/22.84 | | (16) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.84 | | % 153.19/22.84 | | REF_CLOSE: (2), (6), (7), (9), (11), (16) are inconsistent by sub-proof % 153.19/22.84 | | #284. % 153.19/22.84 | | % 153.19/22.84 | End of split % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #161 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_56_11 = all_52_14 % 153.19/22.84 (2) all_56_11 = e2 | all_56_15 = e2 % 153.19/22.84 (3) all_56_15 = e3 % 153.19/22.84 (4) ~ (all_52_14 = e2) % 153.19/22.84 (5) ~ (e3 = e2) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | BETA: splitting (2) gives: % 153.19/22.84 | % 153.19/22.84 | Case 1: % 153.19/22.84 | | % 153.19/22.84 | | (6) all_56_11 = e2 % 153.19/22.84 | | % 153.19/22.84 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #494. % 153.19/22.84 | | % 153.19/22.84 | Case 2: % 153.19/22.84 | | % 153.19/22.84 | | (7) all_56_15 = e2 % 153.19/22.84 | | % 153.19/22.84 | | COMBINE_EQS: (3), (7) imply: % 153.19/22.84 | | (8) e3 = e2 % 153.19/22.84 | | % 153.19/22.84 | | SIMP: (8) implies: % 153.19/22.84 | | (9) e3 = e2 % 153.19/22.84 | | % 153.19/22.84 | | REDUCE: (5), (9) imply: % 153.19/22.84 | | (10) $false % 153.19/22.84 | | % 153.19/22.84 | | CLOSE: (10) is inconsistent. % 153.19/22.84 | | % 153.19/22.84 | End of split % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #162 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_30 = e2 % 153.19/22.84 (2) all_58_6 = e0 % 153.19/22.84 (3) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3 % 153.19/22.84 (4) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (5) all_58_31 = e3 % 153.19/22.84 (6) ~ (e2 = e0) % 153.19/22.84 (7) all_58_22 = e2 % 153.19/22.84 (8) ~ (e3 = e2) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | ALPHA: (3) implies: % 153.19/22.84 | (9) all_58_22 = e3 % 153.19/22.84 | (10) all_58_6 = e3 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (2), (10) imply: % 153.19/22.84 | (11) e3 = e0 % 153.19/22.84 | % 153.19/22.84 | SIMP: (11) implies: % 153.19/22.84 | (12) e3 = e0 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (7), (9) imply: % 153.19/22.84 | (13) e3 = e2 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (1), (4), (5), (6), (8), (12), (13) are inconsistent by sub-proof % 153.19/22.84 | #166. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #163 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.19/22.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.19/22.84 (2) op(all_10_2, all_10_1) = e0 % 153.19/22.84 (3) ~ (all_10_2 = e0) % 153.19/22.84 (4) op(e3, e3) = all_10_2 % 153.19/22.84 (5) all_58_30 = e2 % 153.19/22.84 (6) ~ (e3 = e1) % 153.19/22.84 (7) all_58_29 = e0 % 153.19/22.84 (8) ~ (e2 = e1) % 153.19/22.84 (9) op(e3, all_10_2) = all_58_0 % 153.19/22.84 (10) ~ (e3 = e0) % 153.19/22.84 (11) all_58_28 = all_10_2 % 153.19/22.84 (12) ~ (e2 = e0) % 153.19/22.84 (13) all_56_0 = all_10_2 % 153.19/22.84 (14) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (15) all_58_24 = e1 % 153.19/22.84 (16) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.84 (17) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.19/22.84 (18) all_58_24 = e2 % 153.19/22.84 (19) ~ (e3 = e2) % 153.19/22.84 (20) op(all_10_2, e3) = all_10_1 % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (15), (18) imply: % 153.19/22.84 | (21) e2 = e1 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (5), (21) imply: % 153.19/22.84 | (22) all_58_30 = e1 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), % 153.19/22.84 | (14), (16), (17), (19), (20), (22) are inconsistent by sub-proof % 153.19/22.84 | #250. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #164 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_30 = e2 % 153.19/22.84 (2) all_58_24 = e0 % 153.19/22.84 (3) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (4) all_58_31 = e3 % 153.19/22.84 (5) ~ (e2 = e0) % 153.19/22.84 (6) all_58_24 = e2 % 153.19/22.84 (7) ~ (e3 = e2) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (2), (6) imply: % 153.19/22.84 | (8) e2 = e0 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (8) imply: % 153.19/22.84 | (9) all_58_30 = e0 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #705. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #165 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_4 = e1 % 153.19/22.84 (2) all_58_4 = e0 % 153.19/22.84 (3) ~ (e1 = e0) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (2) imply: % 153.19/22.84 | (4) e1 = e0 % 153.19/22.84 | % 153.19/22.84 | SIMP: (4) implies: % 153.19/22.84 | (5) e1 = e0 % 153.19/22.84 | % 153.19/22.84 | REDUCE: (3), (5) imply: % 153.19/22.84 | (6) $false % 153.19/22.84 | % 153.19/22.84 | CLOSE: (6) is inconsistent. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #166 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_30 = e2 % 153.19/22.84 (2) e3 = e0 % 153.19/22.84 (3) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (4) all_58_31 = e3 % 153.19/22.84 (5) ~ (e2 = e0) % 153.19/22.84 (6) ~ (e3 = e2) % 153.19/22.84 (7) e3 = e2 % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (2), (7) imply: % 153.19/22.84 | (8) e2 = e0 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (8) imply: % 153.19/22.84 | (9) all_58_30 = e0 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (3), (4), (5), (6), (9) are inconsistent by sub-proof #705. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #167 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_6 = e2 % 153.19/22.84 (2) all_58_30 = e2 % 153.19/22.84 (3) all_58_6 = e0 % 153.19/22.84 (4) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (5) all_58_31 = e3 % 153.19/22.84 (6) ~ (e2 = e0) % 153.19/22.84 (7) ~ (e3 = e2) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (3) imply: % 153.19/22.84 | (8) e2 = e0 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (2), (8) imply: % 153.19/22.84 | (9) all_58_30 = e0 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (4), (5), (6), (7), (9) are inconsistent by sub-proof #705. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #168 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_15 = e1 % 153.19/22.84 (2) all_58_30 = e2 % 153.19/22.84 (3) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (4) all_58_31 = e3 % 153.19/22.84 (5) ~ (e2 = e0) % 153.19/22.84 (6) all_58_15 = e3 % 153.19/22.84 (7) e1 = e0 % 153.19/22.84 (8) ~ (e3 = e2) % 153.19/22.84 (9) e3 = e2 % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (6) imply: % 153.19/22.84 | (10) e3 = e1 % 153.19/22.84 | % 153.19/22.84 | SIMP: (10) implies: % 153.19/22.84 | (11) e3 = e1 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (9), (11) imply: % 153.19/22.84 | (12) e2 = e1 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (12) are inconsistent by sub-proof % 153.19/22.84 | #169. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #169 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_30 = e2 % 153.19/22.84 (2) e2 = e1 % 153.19/22.84 (3) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (4) all_58_31 = e3 % 153.19/22.84 (5) ~ (e2 = e0) % 153.19/22.84 (6) e1 = e0 % 153.19/22.84 (7) ~ (e3 = e2) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (2), (6) imply: % 153.19/22.84 | (8) e2 = e0 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (8) imply: % 153.19/22.84 | (9) all_58_30 = e0 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #705. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #170 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) e2 = e0 % 153.19/22.84 (2) all_58_30 = e2 % 153.19/22.84 (3) all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (4) all_58_31 = e3 % 153.19/22.84 (5) ~ (e2 = e0) % 153.19/22.84 (6) ~ (e3 = e2) % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | SIMP: (1) implies: % 153.19/22.84 | (7) e2 = e0 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (2), (7) imply: % 153.19/22.84 | (8) all_58_30 = e0 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #705. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #171 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) all_58_31 = all_4_2 % 153.19/22.84 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.19/22.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.19/22.84 (3) op(all_10_2, all_10_1) = e0 % 153.19/22.84 (4) all_54_10 = all_6_2 % 153.19/22.84 (5) ~ (all_10_2 = e0) % 153.19/22.84 (6) op(e3, e3) = all_10_2 % 153.19/22.84 (7) ~ (e3 = e1) % 153.19/22.84 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 153.19/22.84 (9) all_58_29 = e0 % 153.19/22.84 (10) op(e3, all_10_2) = all_58_0 % 153.19/22.84 (11) ~ (e3 = e0) % 153.19/22.84 (12) all_58_28 = all_10_2 % 153.19/22.84 (13) ~ (all_6_2 = e3) % 153.19/22.84 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.84 (15) all_58_30 = all_6_2 % 153.19/22.84 (16) ~ (e3 = e2) % 153.19/22.84 (17) op(all_10_2, e3) = all_10_1 % 153.19/22.84 (18) all_4_2 = e2 % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | SIMP: (18) implies: % 153.19/22.84 | (19) all_4_2 = e2 % 153.19/22.84 | % 153.19/22.84 | COMBINE_EQS: (1), (19) imply: % 153.19/22.84 | (20) all_58_31 = e2 % 153.19/22.84 | % 153.19/22.84 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 153.19/22.84 | (14), (15), (16), (17), (20) are inconsistent by sub-proof #172. % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #172 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.19/22.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.19/22.84 (2) all_58_31 = e2 % 153.19/22.84 (3) op(all_10_2, all_10_1) = e0 % 153.19/22.84 (4) all_54_10 = all_6_2 % 153.19/22.84 (5) ~ (all_10_2 = e0) % 153.19/22.84 (6) op(e3, e3) = all_10_2 % 153.19/22.84 (7) ~ (e3 = e1) % 153.19/22.84 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 153.19/22.84 (9) all_58_29 = e0 % 153.19/22.84 (10) op(e3, all_10_2) = all_58_0 % 153.19/22.84 (11) ~ (e3 = e0) % 153.19/22.84 (12) all_58_28 = all_10_2 % 153.19/22.84 (13) ~ (all_6_2 = e3) % 153.19/22.84 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.84 (15) all_58_30 = all_6_2 % 153.19/22.84 (16) ~ (e3 = e2) % 153.19/22.84 (17) op(all_10_2, e3) = all_10_1 % 153.19/22.84 % 153.19/22.84 Begin of proof % 153.19/22.84 | % 153.19/22.84 | BETA: splitting (14) gives: % 153.19/22.84 | % 153.19/22.84 | Case 1: % 153.19/22.84 | | % 153.19/22.84 | | (18) all_58_28 = e3 % 153.19/22.84 | | % 153.19/22.84 | | COMBINE_EQS: (12), (18) imply: % 153.19/22.84 | | (19) all_10_2 = e3 % 153.19/22.84 | | % 153.19/22.84 | | REF_CLOSE: (1), (3), (5), (6), (10), (17), (19) are inconsistent by % 153.19/22.84 | | sub-proof #251. % 153.19/22.84 | | % 153.19/22.84 | Case 2: % 153.19/22.84 | | % 153.19/22.84 | | (20) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.84 | | % 153.19/22.84 | | REF_CLOSE: (2), (4), (7), (8), (9), (11), (13), (15), (16), (20) are % 153.19/22.84 | | inconsistent by sub-proof #356. % 153.19/22.84 | | % 153.19/22.84 | End of split % 153.19/22.84 | % 153.19/22.84 End of proof % 153.19/22.84 % 153.19/22.84 Sub-proof #173 shows that the following formulas are inconsistent: % 153.19/22.84 ---------------------------------------------------------------- % 153.19/22.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.19/22.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.19/22.84 (2) all_56_7 = all_52_6 % 153.19/22.84 (3) op(all_10_2, all_10_1) = e0 % 153.19/22.84 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.19/22.84 (5) ~ (all_6_2 = e0) % 153.19/22.84 (6) op(e3, e3) = all_10_2 % 153.19/22.84 (7) ~ (e3 = e1) % 153.19/22.84 (8) ~ (all_52_6 = e0) % 153.19/22.84 (9) all_56_11 = all_52_14 % 153.19/22.84 (10) all_58_29 = e0 % 153.19/22.84 (11) ~ (e2 = e1) % 153.19/22.84 (12) all_56_6 = all_52_2 % 153.19/22.84 (13) op(e3, all_10_2) = all_58_0 % 153.19/22.84 (14) ~ (e3 = e0) % 153.19/22.84 (15) all_58_28 = all_10_2 % 153.19/22.84 (16) ~ (e2 = e0) % 153.19/22.85 (17) ~ (all_52_2 = all_10_2) % 153.19/22.85 (18) all_56_0 = all_10_2 % 153.19/22.85 (19) all_58_31 = e0 % 153.19/22.85 (20) all_56_8 = all_6_2 % 153.19/22.85 (21) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.85 (22) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.19/22.85 (23) ~ (e1 = e0) % 153.19/22.85 (24) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.19/22.85 (25) ~ (all_52_14 = e0) % 153.19/22.85 (26) all_58_30 = all_6_2 % 153.19/22.85 (27) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.19/22.85 (28) ~ (e3 = e2) % 153.19/22.85 (29) op(all_10_2, e3) = all_10_1 % 153.19/22.85 % 153.19/22.85 Begin of proof % 153.19/22.85 | % 153.19/22.85 | BETA: splitting (22) gives: % 153.19/22.85 | % 153.19/22.85 | Case 1: % 153.19/22.85 | | % 153.19/22.85 | | (30) all_56_6 = e0 % 153.19/22.85 | | % 153.19/22.85 | | COMBINE_EQS: (12), (30) imply: % 153.19/22.85 | | (31) all_52_2 = e0 % 153.19/22.85 | | % 153.19/22.85 | | REDUCE: (17), (31) imply: % 153.19/22.85 | | (32) ~ (all_10_2 = e0) % 153.19/22.85 | | % 153.19/22.85 | | SIMP: (32) implies: % 153.19/22.85 | | (33) ~ (all_10_2 = e0) % 153.19/22.85 | | % 153.19/22.85 | | REF_CLOSE: (1), (3), (4), (6), (7), (10), (11), (13), (14), (15), (16), % 153.19/22.85 | | (18), (19), (21), (23), (24), (26), (27), (28), (29), (33) are % 153.19/22.85 | | inconsistent by sub-proof #249. % 153.19/22.85 | | % 153.19/22.85 | Case 2: % 153.19/22.85 | | % 153.19/22.85 | | (34) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.19/22.85 | | % 153.19/22.85 | | REF_CLOSE: (2), (5), (8), (9), (20), (25), (34) are inconsistent by % 153.19/22.85 | | sub-proof #287. % 153.19/22.85 | | % 153.19/22.85 | End of split % 153.19/22.85 | % 153.19/22.85 End of proof % 153.19/22.85 % 153.19/22.85 Sub-proof #174 shows that the following formulas are inconsistent: % 153.19/22.85 ---------------------------------------------------------------- % 153.19/22.85 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.19/22.85 (2) all_58_31 = all_4_2 % 153.19/22.85 (3) ~ (all_52_8 = all_52_9) % 153.19/22.85 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.19/22.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.19/22.85 (5) ~ (all_52_2 = all_52_3) % 153.19/22.85 (6) all_58_11 = all_52_9 % 153.19/22.85 (7) all_56_15 = all_4_2 % 153.19/22.85 (8) all_56_7 = all_52_6 % 153.19/22.85 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 153.19/22.85 (10) all_54_2 = all_52_8 % 153.19/22.85 (11) all_54_8 = all_52_2 % 153.19/22.85 (12) op(e3, all_52_4) = all_58_1 % 153.19/22.85 (13) op(all_10_2, all_10_1) = e0 % 153.19/22.85 (14) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.19/22.85 (15) ~ (all_52_8 = all_10_2) % 153.19/22.85 (16) ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 153.19/22.85 (17) all_58_15 = all_52_2 % 153.19/22.85 (18) all_58_26 = all_52_11 % 153.19/22.85 (19) op(e1, all_52_14) = all_58_19 % 153.19/22.85 (20) ~ (all_52_8 = all_52_11) % 153.19/22.85 (21) ~ (all_52_11 = all_4_2) % 153.19/22.85 (22) all_54_7 = all_52_13 % 153.19/22.85 (23) all_58_6 = all_52_12 % 153.19/22.85 (24) ~ (all_52_6 = all_8_2) % 153.19/22.85 (25) all_56_4 = all_52_8 % 153.19/22.85 (26) all_54_3 = all_52_12 % 153.19/22.85 (27) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.19/22.85 (28) all_54_1 = all_52_4 % 153.19/22.85 (29) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.19/22.85 (30) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 153.19/22.85 (31) ~ (all_52_4 = all_52_6) % 153.19/22.85 (32) all_58_13 = all_52_13 % 153.19/22.85 (33) op(e0, e1) = all_52_11 % 153.19/22.85 (34) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 153.19/22.85 (35) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.19/22.85 (36) ~ (all_52_6 = all_52_7) % 153.19/22.85 (37) op(e3, e2) = all_52_4 % 153.19/22.85 (38) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 153.19/22.85 (39) all_58_20 = all_52_14 % 153.19/22.85 (40) ~ (all_52_12 = all_52_13) % 153.19/22.85 (41) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.19/22.85 (42) op(e0, all_52_3) = all_58_21 % 153.19/22.85 (43) all_54_5 = all_8_2 % 153.19/22.85 (44) ~ (all_52_6 = all_52_14) % 153.19/22.85 (45) all_54_6 = all_52_9 % 153.19/22.85 (46) ~ (all_52_4 = all_52_7) % 153.19/22.85 (47) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 153.19/22.85 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 153.19/22.85 (48) op(e3, e3) = all_10_2 % 153.19/22.85 (49) ~ (all_52_8 = all_52_12) % 153.19/22.85 (50) all_54_9 = all_52_6 % 153.19/22.85 (51) ~ (all_52_13 = all_4_2) % 153.19/22.85 (52) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 153.19/22.85 (53) ~ (all_52_13 = all_8_2) % 153.19/22.85 (54) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 153.19/22.85 (55) ~ (e3 = e1) % 153.19/22.85 (56) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 153.19/22.85 (57) all_56_8 = e0 % 153.19/22.85 (58) ~ (all_52_6 = e0) % 153.19/22.85 (59) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.19/22.85 (60) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 153.19/22.85 (61) ~ (all_52_1 = all_52_13) % 153.19/22.85 (62) all_56_5 = all_52_9 % 153.19/22.85 (63) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.19/22.85 (64) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 153.19/22.85 (65) all_56_12 = all_52_3 % 153.19/22.85 (66) ~ (all_52_3 = all_52_7) % 153.19/22.85 (67) all_58_2 = all_52_4 % 153.19/22.85 (68) all_20_2 = all_4_2 % 153.19/22.85 (69) all_56_11 = all_52_14 % 153.19/22.85 (70) all_56_1 = all_52_4 % 153.19/22.85 (71) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.19/22.85 (72) ~ (all_52_3 = all_4_2) % 153.19/22.85 (73) op(e1, e3) = all_52_2 % 153.19/22.85 (74) op(e1, e0) = all_52_14 % 153.19/22.85 (75) ~ (all_52_9 = all_52_11) % 153.19/22.85 (76) ~ (all_52_9 = e0) % 153.19/22.85 (77) ~ (all_52_1 = all_8_2) % 153.19/22.85 (78) all_56_3 = all_8_2 % 153.19/22.85 (79) all_58_24 = all_52_7 % 153.19/22.85 (80) ~ (all_52_13 = all_52_14) % 153.19/22.85 (81) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.19/22.85 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.19/22.85 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.19/22.85 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.19/22.85 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.19/22.85 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.19/22.85 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.19/22.85 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.19/22.85 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.19/22.85 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.19/22.85 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.19/22.85 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.19/22.85 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.19/22.85 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.19/22.85 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.19/22.85 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.19/22.85 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.19/22.85 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.19/22.85 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.19/22.85 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.19/22.85 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.19/22.85 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.19/22.85 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.19/22.85 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.19/22.85 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.19/22.85 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.19/22.85 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.19/22.85 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.19/22.85 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.85 e0) % 153.19/22.85 (82) ~ (all_52_4 = all_52_8) % 153.19/22.85 (83) all_56_9 = all_52_12 % 153.19/22.85 (84) all_58_29 = all_8_2 % 153.19/22.85 (85) ~ (all_52_12 = all_52_14) % 153.19/22.85 (86) all_58_30 = e0 % 153.19/22.85 (87) all_58_8 = all_52_1 % 153.19/22.85 (88) ~ (e2 = e1) % 153.19/22.85 (89) op(e3, e0) = all_52_12 % 153.19/22.85 (90) all_56_6 = all_52_2 % 153.19/22.85 (91) ~ (all_52_2 = all_52_6) % 153.19/22.85 (92) all_56_13 = all_52_7 % 153.19/22.85 (93) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.19/22.85 (94) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 153.19/22.85 (95) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.19/22.85 (96) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.19/22.85 (97) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.19/22.85 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 153.19/22.85 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 153.19/22.85 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 153.19/22.85 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 153.19/22.85 (all_58_27 = e0)) % 153.19/22.85 (98) ~ (all_52_9 = all_52_13) % 153.19/22.85 (99) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.19/22.85 (100) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.19/22.85 (101) op(e3, all_10_2) = all_58_0 % 153.19/22.85 (102) op(e1, e1) = e0 % 153.19/22.85 (103) ~ (e3 = e0) % 153.19/22.85 (104) all_56_2 = all_52_1 % 153.19/22.85 (105) ~ (all_52_11 = e0) % 153.19/22.85 (106) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.19/22.85 (107) all_56_10 = all_52_13 % 153.19/22.85 (108) ~ (all_52_12 = all_10_2) % 153.19/22.85 (109) ~ (all_52_1 = all_52_3) % 153.19/22.85 (110) op(e0, e1) = all_6_1 % 153.19/22.85 (111) ~ (all_52_9 = all_8_2) % 153.19/22.85 (112) all_56_14 = all_52_11 % 153.19/22.85 (113) all_58_28 = all_10_2 % 153.19/22.85 (114) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 153.19/22.85 (115) all_58_17 = all_52_6 % 153.19/22.85 (116) ~ (all_52_1 = all_52_9) % 153.19/22.85 (117) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 153.19/22.85 (118) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.19/22.85 (119) ~ (all_52_7 = all_52_11) % 153.19/22.85 (120) op(all_8_2, e2) = all_8_1 % 153.19/22.85 (121) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.19/22.85 (122) ~ (e2 = e0) % 153.19/22.85 (123) ~ (all_52_2 = all_10_2) % 153.19/22.85 (124) all_56_0 = all_10_2 % 153.19/22.85 (125) op(e0, e0) = all_4_2 % 153.19/22.85 (126) ~ (all_52_3 = all_52_11) % 153.19/22.85 (127) all_58_22 = all_52_3 % 153.19/22.85 (128) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 153.19/22.85 (129) ~ (all_52_12 = all_4_2) % 153.19/22.85 (130) ~ (all_52_3 = all_10_2) % 153.19/22.85 (131) ~ (all_52_1 = all_52_2) % 153.19/22.85 (132) ~ (all_52_7 = all_8_2) % 153.19/22.85 (133) op(e2, e0) = all_52_13 % 153.19/22.85 (134) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 153.19/22.85 (135) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.19/22.85 (136) op(e2, all_52_13) = all_58_12 % 153.19/22.85 (137) all_58_4 = all_52_8 % 153.19/22.85 (138) ~ (all_8_1 = e0) % 153.19/22.85 (139) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.85 (140) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 153.19/22.85 (141) all_54_0 = all_10_2 % 153.19/22.85 (142) ~ (all_52_2 = all_52_14) % 153.19/22.85 (143) ~ (all_52_14 = all_4_2) % 153.19/22.85 (144) ~ (e1 = e0) % 153.19/22.85 (145) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.19/22.85 (146) ~ (all_52_7 = all_4_2) % 153.19/22.85 (147) ~ (all_52_14 = e0) % 153.19/22.85 (148) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 153.19/22.85 (149) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 153.19/22.85 (150) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 153.19/22.85 (151) ~ (all_52_8 = e0) % 153.19/22.85 (152) ~ (all_52_4 = all_10_2) % 153.19/22.85 (153) all_58_30 = all_6_2 % 153.19/22.85 (154) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.19/22.85 (155) ~ (e3 = e2) % 153.19/22.85 (156) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.19/22.85 (157) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 153.19/22.85 (158) op(all_4_2, e0) = all_4_1 % 153.19/22.85 (159) op(all_10_2, e3) = all_10_1 % 153.19/22.85 (160) op(e1, e0) = all_58_18 % 153.19/22.85 (161) ~ (all_8_2 = e0) % 153.19/22.85 (162) ~ (all_52_4 = all_52_12) % 153.19/22.85 (163) all_54_12 = all_52_3 % 153.19/22.85 (164) all_54_4 = all_52_1 % 153.19/22.85 (165) ~ (all_52_1 = all_10_2) % 153.19/22.85 % 153.19/22.85 Begin of proof % 153.19/22.85 | % 153.19/22.85 | GROUND_INST: instantiating (4) with all_52_11, all_6_1, e1, e0, simplifying % 153.19/22.85 | with (33), (110) gives: % 153.19/22.85 | (166) all_52_11 = all_6_1 % 153.19/22.85 | % 153.19/22.85 | GROUND_INST: instantiating (4) with all_52_14, all_58_18, e0, e1, simplifying % 153.19/22.85 | with (74), (160) gives: % 153.19/22.85 | (167) all_58_18 = all_52_14 % 153.19/22.85 | % 153.19/22.85 | COMBINE_EQS: (112), (166) imply: % 153.19/22.85 | (168) all_56_14 = all_6_1 % 153.19/22.85 | % 153.19/22.85 | COMBINE_EQS: (18), (166) imply: % 153.19/22.85 | (169) all_58_26 = all_6_1 % 153.19/22.85 | % 153.19/22.85 | REDUCE: (126), (166) imply: % 153.19/22.85 | (170) ~ (all_52_3 = all_6_1) % 153.19/22.85 | % 153.19/22.85 | REDUCE: (119), (166) imply: % 153.19/22.85 | (171) ~ (all_52_7 = all_6_1) % 153.19/22.85 | % 153.19/22.85 | REDUCE: (20), (166) imply: % 153.19/22.85 | (172) ~ (all_52_8 = all_6_1) % 153.19/22.85 | % 153.19/22.85 | REDUCE: (75), (166) imply: % 153.19/22.85 | (173) ~ (all_52_9 = all_6_1) % 153.19/22.85 | % 153.19/22.85 | REDUCE: (21), (166) imply: % 153.19/22.85 | (174) ~ (all_6_1 = all_4_2) % 153.19/22.85 | % 153.19/22.85 | BETA: splitting (117) gives: % 153.19/22.85 | % 153.19/22.85 | Case 1: % 153.19/22.85 | | % 153.19/22.85 | | (175) ~ (all_20_2 = e1) % 153.19/22.85 | | % 153.19/22.85 | | REDUCE: (68), (175) imply: % 153.19/22.85 | | (176) ~ (all_4_2 = e1) % 153.19/22.85 | | % 153.19/22.85 | | BETA: splitting (47) gives: % 153.19/22.85 | | % 153.19/22.85 | | Case 1: % 153.19/22.85 | | | % 153.19/22.85 | | | (177) all_56_15 = e0 % 153.19/22.85 | | | % 153.19/22.85 | | | COMBINE_EQS: (7), (177) imply: % 153.19/22.85 | | | (178) all_4_2 = e0 % 153.19/22.85 | | | % 153.19/22.85 | | | SIMP: (178) implies: % 153.19/22.85 | | | (179) all_4_2 = e0 % 153.19/22.85 | | | % 153.19/22.85 | | | COMBINE_EQS: (2), (179) imply: % 153.19/22.85 | | | (180) all_58_31 = e0 % 153.19/22.85 | | | % 153.19/22.85 | | | REDUCE: (51), (179) imply: % 153.19/22.85 | | | (181) ~ (all_52_13 = e0) % 153.19/22.85 | | | % 153.19/22.85 | | | REDUCE: (176), (179) imply: % 153.19/22.85 | | | (182) ~ (e1 = e0) % 153.19/22.85 | | | % 153.19/22.85 | | | BETA: splitting (29) gives: % 153.19/22.85 | | | % 153.19/22.85 | | | Case 1: % 153.19/22.85 | | | | % 153.19/22.85 | | | | (183) all_56_2 = e0 % 153.19/22.85 | | | | % 153.19/22.85 | | | | COMBINE_EQS: (104), (183) imply: % 153.19/22.85 | | | | (184) all_52_1 = e0 % 153.19/22.85 | | | | % 153.19/22.85 | | | | REDUCE: (131), (184) imply: % 153.19/22.85 | | | | (185) ~ (all_52_2 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | SIMP: (185) implies: % 153.19/22.85 | | | | (186) ~ (all_52_2 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | REDUCE: (165), (184) imply: % 153.19/22.85 | | | | (187) ~ (all_10_2 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | SIMP: (187) implies: % 153.19/22.85 | | | | (188) ~ (all_10_2 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | BETA: splitting (154) gives: % 153.19/22.85 | | | | % 153.19/22.85 | | | | Case 1: % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | (189) all_58_28 = e1 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | COMBINE_EQS: (113), (189) imply: % 153.19/22.85 | | | | | (190) all_10_2 = e1 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | SIMP: (190) implies: % 153.19/22.85 | | | | | (191) all_10_2 = e1 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | REF_CLOSE: (4), (13), (16), (55), (71), (73), (88), (90), (103), % 153.19/22.85 | | | | | (114), (122), (124), (155), (159), (183), (186), (191) are % 153.19/22.85 | | | | | inconsistent by sub-proof #190. % 153.19/22.85 | | | | | % 153.19/22.85 | | | | Case 2: % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | (192) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | BETA: splitting (192) gives: % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | Case 1: % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | (193) all_58_29 = e1 % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | BETA: splitting (139) gives: % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | Case 1: % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | (194) all_58_28 = e3 % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | COMBINE_EQS: (113), (194) imply: % 153.19/22.85 | | | | | | | (195) all_10_2 = e3 % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | SIMP: (195) implies: % 153.19/22.85 | | | | | | | (196) all_10_2 = e3 % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | REF_CLOSE: (4), (13), (48), (101), (159), (188), (196) are % 153.19/22.85 | | | | | | | inconsistent by sub-proof #251. % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | Case 2: % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | (197) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | REF_CLOSE: (55), (86), (103), (180), (193), (197) are inconsistent % 153.19/22.85 | | | | | | | by sub-proof #714. % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | End of split % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | Case 2: % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | (198) all_58_30 = e1 | all_58_31 = e1 % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | REF_CLOSE: (2), (86), (144), (176), (198) are inconsistent by % 153.19/22.85 | | | | | | sub-proof #711. % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | End of split % 153.19/22.85 | | | | | % 153.19/22.85 | | | | End of split % 153.19/22.85 | | | | % 153.19/22.85 | | | Case 2: % 153.19/22.85 | | | | % 153.19/22.85 | | | | (199) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.19/22.85 | | | | % 153.19/22.85 | | | | REF_CLOSE: (62), (76), (78), (107), (161), (181), (199) are inconsistent % 153.19/22.85 | | | | by sub-proof #573. % 153.19/22.85 | | | | % 153.19/22.85 | | | End of split % 153.19/22.85 | | | % 153.19/22.85 | | Case 2: % 153.19/22.85 | | | % 153.19/22.85 | | | (200) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 = % 153.19/22.85 | | | e0 | all_56_13 = e0 | all_56_14 = e0) % 153.19/22.85 | | | % 153.19/22.85 | | | ALPHA: (200) implies: % 153.19/22.85 | | | (201) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.19/22.85 | | | (202) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.19/22.85 | | | % 153.19/22.85 | | | BETA: splitting (99) gives: % 153.19/22.85 | | | % 153.19/22.85 | | | Case 1: % 153.19/22.85 | | | | % 153.19/22.85 | | | | (203) all_56_1 = e0 % 153.19/22.85 | | | | % 153.19/22.85 | | | | COMBINE_EQS: (70), (203) imply: % 153.19/22.85 | | | | (204) all_52_4 = e0 % 153.19/22.85 | | | | % 153.19/22.85 | | | | COMBINE_EQS: (67), (204) imply: % 153.19/22.85 | | | | (205) all_58_2 = e0 % 153.19/22.85 | | | | % 153.19/22.85 | | | | REDUCE: (31), (204) imply: % 153.19/22.85 | | | | (206) ~ (all_52_6 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | REDUCE: (46), (204) imply: % 153.19/22.85 | | | | (207) ~ (all_52_7 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | SIMP: (207) implies: % 153.19/22.85 | | | | (208) ~ (all_52_7 = e0) % 153.19/22.85 | | | | % 153.19/22.85 | | | | REDUCE: (12), (204) imply: % 153.19/22.85 | | | | (209) op(e3, e0) = all_58_1 % 153.19/22.85 | | | | % 153.19/22.85 | | | | BETA: splitting (201) gives: % 153.19/22.85 | | | | % 153.19/22.85 | | | | Case 1: % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | (210) all_56_12 = e0 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | COMBINE_EQS: (65), (210) imply: % 153.19/22.85 | | | | | (211) all_52_3 = e0 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | SIMP: (211) implies: % 153.19/22.85 | | | | | (212) all_52_3 = e0 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | COMBINE_EQS: (127), (212) imply: % 153.19/22.85 | | | | | (213) all_58_22 = e0 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | REDUCE: (109), (212) imply: % 153.19/22.85 | | | | | (214) ~ (all_52_1 = e0) % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | REDUCE: (5), (212) imply: % 153.19/22.85 | | | | | (215) ~ (all_52_2 = e0) % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | REDUCE: (130), (212) imply: % 153.19/22.85 | | | | | (216) ~ (all_10_2 = e0) % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | SIMP: (216) implies: % 153.19/22.85 | | | | | (217) ~ (all_10_2 = e0) % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | REDUCE: (170), (212) imply: % 153.19/22.85 | | | | | (218) ~ (all_6_1 = e0) % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | SIMP: (218) implies: % 153.19/22.85 | | | | | (219) ~ (all_6_1 = e0) % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | REDUCE: (42), (212) imply: % 153.19/22.85 | | | | | (220) op(e0, e0) = all_58_21 % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | BETA: splitting (29) gives: % 153.19/22.85 | | | | | % 153.19/22.85 | | | | | Case 1: % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | (221) all_56_2 = e0 % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | COMBINE_EQS: (104), (221) imply: % 153.19/22.85 | | | | | | (222) all_52_1 = e0 % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | REDUCE: (214), (222) imply: % 153.19/22.85 | | | | | | (223) $false % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | CLOSE: (223) is inconsistent. % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | Case 2: % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | (224) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | BETA: splitting (224) gives: % 153.19/22.85 | | | | | | % 153.19/22.85 | | | | | | Case 1: % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | (225) all_56_3 = e0 % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | REF_CLOSE: (2), (27), (55), (78), (84), (86), (88), (103), (113), % 153.19/22.85 | | | | | | | (122), (139), (144), (154), (155), (176), (225) are % 153.19/22.85 | | | | | | | inconsistent by sub-proof #189. % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | Case 2: % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | (226) all_56_5 = e0 | all_56_10 = e0 % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | BETA: splitting (226) gives: % 153.19/22.85 | | | | | | | % 153.19/22.85 | | | | | | | Case 1: % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | (227) all_56_5 = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | COMBINE_EQS: (62), (227) imply: % 153.19/22.85 | | | | | | | | (228) all_52_9 = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (76), (228) imply: % 153.19/22.85 | | | | | | | | (229) $false % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | CLOSE: (229) is inconsistent. % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | Case 2: % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | (230) all_56_10 = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | COMBINE_EQS: (107), (230) imply: % 153.19/22.85 | | | | | | | | (231) all_52_13 = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | COMBINE_EQS: (32), (231) imply: % 153.19/22.85 | | | | | | | | (232) all_58_13 = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (40), (231) imply: % 153.19/22.85 | | | | | | | | (233) ~ (all_52_12 = e0) % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (80), (231) imply: % 153.19/22.85 | | | | | | | | (234) ~ (all_52_14 = e0) % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (53), (231) imply: % 153.19/22.85 | | | | | | | | (235) ~ (all_8_2 = e0) % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (51), (231) imply: % 153.19/22.85 | | | | | | | | (236) ~ (all_4_2 = e0) % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | SIMP: (236) implies: % 153.19/22.85 | | | | | | | | (237) ~ (all_4_2 = e0) % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (136), (231) imply: % 153.19/22.85 | | | | | | | | (238) op(e2, e0) = all_58_12 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | REDUCE: (133), (231) imply: % 153.19/22.85 | | | | | | | | (239) op(e2, e0) = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_21, e0, e0, % 153.19/22.85 | | | | | | | | simplifying with (125), (220) gives: % 153.19/22.85 | | | | | | | | (240) all_58_21 = all_4_2 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e0, e2, % 153.19/22.85 | | | | | | | | simplifying with (238), (239) gives: % 153.19/22.85 | | | | | | | | (241) all_58_12 = e0 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | GROUND_INST: instantiating (4) with all_52_12, all_58_1, e0, e3, % 153.19/22.85 | | | | | | | | simplifying with (89), (209) gives: % 153.19/22.85 | | | | | | | | (242) all_58_1 = all_52_12 % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | BETA: splitting (60) gives: % 153.19/22.85 | | | | | | | | % 153.19/22.85 | | | | | | | | Case 1: % 153.19/22.85 | | | | | | | | | % 153.19/22.85 | | | | | | | | | (243) all_54_0 = e0 % 153.19/22.85 | | | | | | | | | % 153.19/22.85 | | | | | | | | | REF_CLOSE: (141), (217), (243) are inconsistent by sub-proof % 153.19/22.85 | | | | | | | | | #861. % 153.19/22.85 | | | | | | | | | % 153.19/22.85 | | | | | | | | Case 2: % 153.19/22.85 | | | | | | | | | % 153.19/22.85 | | | | | | | | | (244) ~ (all_54_0 = e0) % 153.19/22.85 | | | | | | | | | (245) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.19/22.85 | | | | | | | | | % 153.19/22.85 | | | | | | | | | BETA: splitting (9) gives: % 153.19/22.85 | | | | | | | | | % 153.19/22.85 | | | | | | | | | Case 1: % 153.19/22.85 | | | | | | | | | | % 153.19/22.85 | | | | | | | | | | (246) all_54_3 = e0 % 153.19/22.85 | | | | | | | | | | % 153.19/22.85 | | | | | | | | | | REF_CLOSE: (26), (233), (246) are inconsistent by sub-proof % 153.19/22.85 | | | | | | | | | | #733. % 153.19/22.85 | | | | | | | | | | % 153.19/22.85 | | | | | | | | | Case 2: % 153.19/22.85 | | | | | | | | | | % 153.19/22.85 | | | | | | | | | | (247) ~ (all_54_3 = e0) % 153.19/22.85 | | | | | | | | | | (248) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.19/22.86 | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | BETA: splitting (150) gives: % 153.19/22.86 | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | (249) all_54_6 = e0 % 153.19/22.86 | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | REF_CLOSE: (45), (76), (249) are inconsistent by sub-proof % 153.19/22.86 | | | | | | | | | | | #797. % 153.19/22.86 | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | (250) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 153.19/22.86 | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | BETA: splitting (100) gives: % 153.19/22.86 | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | (251) all_56_9 = e1 % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | COMBINE_EQS: (83), (251) imply: % 153.19/22.86 | | | | | | | | | | | | (252) all_52_12 = e1 % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | SIMP: (252) implies: % 153.19/22.86 | | | | | | | | | | | | (253) all_52_12 = e1 % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | COMBINE_EQS: (23), (253) imply: % 153.19/22.86 | | | | | | | | | | | | (254) all_58_6 = e1 % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | REDUCE: (49), (253) imply: % 153.19/22.86 | | | | | | | | | | | | (255) ~ (all_52_8 = e1) % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | REDUCE: (108), (253) imply: % 153.19/22.86 | | | | | | | | | | | | (256) ~ (all_10_2 = e1) % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | SIMP: (256) implies: % 153.19/22.86 | | | | | | | | | | | | (257) ~ (all_10_2 = e1) % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | REDUCE: (129), (253) imply: % 153.19/22.86 | | | | | | | | | | | | (258) ~ (all_4_2 = e1) % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | BETA: splitting (154) gives: % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | (259) all_58_28 = e1 % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | COMBINE_EQS: (113), (259) imply: % 153.19/22.86 | | | | | | | | | | | | | (260) all_10_2 = e1 % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | REDUCE: (257), (260) imply: % 153.19/22.86 | | | | | | | | | | | | | (261) $false % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | CLOSE: (261) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | (262) ~ (all_58_28 = e1) % 153.19/22.86 | | | | | | | | | | | | | (263) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | BETA: splitting (263) gives: % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | (264) all_58_29 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | COMBINE_EQS: (84), (264) imply: % 153.19/22.86 | | | | | | | | | | | | | | (265) all_8_2 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (77), (265) imply: % 153.19/22.86 | | | | | | | | | | | | | | (266) ~ (all_52_1 = e1) % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (111), (265) imply: % 153.19/22.86 | | | | | | | | | | | | | | (267) ~ (all_52_9 = e1) % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | BETA: splitting (41) gives: % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | (268) all_56_4 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | COMBINE_EQS: (25), (268) imply: % 153.19/22.86 | | | | | | | | | | | | | | | (269) all_52_8 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | REDUCE: (255), (269) imply: % 153.19/22.86 | | | | | | | | | | | | | | | (270) $false % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | (271) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | (272) all_56_0 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (272) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | (273) all_10_2 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | REDUCE: (257), (273) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | (274) $false % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | (275) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | (276) all_58_31 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (276) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | (277) all_4_2 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | REDUCE: (237), (277) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | (278) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | (279) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 153.19/22.86 | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.86 | | | | | | | | | | | | | | | | | e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | (280) all_58_30 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (280) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (281) e1 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.19/22.86 | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (264), (281) % 153.19/22.86 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | (282) ~ (all_58_30 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | (283) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 153.19/22.86 | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.19/22.86 | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 153.19/22.86 | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 153.19/22.86 | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.19/22.86 | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 153.19/22.86 | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 153.19/22.86 | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | REDUCE: (86), (282) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (284) ~ (e1 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (285) all_56_5 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (285) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (286) all_52_9 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | REDUCE: (267), (286) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (287) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (288) all_56_8 = e1 | all_56_14 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (289) all_56_8 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (289) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (290) e1 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (264), (290) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (291) all_56_14 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (291) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (292) all_6_1 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (293) all_6_1 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (293) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (294) all_58_26 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (295) all_56_6 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (295) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (296) all_52_2 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (296) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (297) all_58_15 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (296) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (298) ~ (all_52_14 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (299) ~ (all_52_14 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (300) all_58_29 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (300) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (301) e2 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (301) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (302) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (303) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_28 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (304) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (305) all_10_2 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (306) all_10_2 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (101), (159), (217), (306) are % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (307) ~ (all_58_28 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (308) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (307) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (309) ~ (all_10_2 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (310) all_56_0 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (309), (310) are inconsistent by sub-proof % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | #188. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (311) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_56_1 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (312) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (313) e3 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (313) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (314) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_56_4 = e3 | all_56_9 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (25), (27), (38), (39), (55), (79), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (86), (87), (94), (104), (113), (124), (137), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (139), (140), (141), (144), (153), (154), (164), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (165), (176), (205), (208), (213), (214), (217), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (232), (245), (251), (254), (257), (263), (264), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (266), (294), (297), (299), (308), (315) are % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (316) ~ (all_56_6 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (316) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_52_2 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (104), (144), (210), (266), (275), (317) are % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #637. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | (318) all_58_30 = e1 | all_58_31 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REF_CLOSE: (2), (86), (144), (176), (318) are inconsistent by % 153.19/22.86 | | | | | | | | | | | | | | sub-proof #711. % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | (319) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | BETA: splitting (319) gives: % 153.19/22.86 | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | (320) all_56_10 = e1 % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | COMBINE_EQS: (230), (320) imply: % 153.19/22.86 | | | | | | | | | | | | | (321) e1 = e0 % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | REDUCE: (144), (321) imply: % 153.19/22.86 | | | | | | | | | | | | | (322) $false % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | (323) all_56_11 = e1 | all_56_15 = e1 % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | BETA: splitting (323) gives: % 153.19/22.86 | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | (324) all_56_11 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | COMBINE_EQS: (69), (324) imply: % 153.19/22.86 | | | | | | | | | | | | | | (325) all_52_14 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | SIMP: (325) implies: % 153.19/22.86 | | | | | | | | | | | | | | (326) all_52_14 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | COMBINE_EQS: (39), (326) imply: % 153.19/22.86 | | | | | | | | | | | | | | (327) all_58_20 = e1 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (142), (326) imply: % 153.19/22.86 | | | | | | | | | | | | | | (328) ~ (all_52_2 = e1) % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (44), (326) imply: % 153.19/22.86 | | | | | | | | | | | | | | (329) ~ (all_52_6 = e1) % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (85), (326) imply: % 153.19/22.86 | | | | | | | | | | | | | | (330) ~ (all_52_12 = e1) % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (143), (326) imply: % 153.19/22.86 | | | | | | | | | | | | | | (331) ~ (all_4_2 = e1) % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | REDUCE: (19), (326) imply: % 153.19/22.86 | | | | | | | | | | | | | | (332) op(e1, e1) = all_58_19 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_19, e1, e1, % 153.19/22.86 | | | | | | | | | | | | | | simplifying with (102), (332) gives: % 153.19/22.86 | | | | | | | | | | | | | | (333) all_58_19 = e0 % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | BETA: splitting (56) gives: % 153.19/22.86 | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | (334) all_54_9 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | REF_CLOSE: (50), (58), (334) are inconsistent by sub-proof % 153.19/22.86 | | | | | | | | | | | | | | | #572. % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | (335) ~ (all_54_9 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | (336) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | BETA: splitting (30) gives: % 153.19/22.86 | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | (337) all_54_8 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (215), (337) are inconsistent by sub-proof % 153.19/22.86 | | | | | | | | | | | | | | | | #731. % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | (338) ~ (all_54_8 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | (339) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | (340) all_54_4 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (214), (340) are inconsistent by sub-proof % 153.19/22.86 | | | | | | | | | | | | | | | | | #859. % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | (341) ~ (all_54_4 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | (342) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | (343) all_56_6 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (343) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (344) all_52_2 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (344) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (345) all_58_15 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | REDUCE: (131), (344) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (346) ~ (all_52_1 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | REDUCE: (91), (344) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (347) ~ (all_52_6 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | SIMP: (347) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (348) ~ (all_52_6 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | REDUCE: (123), (344) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (349) ~ (all_10_2 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | SIMP: (349) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | (350) ~ (all_10_2 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (351) all_56_6 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (351) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (352) e3 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | REDUCE: (155), (352) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (353) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | CLOSE: (353) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | (354) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (355) all_56_7 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (355) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (356) all_52_6 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | SIMP: (356) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (357) all_52_6 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (357) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (358) all_58_17 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (357) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (359) ~ (all_8_2 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | SIMP: (359) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | (360) ~ (all_8_2 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (361) all_56_1 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (361) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (362) e1 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (324), (362) are % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_56_1 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (364) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (363) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | (365) ~ (e1 = e0) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (366) all_56_9 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (366) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (367) all_52_12 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (367) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (368) all_52_12 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (368) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_10_2 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (369) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (370) ~ (all_10_2 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_28 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (23), (45), (77), (79), (81), (84), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (86), (87), (103), (113), (116), (137), (164), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (165), (169), (173), (205), (208), (213), (214), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (217), (232), (233), (237), (250), (327), (342), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (345), (346), (350), (358), (371) are inconsistent % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #623. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (372) ~ (all_58_28 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (372) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (373) ~ (all_10_2 = e1) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (101), (124), (141), (145), % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (159), (217), (245), (370), (373) are inconsistent % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #248. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | (374) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (375) all_56_10 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (375) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (376) e2 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (376) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (377) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | (378) all_56_11 = e2 | all_56_15 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (379) all_56_11 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (379) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (380) e2 = e1 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (380) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (381) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (381) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (382) all_56_15 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (382) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (383) all_4_2 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (383) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (384) all_4_2 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (384) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (385) all_58_31 = e2 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (384) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (386) ~ (all_52_7 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (384) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (387) ~ (all_52_12 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (384) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | (388) ~ (all_6_1 = e2) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_56_9 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (389) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_52_12 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_52_12 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (391) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_58_6 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (391) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | (393) ~ (all_52_8 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_58_28 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (394) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_10_2 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (395) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (396) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (396) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (397) ~ (all_58_28 = e3) % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_58_31 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (399) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) e2 = e0 % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (400) imply: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) $false % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (401) is inconsistent. % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_58_31 = e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_58_30 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (404) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) e1 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (324), (405) are % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_58_29 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (407) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_8_2 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (408) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_56_3 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (408) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) ~ (all_52_7 = e3) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (408) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) ~ (all_52_9 = e3) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_58_29 = e2 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (412) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) e3 = e2 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (413) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) $false % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) ~ (all_58_29 = e2) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_56_4 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (417) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_52_8 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (418) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) $false % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (419) is inconsistent. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (364) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_56_3 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (421) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) e3 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (422) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) $false % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (423) is inconsistent. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_56_7 = e1 | all_56_13 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (424) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_56_7 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (355), (425) are inconsistent by sub-proof % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #387. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_56_13 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (426) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_52_7 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (427) implies: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_52_7 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (428) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_58_24 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (428) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) ~ (all_6_1 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (430) implies: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_6_1 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (410), (428) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) ~ (e3 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (428) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) ~ (e2 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_56_5 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (411), (434) are inconsistent by sub-proof % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #267. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_56_8 = e3 | all_56_14 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_56_8 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (436) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) e3 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (437) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_58_29 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (438) are % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #698. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_56_14 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (439) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_6_1 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (440) implies: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_6_1 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (441) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_58_26 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_58_28 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (350), (443) are inconsistent by sub-proof % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #783. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (445) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (447) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_58_2 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (449) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) e3 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (450) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (451) gives: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (452) implies: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_58_6 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (392), (407), % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) are inconsistent by sub-proof #186. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_58_2 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (455) imply: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) e3 = e0 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (456) % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.19/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_58_2 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (460) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) e3 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (461) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_2 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (205), (463) are inconsistent by sub-proof % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #648. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (465) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_58_22 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (466) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) e3 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (467) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (468) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_58_17 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_58_2 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (470) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) e2 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (471) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) e2 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (358), (469) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) e2 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (473) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) e2 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (474) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) e1 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (475) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_56_11 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (476) are inconsistent % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #334. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (477) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_58_24 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (481) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) e1 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (324), (482) are % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) e3 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_58_2 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (485) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) e2 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (486) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) e2 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (484), (487) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) e3 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (488) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_58_29 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (489) are % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #698. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_58_6 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (392), (407), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) are inconsistent by sub-proof #186. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (493) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_58_17 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (358), (494) are inconsistent by sub-proof % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #630. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (496) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (497) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_58_26 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (442), (498) are inconsistent by sub-proof % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #185. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_58_22 = e3 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_58_15 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (345), (501) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) e3 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (502) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) e3 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (500) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) e3 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (504) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) e3 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (503), (505) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) e1 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (503), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) are inconsistent by sub-proof #184. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_58_15 = e1 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (345), (509) are inconsistent by sub-proof % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #629. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (510) implies: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_58_26 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (442), (511) imply: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) e3 = e0 % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (512) % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (513) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (515) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (516) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_58_15 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (345), (517) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #629. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (518) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (519) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_58_22 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (520) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) e3 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (521) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_58_29 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (522) are % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #698. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (523) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (442), (524) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) e3 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (525) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (527) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (528) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_58_6 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (392), (407), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) are inconsistent by sub-proof #186. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_58_6 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (392), (407), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) are inconsistent by sub-proof #186. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (532) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (533) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_58_6 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (392), (407), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) are inconsistent by sub-proof #186. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (535) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_58_24 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (536) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) e1 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (324), (537) are % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (539) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (540) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (541) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_58_26 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (442), (542) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #185. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (543) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) all_58_24 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_58_13 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (545) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) e2 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (546) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) e2 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (544) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) e2 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (547), (548) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) e1 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (324), (549) are % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (550) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (551) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (442), (552) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) e3 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (553) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_58_17 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (358), (555) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #630. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (557) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (442), (559) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) e3 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (560) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (561) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_58_26 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_58_24 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (563) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) e1 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (564) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) e1 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (442), (562) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) e3 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (566) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) e3 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (565), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) are inconsistent by sub-proof #184. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (568) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (569) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_58_24 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (570) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) e1 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (176), (323), (324), (571) are % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (572) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_58_26 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (442), (573) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) e3 = e0 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (407), (574) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #187. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_58_30 = e3 | all_58_31 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (26), (83), (86), (97), (103), (129), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (241), (242), (248), (330), (333), (575) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #611. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | (576) ~ (all_56_9 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (576) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | (577) ~ (all_52_12 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (248), (330), (387), (577) are inconsistent % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (578) ~ (all_56_7 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (578) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (579) ~ (all_52_6 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (329), (336), (348), (579) are inconsistent % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | by sub-proof #619. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | (580) ~ (all_56_6 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | (581) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | REDUCE: (90), (580) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | (582) ~ (all_52_2 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | (583) all_54_8 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (328), (583) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | | | | | | #618. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | (584) all_54_8 = e3 | all_54_8 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | BETA: splitting (584) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (585) all_54_8 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (585) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (586) all_52_2 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | SIMP: (586) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (587) all_52_2 = e2 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (587) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (588) ~ (all_52_6 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | SIMP: (588) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (589) ~ (all_52_6 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (587) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (590) ~ (all_10_2 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | SIMP: (590) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (591) ~ (all_10_2 = e2) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | BETA: splitting (581) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (592) all_56_7 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (592) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (593) all_52_6 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | SIMP: (593) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (594) all_52_6 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (594) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (595) ~ (all_8_2 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | SIMP: (595) implies: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (596) ~ (all_8_2 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (597) all_56_0 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (597) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (598) all_10_2 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (598) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (599) all_58_28 = e1 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (26), (55), (83), (84), (86), (97), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (103), (129), (139), (240), (241), (242), (248), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (330), (333), (596), (599) are inconsistent by % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | sub-proof #183. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (600) ~ (all_56_0 = e1) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (600) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (601) ~ (all_10_2 = e1) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (101), (124), (141), (145), % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | (159), (217), (245), (591), (601) are inconsistent % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #248. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (602) ~ (all_56_7 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (602) imply: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | (603) ~ (all_52_6 = e3) % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (329), (336), (589), (603) are inconsistent % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | by sub-proof #619. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | (604) all_54_8 = e3 % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (582), (604) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | #786. % 153.33/22.88 | | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | (605) all_56_15 = e1 % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | REF_CLOSE: (7), (176), (605) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | #671. % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | End of split % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | End of split % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | End of split % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | End of split % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | End of split % 153.33/22.88 | | | | | % 153.33/22.88 | | | | Case 2: % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | (606) all_56_13 = e0 | all_56_14 = e0 % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | REF_CLOSE: (92), (105), (112), (208), (606) are inconsistent by % 153.33/22.88 | | | | | sub-proof #609. % 153.33/22.88 | | | | | % 153.33/22.88 | | | | End of split % 153.33/22.88 | | | | % 153.33/22.88 | | | Case 2: % 153.33/22.88 | | | | % 153.33/22.88 | | | | (607) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.33/22.88 | | | | % 153.33/22.88 | | | | BETA: splitting (607) gives: % 153.33/22.88 | | | | % 153.33/22.88 | | | | Case 1: % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | (608) all_56_3 = e0 % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | REF_CLOSE: (2), (27), (55), (78), (84), (86), (88), (103), (113), % 153.33/22.88 | | | | | (122), (139), (144), (154), (155), (176), (608) are % 153.33/22.88 | | | | | inconsistent by sub-proof #189. % 153.33/22.88 | | | | | % 153.33/22.88 | | | | Case 2: % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | (609) all_56_7 = e0 | all_56_13 = e0 % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | BETA: splitting (609) gives: % 153.33/22.88 | | | | | % 153.33/22.88 | | | | | Case 1: % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | (610) all_56_7 = e0 % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | COMBINE_EQS: (8), (610) imply: % 153.33/22.88 | | | | | | (611) all_52_6 = e0 % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | REDUCE: (58), (611) imply: % 153.33/22.88 | | | | | | (612) $false % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | CLOSE: (612) is inconsistent. % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | Case 2: % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | (613) all_56_13 = e0 % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | COMBINE_EQS: (92), (613) imply: % 153.33/22.88 | | | | | | (614) all_52_7 = e0 % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | SIMP: (614) implies: % 153.33/22.88 | | | | | | (615) all_52_7 = e0 % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | COMBINE_EQS: (79), (615) imply: % 153.33/22.88 | | | | | | (616) all_58_24 = e0 % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | REDUCE: (46), (615) imply: % 153.33/22.88 | | | | | | (617) ~ (all_52_4 = e0) % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | REDUCE: (132), (615) imply: % 153.33/22.88 | | | | | | (618) ~ (all_8_2 = e0) % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | REDUCE: (171), (615) imply: % 153.33/22.88 | | | | | | (619) ~ (all_6_1 = e0) % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | SIMP: (619) implies: % 153.33/22.88 | | | | | | (620) ~ (all_6_1 = e0) % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | BETA: splitting (63) gives: % 153.33/22.88 | | | | | | % 153.33/22.88 | | | | | | Case 1: % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | (621) all_56_0 = e0 % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | COMBINE_EQS: (124), (621) imply: % 153.33/22.88 | | | | | | | (622) all_10_2 = e0 % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | COMBINE_EQS: (113), (622) imply: % 153.33/22.88 | | | | | | | (623) all_58_28 = e0 % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | REF_CLOSE: (2), (27), (55), (84), (86), (88), (103), (122), (139), % 153.33/22.88 | | | | | | | (144), (154), (155), (176), (623) are inconsistent by % 153.33/22.88 | | | | | | | sub-proof #684. % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | Case 2: % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | (624) ~ (all_56_0 = e0) % 153.33/22.88 | | | | | | | (625) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | REDUCE: (124), (624) imply: % 153.33/22.88 | | | | | | | (626) ~ (all_10_2 = e0) % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | BETA: splitting (128) gives: % 153.33/22.88 | | | | | | | % 153.33/22.88 | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | (627) all_56_0 = e0 % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | COMBINE_EQS: (124), (627) imply: % 153.33/22.88 | | | | | | | | (628) all_10_2 = e0 % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | REDUCE: (626), (628) imply: % 153.33/22.88 | | | | | | | | (629) $false % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | CLOSE: (629) is inconsistent. % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | (630) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | BETA: splitting (630) gives: % 153.33/22.88 | | | | | | | | % 153.33/22.88 | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | (631) all_56_2 = e0 % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | COMBINE_EQS: (104), (631) imply: % 153.33/22.88 | | | | | | | | | (632) all_52_1 = e0 % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | COMBINE_EQS: (87), (632) imply: % 153.33/22.88 | | | | | | | | | (633) all_58_8 = e0 % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | REDUCE: (131), (632) imply: % 153.33/22.88 | | | | | | | | | (634) ~ (all_52_2 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | SIMP: (634) implies: % 153.33/22.88 | | | | | | | | | (635) ~ (all_52_2 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | REDUCE: (109), (632) imply: % 153.33/22.88 | | | | | | | | | (636) ~ (all_52_3 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | SIMP: (636) implies: % 153.33/22.88 | | | | | | | | | (637) ~ (all_52_3 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | REDUCE: (116), (632) imply: % 153.33/22.88 | | | | | | | | | (638) ~ (all_52_9 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | REDUCE: (61), (632) imply: % 153.33/22.88 | | | | | | | | | (639) ~ (all_52_13 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | SIMP: (639) implies: % 153.33/22.88 | | | | | | | | | (640) ~ (all_52_13 = e0) % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | BETA: splitting (202) gives: % 153.33/22.88 | | | | | | | | | % 153.33/22.88 | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | (641) all_56_9 = e0 % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | COMBINE_EQS: (83), (641) imply: % 153.33/22.88 | | | | | | | | | | (642) all_52_12 = e0 % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | COMBINE_EQS: (23), (642) imply: % 153.33/22.88 | | | | | | | | | | (643) all_58_6 = e0 % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | REDUCE: (85), (642) imply: % 153.33/22.88 | | | | | | | | | | (644) ~ (all_52_14 = e0) % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | REDUCE: (108), (642) imply: % 153.33/22.88 | | | | | | | | | | (645) ~ (all_10_2 = e0) % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | REDUCE: (129), (642) imply: % 153.33/22.88 | | | | | | | | | | (646) ~ (all_4_2 = e0) % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | SIMP: (646) implies: % 153.33/22.88 | | | | | | | | | | (647) ~ (all_4_2 = e0) % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | BETA: splitting (56) gives: % 153.33/22.88 | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | (648) all_54_9 = e0 % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | REF_CLOSE: (50), (58), (648) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | #572. % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | (649) ~ (all_54_9 = e0) % 153.33/22.88 | | | | | | | | | | | (650) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | BETA: splitting (150) gives: % 153.33/22.88 | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | (651) all_54_6 = e0 % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | REF_CLOSE: (45), (76), (651) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | #797. % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | (652) ~ (all_54_6 = e0) % 153.33/22.88 | | | | | | | | | | | | (653) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | BETA: splitting (134) gives: % 153.33/22.88 | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | (654) all_54_1 = e0 % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | REF_CLOSE: (28), (617), (654) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | #798. % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | (655) ~ (all_54_1 = e0) % 153.33/22.88 | | | | | | | | | | | | | (656) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | BETA: splitting (157) gives: % 153.33/22.88 | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | Case 1: % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | (657) all_54_7 = e0 % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | | REF_CLOSE: (22), (640), (657) are inconsistent by sub-proof % 153.33/22.88 | | | | | | | | | | | | | | #742. % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.88 | | | | | | | | | | | | | Case 2: % 153.33/22.88 | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | (658) ~ (all_54_7 = e0) % 153.33/22.89 | | | | | | | | | | | | | | (659) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 153.33/22.89 | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | BETA: splitting (100) gives: % 153.33/22.89 | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | (660) all_56_9 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | COMBINE_EQS: (641), (660) imply: % 153.33/22.89 | | | | | | | | | | | | | | | (661) e1 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | REDUCE: (144), (661) imply: % 153.33/22.89 | | | | | | | | | | | | | | | (662) $false % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | CLOSE: (662) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | (663) ~ (all_56_9 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | (664) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | REDUCE: (641), (663) imply: % 153.33/22.89 | | | | | | | | | | | | | | | (665) ~ (e1 = e0) % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 153.33/22.89 | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | (666) all_56_12 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (666) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | (667) all_52_3 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | SIMP: (667) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | (668) all_52_3 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (668) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | (669) all_58_22 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | REDUCE: (130), (668) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | (670) ~ (all_10_2 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | SIMP: (670) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | (671) ~ (all_10_2 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | REDUCE: (170), (668) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | (672) ~ (all_6_1 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | SIMP: (672) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | (673) ~ (all_6_1 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | REDUCE: (72), (668) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | (674) ~ (all_4_2 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | (675) all_58_28 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (675) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | (676) all_10_2 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | REDUCE: (671), (676) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | (677) $false % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | CLOSE: (677) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | (678) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | BETA: splitting (678) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | (679) all_58_29 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (679) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | (680) all_8_2 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | REDUCE: (111), (680) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | (681) ~ (all_52_9 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | REDUCE: (53), (680) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | (682) ~ (all_52_13 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | (683) all_56_4 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (683) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | (684) all_52_8 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (684) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | (685) all_58_4 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | REDUCE: (82), (684) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | (686) ~ (all_52_4 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | REDUCE: (3), (684) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | (687) ~ (all_52_9 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (664) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | (688) all_56_10 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (682), (688) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | #606. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | (689) all_56_11 = e1 | all_56_15 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | (690) all_56_11 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (690) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | (691) all_52_14 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | SIMP: (691) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | (692) all_52_14 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (692) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | (693) all_58_20 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (692) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | (694) ~ (all_52_6 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | (695) all_58_31 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (647), (695) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | #635. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | (696) ~ (all_58_31 = e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | (697) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (698) all_58_30 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (698) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (699) e1 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (679), (699) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (700) all_58_29 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (700) are % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #698. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (701) ~ (all_58_30 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (702) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_29 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (679), (703) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (704) e2 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (704) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (705) $false % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (705) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (706) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (706) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (707) all_58_28 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (707) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (708) all_10_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (708) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (709) all_10_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (101), (159), (626), (709) are % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (710) ~ (all_58_28 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (711) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (710) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | (712) ~ (all_10_2 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_54_0 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (626), (713) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | #861. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) all_56_0 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (712), (715) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | #188. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (716) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_56_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (631), (717) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) e3 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (718) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) $false % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (719) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_56_6 = e3 | all_56_12 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (720) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) all_56_6 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (721) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) all_52_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (722) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_52_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (723) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_58_15 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (723) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) ~ (all_52_6 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (725) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) ~ (all_52_6 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_56_1 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (727) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_52_4 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (728) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_52_4 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (729) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_58_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (729) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) ~ (all_10_2 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_54_0 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (671), (732) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #841. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_54_0 = e3 | all_54_0 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) all_56_0 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (734) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_10_2 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (735) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) all_10_2 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (736) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_58_28 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (712), (736) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) ~ (e3 = e2) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) all_58_28 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (737), (739) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) e3 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (740) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) $false % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (741) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (742) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_58_29 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (679), (743) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) e3 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (744) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) $false % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (745) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) ~ (all_58_29 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_58_30 = e3 | all_58_31 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (679), (746) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) ~ (e3 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (747) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) all_58_30 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (749) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) e3 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (721), (750) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_56_6 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (103), (666), (720), (751) are inconsistent % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #838. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_58_31 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (752) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_4_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (753) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_4_2 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (754) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) ~ (all_52_13 = e3) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_56_4 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (683), (756) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) e3 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (752), (757) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) all_58_31 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (747), (758) are inconsistent % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #694. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (650) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) all_54_9 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (694), (760) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_54_9 = e3 | all_54_9 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (761) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) all_54_9 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (762) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_52_6 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (763) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_52_6 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (764) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_58_17 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_56_9 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (641), (766) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) e2 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (767) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) $false % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (768) is inconsistent. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_56_10 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (770) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_52_13 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (771) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_58_13 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (771) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) ~ (all_52_9 = e2) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (653) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_54_6 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (681), (774) are inconsistent by sub-proof % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) ~ (all_54_6 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_54_6 = e3 | all_54_6 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_56_5 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (777) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_52_9 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (778) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_52_9 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (779) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_11 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (711) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (781) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (782) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (784) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_58_15 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_58_8 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (786) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) e3 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (724), (785) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) e3 = e1 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (787), (788) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) e1 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (789) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (790) gives: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_58_22 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (792) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) e1 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (793) % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (794) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_58_11 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_58_8 = e3 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (796) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) e3 = e0 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (795) imply: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) e3 = e2 % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (798) implies: % 153.33/22.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (797), (799) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (103), (666), (720), (721), (799), (800) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #182. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (801) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (802) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_58_8 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (804) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (721), (805) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_56_6 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (103), (666), (720), (806) are inconsistent % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #838. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) all_58_4 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_58_2 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (730), (810) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (685), (809) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (812) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (808) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (811), (813), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) are inconsistent by sub-proof #649. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (815) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (816) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_58_22 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_58_6 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_58_2 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (730), (819) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (643), (818) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (821) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (817) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (822), (823) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (824) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (820), (822) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (826) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (825), (827) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (828) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_58_11 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) all_58_2 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (730), (831) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (830) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (829) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (834) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (832), (835) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (836) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (833), (837) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (833), (838) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (839) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (840) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (841) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (842) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) all_58_13 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) all_58_2 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (730), (844) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (772), (843) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (103), (666), (720), (721), (845), (846) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #182. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_58_8 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_58_2 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (730), (849) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (848) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (103), (666), (720), (721), (850), (851) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #182. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (852) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (853) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) all_58_22 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (854) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (855) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (856) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_58_11 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (857) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (747), (752), (858) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (860) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (861) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) all_58_4 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (685), (862) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (747), (752), (863) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (864) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_58_22 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_58_6 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (643), (866) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (867) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (865) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (868), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) are inconsistent by sub-proof #645. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (870) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (871) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_58_15 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (724), (747), (752), (872) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (873) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (874) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (875) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (876) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (877) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (878) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (879) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_58_15 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (724), (747), (752), (880) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (881) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (882) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_58_22 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_58_13 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_58_6 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (643), (885) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (886) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (772), (884) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (883) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (889) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (890) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (888), (891) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (892) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) all_58_22 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_58_6 = e3 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (643), (894) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (895) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (893) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (896), (897) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (898) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (899) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (900) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (901) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_58_22 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (903) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (904) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (616), (902) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (905), (906) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (907) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_58_22 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (908) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (909) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (910) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (911) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) all_58_22 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (669), (912) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (913) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (914) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_58_13 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_58_11 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (916) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (917) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (772), (915) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (103), (666), (720), (721), (918), (919) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #182. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (920) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (921) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (922) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (923) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) all_58_11 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (924) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (925) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) e3 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (926) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) $false % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (927) is inconsistent. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (928) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) all_58_17 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (765), (930) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (931) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (616), (929) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (933) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (933), (934) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (935) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (936) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) all_58_17 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (765), (938) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (939) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (937) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (941) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (940), (942) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (942), (943) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (944) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_58_11 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (945) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) e3 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (747), (752), (946) are % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (947) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (948) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (949) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_58_24 = e2 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (951) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (952) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (616), (950) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (88), (103), (122), (139), (144), % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (155), (678), (679), (737), (953), (954) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #650. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (955) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_58_13 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (772), (956) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (957) imply: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) $false % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (958) is inconsistent. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (772), (960) are inconsistent by sub-proof % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #407. % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (961) implies: % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_58_20 = e0 % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (962) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) e1 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (27), (55), (86), (88), (103), (113), (122), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (144), (154), (155), (176), (679), (963) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) ~ (all_56_5 = e3) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (964) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) ~ (all_52_9 = e3) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (773), (776), (965) are inconsistent by % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #552. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) ~ (all_56_10 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (966) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) ~ (all_52_13 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (659), (682), (755), (967) are inconsistent % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #601. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_54_9 = e3 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (726), (968) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #620. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) ~ (all_56_0 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (141), (712), (733), (969) are inconsistent % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #821. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) ~ (all_56_1 = e3) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (970) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) ~ (all_52_4 = e3) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (656) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_54_1 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (686), (972) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) all_54_1 = e3 | all_54_1 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (650) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) all_54_9 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (694), (974) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) all_54_9 = e3 | all_54_9 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (975) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_54_9 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (976) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) all_52_6 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (977) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_52_6 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (978) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) ~ (all_52_4 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (971), (973), (979) are inconsistent by % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #722. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) all_54_9 = e3 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (726), (980) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #620. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_56_12 = e3 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (666), (981) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) e3 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (982) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) $false % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (983) is inconsistent. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (984) all_56_15 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (176), (984) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | #671. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (985) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (62), (144), (168), (673), (681), (985) are % 153.33/22.91 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #179. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (986) all_58_30 = e1 | all_58_31 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (86), (144), (176), (986) are inconsistent by % 153.33/22.91 | | | | | | | | | | | | | | | | | | sub-proof #711. % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | (987) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | BETA: splitting (987) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | (988) all_56_13 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (613), (988) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | (989) e1 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | REDUCE: (144), (989) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | (990) $false % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | CLOSE: (990) is inconsistent. % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | (991) all_56_14 = e1 | all_56_15 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | BETA: splitting (991) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (992) all_56_14 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (992) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (993) all_6_1 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | SIMP: (993) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (994) all_6_1 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REDUCE: (170), (994) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (995) ~ (all_52_3 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REDUCE: (174), (994) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (996) ~ (all_4_2 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (997) all_56_0 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (997) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (998) all_10_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (16), (55), (71), (73), (88), (90), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (103), (114), (122), (124), (155), (159), (631), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (635), (998) are inconsistent by sub-proof #190. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (999) ~ (all_56_0 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1000) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (51), (53), (65), (69), (84), (86), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (90), (107), (113), (124), (142), (144), (154), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (176), (631), (640), (664), (991), (992), (995), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (999), (1000) are inconsistent by sub-proof #576. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1001) all_56_15 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (176), (1001) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | #671. % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | (1002) all_56_10 = e0 | all_56_11 = e0 % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | REF_CLOSE: (69), (107), (147), (640), (1002) are inconsistent % 153.33/22.91 | | | | | | | | | | by sub-proof #294. % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | (1003) ~ (all_56_2 = e0) % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | REDUCE: (104), (1003) imply: % 153.33/22.91 | | | | | | | | | (1004) ~ (all_52_1 = e0) % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | REF_CLOSE: (25), (29), (40), (62), (70), (76), (78), (83), % 153.33/22.91 | | | | | | | | | (104), (107), (151), (161), (617), (625), (1004) % 153.33/22.91 | | | | | | | | | are inconsistent by sub-proof #456. % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | End of split % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | End of split % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | End of split % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | End of split % 153.33/22.91 | | | | | % 153.33/22.91 | | | | End of split % 153.33/22.91 | | | | % 153.33/22.91 | | | End of split % 153.33/22.91 | | | % 153.33/22.91 | | End of split % 153.33/22.91 | | % 153.33/22.91 | Case 2: % 153.33/22.91 | | % 153.33/22.91 | | (1005) all_20_2 = e1 % 153.33/22.91 | | % 153.33/22.91 | | COMBINE_EQS: (68), (1005) imply: % 153.33/22.91 | | (1006) all_4_2 = e1 % 153.33/22.91 | | % 153.33/22.91 | | SIMP: (1006) implies: % 153.33/22.91 | | (1007) all_4_2 = e1 % 153.33/22.91 | | % 153.33/22.91 | | COMBINE_EQS: (7), (1007) imply: % 153.33/22.91 | | (1008) all_56_15 = e1 % 153.33/22.91 | | % 153.33/22.91 | | COMBINE_EQS: (2), (1007) imply: % 153.33/22.91 | | (1009) all_58_31 = e1 % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (72), (1007) imply: % 153.33/22.91 | | (1010) ~ (all_52_3 = e1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (146), (1007) imply: % 153.33/22.91 | | (1011) ~ (all_52_7 = e1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (129), (1007) imply: % 153.33/22.91 | | (1012) ~ (all_52_12 = e1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (51), (1007) imply: % 153.33/22.91 | | (1013) ~ (all_52_13 = e1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (174), (1007) imply: % 153.33/22.91 | | (1014) ~ (all_6_1 = e1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (158), (1007) imply: % 153.33/22.91 | | (1015) op(e1, e0) = all_4_1 % 153.33/22.91 | | % 153.33/22.91 | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, simplifying % 153.33/22.91 | | with (74), (1015) gives: % 153.33/22.91 | | (1016) all_52_14 = all_4_1 % 153.33/22.91 | | % 153.33/22.91 | | COMBINE_EQS: (69), (1016) imply: % 153.33/22.91 | | (1017) all_56_11 = all_4_1 % 153.33/22.91 | | % 153.33/22.91 | | COMBINE_EQS: (39), (1016) imply: % 153.33/22.91 | | (1018) all_58_20 = all_4_1 % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (142), (1016) imply: % 153.33/22.91 | | (1019) ~ (all_52_2 = all_4_1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (85), (1016) imply: % 153.33/22.91 | | (1020) ~ (all_52_12 = all_4_1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (80), (1016) imply: % 153.33/22.91 | | (1021) ~ (all_52_13 = all_4_1) % 153.33/22.91 | | % 153.33/22.91 | | REDUCE: (147), (1016) imply: % 153.33/22.91 | | (1022) ~ (all_4_1 = e0) % 153.33/22.91 | | % 153.33/22.91 | | BETA: splitting (29) gives: % 153.33/22.91 | | % 153.33/22.91 | | Case 1: % 153.33/22.91 | | | % 153.33/22.91 | | | (1023) all_56_2 = e0 % 153.33/22.91 | | | % 153.33/22.91 | | | COMBINE_EQS: (104), (1023) imply: % 153.33/22.91 | | | (1024) all_52_1 = e0 % 153.33/22.91 | | | % 153.33/22.91 | | | COMBINE_EQS: (87), (1024) imply: % 153.33/22.91 | | | (1025) all_58_8 = e0 % 153.33/22.91 | | | % 153.33/22.91 | | | REDUCE: (131), (1024) imply: % 153.33/22.91 | | | (1026) ~ (all_52_2 = e0) % 153.33/22.91 | | | % 153.33/22.91 | | | SIMP: (1026) implies: % 153.33/22.91 | | | (1027) ~ (all_52_2 = e0) % 153.33/22.91 | | | % 153.33/22.91 | | | REDUCE: (116), (1024) imply: % 153.33/22.91 | | | (1028) ~ (all_52_9 = e0) % 153.33/22.91 | | | % 153.33/22.91 | | | REDUCE: (61), (1024) imply: % 153.33/22.91 | | | (1029) ~ (all_52_13 = e0) % 153.33/22.91 | | | % 153.33/22.91 | | | SIMP: (1029) implies: % 153.33/22.91 | | | (1030) ~ (all_52_13 = e0) % 153.33/22.91 | | | % 153.33/22.91 | | | BETA: splitting (47) gives: % 153.33/22.91 | | | % 153.33/22.91 | | | Case 1: % 153.33/22.91 | | | | % 153.33/22.91 | | | | (1031) all_56_15 = e0 % 153.33/22.91 | | | | % 153.33/22.91 | | | | REF_CLOSE: (144), (1008), (1031) are inconsistent by sub-proof #550. % 153.33/22.91 | | | | % 153.33/22.91 | | | Case 2: % 153.33/22.91 | | | | % 153.33/22.91 | | | | (1032) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 % 153.33/22.91 | | | | = e0 | all_56_13 = e0 | all_56_14 = e0) % 153.33/22.91 | | | | % 153.33/22.91 | | | | ALPHA: (1032) implies: % 153.33/22.91 | | | | (1033) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.33/22.91 | | | | % 153.33/22.91 | | | | BETA: splitting (1033) gives: % 153.33/22.91 | | | | % 153.33/22.91 | | | | Case 1: % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | (1034) all_56_9 = e0 % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | COMBINE_EQS: (83), (1034) imply: % 153.33/22.91 | | | | | (1035) all_52_12 = e0 % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | COMBINE_EQS: (23), (1035) imply: % 153.33/22.91 | | | | | (1036) all_58_6 = e0 % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | REDUCE: (162), (1035) imply: % 153.33/22.91 | | | | | (1037) ~ (all_52_4 = e0) % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | REDUCE: (108), (1035) imply: % 153.33/22.91 | | | | | (1038) ~ (all_10_2 = e0) % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | SIMP: (1038) implies: % 153.33/22.91 | | | | | (1039) ~ (all_10_2 = e0) % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | REDUCE: (1020), (1035) imply: % 153.33/22.91 | | | | | (1040) ~ (all_4_1 = e0) % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | BETA: splitting (99) gives: % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | Case 1: % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | (1041) all_56_1 = e0 % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | COMBINE_EQS: (70), (1041) imply: % 153.33/22.91 | | | | | | (1042) all_52_4 = e0 % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | REDUCE: (1037), (1042) imply: % 153.33/22.91 | | | | | | (1043) $false % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | CLOSE: (1043) is inconsistent. % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | Case 2: % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | (1044) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | BETA: splitting (1044) gives: % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | | Case 1: % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | (1045) all_56_3 = e0 % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | COMBINE_EQS: (78), (1045) imply: % 153.33/22.91 | | | | | | | (1046) all_8_2 = e0 % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | COMBINE_EQS: (84), (1046) imply: % 153.33/22.91 | | | | | | | (1047) all_58_29 = e0 % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | REF_CLOSE: (4), (13), (48), (55), (86), (101), (103), (113), % 153.33/22.91 | | | | | | | (139), (159), (1009), (1039), (1047) are inconsistent % 153.33/22.91 | | | | | | | by sub-proof #178. % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | Case 2: % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | (1048) all_56_7 = e0 | all_56_13 = e0 % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | BETA: splitting (1048) gives: % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | (1049) all_56_7 = e0 % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | COMBINE_EQS: (8), (1049) imply: % 153.33/22.91 | | | | | | | | (1050) all_52_6 = e0 % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | REDUCE: (58), (1050) imply: % 153.33/22.91 | | | | | | | | (1051) $false % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | CLOSE: (1051) is inconsistent. % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | (1052) all_56_13 = e0 % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | COMBINE_EQS: (92), (1052) imply: % 153.33/22.91 | | | | | | | | (1053) all_52_7 = e0 % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | SIMP: (1053) implies: % 153.33/22.91 | | | | | | | | (1054) all_52_7 = e0 % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | COMBINE_EQS: (79), (1054) imply: % 153.33/22.91 | | | | | | | | (1055) all_58_24 = e0 % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | REDUCE: (66), (1054) imply: % 153.33/22.91 | | | | | | | | (1056) ~ (all_52_3 = e0) % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | REDUCE: (171), (1054) imply: % 153.33/22.91 | | | | | | | | (1057) ~ (all_6_1 = e0) % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | SIMP: (1057) implies: % 153.33/22.91 | | | | | | | | (1058) ~ (all_6_1 = e0) % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | REDUCE: (1011), (1054) imply: % 153.33/22.91 | | | | | | | | (1059) ~ (e1 = e0) % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | BETA: splitting (106) gives: % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | (1060) all_54_12 = e0 % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | REF_CLOSE: (163), (1056), (1060) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | #762. % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | (1061) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | BETA: splitting (60) gives: % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | (1062) all_54_0 = e0 % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | COMBINE_EQS: (141), (1062) imply: % 153.33/22.91 | | | | | | | | | | (1063) all_10_2 = e0 % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | SIMP: (1063) implies: % 153.33/22.91 | | | | | | | | | | (1064) all_10_2 = e0 % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | COMBINE_EQS: (113), (1064) imply: % 153.33/22.91 | | | | | | | | | | (1065) all_58_28 = e0 % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | REF_CLOSE: (27), (55), (84), (86), (88), (103), (122), (139), % 153.33/22.91 | | | | | | | | | | (155), (1009), (1065) are inconsistent by % 153.33/22.91 | | | | | | | | | | sub-proof #680. % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | (1066) ~ (all_54_0 = e0) % 153.33/22.91 | | | | | | | | | | (1067) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | BETA: splitting (56) gives: % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | (1068) all_54_9 = e0 % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | COMBINE_EQS: (50), (1068) imply: % 153.33/22.91 | | | | | | | | | | | (1069) all_52_6 = e0 % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | REDUCE: (58), (1069) imply: % 153.33/22.91 | | | | | | | | | | | (1070) $false % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | CLOSE: (1070) is inconsistent. % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | (1071) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | BETA: splitting (35) gives: % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | (1072) all_56_0 = e1 % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | COMBINE_EQS: (124), (1072) imply: % 153.33/22.91 | | | | | | | | | | | | (1073) all_10_2 = e1 % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | REF_CLOSE: (4), (13), (16), (55), (71), (73), (88), (90), % 153.33/22.91 | | | | | | | | | | | | (103), (114), (122), (124), (155), (159), (1023), % 153.33/22.91 | | | | | | | | | | | | (1027), (1073) are inconsistent by sub-proof #190. % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | (1074) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | BETA: splitting (1074) gives: % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | (1075) all_56_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | REF_CLOSE: (144), (1023), (1075) are inconsistent by % 153.33/22.91 | | | | | | | | | | | | | sub-proof #549. % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | (1076) all_56_6 = e1 | all_56_12 = e1 % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | BETA: splitting (1076) gives: % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | (1077) all_56_6 = e1 % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | COMBINE_EQS: (90), (1077) imply: % 153.33/22.91 | | | | | | | | | | | | | | (1078) all_52_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | SIMP: (1078) implies: % 153.33/22.91 | | | | | | | | | | | | | | (1079) all_52_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | COMBINE_EQS: (17), (1079) imply: % 153.33/22.91 | | | | | | | | | | | | | | (1080) all_58_15 = e1 % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | REDUCE: (5), (1079) imply: % 153.33/22.91 | | | | | | | | | | | | | | (1081) ~ (all_52_3 = e1) % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | REDUCE: (123), (1079) imply: % 153.33/22.91 | | | | | | | | | | | | | | (1082) ~ (all_10_2 = e1) % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | SIMP: (1082) implies: % 153.33/22.91 | | | | | | | | | | | | | | (1083) ~ (all_10_2 = e1) % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | REDUCE: (1019), (1079) imply: % 153.33/22.91 | | | | | | | | | | | | | | (1084) ~ (all_4_1 = e1) % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | SIMP: (1084) implies: % 153.33/22.91 | | | | | | | | | | | | | | (1085) ~ (all_4_1 = e1) % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | BETA: splitting (64) gives: % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | (1086) all_54_5 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | COMBINE_EQS: (43), (1086) imply: % 153.33/22.91 | | | | | | | | | | | | | | | (1087) all_8_2 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | SIMP: (1087) implies: % 153.33/22.91 | | | | | | | | | | | | | | | (1088) all_8_2 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | COMBINE_EQS: (84), (1088) imply: % 153.33/22.91 | | | | | | | | | | | | | | | (1089) all_58_29 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (55), (86), (101), (103), (113), % 153.33/22.91 | | | | | | | | | | | | | | | (139), (159), (1009), (1039), (1089) are % 153.33/22.91 | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | (1090) ~ (all_54_5 = e0) % 153.33/22.91 | | | | | | | | | | | | | | | (1091) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | (1092) all_56_4 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (1092) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | (1093) all_52_8 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | REDUCE: (3), (1093) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | (1094) ~ (all_52_9 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | SIMP: (1094) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | (1095) ~ (all_52_9 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | (1096) all_56_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1023), (1096) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | (1097) e1 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | SIMP: (1097) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | (1098) e1 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1077), (1098) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | (1099) all_56_6 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (144), (1010), (1076), (1099) are % 153.33/22.91 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #807. % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | (1100) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | BETA: splitting (1100) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1101) all_56_3 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (1101) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1102) all_8_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (1102) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1103) all_58_29 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1104) all_58_28 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (1104) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1105) all_10_2 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (86), (103), (139), (155), (1009), (1103), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1104) are inconsistent by sub-proof #548. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1106) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (55), (86), (88), (101), (103), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (113), (122), (139), (155), (159), (1009), (1039), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1106) are inconsistent by sub-proof #177. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1107) all_56_5 = e1 | all_56_10 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (107), (1013), (1095), (1107) are % 153.33/22.91 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #176. % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | (1108) ~ (all_56_4 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | (1109) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | REDUCE: (25), (1108) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | (1110) ~ (all_52_8 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | BETA: splitting (93) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | (1111) all_56_0 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (1111) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | (1112) all_10_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | REDUCE: (1083), (1112) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | (1113) $false % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | CLOSE: (1113) is inconsistent. % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | (1114) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | BETA: splitting (1114) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1115) all_56_1 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (1115) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1116) all_52_4 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (1116) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1117) all_58_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REDUCE: (31), (1116) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1118) ~ (all_52_6 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | SIMP: (1118) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1119) ~ (all_52_6 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | BETA: splitting (1109) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1120) all_56_5 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (1120) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1121) all_52_9 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (1121) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1122) all_58_11 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REDUCE: (98), (1121) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1123) ~ (all_52_13 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REDUCE: (111), (1121) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1124) ~ (all_8_2 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | SIMP: (1124) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1125) ~ (all_8_2 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REDUCE: (173), (1121) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1126) ~ (all_6_1 = e1) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | (1127) all_54_2 = e0 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (151), (1127) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | #860. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | (1128) ~ (all_54_2 = e0) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | (1129) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1130) all_56_12 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (1130) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1131) all_52_3 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | SIMP: (1131) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1132) all_52_3 = e2 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (1132) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1133) ~ (all_10_2 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | SIMP: (1133) implies: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1134) ~ (all_10_2 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (48), (101), (124), (141), (145), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (159), (1039), (1067), (1083), (1134) are % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #248. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1135) ~ (all_56_12 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (1135) imply: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1136) ~ (all_52_3 = e2) % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (10), (15), (24), (25), (27), (32), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (34), (43), (50), (52), (53), (54), (57), (65), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (78), (81), (84), (86), (107), (113), (114), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (115), (124), (127), (130), (137), (139), (141), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (144), (149), (151), (161), (163), (168), (169), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (172), (1009), (1010), (1013), (1014), (1017), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1018), (1021), (1022), (1023), (1025), (1030), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1036), (1039), (1055), (1058), (1061), (1067), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1071), (1076), (1077), (1080), (1083), (1085), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1091), (1110), (1115), (1117), (1119), (1120), % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | (1122), (1125), (1129), (1136) are inconsistent by % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | sub-proof #530. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | (1137) all_56_8 = e1 | all_56_14 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (144), (168), (1014), (1137) are % 153.33/22.91 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #527. % 153.33/22.91 | | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | (1138) all_56_4 = e1 | all_56_9 = e1 % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (83), (1012), (1110), (1138) are % 153.33/22.91 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #485. % 153.33/22.91 | | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | Case 2: % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | (1139) all_56_12 = e1 % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | | REF_CLOSE: (65), (1010), (1139) are inconsistent by sub-proof % 153.33/22.91 | | | | | | | | | | | | | | #577. % 153.33/22.91 | | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | | % 153.33/22.91 | | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | | % 153.33/22.91 | | | | | | | | | End of split % 153.33/22.91 | | | | | | | | | % 153.33/22.91 | | | | | | | | End of split % 153.33/22.91 | | | | | | | | % 153.33/22.91 | | | | | | | End of split % 153.33/22.91 | | | | | | | % 153.33/22.91 | | | | | | End of split % 153.33/22.91 | | | | | | % 153.33/22.91 | | | | | End of split % 153.33/22.91 | | | | | % 153.33/22.91 | | | | Case 2: % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | (1140) all_56_10 = e0 | all_56_11 = e0 % 153.33/22.91 | | | | | % 153.33/22.91 | | | | | REF_CLOSE: (107), (1017), (1022), (1030), (1140) are inconsistent by % 153.33/22.91 | | | | | sub-proof #524. % 153.33/22.91 | | | | | % 153.33/22.91 | | | | End of split % 153.33/22.91 | | | | % 153.33/22.91 | | | End of split % 153.33/22.91 | | | % 153.33/22.91 | | Case 2: % 153.33/22.91 | | | % 153.33/22.91 | | | (1141) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.33/22.91 | | | % 153.33/22.91 | | | BETA: splitting (1141) gives: % 153.33/22.91 | | | % 153.33/22.91 | | | Case 1: % 153.33/22.91 | | | | % 153.33/22.91 | | | | (1142) all_56_3 = e0 % 153.33/22.92 | | | | % 153.33/22.92 | | | | COMBINE_EQS: (78), (1142) imply: % 153.33/22.92 | | | | (1143) all_8_2 = e0 % 153.33/22.92 | | | | % 153.33/22.92 | | | | SIMP: (1143) implies: % 153.33/22.92 | | | | (1144) all_8_2 = e0 % 153.33/22.92 | | | | % 153.33/22.92 | | | | REDUCE: (161), (1144) imply: % 153.33/22.92 | | | | (1145) $false % 153.33/22.92 | | | | % 153.33/22.92 | | | | CLOSE: (1145) is inconsistent. % 153.33/22.92 | | | | % 153.33/22.92 | | | Case 2: % 153.33/22.92 | | | | % 153.33/22.92 | | | | (1146) all_56_5 = e0 | all_56_10 = e0 % 153.33/22.92 | | | | % 153.33/22.92 | | | | BETA: splitting (1146) gives: % 153.33/22.92 | | | | % 153.33/22.92 | | | | Case 1: % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | (1147) all_56_5 = e0 % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | REF_CLOSE: (62), (76), (1147) are inconsistent by sub-proof #767. % 153.33/22.92 | | | | | % 153.33/22.92 | | | | Case 2: % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | (1148) all_56_10 = e0 % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | COMBINE_EQS: (107), (1148) imply: % 153.33/22.92 | | | | | (1149) all_52_13 = e0 % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | SIMP: (1149) implies: % 153.33/22.92 | | | | | (1150) all_52_13 = e0 % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | REDUCE: (61), (1150) imply: % 153.33/22.92 | | | | | (1151) ~ (all_52_1 = e0) % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | REDUCE: (40), (1150) imply: % 153.33/22.92 | | | | | (1152) ~ (all_52_12 = e0) % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | REDUCE: (53), (1150) imply: % 153.33/22.92 | | | | | (1153) ~ (all_8_2 = e0) % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | BETA: splitting (9) gives: % 153.33/22.92 | | | | | % 153.33/22.92 | | | | | Case 1: % 153.33/22.92 | | | | | | % 153.33/22.92 | | | | | | (1154) all_54_3 = e0 % 153.33/22.92 | | | | | | % 153.33/22.92 | | | | | | REF_CLOSE: (26), (1152), (1154) are inconsistent by sub-proof #733. % 153.33/22.92 | | | | | | % 153.33/22.92 | | | | | Case 2: % 153.33/22.92 | | | | | | % 153.33/22.92 | | | | | | (1155) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.33/22.92 | | | | | | % 153.33/22.92 | | | | | | REF_CLOSE: (4), (13), (14), (25), (26), (27), (29), (37), (40), % 153.33/22.92 | | | | | | (48), (55), (62), (63), (70), (76), (78), (83), (84), % 153.33/22.92 | | | | | | (86), (88), (96), (99), (101), (103), (104), (107), % 153.33/22.92 | | | | | | (108), (113), (120), (122), (124), (138), (139), (151), % 153.33/22.92 | | | | | | (152), (155), (159), (161), (162), (1009), (1012), % 153.33/22.92 | | | | | | (1151), (1155) are inconsistent by sub-proof #175. % 153.33/22.92 | | | | | | % 153.33/22.92 | | | | | End of split % 153.33/22.92 | | | | | % 153.33/22.92 | | | | End of split % 153.33/22.92 | | | | % 153.33/22.92 | | | End of split % 153.33/22.92 | | | % 153.33/22.92 | | End of split % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #175 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.33/22.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.33/22.92 (2) all_58_31 = e1 % 153.33/22.92 (3) op(all_10_2, all_10_1) = e0 % 153.33/22.92 (4) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.33/22.92 (5) all_56_4 = all_52_8 % 153.33/22.92 (6) all_54_3 = all_52_12 % 153.33/22.92 (7) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (8) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.33/22.92 (9) op(e3, e2) = all_52_4 % 153.33/22.92 (10) ~ (all_52_12 = all_52_13) % 153.33/22.92 (11) op(e3, e3) = all_10_2 % 153.33/22.92 (12) ~ (e3 = e1) % 153.33/22.92 (13) all_56_5 = all_52_9 % 153.33/22.92 (14) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.33/22.92 (15) all_56_1 = all_52_4 % 153.33/22.92 (16) ~ (all_52_9 = e0) % 153.33/22.92 (17) all_56_3 = all_8_2 % 153.33/22.92 (18) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.33/22.92 (19) all_56_9 = all_52_12 % 153.33/22.92 (20) all_58_29 = all_8_2 % 153.33/22.92 (21) all_58_30 = e0 % 153.33/22.92 (22) ~ (e2 = e1) % 153.33/22.92 (23) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.33/22.92 (24) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.33/22.92 (25) op(e3, all_10_2) = all_58_0 % 153.33/22.92 (26) ~ (e3 = e0) % 153.33/22.92 (27) all_56_2 = all_52_1 % 153.33/22.92 (28) all_56_10 = all_52_13 % 153.33/22.92 (29) ~ (all_52_12 = all_10_2) % 153.33/22.92 (30) ~ (all_52_12 = e1) % 153.33/22.92 (31) all_58_28 = all_10_2 % 153.33/22.92 (32) op(all_8_2, e2) = all_8_1 % 153.33/22.92 (33) ~ (e2 = e0) % 153.33/22.92 (34) all_56_0 = all_10_2 % 153.33/22.92 (35) ~ (all_52_1 = e0) % 153.33/22.92 (36) ~ (all_8_1 = e0) % 153.33/22.92 (37) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (38) ~ (all_52_8 = e0) % 153.33/22.92 (39) ~ (all_52_4 = all_10_2) % 153.33/22.92 (40) ~ (e3 = e2) % 153.33/22.92 (41) op(all_10_2, e3) = all_10_1 % 153.33/22.92 (42) ~ (all_8_2 = e0) % 153.33/22.92 (43) ~ (all_52_4 = all_52_12) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | BETA: splitting (24) gives: % 153.33/22.92 | % 153.33/22.92 | Case 1: % 153.33/22.92 | | % 153.33/22.92 | | (44) all_56_1 = e0 % 153.33/22.92 | | % 153.33/22.92 | | COMBINE_EQS: (15), (44) imply: % 153.33/22.92 | | (45) all_52_4 = e0 % 153.33/22.92 | | % 153.33/22.92 | | SIMP: (45) implies: % 153.33/22.92 | | (46) all_52_4 = e0 % 153.33/22.92 | | % 153.33/22.92 | | REDUCE: (43), (46) imply: % 153.33/22.92 | | (47) ~ (all_52_12 = e0) % 153.33/22.92 | | % 153.33/22.92 | | SIMP: (47) implies: % 153.33/22.92 | | (48) ~ (all_52_12 = e0) % 153.33/22.92 | | % 153.33/22.92 | | REDUCE: (39), (46) imply: % 153.33/22.92 | | (49) ~ (all_10_2 = e0) % 153.33/22.92 | | % 153.33/22.92 | | SIMP: (49) implies: % 153.33/22.92 | | (50) ~ (all_10_2 = e0) % 153.33/22.92 | | % 153.33/22.92 | | REDUCE: (9), (46) imply: % 153.33/22.92 | | (51) op(e3, e2) = e0 % 153.33/22.92 | | % 153.33/22.92 | | BETA: splitting (4) gives: % 153.33/22.92 | | % 153.33/22.92 | | Case 1: % 153.33/22.92 | | | % 153.33/22.92 | | | (52) all_56_9 = e2 % 153.33/22.92 | | | % 153.33/22.92 | | | COMBINE_EQS: (19), (52) imply: % 153.33/22.92 | | | (53) all_52_12 = e2 % 153.33/22.92 | | | % 153.33/22.92 | | | SIMP: (53) implies: % 153.33/22.92 | | | (54) all_52_12 = e2 % 153.33/22.92 | | | % 153.33/22.92 | | | REDUCE: (29), (54) imply: % 153.33/22.92 | | | (55) ~ (all_10_2 = e2) % 153.33/22.92 | | | % 153.33/22.92 | | | SIMP: (55) implies: % 153.33/22.92 | | | (56) ~ (all_10_2 = e2) % 153.33/22.92 | | | % 153.33/22.92 | | | BETA: splitting (7) gives: % 153.33/22.92 | | | % 153.33/22.92 | | | Case 1: % 153.33/22.92 | | | | % 153.33/22.92 | | | | (57) all_58_28 = e2 % 153.33/22.92 | | | | % 153.33/22.92 | | | | REF_CLOSE: (31), (56), (57) are inconsistent by sub-proof #388. % 153.33/22.92 | | | | % 153.33/22.92 | | | Case 2: % 153.33/22.92 | | | | % 153.33/22.92 | | | | (58) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 | | | | % 153.33/22.92 | | | | REF_CLOSE: (1), (2), (3), (11), (12), (21), (22), (25), (26), (31), % 153.33/22.92 | | | | (33), (37), (40), (41), (50), (58) are inconsistent by % 153.33/22.92 | | | | sub-proof #177. % 153.33/22.92 | | | | % 153.33/22.92 | | | End of split % 153.33/22.92 | | | % 153.33/22.92 | | Case 2: % 153.33/22.92 | | | % 153.33/22.92 | | | (59) ~ (all_56_9 = e2) % 153.33/22.92 | | | % 153.33/22.92 | | | REDUCE: (19), (59) imply: % 153.33/22.92 | | | (60) ~ (all_52_12 = e2) % 153.33/22.92 | | | % 153.33/22.92 | | | REF_CLOSE: (1), (2), (6), (7), (18), (19), (20), (21), (22), (23), (25), % 153.33/22.92 | | | (29), (30), (31), (32), (33), (36), (37), (48), (51), (60) are % 153.33/22.92 | | | inconsistent by sub-proof #522. % 153.33/22.92 | | | % 153.33/22.92 | | End of split % 153.33/22.92 | | % 153.33/22.92 | Case 2: % 153.33/22.92 | | % 153.33/22.92 | | (61) ~ (all_56_1 = e0) % 153.33/22.92 | | % 153.33/22.92 | | REDUCE: (15), (61) imply: % 153.33/22.92 | | (62) ~ (all_52_4 = e0) % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (2), (5), (7), (8), (10), (12), (13), (14), (15), (16), (17), % 153.33/22.92 | | (19), (20), (21), (22), (26), (27), (28), (31), (33), (34), (35), % 153.33/22.92 | | (37), (38), (40), (42), (62) are inconsistent by sub-proof #455. % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #176 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ~ (all_52_13 = e1) % 153.33/22.92 (2) all_56_5 = e1 | all_56_10 = e1 % 153.33/22.92 (3) all_56_5 = all_52_9 % 153.33/22.92 (4) all_56_10 = all_52_13 % 153.33/22.92 (5) ~ (all_52_9 = e1) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | BETA: splitting (2) gives: % 153.33/22.92 | % 153.33/22.92 | Case 1: % 153.33/22.92 | | % 153.33/22.92 | | (6) all_56_5 = e1 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #285. % 153.33/22.92 | | % 153.33/22.92 | Case 2: % 153.33/22.92 | | % 153.33/22.92 | | (7) all_56_10 = e1 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #606. % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #177 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.33/22.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.33/22.92 (2) all_58_31 = e1 % 153.33/22.92 (3) op(all_10_2, all_10_1) = e0 % 153.33/22.92 (4) ~ (all_10_2 = e0) % 153.33/22.92 (5) op(e3, e3) = all_10_2 % 153.33/22.92 (6) ~ (e3 = e1) % 153.33/22.92 (7) all_58_30 = e0 % 153.33/22.92 (8) ~ (e2 = e1) % 153.33/22.92 (9) op(e3, all_10_2) = all_58_0 % 153.33/22.92 (10) ~ (e3 = e0) % 153.33/22.92 (11) all_58_28 = all_10_2 % 153.33/22.92 (12) ~ (e2 = e0) % 153.33/22.92 (13) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (15) ~ (e3 = e2) % 153.33/22.92 (16) op(all_10_2, e3) = all_10_1 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | BETA: splitting (14) gives: % 153.33/22.92 | % 153.33/22.92 | Case 1: % 153.33/22.92 | | % 153.33/22.92 | | (17) all_58_28 = e3 % 153.33/22.92 | | % 153.33/22.92 | | COMBINE_EQS: (11), (17) imply: % 153.33/22.92 | | (18) all_10_2 = e3 % 153.33/22.92 | | % 153.33/22.92 | | SIMP: (18) implies: % 153.33/22.92 | | (19) all_10_2 = e3 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (1), (3), (4), (5), (9), (16), (19) are inconsistent by sub-proof % 153.33/22.92 | | #251. % 153.33/22.92 | | % 153.33/22.92 | Case 2: % 153.33/22.92 | | % 153.33/22.92 | | (20) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (2), (6), (7), (8), (10), (12), (13), (15), (20) are inconsistent % 153.33/22.92 | | by sub-proof #451. % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #178 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.33/22.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.33/22.92 (2) all_58_31 = e1 % 153.33/22.92 (3) op(all_10_2, all_10_1) = e0 % 153.33/22.92 (4) ~ (all_10_2 = e0) % 153.33/22.92 (5) op(e3, e3) = all_10_2 % 153.33/22.92 (6) ~ (e3 = e1) % 153.33/22.92 (7) all_58_29 = e0 % 153.33/22.92 (8) all_58_30 = e0 % 153.33/22.92 (9) op(e3, all_10_2) = all_58_0 % 153.33/22.92 (10) ~ (e3 = e0) % 153.33/22.92 (11) all_58_28 = all_10_2 % 153.33/22.92 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (13) op(all_10_2, e3) = all_10_1 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | BETA: splitting (12) gives: % 153.33/22.92 | % 153.33/22.92 | Case 1: % 153.33/22.92 | | % 153.33/22.92 | | (14) all_58_28 = e3 % 153.33/22.92 | | % 153.33/22.92 | | COMBINE_EQS: (11), (14) imply: % 153.33/22.92 | | (15) all_10_2 = e3 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (1), (3), (4), (5), (9), (13), (15) are inconsistent by sub-proof % 153.33/22.92 | | #251. % 153.33/22.92 | | % 153.33/22.92 | Case 2: % 153.33/22.92 | | % 153.33/22.92 | | (16) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (2), (6), (7), (8), (10), (16) are inconsistent by sub-proof % 153.33/22.92 | | #693. % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #179 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ~ (all_6_1 = e1) % 153.33/22.92 (2) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.33/22.92 (3) all_56_14 = all_6_1 % 153.33/22.92 (4) all_56_8 = e0 % 153.33/22.92 (5) all_56_5 = all_52_9 % 153.33/22.92 (6) ~ (all_52_9 = e1) % 153.33/22.92 (7) ~ (e1 = e0) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | BETA: splitting (2) gives: % 153.33/22.92 | % 153.33/22.92 | Case 1: % 153.33/22.92 | | % 153.33/22.92 | | (8) all_56_5 = e1 % 153.33/22.92 | | % 153.33/22.92 | | COMBINE_EQS: (5), (8) imply: % 153.33/22.92 | | (9) all_52_9 = e1 % 153.33/22.92 | | % 153.33/22.92 | | REDUCE: (6), (9) imply: % 153.33/22.92 | | (10) $false % 153.33/22.92 | | % 153.33/22.92 | | CLOSE: (10) is inconsistent. % 153.33/22.92 | | % 153.33/22.92 | Case 2: % 153.33/22.92 | | % 153.33/22.92 | | (11) all_56_8 = e1 | all_56_14 = e1 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (1), (3), (4), (7), (11) are inconsistent by sub-proof #527. % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #180 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_15 = e1 % 153.33/22.92 (2) ~ (e3 = e1) % 153.33/22.92 (3) all_58_30 = e0 % 153.33/22.92 (4) ~ (e3 = e0) % 153.33/22.92 (5) all_58_31 = e3 % 153.33/22.92 (6) all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (7) all_58_15 = e3 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (1), (7) imply: % 153.33/22.92 | (8) e3 = e1 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (5), (8) imply: % 153.33/22.92 | (9) all_58_31 = e1 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #694. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #181 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ~ (e3 = e1) % 153.33/22.92 (2) all_58_30 = e0 % 153.33/22.92 (3) ~ (e3 = e0) % 153.33/22.92 (4) all_58_31 = e3 % 153.33/22.92 (5) all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (6) e3 = e1 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | SIMP: (6) implies: % 153.33/22.92 | (7) e3 = e1 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (4), (7) imply: % 153.33/22.92 | (8) all_58_31 = e1 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (2), (3), (5), (8) are inconsistent by sub-proof #694. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #182 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_56_6 = e3 | all_56_12 = e3 % 153.33/22.92 (2) ~ (e3 = e1) % 153.33/22.92 (3) all_56_12 = e1 % 153.33/22.92 (4) all_56_6 = e3 % 153.33/22.92 (5) ~ (e3 = e0) % 153.33/22.92 (6) e2 = e0 % 153.33/22.92 (7) e3 = e2 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (6), (7) imply: % 153.33/22.92 | (8) e3 = e0 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (4), (8) imply: % 153.33/22.92 | (9) all_56_6 = e0 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (2), (3), (5), (9) are inconsistent by sub-proof #838. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #183 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_12 = e0 % 153.33/22.92 (2) all_58_31 = all_4_2 % 153.33/22.92 (3) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.33/22.92 (4) all_54_3 = all_52_12 % 153.33/22.92 (5) ~ (all_8_2 = e3) % 153.33/22.92 (6) all_58_19 = e0 % 153.33/22.92 (7) ~ (e3 = e1) % 153.33/22.92 (8) all_58_28 = e1 % 153.33/22.92 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.33/22.92 (10) all_56_9 = all_52_12 % 153.33/22.92 (11) all_58_29 = all_8_2 % 153.33/22.92 (12) all_58_30 = e0 % 153.33/22.92 (13) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.33/22.92 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 153.33/22.92 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 153.33/22.92 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 153.33/22.92 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 153.33/22.92 (all_58_27 = e0)) % 153.33/22.92 (14) ~ (e3 = e0) % 153.33/22.92 (15) ~ (all_52_12 = e1) % 153.33/22.92 (16) all_58_21 = all_4_2 % 153.33/22.92 (17) ~ (all_52_12 = all_4_2) % 153.33/22.92 (18) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (19) all_58_1 = all_52_12 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | BETA: splitting (18) gives: % 153.33/22.92 | % 153.33/22.92 | Case 1: % 153.33/22.92 | | % 153.33/22.92 | | (20) all_58_28 = e3 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (7), (8), (20) are inconsistent by sub-proof #857. % 153.33/22.92 | | % 153.33/22.92 | Case 2: % 153.33/22.92 | | % 153.33/22.92 | | (21) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 | | % 153.33/22.92 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14), % 153.33/22.92 | | (15), (16), (17), (19), (21) are inconsistent by sub-proof #610. % 153.33/22.92 | | % 153.33/22.92 | End of split % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #184 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_31 = all_4_2 % 153.33/22.92 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (3) ~ (e3 = e1) % 153.33/22.92 (4) e3 = e1 % 153.33/22.92 (5) all_58_29 = e3 % 153.33/22.92 (6) all_58_30 = e0 % 153.33/22.92 (7) ~ (e2 = e1) % 153.33/22.92 (8) ~ (e3 = e0) % 153.33/22.92 (9) all_58_28 = all_10_2 % 153.33/22.92 (10) ~ (e2 = e0) % 153.33/22.92 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (12) ~ (e1 = e0) % 153.33/22.92 (13) e1 = e0 % 153.33/22.92 (14) ~ (all_4_2 = e1) % 153.33/22.92 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.33/22.92 (16) ~ (e3 = e2) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (4), (13) imply: % 153.33/22.92 | (17) e3 = e0 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (5), (17) imply: % 153.33/22.92 | (18) all_58_29 = e0 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (14), (15), % 153.33/22.92 | (16), (18) are inconsistent by sub-proof #698. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #185 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_26 = e3 % 153.33/22.92 (2) all_58_26 = e1 % 153.33/22.92 (3) ~ (e3 = e1) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (1), (2) imply: % 153.33/22.92 | (4) e3 = e1 % 153.33/22.92 | % 153.33/22.92 | SIMP: (4) implies: % 153.33/22.92 | (5) e3 = e1 % 153.33/22.92 | % 153.33/22.92 | REDUCE: (3), (5) imply: % 153.33/22.92 | (6) $false % 153.33/22.92 | % 153.33/22.92 | CLOSE: (6) is inconsistent. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #186 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_31 = all_4_2 % 153.33/22.92 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (3) ~ (e3 = e1) % 153.33/22.92 (4) all_58_6 = e0 % 153.33/22.92 (5) all_58_29 = e3 % 153.33/22.92 (6) all_58_30 = e0 % 153.33/22.92 (7) ~ (e2 = e1) % 153.33/22.92 (8) ~ (e3 = e0) % 153.33/22.92 (9) all_58_6 = e3 % 153.33/22.92 (10) all_58_28 = all_10_2 % 153.33/22.92 (11) ~ (e2 = e0) % 153.33/22.92 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (13) ~ (e1 = e0) % 153.33/22.92 (14) ~ (all_4_2 = e1) % 153.33/22.92 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.33/22.92 (16) ~ (e3 = e2) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (4), (9) imply: % 153.33/22.92 | (17) e3 = e0 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (5), (17) imply: % 153.33/22.92 | (18) all_58_29 = e0 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), (15), % 153.33/22.92 | (16), (18) are inconsistent by sub-proof #698. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #187 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_31 = all_4_2 % 153.33/22.92 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (3) ~ (e3 = e1) % 153.33/22.92 (4) all_58_29 = e3 % 153.33/22.92 (5) all_58_30 = e0 % 153.33/22.92 (6) ~ (e2 = e1) % 153.33/22.92 (7) ~ (e3 = e0) % 153.33/22.92 (8) e3 = e0 % 153.33/22.92 (9) all_58_28 = all_10_2 % 153.33/22.92 (10) ~ (e2 = e0) % 153.33/22.92 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (12) ~ (e1 = e0) % 153.33/22.92 (13) ~ (all_4_2 = e1) % 153.33/22.92 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.33/22.92 (15) ~ (e3 = e2) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | SIMP: (8) implies: % 153.33/22.92 | (16) e3 = e0 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (4), (16) imply: % 153.33/22.92 | (17) all_58_29 = e0 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14), % 153.33/22.92 | (15), (17) are inconsistent by sub-proof #698. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #188 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_56_0 = all_10_2 % 153.33/22.92 (2) all_56_0 = e3 % 153.33/22.92 (3) ~ (all_10_2 = e3) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (1), (2) imply: % 153.33/22.92 | (4) all_10_2 = e3 % 153.33/22.92 | % 153.33/22.92 | SIMP: (4) implies: % 153.33/22.92 | (5) all_10_2 = e3 % 153.33/22.92 | % 153.33/22.92 | REDUCE: (3), (5) imply: % 153.33/22.92 | (6) $false % 153.33/22.92 | % 153.33/22.92 | CLOSE: (6) is inconsistent. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #189 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) all_58_31 = all_4_2 % 153.33/22.92 (2) all_56_3 = e0 % 153.33/22.92 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (4) ~ (e3 = e1) % 153.33/22.92 (5) all_56_3 = all_8_2 % 153.33/22.92 (6) all_58_29 = all_8_2 % 153.33/22.92 (7) all_58_30 = e0 % 153.33/22.92 (8) ~ (e2 = e1) % 153.33/22.92 (9) ~ (e3 = e0) % 153.33/22.92 (10) all_58_28 = all_10_2 % 153.33/22.92 (11) ~ (e2 = e0) % 153.33/22.92 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.92 (13) ~ (e1 = e0) % 153.33/22.92 (14) ~ (all_4_2 = e1) % 153.33/22.92 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.33/22.92 (16) ~ (e3 = e2) % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (2), (5) imply: % 153.33/22.92 | (17) all_8_2 = e0 % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (6), (17) imply: % 153.33/22.92 | (18) all_58_29 = e0 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15), % 153.33/22.92 | (16), (18) are inconsistent by sub-proof #698. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #190 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.33/22.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.33/22.92 (2) ~ (all_52_2 = e0) % 153.33/22.92 (3) op(all_10_2, all_10_1) = e0 % 153.33/22.92 (4) ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 153.33/22.92 (5) ~ (e3 = e1) % 153.33/22.92 (6) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.33/22.92 (7) op(e1, e3) = all_52_2 % 153.33/22.92 (8) all_10_2 = e1 % 153.33/22.92 (9) ~ (e2 = e1) % 153.33/22.92 (10) all_56_6 = all_52_2 % 153.33/22.92 (11) all_56_2 = e0 % 153.33/22.92 (12) ~ (e3 = e0) % 153.33/22.92 (13) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 153.33/22.92 (14) ~ (e2 = e0) % 153.33/22.92 (15) all_56_0 = all_10_2 % 153.33/22.92 (16) ~ (e3 = e2) % 153.33/22.92 (17) op(all_10_2, e3) = all_10_1 % 153.33/22.92 % 153.33/22.92 Begin of proof % 153.33/22.92 | % 153.33/22.92 | COMBINE_EQS: (8), (15) imply: % 153.33/22.92 | (18) all_56_0 = e1 % 153.33/22.92 | % 153.33/22.92 | REDUCE: (3), (8) imply: % 153.33/22.92 | (19) op(e1, all_10_1) = e0 % 153.33/22.92 | % 153.33/22.92 | REDUCE: (8), (17) imply: % 153.33/22.92 | (20) op(e1, e3) = all_10_1 % 153.33/22.92 | % 153.33/22.92 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 153.33/22.92 | (14), (16), (18), (19), (20) are inconsistent by sub-proof #242. % 153.33/22.92 | % 153.33/22.92 End of proof % 153.33/22.92 % 153.33/22.92 Sub-proof #191 shows that the following formulas are inconsistent: % 153.33/22.92 ---------------------------------------------------------------- % 153.33/22.92 (1) ~ (all_52_8 = all_52_9) % 153.33/22.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.33/22.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.33/22.92 (3) ~ (all_52_2 = all_52_3) % 153.33/22.92 (4) all_58_11 = all_52_9 % 153.33/22.92 (5) all_56_7 = all_52_6 % 153.33/22.92 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 153.33/22.92 (7) ~ (all_52_13 = e1) % 153.33/22.92 (8) all_54_8 = all_52_2 % 153.33/22.92 (9) all_58_31 = e1 % 153.33/22.92 (10) op(all_10_2, all_10_1) = e0 % 153.33/22.92 (11) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.33/22.92 (12) ~ (all_52_8 = all_10_2) % 153.33/22.92 (13) all_58_15 = all_52_2 % 153.33/22.92 (14) all_58_26 = all_52_11 % 153.33/22.92 (15) op(e1, all_52_14) = all_58_19 % 153.33/22.92 (16) ~ (all_52_8 = all_52_11) % 153.33/22.92 (17) all_54_7 = all_52_13 % 153.33/22.92 (18) all_58_6 = all_52_12 % 153.33/22.92 (19) ~ (all_52_6 = all_8_2) % 153.33/22.92 (20) all_56_4 = all_52_8 % 153.33/22.92 (21) ~ (all_52_4 = all_8_2) % 153.33/22.92 (22) all_54_3 = all_52_12 % 153.33/22.92 (23) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.33/22.92 (24) all_54_1 = all_52_4 % 153.33/22.92 (25) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.33/22.92 (26) ~ (all_6_2 = e0) % 153.33/22.92 (27) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 153.33/22.92 (28) ~ (all_52_4 = all_52_6) % 153.33/22.92 (29) all_58_13 = all_52_13 % 153.33/22.92 (30) op(e0, e1) = all_52_11 % 153.33/22.92 (31) ~ (all_52_6 = all_52_7) % 153.33/22.92 (32) all_58_20 = all_52_14 % 153.33/22.92 (33) op(e1, all_4_1) = all_4_0 % 153.33/22.92 (34) ~ (all_52_3 = e1) % 153.33/22.92 (35) ~ (all_52_12 = all_52_13) % 153.33/22.92 (36) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.33/22.92 (37) op(e0, all_52_3) = all_58_21 % 153.33/22.92 (38) all_54_5 = all_8_2 % 153.33/22.92 (39) ~ (all_52_4 = all_52_7) % 153.33/22.92 (40) ~ (all_52_2 = all_6_2) % 153.33/22.92 (41) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 153.33/22.92 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 153.33/22.92 (42) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 153.33/22.92 (43) ~ (all_52_8 = all_52_12) % 153.33/22.92 (44) ~ (all_52_13 = all_8_2) % 153.33/22.92 (45) ~ (e3 = e1) % 153.33/22.92 (46) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.33/22.92 (47) ~ (all_4_0 = e1) % 153.33/22.92 (48) all_56_5 = all_52_9 % 153.33/22.92 (49) all_54_14 = all_52_11 % 153.33/22.92 (50) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.33/22.93 (51) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 153.33/22.93 (52) all_56_12 = all_52_3 % 153.33/22.93 (53) ~ (all_52_3 = all_52_7) % 153.33/22.93 (54) all_58_2 = all_52_4 % 153.33/22.93 (55) all_56_11 = all_52_14 % 153.33/22.93 (56) all_56_1 = all_52_4 % 153.33/22.93 (57) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.33/22.93 (58) op(e1, e0) = all_52_14 % 153.33/22.93 (59) ~ (all_52_9 = all_52_11) % 153.33/22.93 (60) ~ (all_52_1 = all_8_2) % 153.33/22.93 (61) all_56_3 = all_8_2 % 153.33/22.93 (62) all_58_24 = all_52_7 % 153.33/22.93 (63) ~ (all_52_11 = e1) % 153.33/22.93 (64) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 153.33/22.93 (65) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.33/22.93 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.33/22.93 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.33/22.93 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.33/22.93 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.33/22.93 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.33/22.93 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.33/22.93 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.33/22.93 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.33/22.93 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.33/22.93 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.33/22.93 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.33/22.93 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.33/22.93 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.33/22.93 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.33/22.93 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.33/22.93 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.33/22.93 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.33/22.93 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.33/22.93 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.33/22.93 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.33/22.93 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.33/22.93 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.33/22.93 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.33/22.93 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.33/22.93 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.33/22.93 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.33/22.93 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.33/22.93 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.33/22.93 e0) % 153.33/22.93 (66) ~ (all_52_4 = all_52_8) % 153.33/22.93 (67) all_56_9 = all_52_12 % 153.33/22.93 (68) all_58_29 = all_8_2 % 153.33/22.93 (69) op(e0, e1) = all_58_27 % 153.33/22.93 (70) ~ (all_52_12 = all_52_14) % 153.33/22.93 (71) all_58_8 = all_52_1 % 153.33/22.93 (72) ~ (e2 = e1) % 153.33/22.93 (73) all_56_6 = all_52_2 % 153.33/22.93 (74) ~ (all_52_2 = all_52_6) % 153.33/22.93 (75) all_56_13 = all_52_7 % 153.33/22.93 (76) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.33/22.93 (77) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.33/22.93 (78) ~ (all_52_9 = all_52_13) % 153.33/22.93 (79) ~ (all_52_11 = all_6_2) % 153.33/22.93 (80) ~ (e3 = e0) % 153.33/22.93 (81) all_56_2 = all_52_1 % 153.33/22.93 (82) op(e0, e3) = all_52_3 % 153.33/22.93 (83) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.33/22.93 (84) all_56_10 = all_52_13 % 153.33/22.93 (85) ~ (all_52_12 = all_10_2) % 153.33/22.93 (86) ~ (all_52_1 = all_52_3) % 153.33/22.93 (87) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 153.33/22.93 (88) all_56_14 = all_52_11 % 153.33/22.93 (89) all_58_28 = all_10_2 % 153.33/22.93 (90) all_58_17 = all_52_6 % 153.33/22.93 (91) ~ (all_52_1 = all_52_9) % 153.33/22.93 (92) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.33/22.93 (93) ~ (all_52_7 = all_52_11) % 153.33/22.93 (94) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.33/22.93 (95) ~ (e2 = e0) % 153.33/22.93 (96) ~ (all_52_2 = all_10_2) % 153.33/22.93 (97) all_56_0 = all_10_2 % 153.33/22.93 (98) ~ (all_52_3 = all_52_11) % 153.33/22.93 (99) all_58_22 = all_52_3 % 153.33/22.93 (100) ~ (all_52_3 = all_10_2) % 153.33/22.93 (101) all_56_8 = all_6_2 % 153.33/22.93 (102) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.33/22.93 (103) ~ (all_52_1 = all_52_2) % 153.33/22.93 (104) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 153.33/22.93 (105) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.33/22.93 (106) all_58_4 = all_52_8 % 153.33/22.93 (107) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.33/22.93 (108) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 153.33/22.93 (109) ~ (all_52_2 = all_52_14) % 153.33/22.93 (110) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.33/22.93 (111) ~ (e1 = e0) % 153.33/22.93 (112) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 153.33/22.93 (113) op(e0, e2) = all_52_7 % 153.33/22.93 (114) all_58_30 = all_6_2 % 153.33/22.93 (115) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.33/22.93 (116) ~ (e3 = e2) % 153.33/22.93 (117) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.33/22.93 (118) ~ (all_52_14 = all_6_2) % 153.33/22.93 (119) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 153.33/22.93 (120) all_56_15 = e1 % 153.33/22.93 (121) op(all_10_2, e3) = all_10_1 % 153.33/22.93 (122) ~ (all_8_2 = e0) % 153.33/22.93 (123) ~ (all_52_4 = all_52_12) % 153.33/22.93 (124) all_54_12 = all_52_3 % 153.33/22.93 (125) op(e1, e0) = all_4_1 % 153.33/22.93 (126) ~ (all_52_1 = all_10_2) % 153.33/22.93 % 153.33/22.93 Begin of proof % 153.33/22.93 | % 153.33/22.93 | BETA: splitting (42) gives: % 153.33/22.93 | % 153.33/22.93 | Case 1: % 153.33/22.93 | | % 153.33/22.93 | | (127) all_58_28 = e0 % 153.33/22.93 | | % 153.33/22.93 | | COMBINE_EQS: (89), (127) imply: % 153.33/22.93 | | (128) all_10_2 = e0 % 153.33/22.93 | | % 153.33/22.93 | | SIMP: (128) implies: % 153.33/22.93 | | (129) all_10_2 = e0 % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (126), (129) imply: % 153.33/22.93 | | (130) ~ (all_52_1 = e0) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (96), (129) imply: % 153.33/22.93 | | (131) ~ (all_52_2 = e0) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (100), (129) imply: % 153.33/22.93 | | (132) ~ (all_52_3 = e0) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (12), (129) imply: % 153.33/22.93 | | (133) ~ (all_52_8 = e0) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (85), (129) imply: % 153.33/22.93 | | (134) ~ (all_52_12 = e0) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (10), (129) imply: % 153.33/22.93 | | (135) op(e0, all_10_1) = e0 % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (121), (129) imply: % 153.33/22.93 | | (136) op(e0, e3) = all_10_1 % 153.33/22.93 | | % 153.33/22.93 | | GROUND_INST: instantiating (2) with all_52_11, all_58_27, e1, e0, % 153.33/22.93 | | simplifying with (30), (69) gives: % 153.33/22.93 | | (137) all_58_27 = all_52_11 % 153.33/22.93 | | % 153.33/22.93 | | GROUND_INST: instantiating (2) with all_52_3, all_10_1, e3, e0, simplifying % 153.33/22.93 | | with (82), (136) gives: % 153.33/22.93 | | (138) all_52_3 = all_10_1 % 153.33/22.93 | | % 153.33/22.93 | | GROUND_INST: instantiating (2) with all_52_14, all_4_1, e0, e1, simplifying % 153.33/22.93 | | with (58), (125) gives: % 153.33/22.93 | | (139) all_52_14 = all_4_1 % 153.33/22.93 | | % 153.33/22.93 | | COMBINE_EQS: (124), (138) imply: % 153.33/22.93 | | (140) all_54_12 = all_10_1 % 153.33/22.93 | | % 153.33/22.93 | | COMBINE_EQS: (52), (138) imply: % 153.33/22.93 | | (141) all_56_12 = all_10_1 % 153.33/22.93 | | % 153.33/22.93 | | COMBINE_EQS: (55), (139) imply: % 153.33/22.93 | | (142) all_56_11 = all_4_1 % 153.33/22.93 | | % 153.33/22.93 | | COMBINE_EQS: (99), (138) imply: % 153.33/22.93 | | (143) all_58_22 = all_10_1 % 153.33/22.93 | | % 153.33/22.93 | | COMBINE_EQS: (32), (139) imply: % 153.33/22.93 | | (144) all_58_20 = all_4_1 % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (86), (138) imply: % 153.33/22.93 | | (145) ~ (all_52_1 = all_10_1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (3), (138) imply: % 153.33/22.93 | | (146) ~ (all_52_2 = all_10_1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (109), (139) imply: % 153.33/22.93 | | (147) ~ (all_52_2 = all_4_1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (53), (138) imply: % 153.33/22.93 | | (148) ~ (all_52_7 = all_10_1) % 153.33/22.93 | | % 153.33/22.93 | | SIMP: (148) implies: % 153.33/22.93 | | (149) ~ (all_52_7 = all_10_1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (98), (138) imply: % 153.33/22.93 | | (150) ~ (all_52_11 = all_10_1) % 153.33/22.93 | | % 153.33/22.93 | | SIMP: (150) implies: % 153.33/22.93 | | (151) ~ (all_52_11 = all_10_1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (34), (138) imply: % 153.33/22.93 | | (152) ~ (all_10_1 = e1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (132), (138) imply: % 153.33/22.93 | | (153) ~ (all_10_1 = e0) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (118), (139) imply: % 153.33/22.93 | | (154) ~ (all_6_2 = all_4_1) % 153.33/22.93 | | % 153.33/22.93 | | SIMP: (154) implies: % 153.33/22.93 | | (155) ~ (all_6_2 = all_4_1) % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (15), (139) imply: % 153.33/22.93 | | (156) op(e1, all_4_1) = all_58_19 % 153.33/22.93 | | % 153.33/22.93 | | REDUCE: (37), (138) imply: % 153.33/22.93 | | (157) op(e0, all_10_1) = all_58_21 % 153.33/22.93 | | % 153.33/22.93 | | GROUND_INST: instantiating (2) with e0, all_58_21, all_10_1, e0, simplifying % 153.33/22.93 | | with (135), (157) gives: % 153.33/22.93 | | (158) all_58_21 = e0 % 153.33/22.93 | | % 153.33/22.93 | | GROUND_INST: instantiating (2) with all_4_0, all_58_19, all_4_1, e1, % 153.33/22.93 | | simplifying with (33), (156) gives: % 153.33/22.93 | | (159) all_58_19 = all_4_0 % 153.33/22.93 | | % 153.33/22.93 | | BETA: splitting (6) gives: % 153.33/22.93 | | % 153.33/22.93 | | Case 1: % 153.33/22.93 | | | % 153.33/22.93 | | | (160) all_54_3 = e0 % 153.33/22.93 | | | % 153.33/22.93 | | | REF_CLOSE: (22), (134), (160) are inconsistent by sub-proof #733. % 153.33/22.93 | | | % 153.33/22.93 | | Case 2: % 153.33/22.93 | | | % 153.33/22.93 | | | (161) ~ (all_54_3 = e0) % 153.33/22.93 | | | (162) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.33/22.93 | | | % 153.33/22.93 | | | BETA: splitting (83) gives: % 153.33/22.93 | | | % 153.33/22.93 | | | Case 1: % 153.33/22.93 | | | | % 153.33/22.93 | | | | (163) all_54_12 = e0 % 153.33/22.93 | | | | % 153.33/22.93 | | | | COMBINE_EQS: (140), (163) imply: % 153.33/22.93 | | | | (164) all_10_1 = e0 % 153.33/22.93 | | | | % 153.33/22.93 | | | | REDUCE: (153), (164) imply: % 153.33/22.93 | | | | (165) $false % 153.33/22.93 | | | | % 153.33/22.93 | | | | CLOSE: (165) is inconsistent. % 153.33/22.93 | | | | % 153.33/22.93 | | | Case 2: % 153.33/22.93 | | | | % 153.33/22.93 | | | | (166) ~ (all_54_12 = e0) % 153.33/22.93 | | | | (167) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.33/22.93 | | | | % 153.33/22.93 | | | | BETA: splitting (110) gives: % 153.33/22.93 | | | | % 153.33/22.93 | | | | Case 1: % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | (168) all_56_6 = e0 % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | COMBINE_EQS: (73), (168) imply: % 153.33/22.93 | | | | | (169) all_52_2 = e0 % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | REDUCE: (131), (169) imply: % 153.33/22.93 | | | | | (170) $false % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | CLOSE: (170) is inconsistent. % 153.33/22.93 | | | | | % 153.33/22.93 | | | | Case 2: % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | (171) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | BETA: splitting (57) gives: % 153.33/22.93 | | | | | % 153.33/22.93 | | | | | Case 1: % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | (172) all_56_4 = e0 % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | COMBINE_EQS: (20), (172) imply: % 153.33/22.93 | | | | | | (173) all_52_8 = e0 % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | REDUCE: (133), (173) imply: % 153.33/22.93 | | | | | | (174) $false % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | CLOSE: (174) is inconsistent. % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | Case 2: % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | (175) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | BETA: splitting (25) gives: % 153.33/22.93 | | | | | | % 153.33/22.93 | | | | | | Case 1: % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | (176) all_56_2 = e0 % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | COMBINE_EQS: (81), (176) imply: % 153.33/22.93 | | | | | | | (177) all_52_1 = e0 % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | REDUCE: (130), (177) imply: % 153.33/22.93 | | | | | | | (178) $false % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | CLOSE: (178) is inconsistent. % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | Case 2: % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | (179) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | BETA: splitting (119) gives: % 153.33/22.93 | | | | | | | % 153.33/22.93 | | | | | | | Case 1: % 153.33/22.93 | | | | | | | | % 153.33/22.93 | | | | | | | | (180) all_54_7 = e0 % 153.33/22.93 | | | | | | | | % 153.33/22.93 | | | | | | | | COMBINE_EQS: (17), (180) imply: % 153.33/22.93 | | | | | | | | (181) all_52_13 = e0 % 153.33/22.93 | | | | | | | | % 153.33/22.93 | | | | | | | | REDUCE: (78), (181) imply: % 153.33/22.93 | | | | | | | | (182) ~ (all_52_9 = e0) % 153.33/22.93 | | | | | | | | % 153.33/22.93 | | | | | | | | BETA: splitting (175) gives: % 153.33/22.93 | | | | | | | | % 153.33/22.93 | | | | | | | | Case 1: % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | (183) all_56_5 = e0 % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | COMBINE_EQS: (48), (183) imply: % 153.33/22.93 | | | | | | | | | (184) all_52_9 = e0 % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | REDUCE: (182), (184) imply: % 153.33/22.93 | | | | | | | | | (185) $false % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | CLOSE: (185) is inconsistent. % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | Case 2: % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | (186) all_56_8 = e0 | all_56_14 = e0 % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | BETA: splitting (186) gives: % 153.33/22.93 | | | | | | | | | % 153.33/22.93 | | | | | | | | | Case 1: % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | (187) all_56_8 = e0 % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | COMBINE_EQS: (101), (187) imply: % 153.33/22.93 | | | | | | | | | | (188) all_6_2 = e0 % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | COMBINE_EQS: (114), (188) imply: % 153.33/22.93 | | | | | | | | | | (189) all_58_30 = e0 % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | REF_CLOSE: (9), (23), (45), (68), (72), (80), (95), (107), % 153.33/22.93 | | | | | | | | | | (116), (127), (189) are inconsistent by sub-proof % 153.33/22.93 | | | | | | | | | | #680. % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | Case 2: % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | (190) all_56_14 = e0 % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | COMBINE_EQS: (88), (190) imply: % 153.33/22.93 | | | | | | | | | | (191) all_52_11 = e0 % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | SIMP: (191) implies: % 153.33/22.93 | | | | | | | | | | (192) all_52_11 = e0 % 153.33/22.93 | | | | | | | | | | % 153.33/22.93 | | | | | | | | | | REDUCE: (93), (192) imply: % 153.54/22.93 | | | | | | | | | | (193) ~ (all_52_7 = e0) % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | REDUCE: (151), (192) imply: % 153.54/22.93 | | | | | | | | | | (194) ~ (all_10_1 = e0) % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | REF_CLOSE: (2), (105), (113), (135), (136), (140), (141), % 153.54/22.93 | | | | | | | | | | (152), (153), (167), (193) are inconsistent by % 153.54/22.93 | | | | | | | | | | sub-proof #212. % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | End of split % 153.54/22.93 | | | | | | | | % 153.54/22.93 | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | % 153.54/22.93 | | | | | | | | (195) ~ (all_54_7 = e0) % 153.54/22.93 | | | | | | | | % 153.54/22.93 | | | | | | | | REDUCE: (17), (195) imply: % 153.54/22.93 | | | | | | | | (196) ~ (all_52_13 = e0) % 153.54/22.93 | | | | | | | | % 153.54/22.93 | | | | | | | | BETA: splitting (41) gives: % 153.54/22.93 | | | | | | | | % 153.54/22.93 | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | | (197) all_56_15 = e0 % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | | REF_CLOSE: (111), (120), (197) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | #550. % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | | (198) ~ (all_56_15 = e0) % 153.54/22.93 | | | | | | | | | (199) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 153.54/22.93 | | | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | | ALPHA: (199) implies: % 153.54/22.93 | | | | | | | | | (200) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.54/22.93 | | | | | | | | | (201) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | | BETA: splitting (201) gives: % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | (202) all_56_9 = e0 % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | REF_CLOSE: (67), (134), (202) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | #521. % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | (203) all_56_10 = e0 | all_56_11 = e0 % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | BETA: splitting (179) gives: % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | (204) all_56_3 = e0 % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | COMBINE_EQS: (61), (204) imply: % 153.54/22.93 | | | | | | | | | | | (205) all_8_2 = e0 % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | COMBINE_EQS: (68), (205) imply: % 153.54/22.93 | | | | | | | | | | | (206) all_58_29 = e0 % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | REF_CLOSE: (23), (45), (72), (80), (95), (107), (111), (114), % 153.54/22.93 | | | | | | | | | | | (115), (116), (127), (206) are inconsistent by % 153.54/22.93 | | | | | | | | | | | sub-proof #483. % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | (207) all_56_5 = e0 | all_56_10 = e0 % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | BETA: splitting (207) gives: % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | (208) all_56_5 = e0 % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | COMBINE_EQS: (48), (208) imply: % 153.54/22.93 | | | | | | | | | | | | (209) all_52_9 = e0 % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | COMBINE_EQS: (4), (209) imply: % 153.54/22.93 | | | | | | | | | | | | (210) all_58_11 = e0 % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | REDUCE: (59), (209) imply: % 153.54/22.93 | | | | | | | | | | | | (211) ~ (all_52_11 = e0) % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | SIMP: (211) implies: % 153.54/22.93 | | | | | | | | | | | | (212) ~ (all_52_11 = e0) % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | REDUCE: (78), (209) imply: % 153.54/22.93 | | | | | | | | | | | | (213) ~ (all_52_13 = e0) % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | BETA: splitting (200) gives: % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | (214) all_56_12 = e0 % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | REF_CLOSE: (141), (153), (214) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | | | | #230. % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | (215) all_56_13 = e0 | all_56_14 = e0 % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | BETA: splitting (203) gives: % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | (216) all_56_10 = e0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | REF_CLOSE: (84), (196), (216) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | | | | | #526. % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | (217) all_56_11 = e0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | COMBINE_EQS: (142), (217) imply: % 153.54/22.93 | | | | | | | | | | | | | | (218) all_4_1 = e0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | SIMP: (218) implies: % 153.54/22.93 | | | | | | | | | | | | | | (219) all_4_1 = e0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | COMBINE_EQS: (144), (219) imply: % 153.54/22.93 | | | | | | | | | | | | | | (220) all_58_20 = e0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | REDUCE: (33), (219) imply: % 153.54/22.93 | | | | | | | | | | | | | | (221) op(e1, e0) = all_4_0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | REDUCE: (125), (219) imply: % 153.54/22.93 | | | | | | | | | | | | | | (222) op(e1, e0) = e0 % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | BETA: splitting (215) gives: % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | (223) all_56_13 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | COMBINE_EQS: (75), (223) imply: % 153.54/22.93 | | | | | | | | | | | | | | | (224) all_52_7 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | SIMP: (224) implies: % 153.54/22.93 | | | | | | | | | | | | | | | (225) all_52_7 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | COMBINE_EQS: (62), (225) imply: % 153.54/22.93 | | | | | | | | | | | | | | | (226) all_58_24 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | REDUCE: (39), (225) imply: % 153.54/22.93 | | | | | | | | | | | | | | | (227) ~ (all_52_4 = e0) % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | REDUCE: (31), (225) imply: % 153.54/22.93 | | | | | | | | | | | | | | | (228) ~ (all_52_6 = e0) % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | REDUCE: (149), (225) imply: % 153.54/22.93 | | | | | | | | | | | | | | | (229) ~ (all_10_1 = e0) % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_4_0, e0, e1, % 153.54/22.93 | | | | | | | | | | | | | | | simplifying with (221), (222) gives: % 153.54/22.93 | | | | | | | | | | | | | | | (230) all_4_0 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | REDUCE: (47), (230) imply: % 153.54/22.93 | | | | | | | | | | | | | | | (231) ~ (e1 = e0) % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | BETA: splitting (87) gives: % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | (232) all_54_14 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | REF_CLOSE: (49), (212), (232) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | | | | | | | #517. % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | (233) ~ (all_54_14 = e0) % 153.54/22.93 | | | | | | | | | | | | | | | | (234) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | Case 1: % 153.54/22.93 | | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | | (235) all_54_1 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (227), (235) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | | | | | | | | #798. % 153.54/22.93 | | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | | (236) ~ (all_54_1 = e0) % 153.54/22.93 | | | | | | | | | | | | | | | | | (237) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 153.54/22.93 | | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (11), (13), (14), (16), % 153.54/22.93 | | | | | | | | | | | | | | | | | (18), (19), (20), (21), (22), (23), (24), (26), % 153.54/22.93 | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (35), (36), (38), (40), % 153.54/22.93 | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (49), (50), (51), (54), % 153.54/22.93 | | | | | | | | | | | | | | | | | (55), (56), (60), (61), (63), (64), (65), (66), % 153.54/22.93 | | | | | | | | | | | | | | | | | (67), (68), (70), (71), (72), (73), (74), (76), % 153.54/22.93 | | | | | | | | | | | | | | | | | (77), (79), (80), (81), (84), (88), (89), (90), % 153.54/22.93 | | | | | | | | | | | | | | | | | (92), (94), (95), (97), (101), (102), (103), % 153.54/22.93 | | | | | | | | | | | | | | | | | (105), (106), (107), (108), (111), (112), (114), % 153.54/22.93 | | | | | | | | | | | | | | | | | (115), (116), (117), (120), (123), (127), (130), % 153.54/22.93 | | | | | | | | | | | | | | | | | (131), (133), (135), (136), (140), (141), (143), % 153.54/22.93 | | | | | | | | | | | | | | | | | (145), (146), (151), (152), (153), (162), (167), % 153.54/22.93 | | | | | | | | | | | | | | | | | (171), (208), (210), (212), (217), (220), (223), % 153.54/22.93 | | | | | | | | | | | | | | | | | (226), (227), (228), (234), (237) are inconsistent % 153.54/22.93 | | | | | | | | | | | | | | | | | by sub-proof #193. % 153.54/22.93 | | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | (238) all_56_14 = e0 % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | | REF_CLOSE: (88), (212), (238) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | | | | | | #806. % 153.54/22.93 | | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | Case 2: % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | (239) all_56_10 = e0 % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | | REF_CLOSE: (84), (196), (239) are inconsistent by sub-proof % 153.54/22.93 | | | | | | | | | | | | #526. % 153.54/22.93 | | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | | % 153.54/22.93 | | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | | % 153.54/22.93 | | | | | | | | | End of split % 153.54/22.93 | | | | | | | | | % 153.54/22.93 | | | | | | | | End of split % 153.54/22.93 | | | | | | | | % 153.54/22.93 | | | | | | | End of split % 153.54/22.93 | | | | | | | % 153.54/22.93 | | | | | | End of split % 153.54/22.93 | | | | | | % 153.54/22.93 | | | | | End of split % 153.54/22.93 | | | | | % 153.54/22.93 | | | | End of split % 153.54/22.93 | | | | % 153.54/22.93 | | | End of split % 153.54/22.93 | | | % 153.54/22.93 | | End of split % 153.54/22.93 | | % 153.54/22.93 | Case 2: % 153.54/22.93 | | % 153.54/22.93 | | (240) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 153.54/22.93 | | % 153.54/22.93 | | REF_CLOSE: (9), (26), (68), (111), (114), (122), (240) are inconsistent by % 153.54/22.93 | | sub-proof #192. % 153.54/22.93 | | % 153.54/22.93 | End of split % 153.54/22.93 | % 153.54/22.93 End of proof % 153.54/22.93 % 153.54/22.93 Sub-proof #192 shows that the following formulas are inconsistent: % 153.54/22.93 ---------------------------------------------------------------- % 153.54/22.93 (1) all_58_31 = e1 % 153.54/22.93 (2) ~ (all_6_2 = e0) % 153.54/22.93 (3) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 153.54/22.93 (4) all_58_29 = all_8_2 % 153.54/22.93 (5) ~ (e1 = e0) % 153.54/22.93 (6) all_58_30 = all_6_2 % 153.54/22.93 (7) ~ (all_8_2 = e0) % 153.54/22.93 % 153.54/22.93 Begin of proof % 153.54/22.93 | % 153.54/22.93 | BETA: splitting (3) gives: % 153.54/22.93 | % 153.54/22.93 | Case 1: % 153.54/22.93 | | % 153.54/22.93 | | (8) all_58_29 = e0 % 153.54/22.93 | | % 153.54/22.93 | | COMBINE_EQS: (4), (8) imply: % 153.54/22.93 | | (9) all_8_2 = e0 % 153.54/22.93 | | % 153.54/22.93 | | REDUCE: (7), (9) imply: % 153.54/22.93 | | (10) $false % 153.54/22.93 | | % 153.54/22.93 | | CLOSE: (10) is inconsistent. % 153.54/22.93 | | % 153.54/22.93 | Case 2: % 153.54/22.93 | | % 153.54/22.93 | | (11) all_58_30 = e0 | all_58_31 = e0 % 153.54/22.93 | | % 153.54/22.93 | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #808. % 153.54/22.93 | | % 153.54/22.93 | End of split % 153.54/22.93 | % 153.54/22.93 End of proof % 153.54/22.93 % 153.54/22.93 Sub-proof #193 shows that the following formulas are inconsistent: % 153.54/22.93 ---------------------------------------------------------------- % 153.54/22.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.54/22.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.54/22.93 (2) all_58_28 = e0 % 153.54/22.93 (3) all_56_7 = all_52_6 % 153.54/22.93 (4) ~ (all_52_2 = e0) % 153.54/22.93 (5) ~ (all_10_1 = e0) % 153.54/22.93 (6) ~ (all_52_13 = e1) % 153.54/22.93 (7) all_54_8 = all_52_2 % 153.54/22.93 (8) all_58_31 = e1 % 153.54/22.93 (9) ~ (all_52_11 = all_10_1) % 153.54/22.93 (10) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.54/22.93 (11) all_58_15 = all_52_2 % 153.54/22.93 (12) all_58_26 = all_52_11 % 153.54/22.93 (13) op(e0, all_10_1) = e0 % 153.54/22.93 (14) ~ (all_52_8 = all_52_11) % 153.54/22.93 (15) all_58_6 = all_52_12 % 153.54/22.93 (16) ~ (all_52_6 = all_8_2) % 153.54/22.93 (17) all_56_4 = all_52_8 % 153.54/22.93 (18) ~ (all_52_4 = all_8_2) % 153.54/22.93 (19) all_54_3 = all_52_12 % 153.54/22.93 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.54/22.93 (21) all_54_1 = all_52_4 % 153.54/22.93 (22) ~ (all_6_2 = e0) % 153.54/22.93 (23) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 153.54/22.93 (24) ~ (all_52_4 = all_52_6) % 153.54/22.93 (25) all_58_13 = all_52_13 % 153.54/22.93 (26) op(e0, e1) = all_52_11 % 153.54/22.93 (27) all_56_12 = all_10_1 % 153.54/22.93 (28) all_58_11 = e0 % 153.54/22.93 (29) all_58_20 = e0 % 153.54/22.93 (30) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 153.54/22.93 (31) ~ (all_52_12 = all_52_13) % 153.54/22.93 (32) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.54/22.93 (33) all_56_13 = e0 % 153.54/22.93 (34) all_54_5 = all_8_2 % 153.54/22.93 (35) ~ (all_52_2 = all_6_2) % 153.54/22.93 (36) ~ (all_52_8 = all_52_12) % 153.54/22.93 (37) ~ (all_52_13 = all_8_2) % 153.54/22.93 (38) ~ (e3 = e1) % 153.54/22.93 (39) all_54_12 = all_10_1 % 153.54/22.94 (40) ~ (all_52_6 = e0) % 153.54/22.94 (41) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.54/22.94 (42) all_54_14 = all_52_11 % 153.54/22.94 (43) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.54/22.94 (44) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 153.54/22.94 (45) all_58_2 = all_52_4 % 153.54/22.94 (46) all_56_11 = all_52_14 % 153.54/22.94 (47) all_56_1 = all_52_4 % 153.54/22.94 (48) all_58_24 = e0 % 153.54/22.94 (49) ~ (all_52_1 = all_10_1) % 153.54/22.94 (50) op(e0, e3) = all_10_1 % 153.54/22.94 (51) ~ (all_52_1 = all_8_2) % 153.54/22.94 (52) all_56_3 = all_8_2 % 153.54/22.94 (53) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.54/22.94 (54) ~ (all_52_11 = e1) % 153.54/22.94 (55) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 153.54/22.94 (56) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.54/22.94 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.54/22.94 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.54/22.94 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.54/22.94 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.54/22.94 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.54/22.94 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.54/22.94 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.54/22.94 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.54/22.94 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.54/22.94 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.54/22.94 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.54/22.94 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.54/22.94 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.54/22.94 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.54/22.94 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.54/22.94 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.54/22.94 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.54/22.94 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.54/22.94 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.54/22.94 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.94 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.54/22.94 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.54/22.94 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.54/22.94 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.54/22.94 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.54/22.94 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.54/22.94 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.54/22.94 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.54/22.94 e0) % 153.54/22.94 (57) ~ (all_52_4 = all_52_8) % 153.54/22.94 (58) all_56_9 = all_52_12 % 153.54/22.94 (59) all_58_29 = all_8_2 % 153.54/22.94 (60) ~ (all_52_12 = all_52_14) % 153.54/22.94 (61) all_58_8 = all_52_1 % 153.54/22.94 (62) ~ (e2 = e1) % 153.54/22.94 (63) all_56_6 = all_52_2 % 153.54/22.94 (64) ~ (all_52_2 = all_52_6) % 153.54/22.94 (65) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 153.54/22.94 (66) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.54/22.94 (67) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.54/22.94 (68) ~ (all_52_4 = e0) % 153.54/22.94 (69) ~ (all_52_11 = all_6_2) % 153.54/22.94 (70) ~ (e3 = e0) % 153.54/22.94 (71) all_56_2 = all_52_1 % 153.54/22.94 (72) ~ (all_52_11 = e0) % 153.54/22.94 (73) all_58_22 = all_10_1 % 153.54/22.94 (74) all_56_10 = all_52_13 % 153.54/22.94 (75) all_56_5 = e0 % 153.54/22.94 (76) all_56_14 = all_52_11 % 153.54/22.94 (77) all_58_28 = all_10_2 % 153.54/22.94 (78) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.54/22.94 (79) all_58_17 = all_52_6 % 153.54/22.94 (80) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.54/22.94 (81) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.54/22.94 (82) ~ (e2 = e0) % 153.54/22.94 (83) all_56_0 = all_10_2 % 153.54/22.94 (84) ~ (all_52_1 = e0) % 153.54/22.94 (85) all_56_8 = all_6_2 % 153.54/22.94 (86) ~ (all_10_1 = e1) % 153.54/22.94 (87) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.54/22.94 (88) ~ (all_52_1 = all_52_2) % 153.54/22.94 (89) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.54/22.94 (90) all_58_4 = all_52_8 % 153.54/22.94 (91) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.54/22.94 (92) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 153.54/22.94 (93) ~ (e1 = e0) % 153.54/22.94 (94) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 153.54/22.94 (95) ~ (all_52_8 = e0) % 153.54/22.94 (96) all_58_30 = all_6_2 % 153.54/22.94 (97) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.54/22.94 (98) all_56_11 = e0 % 153.54/22.94 (99) ~ (e3 = e2) % 153.54/22.94 (100) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.54/22.94 (101) all_56_15 = e1 % 153.54/22.94 (102) ~ (all_52_4 = all_52_12) % 153.54/22.94 (103) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.54/22.94 (104) ~ (all_52_2 = all_10_1) % 153.54/22.94 % 153.54/22.94 Begin of proof % 153.54/22.94 | % 153.54/22.94 | BETA: splitting (41) gives: % 153.54/22.94 | % 153.54/22.94 | Case 1: % 153.54/22.94 | | % 153.54/22.94 | | (105) all_56_2 = e1 % 153.54/22.94 | | % 153.54/22.94 | | COMBINE_EQS: (71), (105) imply: % 153.54/22.94 | | (106) all_52_1 = e1 % 153.54/22.94 | | % 153.54/22.94 | | COMBINE_EQS: (61), (106) imply: % 153.54/22.94 | | (107) all_58_8 = e1 % 153.54/22.94 | | % 153.54/22.94 | | REDUCE: (88), (106) imply: % 153.54/22.94 | | (108) ~ (all_52_2 = e1) % 153.54/22.94 | | % 153.54/22.94 | | SIMP: (108) implies: % 153.54/22.94 | | (109) ~ (all_52_2 = e1) % 153.54/22.94 | | % 153.54/22.94 | | REDUCE: (49), (106) imply: % 153.54/22.94 | | (110) ~ (all_10_1 = e1) % 153.54/22.94 | | % 153.54/22.94 | | REDUCE: (51), (106) imply: % 153.54/22.94 | | (111) ~ (all_8_2 = e1) % 153.54/22.94 | | % 153.54/22.94 | | SIMP: (111) implies: % 153.54/22.94 | | (112) ~ (all_8_2 = e1) % 153.54/22.94 | | % 153.54/22.94 | | BETA: splitting (44) gives: % 153.54/22.94 | | % 153.54/22.94 | | Case 1: % 153.54/22.94 | | | % 153.54/22.94 | | | (113) all_54_5 = e0 % 153.54/22.94 | | | % 153.54/22.94 | | | REF_CLOSE: (3), (17), (20), (22), (34), (38), (40), (43), (46), (47), % 153.54/22.94 | | | (58), (59), (60), (62), (68), (70), (77), (78), (82), (83), % 153.54/22.94 | | | (85), (91), (93), (95), (96), (97), (99), (113) are % 153.54/22.94 | | | inconsistent by sub-proof #211. % 153.54/22.94 | | | % 153.54/22.94 | | Case 2: % 153.54/22.94 | | | % 153.54/22.94 | | | (114) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 153.54/22.94 | | | % 153.54/22.94 | | | BETA: splitting (23) gives: % 153.54/22.94 | | | % 153.54/22.94 | | | Case 1: % 153.54/22.94 | | | | % 153.54/22.94 | | | | (115) all_54_8 = e0 % 153.54/22.94 | | | | % 153.54/22.94 | | | | REF_CLOSE: (4), (7), (115) are inconsistent by sub-proof #731. % 153.54/22.94 | | | | % 153.54/22.94 | | | Case 2: % 153.54/22.94 | | | | % 153.54/22.94 | | | | (116) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 153.54/22.94 | | | | % 153.54/22.94 | | | | BETA: splitting (32) gives: % 153.54/22.94 | | | | % 153.54/22.94 | | | | Case 1: % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | (117) all_56_4 = e1 % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | COMBINE_EQS: (17), (117) imply: % 153.54/22.94 | | | | | (118) all_52_8 = e1 % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | SIMP: (118) implies: % 153.54/22.94 | | | | | (119) all_52_8 = e1 % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | COMBINE_EQS: (90), (119) imply: % 153.54/22.94 | | | | | (120) all_58_4 = e1 % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | REDUCE: (57), (119) imply: % 153.54/22.94 | | | | | (121) ~ (all_52_4 = e1) % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | REDUCE: (14), (119) imply: % 153.54/22.94 | | | | | (122) ~ (all_52_11 = e1) % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | REDUCE: (36), (119) imply: % 153.54/22.94 | | | | | (123) ~ (all_52_12 = e1) % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | SIMP: (123) implies: % 153.54/22.94 | | | | | (124) ~ (all_52_12 = e1) % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | BETA: splitting (80) gives: % 153.54/22.94 | | | | | % 153.54/22.94 | | | | | Case 1: % 153.54/22.94 | | | | | | % 153.54/22.94 | | | | | | (125) all_56_6 = e1 % 153.54/22.94 | | | | | | % 153.54/22.94 | | | | | | REF_CLOSE: (63), (109), (125) are inconsistent by sub-proof #639. % 153.54/22.94 | | | | | | % 153.54/22.94 | | | | | Case 2: % 153.54/22.94 | | | | | | % 153.54/22.94 | | | | | | (126) ~ (all_56_6 = e1) % 153.54/22.94 | | | | | | (127) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.54/22.94 | | | | | | % 153.54/22.94 | | | | | | BETA: splitting (56) gives: % 153.54/22.94 | | | | | | % 153.54/22.94 | | | | | | Case 1: % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | (128) all_58_31 = e0 % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | COMBINE_EQS: (8), (128) imply: % 153.54/22.94 | | | | | | | (129) e1 = e0 % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | REDUCE: (93), (129) imply: % 153.54/22.94 | | | | | | | (130) $false % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | CLOSE: (130) is inconsistent. % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | Case 2: % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | (131) ~ (all_58_31 = e0) % 153.54/22.94 | | | | | | | (132) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 153.54/22.94 | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 153.54/22.94 | | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 153.54/22.94 | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.54/22.94 | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.54/22.94 | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 153.54/22.94 | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.54/22.94 | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 153.54/22.94 | | | | | | | all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 153.54/22.94 | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.54/22.94 | | | | | | | e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 153.54/22.94 | | | | | | | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 153.54/22.94 | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.54/22.94 | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 153.54/22.94 | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 153.54/22.94 | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 153.54/22.94 | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.54/22.94 | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 % 153.54/22.94 | | | | | | | = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = % 153.54/22.94 | | | | | | | e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 153.54/22.94 | | | | | | | & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & % 153.54/22.94 | | | | | | | all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 153.54/22.94 | | | | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.54/22.94 | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 % 153.54/22.94 | | | | | | | = e0) | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = % 153.54/22.94 | | | | | | | e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 % 153.54/22.94 | | | | | | | & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 153.54/22.94 | | | | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.54/22.94 | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 153.54/22.94 | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 % 153.54/22.94 | | | | | | | = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = % 153.54/22.94 | | | | | | | e2 & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 % 153.54/22.94 | | | | | | | & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.54/22.94 | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 % 153.54/22.94 | | | | | | | = e0 & e1 = e0) % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | BETA: splitting (132) gives: % 153.54/22.94 | | | | | | | % 153.54/22.94 | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | % 153.54/22.94 | | | | | | | | (133) all_58_30 = e1 % 153.54/22.94 | | | | | | | | % 153.54/22.94 | | | | | | | | REF_CLOSE: (2), (8), (20), (38), (59), (62), (70), (82), (91), % 153.54/22.94 | | | | | | | | (99), (133) are inconsistent by sub-proof #497. % 153.54/22.94 | | | | | | | | % 153.54/22.94 | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | % 153.54/22.94 | | | | | | | | (134) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 153.54/22.94 | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.54/22.94 | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 153.54/22.94 | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.54/22.94 | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.54/22.94 | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 153.54/22.94 | | | | | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.54/22.94 | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.54/22.94 | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 % 153.54/22.94 | | | | | | | | = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = % 153.54/22.94 | | | | | | | | e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.54/22.94 | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 153.54/22.94 | | | | | | | | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 153.54/22.94 | | | | | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 % 153.54/22.94 | | | | | | | | & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.54/22.94 | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 153.54/22.94 | | | | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.54/22.94 | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 % 153.54/22.94 | | | | | | | | = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 153.54/22.94 | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = % 153.54/22.94 | | | | | | | | e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 153.54/22.94 | | | | | | | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.54/22.94 | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = % 153.54/22.94 | | | | | | | | e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.94 | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 153.54/22.94 | | | | | | | | all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 & % 153.54/22.94 | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 153.54/22.94 | | | | | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.54/22.94 | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 153.54/22.94 | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & % 153.54/22.94 | | | | | | | | e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.54/22.94 | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.54/22.94 | | | | | | | | all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.54/22.94 | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.54/22.94 | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.54/22.94 | | | | | | | | % 153.54/22.94 | | | | | | | | BETA: splitting (134) gives: % 153.54/22.94 | | | | | | | | % 153.54/22.94 | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | | (135) all_58_29 = e2 % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | | COMBINE_EQS: (59), (135) imply: % 153.54/22.94 | | | | | | | | | (136) all_8_2 = e2 % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (8), (13), (26), (27), (35), % 153.54/22.94 | | | | | | | | | (38), (39), (50), (63), (70), (72), (81), (91), % 153.54/22.94 | | | | | | | | | (96), (99), (100), (103), (104), (109), (116), % 153.54/22.94 | | | | | | | | | (135) are inconsistent by sub-proof #208. % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | | (137) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 153.54/22.94 | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 153.54/22.94 | | | | | | | | | all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.54/22.94 | | | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 153.54/22.94 | | | | | | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | | | all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.54/22.94 | | | | | | | | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.54/22.94 | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 153.54/22.94 | | | | | | | | | all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.54/22.94 | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 % 153.54/22.94 | | | | | | | | | = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = % 153.54/22.94 | | | | | | | | | e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = % 153.54/22.94 | | | | | | | | | e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.54/22.94 | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.54/22.94 | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 153.54/22.94 | | | | | | | | | e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = % 153.54/22.94 | | | | | | | | | e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 153.54/22.94 | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 153.54/22.94 | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 153.54/22.94 | | | | | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 153.54/22.94 | | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.54/22.94 | | | | | | | | | all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.54/22.94 | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 153.54/22.94 | | | | | | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.54/22.94 | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.94 | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 153.54/22.94 | | | | | | | | | all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 % 153.54/22.94 | | | | | | | | | & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 153.54/22.94 | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = % 153.54/22.94 | | | | | | | | | e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 % 153.54/22.94 | | | | | | | | | = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 153.54/22.94 | | | | | | | | | all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.54/22.94 | | | | | | | | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 153.54/22.94 | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 153.54/22.94 | | | | | | | | | all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 % 153.54/22.94 | | | | | | | | | & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 % 153.54/22.94 | | | | | | | | | = e0) % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | | BETA: splitting (20) gives: % 153.54/22.94 | | | | | | | | | % 153.54/22.94 | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | (138) all_58_28 = e2 % 153.54/22.94 | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | REF_CLOSE: (2), (82), (138) are inconsistent by sub-proof % 153.54/22.94 | | | | | | | | | | #688. % 153.54/22.94 | | | | | | | | | | % 153.54/22.94 | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | (139) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.54/22.94 | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | BETA: splitting (139) gives: % 153.54/22.94 | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | (140) all_58_29 = e2 % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (8), (13), (26), (27), (35), % 153.54/22.94 | | | | | | | | | | | (38), (39), (50), (63), (70), (72), (81), (91), % 153.54/22.94 | | | | | | | | | | | (96), (99), (100), (103), (104), (109), (116), % 153.54/22.94 | | | | | | | | | | | (140) are inconsistent by sub-proof #208. % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | (141) ~ (all_58_29 = e2) % 153.54/22.94 | | | | | | | | | | | (142) all_58_30 = e2 | all_58_31 = e2 % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | REDUCE: (59), (141) imply: % 153.54/22.94 | | | | | | | | | | | (143) ~ (all_8_2 = e2) % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | BETA: splitting (142) gives: % 153.54/22.94 | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | (144) all_58_30 = e2 % 153.54/22.94 | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | COMBINE_EQS: (96), (144) imply: % 153.54/22.94 | | | | | | | | | | | | (145) all_6_2 = e2 % 153.54/22.94 | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | BETA: splitting (127) gives: % 153.54/22.94 | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | (146) all_56_7 = e1 % 153.54/22.94 | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | COMBINE_EQS: (3), (146) imply: % 153.54/22.94 | | | | | | | | | | | | | (147) all_52_6 = e1 % 153.54/22.94 | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | SIMP: (147) implies: % 153.54/22.94 | | | | | | | | | | | | | (148) all_52_6 = e1 % 153.54/22.94 | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | COMBINE_EQS: (79), (148) imply: % 153.54/22.94 | | | | | | | | | | | | | (149) all_58_17 = e1 % 153.54/22.94 | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | BETA: splitting (87) gives: % 153.54/22.94 | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | (150) all_56_1 = e2 % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | COMBINE_EQS: (47), (150) imply: % 153.54/22.94 | | | | | | | | | | | | | | (151) all_52_4 = e2 % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | COMBINE_EQS: (45), (151) imply: % 153.54/22.94 | | | | | | | | | | | | | | (152) all_58_2 = e2 % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | REDUCE: (102), (151) imply: % 153.54/22.94 | | | | | | | | | | | | | | (153) ~ (all_52_12 = e2) % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | SIMP: (153) implies: % 153.54/22.94 | | | | | | | | | | | | | | (154) ~ (all_52_12 = e2) % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | BETA: splitting (10) gives: % 153.54/22.94 | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | (155) all_56_9 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | REF_CLOSE: (58), (154), (155) are inconsistent by sub-proof % 153.54/22.94 | | | | | | | | | | | | | | | #431. % 153.54/22.94 | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | (156) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 153.54/22.94 | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | (157) all_54_14 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (54), (157) are inconsistent by sub-proof % 153.54/22.94 | | | | | | | | | | | | | | | | #207. % 153.54/22.94 | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | (158) ~ (all_54_14 = e1) % 153.54/22.94 | | | | | | | | | | | | | | | | (159) all_54_14 = e3 | all_54_14 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | BETA: splitting (91) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | (160) all_58_28 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (70), (160) are inconsistent by sub-proof % 153.54/22.94 | | | | | | | | | | | | | | | | | #689. % 153.54/22.94 | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | (161) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | (162) all_56_10 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (162) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | (163) all_52_13 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | SIMP: (163) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | (164) all_52_13 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (164) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | (165) all_58_13 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | REDUCE: (37), (164) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | (166) ~ (all_8_2 = e2) % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | (167) all_56_9 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (167) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | (168) all_52_12 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | SIMP: (168) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | (169) all_52_12 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (169) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | (170) all_58_6 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | (171) all_56_12 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (171) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | (172) all_10_1 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | SIMP: (172) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | (173) all_10_1 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (173) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | (174) all_58_22 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (173) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | (175) ~ (all_52_2 = e2) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (173) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | (176) ~ (all_52_11 = e2) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | (177) all_56_2 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (105), (177) are inconsistent by sub-proof % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | #206. % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | (178) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | (179) all_56_6 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (179) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | (180) all_52_2 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | SIMP: (180) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | (181) all_52_2 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (181) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | (182) all_58_15 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | (183) all_56_3 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (183) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | (184) all_8_2 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (184) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | (185) all_58_29 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | (186) all_54_14 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (176), (186) are inconsistent by sub-proof % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | #360. % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | (187) all_54_14 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (187) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | (188) all_52_11 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | (189) all_52_11 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (189) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | (190) all_58_26 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_28 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (191) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (192) e3 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (192) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_29 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (161), (193) are inconsistent by sub-proof #385. % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_58_28 = e3) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (195) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (194) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | (196) ~ (e3 = e0) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (197) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_58_15 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_2 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (202) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) e3 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (203) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) e3 = e2 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (201) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) e3 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) e3 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (206) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) e2 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (207) imply: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_58_30 = e1 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (142), (208) are inconsistent by % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_22 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_8 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_2 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (213) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (212) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (211) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (215), (216), (217) are inconsistent % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #204. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_11 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_8 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_2 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (221) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (220) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (219) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (225) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (224) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (227) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (224), (226), (228) are inconsistent % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #203. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_8 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_2 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (234) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (233) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (232) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (236), (237), (238) are inconsistent % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #204. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (240) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (241) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_30 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (142), (242) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (245) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (246) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_58_30 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (142), (247) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_58_11 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (250) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (62), (82), (142), (144), (249), (251) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_13 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (257) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (256) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (259) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (260) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) e1 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (260) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_30 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (82), (142), (262) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_58_8 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (264) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (265) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_58_30 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (142), (266) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_6 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_4 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (270) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (269) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (272) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) e1 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (272) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (274) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_11 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_4 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (277) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (276) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) e1 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (278), (279) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #205. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_20 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (29), (38), (62), (70), (82), (96), (99), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (161), (185), (190), (283), (284) are % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #201. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_58_22 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_15 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (287) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (286) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (290) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (291) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_58_30 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (142), (292) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_15 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_11 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (297) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (296) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (295) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (299), (301), (302) are inconsistent % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #203. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (304) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (305) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (306) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (307) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_15 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (182), (311) are inconsistent by sub-proof % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #629. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_22 = e3 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_13 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (315) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (316) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (314) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) e3 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (318) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (319) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (320) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (190), (322) are inconsistent by % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #200. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_6 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (326) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (327) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (328) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_6 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (330) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (331) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (332) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_58_6 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (335) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (336) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (337) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_58_13 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (82), (142), (144), (165), (339) are % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #437. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (343) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_58_17 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_11 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (346) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (347) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) e2 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (345) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (344) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) e3 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (348), (349), (350) are inconsistent % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #203. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (351) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (48), (62), (82), (142), (144), (352) are % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (355) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (356) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (357) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (358) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) e2 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_58_11 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (62), (82), (142), (144), (359), (360) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (363) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_26 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (364) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) e3 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (365) imply: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_29 = e0 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (366) are inconsistent by sub-proof #385. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_58_26 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_20 = e1 % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (29), (38), (62), (70), (82), (96), (99), % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (161), (185), (190), (368), (369) are % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #201. % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_58_13 = e0 % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (82), (142), (144), (165), (372) are % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #437. % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_26 = e0 % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (38), (62), (70), (82), (96), (99), (139), % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (185), (190), (374) are inconsistent by % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #200. % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_56_3 = e3) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (375) imply: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | (376) ~ (all_8_2 = e3) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (112), (114), (143), (376) are inconsistent % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #531. % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | (377) ~ (all_56_6 = e3) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (377) imply: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | (378) ~ (all_52_2 = e3) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (109), (116), (175), (378) are inconsistent % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #416. % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | (379) ~ (all_56_12 = e2) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (379) imply: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | (380) ~ (all_10_1 = e2) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (13), (26), (27), (39), (50), (72), % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | (81), (103), (380) are inconsistent by sub-proof % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | #235. % 153.54/22.96 | | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | (381) ~ (all_56_9 = e3) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | REDUCE: (58), (381) imply: % 153.54/22.96 | | | | | | | | | | | | | | | | | | | (382) ~ (all_52_12 = e3) % 153.54/22.96 | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (53), (124), (154), (382) are inconsistent % 153.54/22.96 | | | | | | | | | | | | | | | | | | | by sub-proof #612. % 153.54/22.96 | | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | (383) all_56_11 = e2 | all_56_15 = e2 % 153.54/22.96 | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (82), (98), (101), (383) are inconsistent by % 153.54/22.96 | | | | | | | | | | | | | | | | | | sub-proof #423. % 153.54/22.96 | | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | End of split % 153.54/22.96 | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | Case 2: % 153.54/22.96 | | | | | | | | | | | | | | % 153.54/22.96 | | | | | | | | | | | | | | (384) ~ (all_56_1 = e2) % 153.54/22.96 | | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (30), (34), (47), (112), (114), (121), % 153.63/22.96 | | | | | | | | | | | | | | (143), (384) are inconsistent by sub-proof #198. % 153.63/22.96 | | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | | End of split % 153.63/22.96 | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | Case 2: % 153.63/22.96 | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | | (385) ~ (all_56_7 = e1) % 153.63/22.96 | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | | REDUCE: (3), (385) imply: % 153.63/22.96 | | | | | | | | | | | | | (386) ~ (all_52_6 = e1) % 153.63/22.96 | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | | REF_CLOSE: (3), (33), (47), (52), (66), (93), (112), (121), % 153.63/22.96 | | | | | | | | | | | | | (386) are inconsistent by sub-proof #197. % 153.63/22.96 | | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | End of split % 153.63/22.96 | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | Case 2: % 153.63/22.96 | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | (387) all_58_31 = e2 % 153.63/22.96 | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | | REF_CLOSE: (8), (62), (387) are inconsistent by sub-proof % 153.63/22.96 | | | | | | | | | | | | #697. % 153.63/22.96 | | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | | End of split % 153.63/22.96 | | | | | | | | | | | % 153.63/22.96 | | | | | | | | | | End of split % 153.63/22.96 | | | | | | | | | | % 153.63/22.96 | | | | | | | | | End of split % 153.63/22.96 | | | | | | | | | % 153.63/22.96 | | | | | | | | End of split % 153.63/22.96 | | | | | | | | % 153.63/22.96 | | | | | | | End of split % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | End of split % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | End of split % 153.63/22.96 | | | | | % 153.63/22.96 | | | | Case 2: % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | (388) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | REF_CLOSE: (2), (8), (20), (38), (54), (59), (62), (70), (75), (76), % 153.63/22.96 | | | | | (82), (85), (91), (93), (96), (99), (388) are inconsistent % 153.63/22.96 | | | | | by sub-proof #402. % 153.63/22.96 | | | | | % 153.63/22.96 | | | | End of split % 153.63/22.96 | | | | % 153.63/22.96 | | | End of split % 153.63/22.96 | | | % 153.63/22.96 | | End of split % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (389) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.63/22.96 | | % 153.63/22.96 | | BETA: splitting (389) gives: % 153.63/22.96 | | % 153.63/22.96 | | Case 1: % 153.63/22.96 | | | % 153.63/22.96 | | | (390) all_56_3 = e1 % 153.63/22.96 | | | % 153.63/22.96 | | | COMBINE_EQS: (52), (390) imply: % 153.63/22.96 | | | (391) all_8_2 = e1 % 153.63/22.96 | | | % 153.63/22.96 | | | COMBINE_EQS: (59), (391) imply: % 153.63/22.96 | | | (392) all_58_29 = e1 % 153.63/22.96 | | | % 153.63/22.96 | | | BETA: splitting (91) gives: % 153.63/22.96 | | | % 153.63/22.96 | | | Case 1: % 153.63/22.96 | | | | % 153.63/22.96 | | | | (393) all_58_28 = e3 % 153.63/22.96 | | | | % 153.63/22.96 | | | | REF_CLOSE: (2), (70), (393) are inconsistent by sub-proof #689. % 153.63/22.96 | | | | % 153.63/22.96 | | | Case 2: % 153.63/22.96 | | | | % 153.63/22.96 | | | | (394) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 | | | | % 153.63/22.96 | | | | BETA: splitting (394) gives: % 153.63/22.96 | | | | % 153.63/22.96 | | | | Case 1: % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | (395) all_58_29 = e3 % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | REF_CLOSE: (38), (392), (395) are inconsistent by sub-proof #686. % 153.63/22.96 | | | | | % 153.63/22.96 | | | | Case 2: % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | (396) ~ (all_58_29 = e3) % 153.63/22.96 | | | | | (397) all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | REDUCE: (392), (396) imply: % 153.63/22.96 | | | | | (398) ~ (e3 = e1) % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | BETA: splitting (397) gives: % 153.63/22.96 | | | | | % 153.63/22.96 | | | | | Case 1: % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | (399) all_58_30 = e3 % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | COMBINE_EQS: (96), (399) imply: % 153.63/22.96 | | | | | | (400) all_6_2 = e3 % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | REDUCE: (69), (400) imply: % 153.63/22.96 | | | | | | (401) ~ (all_52_11 = e3) % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | BETA: splitting (55) gives: % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | Case 1: % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | | (402) all_56_12 = e3 % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | | REF_CLOSE: (1), (5), (13), (27), (50), (402) are inconsistent by % 153.63/22.96 | | | | | | | sub-proof #196. % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | Case 2: % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | | (403) ~ (all_56_12 = e3) % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | | REF_CLOSE: (9), (27), (39), (42), (54), (65), (86), (103), (401), % 153.63/22.96 | | | | | | | (403) are inconsistent by sub-proof #195. % 153.63/22.96 | | | | | | | % 153.63/22.96 | | | | | | End of split % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | Case 2: % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | (404) all_58_31 = e3 % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | | REF_CLOSE: (8), (38), (404) are inconsistent by sub-proof #656. % 153.63/22.96 | | | | | | % 153.63/22.96 | | | | | End of split % 153.63/22.96 | | | | | % 153.63/22.96 | | | | End of split % 153.63/22.96 | | | | % 153.63/22.96 | | | End of split % 153.63/22.96 | | | % 153.63/22.96 | | Case 2: % 153.63/22.96 | | | % 153.63/22.96 | | | (405) all_56_5 = e1 | all_56_10 = e1 % 153.63/22.96 | | | % 153.63/22.96 | | | REF_CLOSE: (6), (74), (75), (93), (405) are inconsistent by sub-proof % 153.63/22.96 | | | #194. % 153.63/22.96 | | | % 153.63/22.96 | | End of split % 153.63/22.96 | | % 153.63/22.96 | End of split % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #194 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) ~ (all_52_13 = e1) % 153.63/22.96 (2) all_56_5 = e1 | all_56_10 = e1 % 153.63/22.96 (3) all_56_10 = all_52_13 % 153.63/22.96 (4) all_56_5 = e0 % 153.63/22.96 (5) ~ (e1 = e0) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | BETA: splitting (2) gives: % 153.63/22.96 | % 153.63/22.96 | Case 1: % 153.63/22.96 | | % 153.63/22.96 | | (6) all_56_5 = e1 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #305. % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (7) all_56_10 = e1 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #606. % 153.63/22.96 | | % 153.63/22.96 | End of split % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #195 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) ~ (all_52_11 = all_10_1) % 153.63/22.96 (2) all_56_12 = all_10_1 % 153.63/22.96 (3) all_54_12 = all_10_1 % 153.63/22.96 (4) all_54_14 = all_52_11 % 153.63/22.96 (5) ~ (all_52_11 = e1) % 153.63/22.96 (6) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 153.63/22.96 (7) ~ (all_56_12 = e3) % 153.63/22.96 (8) ~ (all_10_1 = e1) % 153.63/22.96 (9) ~ (all_52_11 = e3) % 153.63/22.96 (10) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | REDUCE: (2), (7) imply: % 153.63/22.96 | (11) ~ (all_10_1 = e3) % 153.63/22.96 | % 153.63/22.96 | BETA: splitting (6) gives: % 153.63/22.96 | % 153.63/22.96 | Case 1: % 153.63/22.96 | | % 153.63/22.96 | | (12) all_54_14 = e1 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #207. % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (13) all_54_14 = e3 | all_54_14 = e2 % 153.63/22.96 | | % 153.63/22.96 | | BETA: splitting (13) gives: % 153.63/22.96 | | % 153.63/22.96 | | Case 1: % 153.63/22.96 | | | % 153.63/22.96 | | | (14) all_54_14 = e2 % 153.63/22.96 | | | % 153.63/22.96 | | | COMBINE_EQS: (4), (14) imply: % 153.63/22.96 | | | (15) all_52_11 = e2 % 153.63/22.96 | | | % 153.63/22.96 | | | SIMP: (15) implies: % 153.63/22.96 | | | (16) all_52_11 = e2 % 153.63/22.96 | | | % 153.63/22.96 | | | REDUCE: (1), (16) imply: % 153.63/22.96 | | | (17) ~ (all_10_1 = e2) % 153.63/22.96 | | | % 153.63/22.96 | | | SIMP: (17) implies: % 153.63/22.96 | | | (18) ~ (all_10_1 = e2) % 153.63/22.96 | | | % 153.63/22.96 | | | REF_CLOSE: (3), (8), (10), (11), (18) are inconsistent by sub-proof #505. % 153.63/22.96 | | | % 153.63/22.96 | | Case 2: % 153.63/22.96 | | | % 153.63/22.96 | | | (19) all_54_14 = e3 % 153.63/22.96 | | | % 153.63/22.96 | | | REF_CLOSE: (4), (9), (19) are inconsistent by sub-proof #359. % 153.63/22.96 | | | % 153.63/22.96 | | End of split % 153.63/22.96 | | % 153.63/22.96 | End of split % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #196 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.96 (2) ~ (all_10_1 = e0) % 153.63/22.96 (3) op(e0, all_10_1) = e0 % 153.63/22.96 (4) all_56_12 = all_10_1 % 153.63/22.96 (5) op(e0, e3) = all_10_1 % 153.63/22.96 (6) all_56_12 = e3 % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (4), (6) imply: % 153.63/22.96 | (7) all_10_1 = e3 % 153.63/22.96 | % 153.63/22.96 | SIMP: (7) implies: % 153.63/22.96 | (8) all_10_1 = e3 % 153.63/22.96 | % 153.63/22.96 | REDUCE: (2), (8) imply: % 153.63/22.96 | (9) ~ (e3 = e0) % 153.63/22.96 | % 153.63/22.96 | REDUCE: (3), (8) imply: % 153.63/22.96 | (10) op(e0, e3) = e0 % 153.63/22.96 | % 153.63/22.96 | REDUCE: (5), (8) imply: % 153.63/22.96 | (11) op(e0, e3) = e3 % 153.63/22.96 | % 153.63/22.96 | GROUND_INST: instantiating (1) with e0, e3, e3, e0, simplifying with (10), % 153.63/22.96 | (11) gives: % 153.63/22.96 | (12) e3 = e0 % 153.63/22.96 | % 153.63/22.96 | REDUCE: (9), (12) imply: % 153.63/22.96 | (13) $false % 153.63/22.96 | % 153.63/22.96 | CLOSE: (13) is inconsistent. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #197 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_56_7 = all_52_6 % 153.63/22.96 (2) ~ (all_52_6 = e1) % 153.63/22.96 (3) all_56_13 = e0 % 153.63/22.96 (4) all_56_1 = all_52_4 % 153.63/22.96 (5) all_56_3 = all_8_2 % 153.63/22.96 (6) ~ (all_52_4 = e1) % 153.63/22.96 (7) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/22.96 (8) ~ (e1 = e0) % 153.63/22.96 (9) ~ (all_8_2 = e1) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | BETA: splitting (7) gives: % 153.63/22.96 | % 153.63/22.96 | Case 1: % 153.63/22.96 | | % 153.63/22.96 | | (10) all_56_1 = e1 % 153.63/22.96 | | % 153.63/22.96 | | COMBINE_EQS: (4), (10) imply: % 153.63/22.96 | | (11) all_52_4 = e1 % 153.63/22.96 | | % 153.63/22.96 | | REDUCE: (6), (11) imply: % 153.63/22.96 | | (12) $false % 153.63/22.96 | | % 153.63/22.96 | | CLOSE: (12) is inconsistent. % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (13) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (13) are inconsistent by sub-proof % 153.63/22.96 | | #528. % 153.63/22.96 | | % 153.63/22.96 | End of split % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #198 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) ~ (all_52_4 = all_8_2) % 153.63/22.96 (2) all_54_1 = all_52_4 % 153.63/22.96 (3) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 153.63/22.96 (4) all_54_5 = all_8_2 % 153.63/22.96 (5) ~ (all_8_2 = e2) % 153.63/22.96 (6) all_56_1 = all_52_4 % 153.63/22.96 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 153.63/22.96 (8) ~ (all_52_4 = e1) % 153.63/22.96 (9) ~ (all_56_1 = e2) % 153.63/22.96 (10) ~ (all_8_2 = e1) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | REDUCE: (6), (9) imply: % 153.63/22.96 | (11) ~ (all_52_4 = e2) % 153.63/22.96 | % 153.63/22.96 | BETA: splitting (3) gives: % 153.63/22.96 | % 153.63/22.96 | Case 1: % 153.63/22.96 | | % 153.63/22.96 | | (12) all_54_1 = e1 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #741. % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (13) all_54_1 = e3 | all_54_1 = e2 % 153.63/22.96 | | % 153.63/22.96 | | BETA: splitting (13) gives: % 153.63/22.96 | | % 153.63/22.96 | | Case 1: % 153.63/22.96 | | | % 153.63/22.96 | | | (14) all_54_1 = e2 % 153.63/22.96 | | | % 153.63/22.96 | | | REF_CLOSE: (2), (11), (14) are inconsistent by sub-proof #740. % 153.63/22.96 | | | % 153.63/22.96 | | Case 2: % 153.63/22.96 | | | % 153.63/22.96 | | | (15) all_54_1 = e3 % 153.63/22.96 | | | % 153.63/22.96 | | | COMBINE_EQS: (2), (15) imply: % 153.63/22.96 | | | (16) all_52_4 = e3 % 153.63/22.96 | | | % 153.63/22.96 | | | SIMP: (16) implies: % 153.63/22.96 | | | (17) all_52_4 = e3 % 153.63/22.96 | | | % 153.63/22.96 | | | REDUCE: (1), (17) imply: % 153.63/22.96 | | | (18) ~ (all_8_2 = e3) % 153.63/22.96 | | | % 153.63/22.96 | | | SIMP: (18) implies: % 153.63/22.96 | | | (19) ~ (all_8_2 = e3) % 153.63/22.96 | | | % 153.63/22.96 | | | REF_CLOSE: (4), (5), (7), (10), (19) are inconsistent by sub-proof #531. % 153.63/22.96 | | | % 153.63/22.96 | | End of split % 153.63/22.96 | | % 153.63/22.96 | End of split % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #199 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_58_31 = e1 % 153.63/22.96 (2) all_58_30 = e2 % 153.63/22.96 (3) all_58_24 = e0 % 153.63/22.96 (4) ~ (e2 = e1) % 153.63/22.96 (5) all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (6) ~ (e2 = e0) % 153.63/22.96 (7) all_58_24 = e2 % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (3), (7) imply: % 153.63/22.96 | (8) e2 = e0 % 153.63/22.96 | % 153.63/22.96 | SIMP: (8) implies: % 153.63/22.96 | (9) e2 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (2), (9) imply: % 153.63/22.96 | (10) all_58_30 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (1), (4), (5), (6), (10) are inconsistent by sub-proof #675. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #200 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_58_31 = e1 % 153.63/22.96 (2) ~ (e3 = e1) % 153.63/22.96 (3) all_58_26 = e3 % 153.63/22.96 (4) all_58_29 = e3 % 153.63/22.96 (5) ~ (e2 = e1) % 153.63/22.96 (6) all_58_26 = e0 % 153.63/22.96 (7) ~ (e3 = e0) % 153.63/22.96 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 (9) ~ (e2 = e0) % 153.63/22.96 (10) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (11) all_58_30 = all_6_2 % 153.63/22.96 (12) ~ (e3 = e2) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (3), (6) imply: % 153.63/22.96 | (13) e3 = e0 % 153.63/22.96 | % 153.63/22.96 | SIMP: (13) implies: % 153.63/22.96 | (14) e3 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (4), (14) imply: % 153.63/22.96 | (15) all_58_29 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (12), (15) are % 153.63/22.96 | inconsistent by sub-proof #385. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #201 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_58_31 = e1 % 153.63/22.96 (2) all_58_20 = e0 % 153.63/22.96 (3) ~ (e3 = e1) % 153.63/22.96 (4) all_58_26 = e1 % 153.63/22.96 (5) all_58_26 = e3 % 153.63/22.96 (6) all_58_29 = e3 % 153.63/22.96 (7) ~ (e2 = e1) % 153.63/22.96 (8) ~ (e3 = e0) % 153.63/22.96 (9) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 (10) ~ (e2 = e0) % 153.63/22.96 (11) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (12) all_58_20 = e1 % 153.63/22.96 (13) all_58_30 = all_6_2 % 153.63/22.96 (14) ~ (e3 = e2) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (2), (12) imply: % 153.63/22.96 | (15) e1 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (4), (5) imply: % 153.63/22.96 | (16) e3 = e1 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (15), (16) imply: % 153.63/22.96 | (17) e3 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (6), (17) imply: % 153.63/22.96 | (18) all_58_29 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (1), (3), (7), (8), (9), (10), (11), (13), (14), (18) are % 153.63/22.96 | inconsistent by sub-proof #385. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #202 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_58_31 = e1 % 153.63/22.96 (2) all_58_11 = e0 % 153.63/22.96 (3) all_58_30 = e2 % 153.63/22.96 (4) all_58_11 = e1 % 153.63/22.96 (5) ~ (e2 = e1) % 153.63/22.96 (6) e2 = e1 % 153.63/22.96 (7) all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (8) ~ (e2 = e0) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (2), (4) imply: % 153.63/22.96 | (9) e1 = e0 % 153.63/22.96 | % 153.63/22.96 | SIMP: (9) implies: % 153.63/22.96 | (10) e1 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (6), (10) imply: % 153.63/22.96 | (11) e2 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (3), (11) imply: % 153.63/22.96 | (12) all_58_30 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (1), (5), (7), (8), (12) are inconsistent by sub-proof #675. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #203 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_58_31 = e1 % 153.63/22.96 (2) ~ (e3 = e1) % 153.63/22.96 (3) e3 = e1 % 153.63/22.96 (4) all_58_29 = e3 % 153.63/22.96 (5) ~ (e2 = e1) % 153.63/22.96 (6) e2 = e1 % 153.63/22.96 (7) ~ (e3 = e0) % 153.63/22.96 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 (9) ~ (e2 = e0) % 153.63/22.96 (10) e2 = e0 % 153.63/22.96 (11) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (12) all_58_30 = all_6_2 % 153.63/22.96 (13) ~ (e3 = e2) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (6), (10) imply: % 153.63/22.96 | (14) e1 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (3), (14) imply: % 153.63/22.96 | (15) e3 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (4), (15) imply: % 153.63/22.96 | (16) all_58_29 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (1), (2), (5), (7), (8), (9), (11), (12), (13), (16) are % 153.63/22.96 | inconsistent by sub-proof #385. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #204 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) e2 = e0 % 153.63/22.96 (2) all_58_31 = e1 % 153.63/22.96 (3) ~ (e3 = e1) % 153.63/22.96 (4) e3 = e1 % 153.63/22.96 (5) all_58_29 = e3 % 153.63/22.96 (6) ~ (e2 = e1) % 153.63/22.96 (7) ~ (e3 = e0) % 153.63/22.96 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 (9) ~ (e2 = e0) % 153.63/22.96 (10) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (11) all_58_30 = all_6_2 % 153.63/22.96 (12) ~ (e3 = e2) % 153.63/22.96 (13) e3 = e2 % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | SIMP: (1) implies: % 153.63/22.96 | (14) e2 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (4), (13) imply: % 153.63/22.96 | (15) e2 = e1 % 153.63/22.96 | % 153.63/22.96 | SIMP: (15) implies: % 153.63/22.96 | (16) e2 = e1 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (14), (16) imply: % 153.63/22.96 | (17) e1 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (17) are % 153.63/22.96 | inconsistent by sub-proof #205. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #205 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_58_31 = e1 % 153.63/22.96 (2) ~ (e3 = e1) % 153.63/22.96 (3) e3 = e1 % 153.63/22.96 (4) all_58_29 = e3 % 153.63/22.96 (5) ~ (e2 = e1) % 153.63/22.96 (6) ~ (e3 = e0) % 153.63/22.96 (7) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 (8) ~ (e2 = e0) % 153.63/22.96 (9) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.96 (10) e1 = e0 % 153.63/22.96 (11) all_58_30 = all_6_2 % 153.63/22.96 (12) ~ (e3 = e2) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | SIMP: (10) implies: % 153.63/22.96 | (13) e1 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (3), (13) imply: % 153.63/22.96 | (14) e3 = e0 % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (4), (14) imply: % 153.63/22.96 | (15) all_58_29 = e0 % 153.63/22.96 | % 153.63/22.96 | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (15) are % 153.63/22.96 | inconsistent by sub-proof #385. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #206 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_56_2 = e3 % 153.63/22.96 (2) all_56_2 = e1 % 153.63/22.96 (3) ~ (e3 = e1) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (1), (2) imply: % 153.63/22.96 | (4) e3 = e1 % 153.63/22.96 | % 153.63/22.96 | SIMP: (4) implies: % 153.63/22.96 | (5) e3 = e1 % 153.63/22.96 | % 153.63/22.96 | REDUCE: (3), (5) imply: % 153.63/22.96 | (6) $false % 153.63/22.96 | % 153.63/22.96 | CLOSE: (6) is inconsistent. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #207 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) all_54_14 = all_52_11 % 153.63/22.96 (2) all_54_14 = e1 % 153.63/22.96 (3) ~ (all_52_11 = e1) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | COMBINE_EQS: (1), (2) imply: % 153.63/22.96 | (4) all_52_11 = e1 % 153.63/22.96 | % 153.63/22.96 | SIMP: (4) implies: % 153.63/22.96 | (5) all_52_11 = e1 % 153.63/22.96 | % 153.63/22.96 | REDUCE: (3), (5) imply: % 153.63/22.96 | (6) $false % 153.63/22.96 | % 153.63/22.96 | CLOSE: (6) is inconsistent. % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #208 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.96 (2) all_58_28 = e0 % 153.63/22.96 (3) ~ (all_10_1 = e0) % 153.63/22.96 (4) all_54_8 = all_52_2 % 153.63/22.96 (5) all_58_31 = e1 % 153.63/22.96 (6) op(e0, all_10_1) = e0 % 153.63/22.96 (7) op(e0, e1) = all_52_11 % 153.63/22.96 (8) all_56_12 = all_10_1 % 153.63/22.96 (9) ~ (all_52_2 = all_6_2) % 153.63/22.96 (10) ~ (e3 = e1) % 153.63/22.96 (11) all_54_12 = all_10_1 % 153.63/22.96 (12) ~ (all_52_2 = e1) % 153.63/22.96 (13) op(e0, e3) = all_10_1 % 153.63/22.96 (14) all_56_6 = all_52_2 % 153.63/22.96 (15) ~ (e3 = e0) % 153.63/22.96 (16) ~ (all_52_11 = e0) % 153.63/22.96 (17) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.96 (18) all_58_29 = e2 % 153.63/22.96 (19) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 153.63/22.96 (20) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 (21) all_58_30 = all_6_2 % 153.63/22.96 (22) ~ (e3 = e2) % 153.63/22.96 (23) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.63/22.96 (24) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/22.96 (25) ~ (all_52_2 = all_10_1) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | BETA: splitting (20) gives: % 153.63/22.96 | % 153.63/22.96 | Case 1: % 153.63/22.96 | | % 153.63/22.96 | | (26) all_58_28 = e3 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (2), (15), (26) are inconsistent by sub-proof #689. % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (27) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 | | % 153.63/22.96 | | BETA: splitting (27) gives: % 153.63/22.96 | | % 153.63/22.96 | | Case 1: % 153.63/22.96 | | | % 153.63/22.96 | | | (28) all_58_29 = e3 % 153.63/22.96 | | | % 153.63/22.96 | | | REF_CLOSE: (18), (22), (28) are inconsistent by sub-proof #780. % 153.63/22.96 | | | % 153.63/22.96 | | Case 2: % 153.63/22.96 | | | % 153.63/22.96 | | | (29) all_58_30 = e3 | all_58_31 = e3 % 153.63/22.96 | | | % 153.63/22.96 | | | BETA: splitting (29) gives: % 153.63/22.96 | | | % 153.63/22.96 | | | Case 1: % 153.63/22.96 | | | | % 153.63/22.96 | | | | (30) all_58_30 = e3 % 153.63/22.96 | | | | % 153.63/22.96 | | | | COMBINE_EQS: (21), (30) imply: % 153.63/22.96 | | | | (31) all_6_2 = e3 % 153.63/22.96 | | | | % 153.63/22.96 | | | | REDUCE: (9), (31) imply: % 153.63/22.96 | | | | (32) ~ (all_52_2 = e3) % 153.63/22.96 | | | | % 153.63/22.96 | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (11), (12), (13), (14), (16), % 153.63/22.96 | | | | (17), (19), (23), (24), (25), (32) are inconsistent by % 153.63/22.96 | | | | sub-proof #209. % 153.63/22.96 | | | | % 153.63/22.96 | | | Case 2: % 153.63/22.96 | | | | % 153.63/22.96 | | | | (33) all_58_31 = e3 % 153.63/22.96 | | | | % 153.63/22.96 | | | | REF_CLOSE: (5), (10), (33) are inconsistent by sub-proof #656. % 153.63/22.96 | | | | % 153.63/22.96 | | | End of split % 153.63/22.96 | | | % 153.63/22.96 | | End of split % 153.63/22.96 | | % 153.63/22.96 | End of split % 153.63/22.96 | % 153.63/22.96 End of proof % 153.63/22.96 % 153.63/22.96 Sub-proof #209 shows that the following formulas are inconsistent: % 153.63/22.96 ---------------------------------------------------------------- % 153.63/22.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.96 (2) ~ (all_10_1 = e0) % 153.63/22.96 (3) all_54_8 = all_52_2 % 153.63/22.96 (4) op(e0, all_10_1) = e0 % 153.63/22.96 (5) op(e0, e1) = all_52_11 % 153.63/22.96 (6) all_56_12 = all_10_1 % 153.63/22.96 (7) all_54_12 = all_10_1 % 153.63/22.96 (8) ~ (all_52_2 = e1) % 153.63/22.96 (9) op(e0, e3) = all_10_1 % 153.63/22.96 (10) all_56_6 = all_52_2 % 153.63/22.96 (11) ~ (all_52_11 = e0) % 153.63/22.96 (12) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.96 (13) ~ (all_52_2 = e3) % 153.63/22.96 (14) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 153.63/22.96 (15) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.63/22.96 (16) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/22.96 (17) ~ (all_52_2 = all_10_1) % 153.63/22.96 % 153.63/22.96 Begin of proof % 153.63/22.96 | % 153.63/22.96 | BETA: splitting (15) gives: % 153.63/22.96 | % 153.63/22.96 | Case 1: % 153.63/22.96 | | % 153.63/22.96 | | (18) all_56_6 = e2 % 153.63/22.96 | | % 153.63/22.96 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (16), (17), % 153.63/22.96 | | (18) are inconsistent by sub-proof #210. % 153.63/22.96 | | % 153.63/22.96 | Case 2: % 153.63/22.96 | | % 153.63/22.96 | | (19) ~ (all_56_6 = e2) % 153.63/22.96 | | % 153.63/22.96 | | REDUCE: (10), (19) imply: % 153.63/22.96 | | (20) ~ (all_52_2 = e2) % 153.63/22.97 | | % 153.63/22.97 | | REF_CLOSE: (3), (8), (13), (14), (20) are inconsistent by sub-proof #416. % 153.63/22.97 | | % 153.63/22.97 | End of split % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #210 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.97 (2) ~ (all_10_1 = e0) % 153.63/22.97 (3) op(e0, all_10_1) = e0 % 153.63/22.97 (4) op(e0, e1) = all_52_11 % 153.63/22.97 (5) all_56_12 = all_10_1 % 153.63/22.97 (6) all_54_12 = all_10_1 % 153.63/22.97 (7) op(e0, e3) = all_10_1 % 153.63/22.97 (8) all_56_6 = all_52_2 % 153.63/22.97 (9) all_56_6 = e2 % 153.63/22.97 (10) ~ (all_52_11 = e0) % 153.63/22.97 (11) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.97 (12) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/22.97 (13) ~ (all_52_2 = all_10_1) % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | COMBINE_EQS: (8), (9) imply: % 153.63/22.97 | (14) all_52_2 = e2 % 153.63/22.97 | % 153.63/22.97 | SIMP: (14) implies: % 153.63/22.97 | (15) all_52_2 = e2 % 153.63/22.97 | % 153.63/22.97 | REDUCE: (13), (15) imply: % 153.63/22.97 | (16) ~ (all_10_1 = e2) % 153.63/22.97 | % 153.63/22.97 | SIMP: (16) implies: % 153.63/22.97 | (17) ~ (all_10_1 = e2) % 153.63/22.97 | % 153.63/22.97 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (17) are % 153.63/22.97 | inconsistent by sub-proof #235. % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #211 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) all_56_7 = all_52_6 % 153.63/22.97 (2) all_56_4 = all_52_8 % 153.63/22.97 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.97 (4) ~ (all_6_2 = e0) % 153.63/22.97 (5) all_54_5 = all_8_2 % 153.63/22.97 (6) ~ (e3 = e1) % 153.63/22.97 (7) ~ (all_52_6 = e0) % 153.63/22.97 (8) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.63/22.97 (9) all_56_11 = all_52_14 % 153.63/22.97 (10) all_56_1 = all_52_4 % 153.63/22.97 (11) all_54_5 = e0 % 153.63/22.97 (12) all_56_9 = all_52_12 % 153.63/22.97 (13) all_58_29 = all_8_2 % 153.63/22.97 (14) ~ (all_52_12 = all_52_14) % 153.63/22.97 (15) ~ (e2 = e1) % 153.63/22.97 (16) ~ (all_52_4 = e0) % 153.63/22.97 (17) ~ (e3 = e0) % 153.63/22.97 (18) all_58_28 = all_10_2 % 153.63/22.97 (19) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.63/22.97 (20) ~ (e2 = e0) % 153.63/22.97 (21) all_56_0 = all_10_2 % 153.63/22.97 (22) all_56_8 = all_6_2 % 153.63/22.97 (23) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.97 (24) ~ (e1 = e0) % 153.63/22.97 (25) ~ (all_52_8 = e0) % 153.63/22.97 (26) all_58_30 = all_6_2 % 153.63/22.97 (27) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/22.97 (28) ~ (e3 = e2) % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | COMBINE_EQS: (5), (11) imply: % 153.63/22.97 | (29) all_8_2 = e0 % 153.63/22.97 | % 153.63/22.97 | SIMP: (29) implies: % 153.63/22.97 | (30) all_8_2 = e0 % 153.63/22.97 | % 153.63/22.97 | COMBINE_EQS: (13), (30) imply: % 153.63/22.97 | (31) all_58_29 = e0 % 153.63/22.97 | % 153.63/22.97 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (14), (15), % 153.63/22.97 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 153.63/22.97 | (27), (28), (31) are inconsistent by sub-proof #481. % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #212 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.97 (2) ~ (all_10_1 = e0) % 153.63/22.97 (3) op(e0, all_10_1) = e0 % 153.63/22.97 (4) all_56_12 = all_10_1 % 153.63/22.97 (5) all_54_12 = all_10_1 % 153.63/22.97 (6) op(e0, e3) = all_10_1 % 153.63/22.97 (7) ~ (all_10_1 = e1) % 153.63/22.97 (8) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.63/22.97 (9) ~ (all_52_7 = e0) % 153.63/22.97 (10) op(e0, e2) = all_52_7 % 153.63/22.97 (11) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | BETA: splitting (8) gives: % 153.63/22.97 | % 153.63/22.97 | Case 1: % 153.63/22.97 | | % 153.63/22.97 | | (12) all_56_12 = e2 % 153.63/22.97 | | % 153.63/22.97 | | REF_CLOSE: (1), (3), (4), (9), (10), (12) are inconsistent by sub-proof % 153.63/22.97 | | #239. % 153.63/22.97 | | % 153.63/22.97 | Case 2: % 153.63/22.97 | | % 153.63/22.97 | | (13) ~ (all_56_12 = e2) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (4), (13) imply: % 153.63/22.97 | | (14) ~ (all_10_1 = e2) % 153.63/22.97 | | % 153.63/22.97 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (11), (14) are inconsistent by % 153.63/22.97 | | sub-proof #236. % 153.63/22.97 | | % 153.63/22.97 | End of split % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #213 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) all_56_1 = e1 % 153.63/22.97 (2) all_56_1 = e0 % 153.63/22.97 (3) ~ (e1 = e0) % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | COMBINE_EQS: (1), (2) imply: % 153.63/22.97 | (4) e1 = e0 % 153.63/22.97 | % 153.63/22.97 | SIMP: (4) implies: % 153.63/22.97 | (5) e1 = e0 % 153.63/22.97 | % 153.63/22.97 | REDUCE: (3), (5) imply: % 153.63/22.97 | (6) $false % 153.63/22.97 | % 153.63/22.97 | CLOSE: (6) is inconsistent. % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #214 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.97 (2) ~ (all_52_6 = all_8_2) % 153.63/22.97 (3) op(all_8_2, all_8_1) = e0 % 153.63/22.97 (4) all_54_9 = all_52_6 % 153.63/22.97 (5) op(e1, e2) = all_52_6 % 153.63/22.97 (6) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 153.63/22.97 (7) ~ (all_52_6 = e0) % 153.63/22.97 (8) all_8_2 = e1 % 153.63/22.97 (9) op(all_8_2, e2) = all_8_1 % 153.63/22.97 (10) ~ (all_30_1 = e3) | ~ (all_30_2 = e1) % 153.63/22.97 (11) all_30_2 = all_8_2 % 153.63/22.97 (12) all_30_1 = all_8_1 % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | SIMP: (8) implies: % 153.63/22.97 | (13) all_8_2 = e1 % 153.63/22.97 | % 153.63/22.97 | COMBINE_EQS: (11), (13) imply: % 153.63/22.97 | (14) all_30_2 = e1 % 153.63/22.97 | % 153.63/22.97 | REDUCE: (2), (13) imply: % 153.63/22.97 | (15) ~ (all_52_6 = e1) % 153.63/22.97 | % 153.63/22.97 | REDUCE: (3), (13) imply: % 153.63/22.97 | (16) op(e1, all_8_1) = e0 % 153.63/22.97 | % 153.63/22.97 | REDUCE: (9), (13) imply: % 153.63/22.97 | (17) op(e1, e2) = all_8_1 % 153.63/22.97 | % 153.63/22.97 | BETA: splitting (10) gives: % 153.63/22.97 | % 153.63/22.97 | Case 1: % 153.63/22.97 | | % 153.63/22.97 | | (18) ~ (all_30_2 = e1) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (14), (18) imply: % 153.63/22.97 | | (19) $false % 153.63/22.97 | | % 153.63/22.97 | | CLOSE: (19) is inconsistent. % 153.63/22.97 | | % 153.63/22.97 | Case 2: % 153.63/22.97 | | % 153.63/22.97 | | (20) ~ (all_30_1 = e3) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (12), (20) imply: % 153.63/22.97 | | (21) ~ (all_8_1 = e3) % 153.63/22.97 | | % 153.63/22.97 | | GROUND_INST: instantiating (1) with all_52_6, all_8_1, e2, e1, simplifying % 153.63/22.97 | | with (5), (17) gives: % 153.63/22.97 | | (22) all_52_6 = all_8_1 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (4), (22) imply: % 153.63/22.97 | | (23) all_54_9 = all_8_1 % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (15), (22) imply: % 153.63/22.97 | | (24) ~ (all_8_1 = e1) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (7), (22) imply: % 153.63/22.97 | | (25) ~ (all_8_1 = e0) % 153.63/22.97 | | % 153.63/22.97 | | BETA: splitting (6) gives: % 153.63/22.97 | | % 153.63/22.97 | | Case 1: % 153.63/22.97 | | | % 153.63/22.97 | | | (26) all_54_9 = e1 % 153.63/22.97 | | | % 153.63/22.97 | | | REF_CLOSE: (23), (24), (26) are inconsistent by sub-proof #835. % 153.63/22.97 | | | % 153.63/22.97 | | Case 2: % 153.63/22.97 | | | % 153.63/22.97 | | | (27) all_54_9 = e3 | all_54_9 = e2 % 153.63/22.97 | | | % 153.63/22.97 | | | BETA: splitting (27) gives: % 153.63/22.97 | | | % 153.63/22.97 | | | Case 1: % 153.63/22.97 | | | | % 153.63/22.97 | | | | (28) all_54_9 = e2 % 153.63/22.97 | | | | % 153.63/22.97 | | | | COMBINE_EQS: (23), (28) imply: % 153.63/22.97 | | | | (29) all_8_1 = e2 % 153.63/22.97 | | | | % 153.63/22.97 | | | | SIMP: (29) implies: % 153.63/22.97 | | | | (30) all_8_1 = e2 % 153.63/22.97 | | | | % 153.63/22.97 | | | | REDUCE: (16), (30) imply: % 153.63/22.97 | | | | (31) op(e1, e2) = e0 % 153.63/22.97 | | | | % 153.63/22.97 | | | | REF_CLOSE: (1), (17), (25), (31) are inconsistent by sub-proof #795. % 153.63/22.97 | | | | % 153.63/22.97 | | | Case 2: % 153.63/22.97 | | | | % 153.63/22.97 | | | | (32) all_54_9 = e3 % 153.63/22.97 | | | | % 153.63/22.97 | | | | REF_CLOSE: (21), (23), (32) are inconsistent by sub-proof #833. % 153.63/22.97 | | | | % 153.63/22.97 | | | End of split % 153.63/22.97 | | | % 153.63/22.97 | | End of split % 153.63/22.97 | | % 153.63/22.97 | End of split % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #215 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.63/22.97 (2) all_58_31 = all_4_2 % 153.63/22.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.97 (4) all_54_13 = all_52_7 % 153.63/22.97 (5) ~ (all_52_2 = all_52_3) % 153.63/22.97 (6) all_58_11 = all_52_9 % 153.63/22.97 (7) all_56_15 = all_4_2 % 153.63/22.97 (8) all_56_7 = all_52_6 % 153.63/22.97 (9) all_54_2 = all_52_8 % 153.63/22.97 (10) op(all_10_2, all_10_1) = e0 % 153.63/22.97 (11) ~ (all_52_8 = all_10_2) % 153.63/22.97 (12) all_58_15 = all_52_2 % 153.63/22.97 (13) all_58_26 = all_52_11 % 153.63/22.97 (14) ~ (all_52_8 = all_52_11) % 153.63/22.97 (15) ~ (all_52_11 = all_4_2) % 153.63/22.97 (16) all_58_6 = all_52_12 % 153.63/22.97 (17) ~ (all_52_6 = all_8_2) % 153.63/22.97 (18) all_56_4 = all_52_8 % 153.63/22.97 (19) ~ (all_52_4 = all_8_2) % 153.63/22.97 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.97 (21) all_54_1 = all_52_4 % 153.63/22.97 (22) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/22.97 (23) ~ (all_6_2 = e0) % 153.63/22.97 (24) ~ (all_52_4 = all_52_6) % 153.63/22.97 (25) all_58_13 = all_52_13 % 153.63/22.97 (26) op(e0, e1) = all_52_11 % 153.63/22.97 (27) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 153.63/22.97 (28) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.63/22.97 (29) ~ (all_52_6 = all_52_7) % 153.63/22.97 (30) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 153.63/22.97 (31) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 = e0 | % 153.63/22.97 all_56_13 = e0 | all_56_14 = e0) % 153.63/22.97 (32) all_58_20 = all_52_14 % 153.63/22.97 (33) ~ (all_52_8 = all_6_2) % 153.63/22.97 (34) ~ (all_52_12 = all_52_13) % 153.63/22.97 (35) op(e0, all_52_3) = all_58_21 % 153.63/22.97 (36) all_54_5 = all_8_2 % 153.63/22.97 (37) ~ (all_52_6 = all_52_14) % 153.63/22.97 (38) ~ (all_52_4 = all_52_7) % 153.63/22.97 (39) ~ (all_52_2 = all_6_2) % 153.63/22.97 (40) all_58_28 = e0 | all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 153.63/22.97 (41) ~ (all_52_8 = all_52_12) % 153.63/22.97 (42) ~ (all_52_13 = all_4_2) % 153.63/22.97 (43) ~ (all_52_13 = all_8_2) % 153.63/22.97 (44) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 153.63/22.97 (45) ~ (e3 = e1) % 153.63/22.97 (46) ~ (all_52_1 = all_52_13) % 153.63/22.97 (47) all_56_5 = all_52_9 % 153.63/22.97 (48) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 153.63/22.97 (49) all_56_12 = all_52_3 % 153.63/22.97 (50) ~ (all_52_3 = all_52_7) % 153.63/22.97 (51) all_56_11 = all_52_14 % 153.63/22.97 (52) all_56_1 = all_52_4 % 153.63/22.97 (53) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.63/22.97 (54) ~ (all_52_3 = all_4_2) % 153.63/22.97 (55) ~ (all_52_9 = all_52_11) % 153.63/22.97 (56) all_56_3 = all_8_2 % 153.63/22.97 (57) all_58_24 = all_52_7 % 153.63/22.97 (58) ~ (all_52_13 = all_52_14) % 153.63/22.97 (59) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 153.63/22.97 (60) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.63/22.97 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.63/22.97 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.63/22.97 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.63/22.97 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.63/22.97 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.63/22.97 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.63/22.97 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.63/22.97 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.63/22.97 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.63/22.97 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/22.97 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.63/22.97 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/22.97 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/22.97 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/22.97 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/22.97 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/22.97 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.63/22.97 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/22.97 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.63/22.97 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/22.97 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.63/22.97 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/22.97 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/22.97 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.63/22.97 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.63/22.97 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.63/22.97 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.63/22.97 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/22.97 e0) % 153.63/22.97 (61) ~ (all_52_4 = all_52_8) % 153.63/22.97 (62) all_56_9 = all_52_12 % 153.63/22.97 (63) all_58_29 = all_8_2 % 153.63/22.97 (64) ~ (all_52_12 = all_52_14) % 153.63/22.97 (65) ~ (e2 = e1) % 153.63/22.97 (66) all_56_6 = all_52_2 % 153.63/22.97 (67) all_56_13 = all_52_7 % 153.63/22.97 (68) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/22.97 (69) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/22.97 (70) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.63/22.97 (71) ~ (all_52_9 = all_52_13) % 153.63/22.97 (72) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.63/22.97 (73) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/22.97 (74) ~ (all_52_11 = all_6_2) % 153.63/22.97 (75) ~ (e3 = e0) % 153.63/22.97 (76) all_56_2 = all_52_1 % 153.63/22.97 (77) op(e0, e3) = all_52_3 % 153.63/22.97 (78) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.63/22.97 (79) all_56_10 = all_52_13 % 153.63/22.97 (80) ~ (all_52_12 = all_10_2) % 153.63/22.97 (81) ~ (all_52_9 = all_8_2) % 153.63/22.97 (82) all_56_14 = all_52_11 % 153.63/22.97 (83) all_58_28 = all_10_2 % 153.63/22.97 (84) all_58_17 = all_52_6 % 153.63/22.97 (85) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.63/22.97 (86) ~ (all_52_7 = all_52_11) % 153.63/22.97 (87) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.97 (88) ~ (all_56_15 = e0) % 153.63/22.97 (89) ~ (e2 = e0) % 153.63/22.97 (90) all_56_0 = all_10_2 % 153.63/22.97 (91) ~ (all_52_3 = all_52_11) % 153.63/22.97 (92) all_58_22 = all_52_3 % 153.63/22.97 (93) ~ (all_52_12 = all_4_2) % 153.63/22.97 (94) ~ (all_52_3 = all_10_2) % 153.63/22.97 (95) all_56_8 = all_6_2 % 153.63/22.97 (96) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.63/22.97 (97) ~ (all_52_7 = all_8_2) % 153.63/22.97 (98) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 153.63/22.97 (99) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.63/22.97 (100) all_58_4 = all_52_8 % 153.63/22.97 (101) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.97 (102) ~ (all_52_2 = all_52_14) % 153.63/22.97 (103) ~ (all_52_14 = all_4_2) % 153.63/22.97 (104) ~ (e1 = e0) % 153.63/22.97 (105) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.63/22.97 (106) ~ (all_52_7 = all_4_2) % 153.63/22.97 (107) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 153.63/22.97 (108) ~ (all_4_2 = e1) % 153.63/22.97 (109) op(e0, e2) = all_52_7 % 153.63/22.97 (110) ~ (all_52_4 = all_10_2) % 153.63/22.97 (111) all_58_30 = all_6_2 % 153.63/22.97 (112) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/22.97 (113) ~ (e3 = e2) % 153.63/22.97 (114) ~ (all_52_14 = all_6_2) % 153.63/22.97 (115) op(all_10_2, e3) = all_10_1 % 153.63/22.97 (116) ~ (all_8_2 = e0) % 153.63/22.97 (117) ~ (all_52_4 = all_52_12) % 153.63/22.97 (118) all_54_12 = all_52_3 % 153.63/22.97 (119) ~ (all_52_1 = all_10_2) % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | ALPHA: (31) implies: % 153.63/22.97 | (120) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.63/22.97 | (121) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.63/22.97 | % 153.63/22.97 | REDUCE: (7), (88) imply: % 153.63/22.97 | (122) ~ (all_4_2 = e0) % 153.63/22.97 | % 153.63/22.97 | BETA: splitting (40) gives: % 153.63/22.97 | % 153.63/22.97 | Case 1: % 153.63/22.97 | | % 153.63/22.97 | | (123) all_58_28 = e0 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (83), (123) imply: % 153.63/22.97 | | (124) all_10_2 = e0 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (90), (124) imply: % 153.63/22.97 | | (125) all_56_0 = e0 % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (119), (124) imply: % 153.63/22.97 | | (126) ~ (all_52_1 = e0) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (94), (124) imply: % 153.63/22.97 | | (127) ~ (all_52_3 = e0) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (110), (124) imply: % 153.63/22.97 | | (128) ~ (all_52_4 = e0) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (11), (124) imply: % 153.63/22.97 | | (129) ~ (all_52_8 = e0) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (80), (124) imply: % 153.63/22.97 | | (130) ~ (all_52_12 = e0) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (10), (124) imply: % 153.63/22.97 | | (131) op(e0, all_10_1) = e0 % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (115), (124) imply: % 153.63/22.97 | | (132) op(e0, e3) = all_10_1 % 153.63/22.97 | | % 153.63/22.97 | | GROUND_INST: instantiating (3) with all_52_3, all_10_1, e3, e0, simplifying % 153.63/22.97 | | with (77), (132) gives: % 153.63/22.97 | | (133) all_52_3 = all_10_1 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (118), (133) imply: % 153.63/22.97 | | (134) all_54_12 = all_10_1 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (49), (133) imply: % 153.63/22.97 | | (135) all_56_12 = all_10_1 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (92), (133) imply: % 153.63/22.97 | | (136) all_58_22 = all_10_1 % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (5), (133) imply: % 153.63/22.97 | | (137) ~ (all_52_2 = all_10_1) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (50), (133) imply: % 153.63/22.97 | | (138) ~ (all_52_7 = all_10_1) % 153.63/22.97 | | % 153.63/22.97 | | SIMP: (138) implies: % 153.63/22.97 | | (139) ~ (all_52_7 = all_10_1) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (91), (133) imply: % 153.63/22.97 | | (140) ~ (all_52_11 = all_10_1) % 153.63/22.97 | | % 153.63/22.97 | | SIMP: (140) implies: % 153.63/22.97 | | (141) ~ (all_52_11 = all_10_1) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (54), (133) imply: % 153.63/22.97 | | (142) ~ (all_10_1 = all_4_2) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (127), (133) imply: % 153.63/22.97 | | (143) ~ (all_10_1 = e0) % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (35), (133) imply: % 153.63/22.97 | | (144) op(e0, all_10_1) = all_58_21 % 153.63/22.97 | | % 153.63/22.97 | | GROUND_INST: instantiating (3) with e0, all_58_21, all_10_1, e0, simplifying % 153.63/22.97 | | with (131), (144) gives: % 153.63/22.97 | | (145) all_58_21 = e0 % 153.63/22.97 | | % 153.63/22.97 | | BETA: splitting (72) gives: % 153.63/22.97 | | % 153.63/22.97 | | Case 1: % 153.63/22.97 | | | % 153.63/22.97 | | | (146) all_56_1 = e0 % 153.63/22.97 | | | % 153.63/22.97 | | | COMBINE_EQS: (52), (146) imply: % 153.63/22.97 | | | (147) all_52_4 = e0 % 153.63/22.97 | | | % 153.63/22.97 | | | REDUCE: (128), (147) imply: % 153.63/22.97 | | | (148) $false % 153.63/22.97 | | | % 153.63/22.97 | | | CLOSE: (148) is inconsistent. % 153.63/22.97 | | | % 153.63/22.97 | | Case 2: % 153.63/22.97 | | | % 153.63/22.97 | | | (149) ~ (all_56_1 = e0) % 153.63/22.97 | | | (150) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.63/22.97 | | | % 153.63/22.97 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (12), (13), (14), (15), % 153.63/22.97 | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 153.63/22.97 | | | (26), (27), (28), (29), (30), (32), (33), (34), (36), (37), % 153.63/22.97 | | | (38), (39), (41), (42), (43), (44), (45), (46), (47), (48), % 153.63/22.97 | | | (51), (52), (53), (55), (56), (57), (58), (59), (60), (61), % 153.63/22.97 | | | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), % 153.63/22.97 | | | (73), (74), (75), (76), (78), (79), (81), (82), (84), (85), % 153.63/22.97 | | | (86), (87), (89), (93), (95), (96), (97), (98), (99), (100), % 153.63/22.97 | | | (101), (102), (103), (104), (105), (106), (107), (108), (109), % 153.63/22.97 | | | (111), (112), (113), (114), (117), (120), (121), (123), (125), % 153.63/22.97 | | | (126), (128), (129), (130), (131), (132), (134), (135), (136), % 153.63/22.97 | | | (137), (139), (141), (142), (143), (150) are inconsistent by % 153.63/22.97 | | | sub-proof #218. % 153.63/22.97 | | | % 153.63/22.97 | | End of split % 153.63/22.97 | | % 153.63/22.97 | Case 2: % 153.63/22.97 | | % 153.63/22.97 | | (151) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 153.63/22.97 | | % 153.63/22.97 | | REF_CLOSE: (2), (23), (63), (111), (116), (122), (151) are inconsistent by % 153.63/22.97 | | sub-proof #216. % 153.63/22.97 | | % 153.63/22.97 | End of split % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #216 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) all_58_31 = all_4_2 % 153.63/22.97 (2) ~ (all_6_2 = e0) % 153.63/22.97 (3) all_58_29 = e0 | all_58_30 = e0 | all_58_31 = e0 % 153.63/22.97 (4) all_58_29 = all_8_2 % 153.63/22.97 (5) ~ (all_4_2 = e0) % 153.63/22.97 (6) all_58_30 = all_6_2 % 153.63/22.97 (7) ~ (all_8_2 = e0) % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | BETA: splitting (3) gives: % 153.63/22.97 | % 153.63/22.97 | Case 1: % 153.63/22.97 | | % 153.63/22.97 | | (8) all_58_29 = e0 % 153.63/22.97 | | % 153.63/22.97 | | COMBINE_EQS: (4), (8) imply: % 153.63/22.97 | | (9) all_8_2 = e0 % 153.63/22.97 | | % 153.63/22.97 | | REDUCE: (7), (9) imply: % 153.63/22.97 | | (10) $false % 153.63/22.97 | | % 153.63/22.97 | | CLOSE: (10) is inconsistent. % 153.63/22.97 | | % 153.63/22.97 | Case 2: % 153.63/22.97 | | % 153.63/22.97 | | (11) all_58_30 = e0 | all_58_31 = e0 % 153.63/22.97 | | % 153.63/22.97 | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #217. % 153.63/22.97 | | % 153.63/22.97 | End of split % 153.63/22.97 | % 153.63/22.97 End of proof % 153.63/22.97 % 153.63/22.97 Sub-proof #217 shows that the following formulas are inconsistent: % 153.63/22.97 ---------------------------------------------------------------- % 153.63/22.97 (1) all_58_31 = all_4_2 % 153.63/22.97 (2) ~ (all_6_2 = e0) % 153.63/22.97 (3) ~ (all_4_2 = e0) % 153.63/22.97 (4) all_58_30 = e0 | all_58_31 = e0 % 153.63/22.97 (5) all_58_30 = all_6_2 % 153.63/22.97 % 153.63/22.97 Begin of proof % 153.63/22.97 | % 153.63/22.97 | BETA: splitting (4) gives: % 153.63/22.97 | % 153.63/22.97 | Case 1: % 153.63/22.97 | | % 153.63/22.97 | | (6) all_58_30 = e0 % 153.63/22.97 | | % 153.63/22.97 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #863. % 153.63/22.97 | | % 153.63/22.97 | Case 2: % 153.63/22.97 | | % 153.63/22.97 | | (7) all_58_31 = e0 % 153.63/22.98 | | % 153.63/22.98 | | COMBINE_EQS: (1), (7) imply: % 153.63/22.98 | | (8) all_4_2 = e0 % 153.63/22.98 | | % 153.63/22.98 | | REDUCE: (3), (8) imply: % 153.63/22.98 | | (9) $false % 153.63/22.98 | | % 153.63/22.98 | | CLOSE: (9) is inconsistent. % 153.63/22.98 | | % 153.63/22.98 | End of split % 153.63/22.98 | % 153.63/22.98 End of proof % 153.63/22.98 % 153.63/22.98 Sub-proof #218 shows that the following formulas are inconsistent: % 153.63/22.98 ---------------------------------------------------------------- % 153.63/22.98 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.63/22.98 (2) all_58_31 = all_4_2 % 153.63/22.98 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.98 (4) all_58_28 = e0 % 153.63/22.98 (5) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.63/22.98 (6) all_54_13 = all_52_7 % 153.63/22.98 (7) all_58_11 = all_52_9 % 153.63/22.98 (8) all_56_15 = all_4_2 % 153.63/22.98 (9) all_56_7 = all_52_6 % 153.63/22.98 (10) all_54_2 = all_52_8 % 153.63/22.98 (11) ~ (all_10_1 = e0) % 153.63/22.98 (12) ~ (all_52_7 = all_10_1) % 153.63/22.98 (13) ~ (all_52_11 = all_10_1) % 153.63/22.98 (14) all_58_15 = all_52_2 % 153.63/22.98 (15) all_58_26 = all_52_11 % 153.63/22.98 (16) op(e0, all_10_1) = e0 % 153.63/22.98 (17) ~ (all_52_8 = all_52_11) % 153.63/22.98 (18) ~ (all_52_11 = all_4_2) % 153.63/22.98 (19) all_58_6 = all_52_12 % 153.63/22.98 (20) ~ (all_52_6 = all_8_2) % 153.63/22.98 (21) all_56_4 = all_52_8 % 153.63/22.98 (22) ~ (all_52_4 = all_8_2) % 153.63/22.98 (23) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.98 (24) all_54_1 = all_52_4 % 153.63/22.98 (25) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/22.98 (26) ~ (all_6_2 = e0) % 153.63/22.98 (27) ~ (all_52_4 = all_52_6) % 153.63/22.98 (28) ~ (all_10_1 = all_4_2) % 153.63/22.98 (29) all_58_13 = all_52_13 % 153.63/22.98 (30) op(e0, e1) = all_52_11 % 153.63/22.98 (31) all_56_12 = all_10_1 % 153.63/22.98 (32) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 153.63/22.98 (33) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.63/22.98 (34) ~ (all_52_6 = all_52_7) % 153.63/22.98 (35) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 153.63/22.98 (36) all_58_20 = all_52_14 % 153.63/22.98 (37) ~ (all_52_8 = all_6_2) % 153.63/22.98 (38) ~ (all_52_12 = all_52_13) % 153.63/22.98 (39) all_56_0 = e0 % 153.63/22.98 (40) all_54_5 = all_8_2 % 153.63/22.98 (41) ~ (all_52_6 = all_52_14) % 153.63/22.98 (42) ~ (all_52_4 = all_52_7) % 153.63/22.98 (43) ~ (all_52_2 = all_6_2) % 153.63/22.98 (44) ~ (all_52_8 = all_52_12) % 153.63/22.98 (45) ~ (all_52_13 = all_4_2) % 153.63/22.98 (46) ~ (all_52_13 = all_8_2) % 153.63/22.98 (47) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 153.63/22.98 (48) ~ (e3 = e1) % 153.63/22.98 (49) all_54_12 = all_10_1 % 153.63/22.98 (50) ~ (all_52_1 = all_52_13) % 153.63/22.98 (51) all_56_5 = all_52_9 % 153.63/22.98 (52) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 153.63/22.98 (53) ~ (all_52_12 = e0) % 153.63/22.98 (54) all_56_11 = all_52_14 % 153.63/22.98 (55) all_56_1 = all_52_4 % 153.63/22.98 (56) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.63/22.98 (57) op(e0, e3) = all_10_1 % 153.63/22.98 (58) ~ (all_52_9 = all_52_11) % 153.63/22.98 (59) all_56_3 = all_8_2 % 153.63/22.98 (60) all_58_24 = all_52_7 % 153.63/22.98 (61) ~ (all_52_13 = all_52_14) % 153.63/22.98 (62) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 153.63/22.98 (63) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.63/22.98 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.63/22.98 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.63/22.98 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.63/22.98 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.63/22.98 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.63/22.98 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.63/22.98 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.63/22.98 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.63/22.98 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.63/22.98 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/22.98 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.63/22.98 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/22.98 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/22.98 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/22.98 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/22.98 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/22.98 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.63/22.98 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/22.98 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.63/22.98 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/22.98 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.63/22.98 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/22.98 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/22.98 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.63/22.98 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.63/22.98 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.63/22.98 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.63/22.98 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/22.98 e0) % 153.63/22.98 (64) ~ (all_52_4 = all_52_8) % 153.63/22.98 (65) all_56_9 = all_52_12 % 153.63/22.98 (66) all_58_29 = all_8_2 % 153.63/22.98 (67) ~ (all_52_12 = all_52_14) % 153.63/22.98 (68) ~ (e2 = e1) % 153.63/22.98 (69) all_56_6 = all_52_2 % 153.63/22.98 (70) all_56_13 = all_52_7 % 153.63/22.98 (71) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/22.98 (72) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/22.98 (73) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.63/22.98 (74) ~ (all_52_9 = all_52_13) % 153.63/22.98 (75) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/22.98 (76) ~ (all_52_4 = e0) % 153.63/22.98 (77) ~ (all_52_11 = all_6_2) % 153.63/22.98 (78) ~ (e3 = e0) % 153.63/22.98 (79) all_56_2 = all_52_1 % 153.63/22.98 (80) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.63/22.98 (81) all_58_22 = all_10_1 % 153.63/22.98 (82) all_56_10 = all_52_13 % 153.63/22.98 (83) ~ (all_52_9 = all_8_2) % 153.63/22.98 (84) all_56_14 = all_52_11 % 153.63/22.98 (85) all_58_17 = all_52_6 % 153.63/22.98 (86) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.63/22.98 (87) ~ (all_52_7 = all_52_11) % 153.63/22.98 (88) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.98 (89) ~ (e2 = e0) % 153.63/22.98 (90) ~ (all_52_1 = e0) % 153.63/22.98 (91) ~ (all_52_12 = all_4_2) % 153.63/22.98 (92) all_56_8 = all_6_2 % 153.63/22.98 (93) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.63/22.98 (94) ~ (all_52_7 = all_8_2) % 153.63/22.98 (95) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 153.63/22.98 (96) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.63/22.98 (97) all_58_4 = all_52_8 % 153.63/22.98 (98) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.98 (99) ~ (all_52_2 = all_52_14) % 153.63/22.98 (100) ~ (all_52_14 = all_4_2) % 153.63/22.98 (101) ~ (e1 = e0) % 153.63/22.98 (102) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.63/22.98 (103) ~ (all_52_7 = all_4_2) % 153.63/22.98 (104) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 153.63/22.98 (105) ~ (all_4_2 = e1) % 153.63/22.98 (106) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.63/22.98 (107) op(e0, e2) = all_52_7 % 153.63/22.98 (108) ~ (all_52_8 = e0) % 153.63/22.98 (109) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.63/22.98 (110) all_58_30 = all_6_2 % 153.63/22.98 (111) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/22.98 (112) ~ (e3 = e2) % 153.63/22.98 (113) ~ (all_52_14 = all_6_2) % 153.63/22.98 (114) ~ (all_52_4 = all_52_12) % 153.63/22.98 (115) ~ (all_52_2 = all_10_1) % 153.63/22.98 % 153.63/22.98 Begin of proof % 153.63/22.98 | % 153.63/22.98 | BETA: splitting (56) gives: % 153.63/22.98 | % 153.63/22.98 | Case 1: % 153.63/22.98 | | % 153.63/22.98 | | (116) all_56_4 = e0 % 153.63/22.98 | | % 153.63/22.98 | | COMBINE_EQS: (21), (116) imply: % 153.63/22.98 | | (117) all_52_8 = e0 % 153.63/22.98 | | % 153.63/22.98 | | REDUCE: (108), (117) imply: % 153.63/22.98 | | (118) $false % 153.63/22.98 | | % 153.63/22.98 | | CLOSE: (118) is inconsistent. % 153.63/22.98 | | % 153.63/22.98 | Case 2: % 153.63/22.98 | | % 153.63/22.98 | | (119) ~ (all_56_4 = e0) % 153.63/22.98 | | (120) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.63/22.98 | | % 153.63/22.98 | | BETA: splitting (25) gives: % 153.63/22.98 | | % 153.63/22.98 | | Case 1: % 153.63/22.98 | | | % 153.63/22.98 | | | (121) all_56_2 = e0 % 153.63/22.98 | | | % 153.63/22.98 | | | COMBINE_EQS: (79), (121) imply: % 153.63/22.98 | | | (122) all_52_1 = e0 % 153.63/22.98 | | | % 153.63/22.98 | | | REDUCE: (90), (122) imply: % 153.63/22.98 | | | (123) $false % 153.63/22.98 | | | % 153.63/22.98 | | | CLOSE: (123) is inconsistent. % 153.63/22.98 | | | % 153.63/22.98 | | Case 2: % 153.63/22.98 | | | % 153.63/22.98 | | | (124) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/22.98 | | | % 153.63/22.98 | | | BETA: splitting (95) gives: % 153.63/22.98 | | | % 153.63/22.98 | | | Case 1: % 153.63/22.98 | | | | % 153.63/22.98 | | | | (125) all_54_1 = e0 % 153.63/22.98 | | | | % 153.63/22.98 | | | | REF_CLOSE: (24), (76), (125) are inconsistent by sub-proof #798. % 153.63/22.98 | | | | % 153.63/22.98 | | | Case 2: % 153.63/22.98 | | | | % 153.63/22.98 | | | | (126) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 153.63/22.98 | | | | % 153.63/22.98 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 153.63/22.98 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 153.63/22.98 | | | | (22), (23), (24), (26), (27), (28), (29), (30), (31), (32), % 153.63/22.98 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42), % 153.63/22.98 | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), % 153.63/22.98 | | | | (53), (54), (55), (57), (58), (59), (60), (61), (62), (63), % 153.63/22.98 | | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 153.63/22.98 | | | | (74), (75), (77), (78), (79), (80), (81), (82), (83), (84), % 153.63/22.98 | | | | (85), (86), (87), (88), (89), (91), (92), (93), (94), (96), % 153.63/22.98 | | | | (97), (98), (99), (100), (101), (102), (103), (104), (105), % 153.63/22.98 | | | | (106), (107), (108), (109), (110), (111), (112), (113), % 153.63/22.98 | | | | (114), (115), (120), (124), (126) are inconsistent by % 153.63/22.98 | | | | sub-proof #219. % 153.63/22.98 | | | | % 153.63/22.98 | | | End of split % 153.63/22.98 | | | % 153.63/22.98 | | End of split % 153.63/22.98 | | % 153.63/22.98 | End of split % 153.63/22.98 | % 153.63/22.98 End of proof % 153.63/22.98 % 153.63/22.98 Sub-proof #219 shows that the following formulas are inconsistent: % 153.63/22.98 ---------------------------------------------------------------- % 153.63/22.98 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.63/22.98 (2) all_58_31 = all_4_2 % 153.63/22.98 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/22.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/22.98 (4) all_58_28 = e0 % 153.63/22.98 (5) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/22.98 (6) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.63/22.98 (7) all_54_13 = all_52_7 % 153.63/22.98 (8) all_58_11 = all_52_9 % 153.63/22.98 (9) all_56_15 = all_4_2 % 153.63/22.98 (10) all_56_7 = all_52_6 % 153.63/22.98 (11) all_54_2 = all_52_8 % 153.63/22.98 (12) ~ (all_10_1 = e0) % 153.63/22.98 (13) ~ (all_52_7 = all_10_1) % 153.63/22.98 (14) ~ (all_52_11 = all_10_1) % 153.63/22.98 (15) all_58_15 = all_52_2 % 153.63/22.98 (16) all_58_26 = all_52_11 % 153.63/22.98 (17) op(e0, all_10_1) = e0 % 153.63/22.98 (18) ~ (all_52_8 = all_52_11) % 153.63/22.98 (19) ~ (all_52_11 = all_4_2) % 153.63/22.98 (20) all_58_6 = all_52_12 % 153.63/22.98 (21) ~ (all_52_6 = all_8_2) % 153.63/22.98 (22) all_56_4 = all_52_8 % 153.63/22.98 (23) ~ (all_52_4 = all_8_2) % 153.63/22.98 (24) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.98 (25) all_54_1 = all_52_4 % 153.63/22.98 (26) ~ (all_6_2 = e0) % 153.63/22.98 (27) ~ (all_52_4 = all_52_6) % 153.63/22.98 (28) ~ (all_10_1 = all_4_2) % 153.63/22.98 (29) all_58_13 = all_52_13 % 153.63/22.98 (30) op(e0, e1) = all_52_11 % 153.63/22.98 (31) all_56_12 = all_10_1 % 153.63/22.98 (32) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 153.63/22.98 (33) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.63/22.98 (34) ~ (all_52_6 = all_52_7) % 153.63/22.98 (35) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 153.63/22.98 (36) all_58_20 = all_52_14 % 153.63/22.98 (37) ~ (all_52_8 = all_6_2) % 153.63/22.98 (38) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 153.63/22.98 (39) ~ (all_52_12 = all_52_13) % 153.63/22.98 (40) all_56_0 = e0 % 153.63/22.98 (41) all_54_5 = all_8_2 % 153.63/22.98 (42) ~ (all_52_6 = all_52_14) % 153.63/22.98 (43) ~ (all_52_4 = all_52_7) % 153.63/22.98 (44) ~ (all_52_2 = all_6_2) % 153.63/22.98 (45) ~ (all_52_8 = all_52_12) % 153.63/22.98 (46) ~ (all_52_13 = all_4_2) % 153.63/22.98 (47) ~ (all_52_13 = all_8_2) % 153.63/22.98 (48) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 153.63/22.98 (49) ~ (e3 = e1) % 153.63/22.98 (50) all_54_12 = all_10_1 % 153.63/22.98 (51) ~ (all_52_1 = all_52_13) % 153.63/22.98 (52) all_56_5 = all_52_9 % 153.63/22.98 (53) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 153.63/22.98 (54) ~ (all_52_12 = e0) % 153.63/22.98 (55) all_56_11 = all_52_14 % 153.63/22.98 (56) all_56_1 = all_52_4 % 153.63/22.98 (57) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.63/22.98 (58) op(e0, e3) = all_10_1 % 153.63/22.98 (59) ~ (all_52_9 = all_52_11) % 153.63/22.98 (60) all_56_3 = all_8_2 % 153.63/22.98 (61) all_58_24 = all_52_7 % 153.63/22.98 (62) ~ (all_52_13 = all_52_14) % 153.63/22.98 (63) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 153.63/22.98 (64) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.63/22.98 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.63/22.98 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.63/22.98 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.63/22.98 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.63/22.98 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.63/22.98 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.63/22.98 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.63/22.98 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.63/22.98 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.63/22.98 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/22.98 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.63/22.98 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/22.98 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/22.98 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/22.98 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/22.98 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/22.98 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.63/22.98 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/22.98 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.63/22.98 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/22.98 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.63/22.98 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/22.98 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/22.98 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.63/22.98 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.63/22.98 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.63/22.98 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.63/22.98 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/22.98 e0) % 153.63/22.98 (65) ~ (all_52_4 = all_52_8) % 153.63/22.98 (66) all_56_9 = all_52_12 % 153.63/22.98 (67) all_58_29 = all_8_2 % 153.63/22.98 (68) ~ (all_52_12 = all_52_14) % 153.63/22.98 (69) ~ (e2 = e1) % 153.63/22.98 (70) all_56_6 = all_52_2 % 153.63/22.98 (71) all_56_13 = all_52_7 % 153.63/22.98 (72) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/22.98 (73) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/22.98 (74) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.63/22.98 (75) ~ (all_52_9 = all_52_13) % 153.63/22.98 (76) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/22.98 (77) ~ (all_52_11 = all_6_2) % 153.63/22.98 (78) ~ (e3 = e0) % 153.63/22.98 (79) all_56_2 = all_52_1 % 153.63/22.98 (80) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.63/22.98 (81) all_58_22 = all_10_1 % 153.63/22.98 (82) all_56_10 = all_52_13 % 153.63/22.98 (83) ~ (all_52_9 = all_8_2) % 153.63/22.98 (84) all_56_14 = all_52_11 % 153.63/22.98 (85) all_58_17 = all_52_6 % 153.63/22.98 (86) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.63/22.98 (87) ~ (all_52_7 = all_52_11) % 153.63/22.98 (88) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.98 (89) ~ (e2 = e0) % 153.63/22.98 (90) ~ (all_52_12 = all_4_2) % 153.63/22.98 (91) all_56_8 = all_6_2 % 153.63/22.98 (92) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.63/22.98 (93) ~ (all_52_7 = all_8_2) % 153.63/22.98 (94) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.63/22.98 (95) all_58_4 = all_52_8 % 153.63/22.98 (96) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/22.98 (97) ~ (all_52_2 = all_52_14) % 153.63/22.98 (98) ~ (all_52_14 = all_4_2) % 153.63/22.98 (99) ~ (e1 = e0) % 153.63/22.98 (100) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.63/22.98 (101) ~ (all_52_7 = all_4_2) % 153.63/22.98 (102) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 153.63/22.98 (103) ~ (all_4_2 = e1) % 153.63/22.98 (104) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 153.63/22.98 (105) op(e0, e2) = all_52_7 % 153.63/22.98 (106) ~ (all_52_8 = e0) % 153.63/22.98 (107) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.63/22.98 (108) all_58_30 = all_6_2 % 153.63/22.98 (109) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/22.98 (110) ~ (e3 = e2) % 153.63/22.98 (111) ~ (all_52_14 = all_6_2) % 153.63/22.98 (112) ~ (all_52_4 = all_52_12) % 153.63/22.98 (113) ~ (all_52_2 = all_10_1) % 153.63/22.98 % 153.63/22.98 Begin of proof % 153.63/22.98 | % 153.63/22.98 | BETA: splitting (80) gives: % 153.63/22.98 | % 153.63/22.98 | Case 1: % 153.63/22.98 | | % 153.63/22.98 | | (114) all_54_12 = e0 % 153.63/22.98 | | % 153.63/22.98 | | REF_CLOSE: (12), (50), (114) are inconsistent by sub-proof #459. % 153.63/22.98 | | % 153.63/22.98 | Case 2: % 153.63/22.98 | | % 153.63/22.98 | | (115) ~ (all_54_12 = e0) % 153.63/22.98 | | (116) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/22.98 | | % 153.63/22.98 | | BETA: splitting (102) gives: % 153.63/22.98 | | % 153.63/22.98 | | Case 1: % 153.63/22.98 | | | % 153.63/22.98 | | | (117) all_54_2 = e0 % 153.63/22.98 | | | % 153.63/22.98 | | | REF_CLOSE: (11), (106), (117) are inconsistent by sub-proof #860. % 153.63/22.98 | | | % 153.63/22.98 | | Case 2: % 153.63/22.98 | | | % 153.63/22.98 | | | (118) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 153.63/22.98 | | | % 153.63/22.98 | | | BETA: splitting (53) gives: % 153.63/22.98 | | | % 153.63/22.98 | | | Case 1: % 153.63/22.98 | | | | % 153.63/22.98 | | | | (119) all_54_5 = e0 % 153.63/22.98 | | | | % 153.63/22.98 | | | | REF_CLOSE: (4), (24), (41), (49), (67), (69), (78), (89), (96), (99), % 153.63/22.98 | | | | (108), (109), (110), (119) are inconsistent by sub-proof % 153.63/22.98 | | | | #231. % 153.63/22.98 | | | | % 153.63/22.98 | | | Case 2: % 153.63/22.98 | | | | % 153.63/22.98 | | | | (120) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 153.63/22.98 | | | | % 153.63/22.98 | | | | BETA: splitting (109) gives: % 153.63/22.98 | | | | % 153.63/22.98 | | | | Case 1: % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | (121) all_58_28 = e1 % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | COMBINE_EQS: (4), (121) imply: % 153.63/22.98 | | | | | (122) e1 = e0 % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | REDUCE: (99), (122) imply: % 153.63/22.98 | | | | | (123) $false % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | CLOSE: (123) is inconsistent. % 153.63/22.98 | | | | | % 153.63/22.98 | | | | Case 2: % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | (124) ~ (all_58_28 = e1) % 153.63/22.98 | | | | | (125) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | REDUCE: (4), (124) imply: % 153.63/22.98 | | | | | (126) ~ (e1 = e0) % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | BETA: splitting (35) gives: % 153.63/22.98 | | | | | % 153.63/22.98 | | | | | Case 1: % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | (127) all_54_13 = e0 % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | COMBINE_EQS: (7), (127) imply: % 153.63/22.98 | | | | | | (128) all_52_7 = e0 % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | SIMP: (128) implies: % 153.63/22.98 | | | | | | (129) all_52_7 = e0 % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | COMBINE_EQS: (71), (129) imply: % 153.63/22.98 | | | | | | (130) all_56_13 = e0 % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | COMBINE_EQS: (61), (129) imply: % 153.63/22.98 | | | | | | (131) all_58_24 = e0 % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | REDUCE: (87), (129) imply: % 153.63/22.98 | | | | | | (132) ~ (all_52_11 = e0) % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | SIMP: (132) implies: % 153.63/22.98 | | | | | | (133) ~ (all_52_11 = e0) % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | BETA: splitting (57) gives: % 153.63/22.98 | | | | | | % 153.63/22.98 | | | | | | Case 1: % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | (134) all_56_5 = e0 % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | COMBINE_EQS: (52), (134) imply: % 153.63/22.98 | | | | | | | (135) all_52_9 = e0 % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | COMBINE_EQS: (8), (135) imply: % 153.63/22.98 | | | | | | | (136) all_58_11 = e0 % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | REDUCE: (75), (135) imply: % 153.63/22.98 | | | | | | | (137) ~ (all_52_13 = e0) % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | SIMP: (137) implies: % 153.63/22.98 | | | | | | | (138) ~ (all_52_13 = e0) % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | REDUCE: (83), (135) imply: % 153.63/22.98 | | | | | | | (139) ~ (all_8_2 = e0) % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | SIMP: (139) implies: % 153.63/22.98 | | | | | | | (140) ~ (all_8_2 = e0) % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | BETA: splitting (6) gives: % 153.63/22.98 | | | | | | | % 153.63/22.98 | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | (141) all_56_9 = e0 % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | COMBINE_EQS: (66), (141) imply: % 153.63/22.98 | | | | | | | | (142) all_52_12 = e0 % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | REDUCE: (54), (142) imply: % 153.63/22.98 | | | | | | | | (143) $false % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | CLOSE: (143) is inconsistent. % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | Case 2: % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | (144) all_56_10 = e0 | all_56_11 = e0 % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | BETA: splitting (144) gives: % 153.63/22.98 | | | | | | | | % 153.63/22.98 | | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | (145) all_56_10 = e0 % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | COMBINE_EQS: (82), (145) imply: % 153.63/22.98 | | | | | | | | | (146) all_52_13 = e0 % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | REDUCE: (138), (146) imply: % 153.63/22.98 | | | | | | | | | (147) $false % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | CLOSE: (147) is inconsistent. % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | Case 2: % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | (148) all_56_11 = e0 % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | COMBINE_EQS: (55), (148) imply: % 153.63/22.98 | | | | | | | | | (149) all_52_14 = e0 % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | SIMP: (149) implies: % 153.63/22.98 | | | | | | | | | (150) all_52_14 = e0 % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | COMBINE_EQS: (36), (150) imply: % 153.63/22.98 | | | | | | | | | (151) all_58_20 = e0 % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | REDUCE: (97), (150) imply: % 153.63/22.98 | | | | | | | | | (152) ~ (all_52_2 = e0) % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | REDUCE: (111), (150) imply: % 153.63/22.98 | | | | | | | | | (153) ~ (all_6_2 = e0) % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | REDUCE: (98), (150) imply: % 153.63/22.98 | | | | | | | | | (154) ~ (all_4_2 = e0) % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | SIMP: (154) implies: % 153.63/22.98 | | | | | | | | | (155) ~ (all_4_2 = e0) % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | BETA: splitting (76) gives: % 153.63/22.98 | | | | | | | | | % 153.63/22.98 | | | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | (156) all_56_9 = e1 % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | COMBINE_EQS: (66), (156) imply: % 153.63/22.98 | | | | | | | | | | (157) all_52_12 = e1 % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | SIMP: (157) implies: % 153.63/22.98 | | | | | | | | | | (158) all_52_12 = e1 % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | COMBINE_EQS: (20), (158) imply: % 153.63/22.98 | | | | | | | | | | (159) all_58_6 = e1 % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | REDUCE: (90), (158) imply: % 153.63/22.98 | | | | | | | | | | (160) ~ (all_4_2 = e1) % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | BETA: splitting (88) gives: % 153.63/22.98 | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | (161) all_56_12 = e1 % 153.63/22.98 | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | REF_CLOSE: (3), (17), (30), (31), (133), (161) are % 153.63/22.98 | | | | | | | | | | | inconsistent by sub-proof #237. % 153.63/22.98 | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | Case 2: % 153.63/22.98 | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | (162) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.98 | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | BETA: splitting (162) gives: % 153.63/22.98 | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | (163) all_56_13 = e1 % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | COMBINE_EQS: (130), (163) imply: % 153.63/22.98 | | | | | | | | | | | | (164) e1 = e0 % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | REDUCE: (99), (164) imply: % 153.63/22.98 | | | | | | | | | | | | (165) $false % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | CLOSE: (165) is inconsistent. % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | Case 2: % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | (166) all_56_14 = e1 | all_56_15 = e1 % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | BETA: splitting (166) gives: % 153.63/22.98 | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | (167) all_56_14 = e1 % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | COMBINE_EQS: (84), (167) imply: % 153.63/22.98 | | | | | | | | | | | | | (168) all_52_11 = e1 % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | SIMP: (168) implies: % 153.63/22.98 | | | | | | | | | | | | | (169) all_52_11 = e1 % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | COMBINE_EQS: (16), (169) imply: % 153.63/22.98 | | | | | | | | | | | | | (170) all_58_26 = e1 % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | REDUCE: (18), (169) imply: % 153.63/22.98 | | | | | | | | | | | | | (171) ~ (all_52_8 = e1) % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | REDUCE: (77), (169) imply: % 153.63/22.98 | | | | | | | | | | | | | (172) ~ (all_6_2 = e1) % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | SIMP: (172) implies: % 153.63/22.98 | | | | | | | | | | | | | (173) ~ (all_6_2 = e1) % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | BETA: splitting (125) gives: % 153.63/22.98 | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | Case 1: % 153.63/22.98 | | | | | | | | | | | | | | % 153.63/22.98 | | | | | | | | | | | | | | (174) all_58_29 = e1 % 153.63/22.98 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | COMBINE_EQS: (67), (174) imply: % 153.63/22.99 | | | | | | | | | | | | | | (175) all_8_2 = e1 % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REDUCE: (21), (175) imply: % 153.63/22.99 | | | | | | | | | | | | | | (176) ~ (all_52_6 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | BETA: splitting (86) gives: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | (177) all_56_6 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | COMBINE_EQS: (70), (177) imply: % 153.63/22.99 | | | | | | | | | | | | | | | (178) all_52_2 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | COMBINE_EQS: (15), (178) imply: % 153.63/22.99 | | | | | | | | | | | | | | | (179) all_58_15 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | (180) all_58_31 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (180) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | (181) all_4_2 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | REDUCE: (155), (181) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | (182) $false % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | (183) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 153.63/22.99 | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.63/22.99 | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.63/22.99 | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.63/22.99 | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.63/22.99 | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.63/22.99 | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.63/22.99 | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.63/22.99 | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.63/22.99 | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.63/22.99 | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.63/22.99 | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.63/22.99 | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.63/22.99 | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.63/22.99 | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.63/22.99 | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.63/22.99 | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.63/22.99 | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.63/22.99 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.63/22.99 | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.63/22.99 | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.63/22.99 | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.63/22.99 | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.63/22.99 | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.63/22.99 | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.63/22.99 | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.63/22.99 | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.63/22.99 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.63/22.99 | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.63/22.99 | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/22.99 | | | | | | | | | | | | | | | | e0) % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (24), (29), (49), (69), (78), (89), % 153.63/22.99 | | | | | | | | | | | | | | | | (95), (96), (99), (103), (108), (110), (125), % 153.63/22.99 | | | | | | | | | | | | | | | | (131), (136), (138), (151), (159), (170), (171), % 153.63/22.99 | | | | | | | | | | | | | | | | (174), (179), (183) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | | | | #466. % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | (184) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (10), (24), (49), (69), (78), (89), % 153.63/22.99 | | | | | | | | | | | | | | | (91), (96), (99), (103), (108), (110), (125), % 153.63/22.99 | | | | | | | | | | | | | | | (148), (173), (174), (176), (184) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | by sub-proof #465. % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | (185) all_58_30 = e1 | all_58_31 = e1 % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REF_CLOSE: (2), (103), (108), (173), (185) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | by sub-proof #673. % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | (186) all_56_15 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | REF_CLOSE: (9), (103), (186) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | #671. % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | (187) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | BETA: splitting (187) gives: % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | (188) all_56_10 = e1 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | COMBINE_EQS: (82), (188) imply: % 153.63/22.99 | | | | | | | | | | | (189) all_52_13 = e1 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | SIMP: (189) implies: % 153.63/22.99 | | | | | | | | | | | (190) all_52_13 = e1 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | REDUCE: (51), (190) imply: % 153.63/22.99 | | | | | | | | | | | (191) ~ (all_52_1 = e1) % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | REDUCE: (47), (190) imply: % 153.63/22.99 | | | | | | | | | | | (192) ~ (all_8_2 = e1) % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | SIMP: (192) implies: % 153.63/22.99 | | | | | | | | | | | (193) ~ (all_8_2 = e1) % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | REDUCE: (46), (190) imply: % 153.63/22.99 | | | | | | | | | | | (194) ~ (all_4_2 = e1) % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | BETA: splitting (125) gives: % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | (195) all_58_29 = e1 % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | COMBINE_EQS: (67), (195) imply: % 153.63/22.99 | | | | | | | | | | | | (196) all_8_2 = e1 % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | REDUCE: (193), (196) imply: % 153.63/22.99 | | | | | | | | | | | | (197) $false % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | (198) all_58_30 = e1 | all_58_31 = e1 % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | BETA: splitting (198) gives: % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | (199) all_58_30 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | COMBINE_EQS: (108), (199) imply: % 153.63/22.99 | | | | | | | | | | | | | (200) all_6_2 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | REDUCE: (44), (200) imply: % 153.63/22.99 | | | | | | | | | | | | | (201) ~ (all_52_2 = e1) % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | BETA: splitting (88) gives: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | (202) all_56_12 = e1 % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (30), (31), (133), (202) are % 153.63/22.99 | | | | | | | | | | | | | | inconsistent by sub-proof #237. % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | (203) ~ (all_56_12 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REDUCE: (31), (203) imply: % 153.63/22.99 | | | | | | | | | | | | | | (204) ~ (all_10_1 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | BETA: splitting (33) gives: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | (205) all_56_0 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | COMBINE_EQS: (40), (205) imply: % 153.63/22.99 | | | | | | | | | | | | | | | (206) e1 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | REF_CLOSE: (2), (99), (103), (198), (199), (206) are % 153.63/22.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #487. % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | (207) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | REF_CLOSE: (31), (70), (79), (191), (201), (204), (207) are % 153.63/22.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #403. % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | (208) all_58_31 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | COMBINE_EQS: (2), (208) imply: % 153.63/22.99 | | | | | | | | | | | | | (209) all_4_2 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | REDUCE: (103), (209) imply: % 153.63/22.99 | | | | | | | | | | | | | (210) $false % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | (211) all_56_11 = e1 | all_56_15 = e1 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | REF_CLOSE: (9), (99), (103), (148), (211) are inconsistent by % 153.63/22.99 | | | | | | | | | | | sub-proof #334. % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | End of split % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | End of split % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | Case 2: % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | (212) all_56_8 = e0 | all_56_14 = e0 % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | REF_CLOSE: (26), (84), (91), (133), (212) are inconsistent by % 153.63/22.99 | | | | | | | sub-proof #805. % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | End of split % 153.63/22.99 | | | | | | % 153.63/22.99 | | | | | Case 2: % 153.63/22.99 | | | | | | % 153.63/22.99 | | | | | | (213) ~ (all_54_13 = e0) % 153.63/22.99 | | | | | | % 153.63/22.99 | | | | | | REDUCE: (7), (213) imply: % 153.63/22.99 | | | | | | (214) ~ (all_52_7 = e0) % 153.63/22.99 | | | | | | % 153.63/22.99 | | | | | | BETA: splitting (104) gives: % 153.63/22.99 | | | | | | % 153.63/22.99 | | | | | | Case 1: % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | (215) all_56_3 = e0 % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | COMBINE_EQS: (60), (215) imply: % 153.63/22.99 | | | | | | | (216) all_8_2 = e0 % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | COMBINE_EQS: (67), (216) imply: % 153.63/22.99 | | | | | | | (217) all_58_29 = e0 % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | REF_CLOSE: (4), (24), (49), (69), (78), (89), (96), (99), (108), % 153.63/22.99 | | | | | | | (109), (110), (217) are inconsistent by sub-proof #483. % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | Case 2: % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | (218) all_56_7 = e0 | all_56_13 = e0 % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | BETA: splitting (218) gives: % 153.63/22.99 | | | | | | | % 153.63/22.99 | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | (219) all_56_7 = e0 % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | COMBINE_EQS: (10), (219) imply: % 153.63/22.99 | | | | | | | | (220) all_52_6 = e0 % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | COMBINE_EQS: (85), (220) imply: % 153.63/22.99 | | | | | | | | (221) all_58_17 = e0 % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | REDUCE: (27), (220) imply: % 153.63/22.99 | | | | | | | | (222) ~ (all_52_4 = e0) % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | REDUCE: (34), (220) imply: % 153.63/22.99 | | | | | | | | (223) ~ (all_52_7 = e0) % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | REDUCE: (42), (220) imply: % 153.63/22.99 | | | | | | | | (224) ~ (all_52_14 = e0) % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | SIMP: (224) implies: % 153.63/22.99 | | | | | | | | (225) ~ (all_52_14 = e0) % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | BETA: splitting (107) gives: % 153.63/22.99 | | | | | | | | % 153.63/22.99 | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | | (226) all_56_12 = e0 % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | | REF_CLOSE: (12), (31), (226) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | #230. % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | | (227) all_56_13 = e0 | all_56_14 = e0 % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | | BETA: splitting (227) gives: % 153.63/22.99 | | | | | | | | | % 153.63/22.99 | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | (228) all_56_13 = e0 % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | REF_CLOSE: (71), (214), (228) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | #802. % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | (229) all_56_14 = e0 % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | COMBINE_EQS: (84), (229) imply: % 153.63/22.99 | | | | | | | | | | (230) all_52_11 = e0 % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | SIMP: (230) implies: % 153.63/22.99 | | | | | | | | | | (231) all_52_11 = e0 % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | COMBINE_EQS: (16), (231) imply: % 153.63/22.99 | | | | | | | | | | (232) all_58_26 = e0 % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | REDUCE: (14), (231) imply: % 153.63/22.99 | | | | | | | | | | (233) ~ (all_10_1 = e0) % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | REDUCE: (77), (231) imply: % 153.63/22.99 | | | | | | | | | | (234) ~ (all_6_2 = e0) % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | BETA: splitting (6) gives: % 153.63/22.99 | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | (235) all_56_9 = e0 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | COMBINE_EQS: (66), (235) imply: % 153.63/22.99 | | | | | | | | | | | (236) all_52_12 = e0 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | REDUCE: (54), (236) imply: % 153.63/22.99 | | | | | | | | | | | (237) $false % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | CLOSE: (237) is inconsistent. % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | (238) all_56_10 = e0 | all_56_11 = e0 % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | BETA: splitting (238) gives: % 153.63/22.99 | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | (239) all_56_10 = e0 % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | COMBINE_EQS: (82), (239) imply: % 153.63/22.99 | | | | | | | | | | | | (240) all_52_13 = e0 % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | REDUCE: (75), (240) imply: % 153.63/22.99 | | | | | | | | | | | | (241) ~ (all_52_9 = e0) % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | REDUCE: (47), (240) imply: % 153.63/22.99 | | | | | | | | | | | | (242) ~ (all_8_2 = e0) % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | SIMP: (242) implies: % 153.63/22.99 | | | | | | | | | | | | (243) ~ (all_8_2 = e0) % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | REDUCE: (46), (240) imply: % 153.63/22.99 | | | | | | | | | | | | (244) ~ (all_4_2 = e0) % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | SIMP: (244) implies: % 153.63/22.99 | | | | | | | | | | | | (245) ~ (all_4_2 = e0) % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | BETA: splitting (88) gives: % 153.63/22.99 | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | (246) all_56_12 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (12), (13), (15), (22), (23), % 153.63/22.99 | | | | | | | | | | | | | (24), (28), (29), (31), (36), (39), (40), (46), % 153.63/22.99 | | | | | | | | | | | | | (47), (49), (52), (55), (56), (60), (61), (62), % 153.63/22.99 | | | | | | | | | | | | | (64), (66), (67), (68), (69), (70), (71), (72), % 153.63/22.99 | | | | | | | | | | | | | (73), (76), (78), (81), (82), (86), (89), (91), % 153.63/22.99 | | | | | | | | | | | | | (95), (96), (97), (98), (108), (109), (110), % 153.63/22.99 | | | | | | | | | | | | | (111), (112), (113), (214), (219), (221), (232), % 153.63/22.99 | | | | | | | | | | | | | (241), (243), (246) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | #222. % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | (247) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | BETA: splitting (247) gives: % 153.63/22.99 | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | (248) all_56_13 = e1 % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | COMBINE_EQS: (71), (248) imply: % 153.63/22.99 | | | | | | | | | | | | | | (249) all_52_7 = e1 % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | SIMP: (249) implies: % 153.63/22.99 | | | | | | | | | | | | | | (250) all_52_7 = e1 % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REDUCE: (43), (250) imply: % 153.63/22.99 | | | | | | | | | | | | | | (251) ~ (all_52_4 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REDUCE: (13), (250) imply: % 153.63/22.99 | | | | | | | | | | | | | | (252) ~ (all_10_1 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | SIMP: (252) implies: % 153.63/22.99 | | | | | | | | | | | | | | (253) ~ (all_10_1 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REDUCE: (93), (250) imply: % 153.63/22.99 | | | | | | | | | | | | | | (254) ~ (all_8_2 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | SIMP: (254) implies: % 153.63/22.99 | | | | | | | | | | | | | | (255) ~ (all_8_2 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | REDUCE: (101), (250) imply: % 153.63/22.99 | | | | | | | | | | | | | | (256) ~ (all_4_2 = e1) % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | BETA: splitting (125) gives: % 153.63/22.99 | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | (257) all_58_29 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | COMBINE_EQS: (67), (257) imply: % 153.63/22.99 | | | | | | | | | | | | | | | (258) all_8_2 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | REDUCE: (255), (258) imply: % 153.63/22.99 | | | | | | | | | | | | | | | (259) $false % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | (260) ~ (all_58_29 = e1) % 153.63/22.99 | | | | | | | | | | | | | | | (261) all_58_30 = e1 | all_58_31 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 153.63/22.99 | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | (262) all_58_30 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (262) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | (263) all_6_2 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | REDUCE: (37), (263) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | (264) ~ (all_52_8 = e1) % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | (265) all_56_0 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (265) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | (266) e1 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (99), (103), (261), (262), (266) are % 153.63/22.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #487. % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | (267) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | (268) all_56_1 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (268) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | (269) all_52_4 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | REDUCE: (251), (269) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | (270) $false % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | (271) all_56_4 = e1 | all_56_9 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | (272) all_56_9 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (272) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | (273) all_52_12 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | SIMP: (273) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | (274) all_52_12 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | REDUCE: (68), (274) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | (275) ~ (all_52_14 = e1) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | SIMP: (275) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | (276) ~ (all_52_14 = e1) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | (277) all_56_4 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (277) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | (278) all_52_8 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (278) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | (279) ~ (all_52_4 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (280) all_56_1 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (280) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (281) all_52_4 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | SIMP: (281) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (282) all_52_4 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (282) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_8_2 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_8_2 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (282) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (285) ~ (e3 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (286) all_58_28 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (89), (286) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | #688. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (287) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (288) all_56_1 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (288) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (289) e3 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (289) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (290) $false % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (291) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (292) all_56_3 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (292) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (293) all_8_2 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (293) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (294) all_58_29 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_58_29 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (17), (28), (31), (49), (50), (78), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | (94), (96), (105), (110), (116), (214), (253), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | (262), (295) are inconsistent by sub-proof #221. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_58_29 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_30 = e2 | all_58_31 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_58_30 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (262), (298) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | #500. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_31 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (299) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_4_2 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_4_2 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (301) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_56_15 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (301) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (303) ~ (all_52_14 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (301) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (304) ~ (all_10_1 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_56_9 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (305) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) e3 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) e3 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (307) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_29 = e1 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (24), (49), (69), (78), (89), (96), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (262), (308) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | #472. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_56_12 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (310) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_10_1 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (311) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_10_1 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (312) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) op(e0, e3) = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (312) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) op(e0, e3) = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_56_10 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (315) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) e3 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (316) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) e3 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (317) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_58_29 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (49), (69), (78), (89), (96), (110), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (318) are inconsistent by sub-proof #660. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_56_10 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_56_11 = e3 | all_56_15 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (239), (319) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) ~ (e3 = e0) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_56_11 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (322) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_52_14 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (323) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_52_14 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, e3, e3, e0, simplifying % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (313), (314) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) e3 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (325) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_58_29 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (49), (69), (78), (89), (96), (110), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (326) are inconsistent by sub-proof #660. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_56_15 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (327) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) e3 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (328) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_29 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (17), (28), (31), (49), (50), (78), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (94), (96), (105), (110), (116), (214), (253), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (329) are inconsistent by sub-proof #221. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (all_56_12 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (330) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (all_10_1 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (116), (253), (304), (331) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #505. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (332) ~ (all_56_3 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (332) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (333) ~ (all_8_2 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (120), (255), (284), (333) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #531. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_56_1 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (334) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_52_4 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (38), (251), (279), (335) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | (336) ~ (all_56_4 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (336) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | (337) ~ (all_52_8 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (338) all_56_0 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (338) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (339) e3 = e0 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (339) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (340) $false % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | (341) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (342) all_56_1 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (342) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (343) all_52_4 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | SIMP: (343) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (344) all_52_4 = e3 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (344) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_8_2 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | SIMP: (345) implies: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_8_2 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (347) all_56_1 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (342), (347) are inconsistent by sub-proof % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | #568. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (348) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (349) all_56_3 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (349) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (350) all_8_2 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (350) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_29 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (350) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (352) ~ (e3 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (17), (28), (31), (49), (50), (78), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (94), (96), (105), (110), (116), (214), (253), % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (262), (351) are inconsistent by sub-proof #221. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_56_3 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (353) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_8_2 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (120), (255), (346), (354) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #531. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (355) ~ (all_56_1 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (355) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | (356) ~ (all_52_4 = e3) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (357) all_56_4 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (357) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (358) all_52_8 = e2 % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (358) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (359) ~ (all_52_4 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (38), (251), (356), (359) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_56_4 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (360) imply: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_52_8 = e2) % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (118), (264), (337), (361) are inconsistent % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #554. % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | End of split % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/22.99 | | | | | | | | | | | | | | | | | | | % 153.63/22.99 | | | | | | | | | | | | | | | | | | | (362) ~ (all_56_9 = e1) % 153.63/23.00 | | | | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | | | | REDUCE: (66), (362) imply: % 153.63/23.00 | | | | | | | | | | | | | | | | | | | (363) ~ (all_52_12 = e1) % 153.63/23.00 | | | | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (66), (264), (271), (363) are inconsistent % 153.63/23.00 | | | | | | | | | | | | | | | | | | | by sub-proof #485. % 153.63/23.00 | | | | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | (364) all_58_31 = e1 % 153.63/23.00 | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (364) imply: % 153.63/23.00 | | | | | | | | | | | | | | | | (365) all_4_2 = e1 % 153.63/23.00 | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | REDUCE: (103), (365) imply: % 153.63/23.00 | | | | | | | | | | | | | | | | (366) $false % 153.63/23.00 | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | | CLOSE: (366) is inconsistent. % 153.63/23.00 | | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | (367) all_56_14 = e1 | all_56_15 = e1 % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | REF_CLOSE: (9), (99), (103), (229), (367) are inconsistent by % 153.63/23.00 | | | | | | | | | | | | | | sub-proof #582. % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | (368) all_56_11 = e0 % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | REF_CLOSE: (55), (225), (368) are inconsistent by sub-proof % 153.63/23.00 | | | | | | | | | | | | #220. % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | End of split % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | End of split % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | (369) all_56_13 = e0 % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | REF_CLOSE: (71), (214), (369) are inconsistent by sub-proof % 153.63/23.00 | | | | | | | | #802. % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | End of split % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | End of split % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | End of split % 153.63/23.00 | | | | | % 153.63/23.00 | | | | End of split % 153.63/23.00 | | | | % 153.63/23.00 | | | End of split % 153.63/23.00 | | | % 153.63/23.00 | | End of split % 153.63/23.00 | | % 153.63/23.00 | End of split % 153.63/23.00 | % 153.63/23.00 End of proof % 153.63/23.00 % 153.63/23.00 Sub-proof #220 shows that the following formulas are inconsistent: % 153.63/23.00 ---------------------------------------------------------------- % 153.63/23.00 (1) all_56_11 = all_52_14 % 153.63/23.00 (2) all_56_11 = e0 % 153.63/23.00 (3) ~ (all_52_14 = e0) % 153.63/23.00 % 153.63/23.00 Begin of proof % 153.63/23.00 | % 153.63/23.00 | COMBINE_EQS: (1), (2) imply: % 153.63/23.00 | (4) all_52_14 = e0 % 153.63/23.00 | % 153.63/23.00 | SIMP: (4) implies: % 153.63/23.00 | (5) all_52_14 = e0 % 153.63/23.00 | % 153.63/23.00 | REDUCE: (3), (5) imply: % 153.63/23.00 | (6) $false % 153.63/23.00 | % 153.63/23.00 | CLOSE: (6) is inconsistent. % 153.63/23.00 | % 153.63/23.00 End of proof % 153.63/23.00 % 153.63/23.00 Sub-proof #221 shows that the following formulas are inconsistent: % 153.63/23.00 ---------------------------------------------------------------- % 153.63/23.00 (1) all_58_31 = all_4_2 % 153.63/23.00 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/23.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/23.00 (3) all_58_28 = e0 % 153.63/23.00 (4) op(e0, all_10_1) = e0 % 153.63/23.00 (5) ~ (all_10_1 = all_4_2) % 153.63/23.00 (6) all_56_12 = all_10_1 % 153.63/23.00 (7) ~ (e3 = e1) % 153.63/23.00 (8) all_54_12 = all_10_1 % 153.63/23.00 (9) ~ (e3 = e0) % 153.63/23.00 (10) all_58_30 = e1 % 153.63/23.00 (11) all_58_29 = e2 % 153.63/23.00 (12) ~ (all_10_1 = e1) % 153.63/23.00 (13) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.63/23.00 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.00 (15) ~ (all_52_7 = e0) % 153.63/23.00 (16) op(e0, e2) = all_52_7 % 153.63/23.00 (17) ~ (e3 = e2) % 153.63/23.00 (18) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.63/23.00 % 153.63/23.00 Begin of proof % 153.63/23.00 | % 153.63/23.00 | BETA: splitting (14) gives: % 153.63/23.00 | % 153.63/23.00 | Case 1: % 153.63/23.00 | | % 153.63/23.00 | | (19) all_58_28 = e3 % 153.63/23.00 | | % 153.63/23.00 | | REF_CLOSE: (3), (9), (19) are inconsistent by sub-proof #689. % 153.63/23.00 | | % 153.63/23.00 | Case 2: % 153.63/23.00 | | % 153.63/23.00 | | (20) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.00 | | % 153.63/23.00 | | BETA: splitting (20) gives: % 153.63/23.00 | | % 153.63/23.00 | | Case 1: % 153.63/23.00 | | | % 153.63/23.00 | | | (21) all_58_29 = e3 % 153.63/23.00 | | | % 153.63/23.00 | | | REF_CLOSE: (11), (17), (21) are inconsistent by sub-proof #780. % 153.63/23.00 | | | % 153.63/23.00 | | Case 2: % 153.63/23.00 | | | % 153.63/23.00 | | | (22) all_58_30 = e3 | all_58_31 = e3 % 153.63/23.00 | | | % 153.63/23.00 | | | BETA: splitting (22) gives: % 153.63/23.00 | | | % 153.63/23.00 | | | Case 1: % 153.63/23.00 | | | | % 153.63/23.00 | | | | (23) all_58_30 = e3 % 153.63/23.00 | | | | % 153.63/23.00 | | | | REF_CLOSE: (7), (10), (23) are inconsistent by sub-proof #290. % 153.63/23.00 | | | | % 153.63/23.00 | | | Case 2: % 153.63/23.00 | | | | % 153.63/23.00 | | | | (24) all_58_31 = e3 % 153.63/23.00 | | | | % 153.63/23.00 | | | | COMBINE_EQS: (1), (24) imply: % 153.63/23.00 | | | | (25) all_4_2 = e3 % 153.63/23.00 | | | | % 153.63/23.00 | | | | SIMP: (25) implies: % 153.63/23.00 | | | | (26) all_4_2 = e3 % 153.63/23.00 | | | | % 153.63/23.00 | | | | REDUCE: (5), (26) imply: % 153.63/23.00 | | | | (27) ~ (all_10_1 = e3) % 153.63/23.00 | | | | % 153.63/23.00 | | | | BETA: splitting (13) gives: % 153.63/23.00 | | | | % 153.63/23.00 | | | | Case 1: % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | (28) all_56_12 = e2 % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | REF_CLOSE: (2), (4), (6), (15), (16), (28) are inconsistent by % 153.63/23.00 | | | | | sub-proof #239. % 153.63/23.00 | | | | | % 153.63/23.00 | | | | Case 2: % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | (29) ~ (all_56_12 = e2) % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | REDUCE: (6), (29) imply: % 153.63/23.00 | | | | | (30) ~ (all_10_1 = e2) % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | REF_CLOSE: (8), (12), (18), (27), (30) are inconsistent by sub-proof % 153.63/23.00 | | | | | #505. % 153.63/23.00 | | | | | % 153.63/23.00 | | | | End of split % 153.63/23.00 | | | | % 153.63/23.00 | | | End of split % 153.63/23.00 | | | % 153.63/23.00 | | End of split % 153.63/23.00 | | % 153.63/23.00 | End of split % 153.63/23.00 | % 153.63/23.00 End of proof % 153.63/23.00 % 153.63/23.00 Sub-proof #222 shows that the following formulas are inconsistent: % 153.63/23.00 ---------------------------------------------------------------- % 153.63/23.00 (1) all_58_31 = all_4_2 % 153.63/23.00 (2) all_58_28 = e0 % 153.63/23.00 (3) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/23.00 (4) all_56_15 = all_4_2 % 153.63/23.00 (5) ~ (all_10_1 = e0) % 153.63/23.00 (6) ~ (all_52_7 = all_10_1) % 153.63/23.00 (7) all_58_15 = all_52_2 % 153.63/23.00 (8) all_58_17 = e0 % 153.63/23.00 (9) all_56_4 = all_52_8 % 153.63/23.00 (10) ~ (all_52_4 = all_8_2) % 153.63/23.00 (11) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/23.00 (12) ~ (all_10_1 = all_4_2) % 153.63/23.00 (13) all_58_13 = all_52_13 % 153.63/23.00 (14) all_56_12 = all_10_1 % 153.63/23.00 (15) all_56_7 = e0 % 153.63/23.00 (16) all_58_20 = all_52_14 % 153.63/23.00 (17) ~ (all_52_12 = all_52_13) % 153.63/23.00 (18) all_56_0 = e0 % 153.63/23.00 (19) ~ (all_52_13 = all_4_2) % 153.63/23.00 (20) ~ (all_52_13 = all_8_2) % 153.63/23.00 (21) ~ (e3 = e1) % 153.63/23.00 (22) all_56_5 = all_52_9 % 153.63/23.00 (23) all_56_12 = e1 % 153.63/23.00 (24) all_56_11 = all_52_14 % 153.63/23.00 (25) all_56_1 = all_52_4 % 153.63/23.00 (26) ~ (all_52_9 = e0) % 153.63/23.00 (27) all_56_3 = all_8_2 % 153.63/23.00 (28) all_58_24 = all_52_7 % 153.63/23.00 (29) ~ (all_52_13 = all_52_14) % 153.63/23.00 (30) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.63/23.00 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.63/23.00 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.63/23.00 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.63/23.00 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.63/23.00 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.63/23.00 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.63/23.00 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.63/23.00 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.63/23.00 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.63/23.00 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/23.00 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.63/23.00 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/23.00 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/23.00 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/23.00 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/23.00 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.00 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.63/23.00 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.00 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.63/23.00 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/23.00 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.63/23.00 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/23.00 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/23.00 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.63/23.00 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.63/23.00 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.63/23.00 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.63/23.00 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/23.00 e0) % 153.63/23.00 (31) all_56_9 = all_52_12 % 153.63/23.00 (32) all_58_29 = all_8_2 % 153.63/23.00 (33) ~ (all_52_12 = all_52_14) % 153.63/23.00 (34) ~ (e2 = e1) % 153.63/23.00 (35) all_56_6 = all_52_2 % 153.63/23.00 (36) all_56_13 = all_52_7 % 153.63/23.00 (37) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/23.00 (38) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/23.00 (39) all_58_26 = e0 % 153.63/23.00 (40) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/23.00 (41) ~ (e3 = e0) % 153.63/23.00 (42) all_58_22 = all_10_1 % 153.63/23.00 (43) all_56_10 = all_52_13 % 153.63/23.00 (44) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.63/23.00 (45) ~ (e2 = e0) % 153.63/23.00 (46) all_56_8 = all_6_2 % 153.63/23.00 (47) all_58_4 = all_52_8 % 153.63/23.00 (48) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.00 (49) ~ (all_52_2 = all_52_14) % 153.63/23.00 (50) ~ (all_52_7 = e0) % 153.63/23.00 (51) ~ (all_52_14 = all_4_2) % 153.63/23.00 (52) all_58_30 = all_6_2 % 153.63/23.00 (53) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/23.00 (54) ~ (e3 = e2) % 153.63/23.00 (55) ~ (all_52_14 = all_6_2) % 153.63/23.00 (56) ~ (all_8_2 = e0) % 153.63/23.00 (57) ~ (all_52_4 = all_52_12) % 153.63/23.00 (58) ~ (all_52_2 = all_10_1) % 153.63/23.00 % 153.63/23.00 Begin of proof % 153.63/23.00 | % 153.63/23.00 | COMBINE_EQS: (14), (23) imply: % 153.63/23.00 | (59) all_10_1 = e1 % 153.63/23.00 | % 153.63/23.00 | SIMP: (59) implies: % 153.63/23.00 | (60) all_10_1 = e1 % 153.63/23.00 | % 153.63/23.00 | COMBINE_EQS: (42), (60) imply: % 153.63/23.00 | (61) all_58_22 = e1 % 153.63/23.00 | % 153.63/23.00 | REDUCE: (58), (60) imply: % 153.63/23.00 | (62) ~ (all_52_2 = e1) % 153.63/23.00 | % 153.63/23.00 | REDUCE: (6), (60) imply: % 153.63/23.00 | (63) ~ (all_52_7 = e1) % 153.63/23.00 | % 153.63/23.00 | REDUCE: (12), (60) imply: % 153.63/23.00 | (64) ~ (all_4_2 = e1) % 153.63/23.00 | % 153.63/23.00 | SIMP: (64) implies: % 153.63/23.00 | (65) ~ (all_4_2 = e1) % 153.63/23.00 | % 153.63/23.00 | REDUCE: (5), (60) imply: % 153.63/23.00 | (66) ~ (e1 = e0) % 153.63/23.00 | % 153.63/23.00 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (13), (15), (16), % 153.63/23.00 | (17), (18), (19), (20), (21), (22), (24), (25), (26), (27), (28), % 153.63/23.00 | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), % 153.63/23.00 | (40), (41), (43), (44), (45), (46), (47), (48), (49), (50), (51), % 153.63/23.00 | (52), (53), (54), (55), (56), (57), (61), (62), (63), (65), (66) % 153.63/23.00 | are inconsistent by sub-proof #223. % 153.63/23.00 | % 153.63/23.00 End of proof % 153.63/23.00 % 153.63/23.00 Sub-proof #223 shows that the following formulas are inconsistent: % 153.63/23.00 ---------------------------------------------------------------- % 153.63/23.00 (1) all_58_31 = all_4_2 % 153.63/23.00 (2) all_58_28 = e0 % 153.63/23.00 (3) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/23.00 (4) all_56_15 = all_4_2 % 153.63/23.00 (5) all_58_15 = all_52_2 % 153.63/23.00 (6) all_58_17 = e0 % 153.63/23.00 (7) all_56_4 = all_52_8 % 153.63/23.00 (8) ~ (all_52_4 = all_8_2) % 153.63/23.00 (9) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/23.00 (10) ~ (all_52_7 = e1) % 153.63/23.00 (11) all_58_13 = all_52_13 % 153.63/23.00 (12) all_56_7 = e0 % 153.63/23.00 (13) all_58_20 = all_52_14 % 153.63/23.00 (14) ~ (all_52_12 = all_52_13) % 153.63/23.00 (15) all_56_0 = e0 % 153.63/23.00 (16) ~ (all_52_13 = all_4_2) % 153.63/23.00 (17) ~ (all_52_13 = all_8_2) % 153.63/23.00 (18) ~ (e3 = e1) % 153.63/23.00 (19) all_56_5 = all_52_9 % 153.63/23.00 (20) ~ (all_52_2 = e1) % 153.63/23.00 (21) all_56_11 = all_52_14 % 153.63/23.00 (22) all_56_1 = all_52_4 % 153.63/23.00 (23) ~ (all_52_9 = e0) % 153.63/23.00 (24) all_56_3 = all_8_2 % 153.63/23.00 (25) all_58_24 = all_52_7 % 153.63/23.00 (26) ~ (all_52_13 = all_52_14) % 153.63/23.00 (27) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.63/23.00 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.63/23.00 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.63/23.00 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.63/23.00 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.63/23.00 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.63/23.00 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.63/23.00 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.63/23.00 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.63/23.00 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.63/23.00 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/23.00 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.63/23.00 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/23.00 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/23.00 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/23.00 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/23.00 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.00 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.63/23.00 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.00 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.63/23.00 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/23.00 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.63/23.00 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/23.00 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/23.00 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.63/23.00 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.63/23.00 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.63/23.00 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.63/23.00 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/23.00 e0) % 153.63/23.00 (28) all_56_9 = all_52_12 % 153.63/23.00 (29) all_58_29 = all_8_2 % 153.63/23.00 (30) ~ (all_52_12 = all_52_14) % 153.63/23.00 (31) ~ (e2 = e1) % 153.63/23.00 (32) all_56_6 = all_52_2 % 153.63/23.00 (33) all_56_13 = all_52_7 % 153.63/23.00 (34) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/23.00 (35) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.63/23.00 (36) all_58_26 = e0 % 153.63/23.00 (37) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/23.00 (38) ~ (e3 = e0) % 153.63/23.00 (39) all_56_10 = all_52_13 % 153.63/23.00 (40) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.63/23.00 (41) ~ (e2 = e0) % 153.63/23.00 (42) all_56_8 = all_6_2 % 153.63/23.00 (43) all_58_4 = all_52_8 % 153.63/23.00 (44) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.00 (45) ~ (all_52_2 = all_52_14) % 153.63/23.00 (46) ~ (all_52_7 = e0) % 153.63/23.00 (47) ~ (all_52_14 = all_4_2) % 153.63/23.00 (48) ~ (e1 = e0) % 153.63/23.00 (49) ~ (all_4_2 = e1) % 153.63/23.00 (50) all_58_30 = all_6_2 % 153.63/23.00 (51) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/23.00 (52) ~ (e3 = e2) % 153.63/23.00 (53) ~ (all_52_14 = all_6_2) % 153.63/23.00 (54) all_58_22 = e1 % 153.63/23.00 (55) ~ (all_8_2 = e0) % 153.63/23.00 (56) ~ (all_52_4 = all_52_12) % 153.63/23.00 % 153.63/23.00 Begin of proof % 153.63/23.00 | % 153.63/23.00 | BETA: splitting (3) gives: % 153.63/23.00 | % 153.63/23.00 | Case 1: % 153.63/23.00 | | % 153.63/23.00 | | (57) all_56_3 = e0 % 153.63/23.00 | | % 153.63/23.00 | | COMBINE_EQS: (24), (57) imply: % 153.63/23.00 | | (58) all_8_2 = e0 % 153.63/23.00 | | % 153.63/23.00 | | REDUCE: (55), (58) imply: % 153.63/23.00 | | (59) $false % 153.63/23.00 | | % 153.63/23.00 | | CLOSE: (59) is inconsistent. % 153.63/23.00 | | % 153.63/23.00 | Case 2: % 153.63/23.00 | | % 153.63/23.00 | | (60) all_56_5 = e0 | all_56_10 = e0 % 153.63/23.00 | | % 153.63/23.00 | | BETA: splitting (60) gives: % 153.63/23.00 | | % 153.63/23.00 | | Case 1: % 153.63/23.00 | | | % 153.63/23.00 | | | (61) all_56_5 = e0 % 153.63/23.00 | | | % 153.63/23.00 | | | COMBINE_EQS: (19), (61) imply: % 153.63/23.00 | | | (62) all_52_9 = e0 % 153.63/23.00 | | | % 153.63/23.00 | | | REDUCE: (23), (62) imply: % 153.63/23.00 | | | (63) $false % 153.63/23.00 | | | % 153.63/23.00 | | | CLOSE: (63) is inconsistent. % 153.63/23.00 | | | % 153.63/23.00 | | Case 2: % 153.63/23.00 | | | % 153.63/23.00 | | | (64) all_56_10 = e0 % 153.63/23.00 | | | % 153.63/23.00 | | | COMBINE_EQS: (39), (64) imply: % 153.63/23.00 | | | (65) all_52_13 = e0 % 153.63/23.00 | | | % 153.63/23.00 | | | SIMP: (65) implies: % 153.63/23.00 | | | (66) all_52_13 = e0 % 153.63/23.00 | | | % 153.63/23.00 | | | COMBINE_EQS: (11), (66) imply: % 153.63/23.00 | | | (67) all_58_13 = e0 % 153.63/23.00 | | | % 153.63/23.00 | | | REDUCE: (14), (66) imply: % 153.63/23.00 | | | (68) ~ (all_52_12 = e0) % 153.63/23.00 | | | % 153.63/23.00 | | | REDUCE: (26), (66) imply: % 153.63/23.00 | | | (69) ~ (all_52_14 = e0) % 153.63/23.00 | | | % 153.63/23.00 | | | SIMP: (69) implies: % 153.63/23.00 | | | (70) ~ (all_52_14 = e0) % 153.63/23.00 | | | % 153.63/23.00 | | | REDUCE: (17), (66) imply: % 153.63/23.00 | | | (71) ~ (all_8_2 = e0) % 153.63/23.00 | | | % 153.63/23.00 | | | REDUCE: (16), (66) imply: % 153.63/23.00 | | | (72) ~ (all_4_2 = e0) % 153.63/23.00 | | | % 153.63/23.00 | | | SIMP: (72) implies: % 153.63/23.00 | | | (73) ~ (all_4_2 = e0) % 153.63/23.00 | | | % 153.63/23.00 | | | BETA: splitting (37) gives: % 153.63/23.00 | | | % 153.63/23.00 | | | Case 1: % 153.63/23.00 | | | | % 153.63/23.00 | | | | (74) all_56_9 = e1 % 153.63/23.00 | | | | % 153.63/23.00 | | | | COMBINE_EQS: (28), (74) imply: % 153.63/23.00 | | | | (75) all_52_12 = e1 % 153.63/23.00 | | | | % 153.63/23.00 | | | | SIMP: (75) implies: % 153.63/23.00 | | | | (76) all_52_12 = e1 % 153.63/23.00 | | | | % 153.63/23.00 | | | | REDUCE: (56), (76) imply: % 153.63/23.00 | | | | (77) ~ (all_52_4 = e1) % 153.63/23.00 | | | | % 153.63/23.00 | | | | REDUCE: (30), (76) imply: % 153.63/23.00 | | | | (78) ~ (all_52_14 = e1) % 153.63/23.00 | | | | % 153.63/23.00 | | | | SIMP: (78) implies: % 153.63/23.00 | | | | (79) ~ (all_52_14 = e1) % 153.63/23.00 | | | | % 153.63/23.00 | | | | REF_CLOSE: (1), (2), (9), (10), (12), (18), (20), (21), (22), (24), % 153.63/23.00 | | | | (29), (31), (32), (33), (35), (38), (40), (41), (42), (44), % 153.63/23.00 | | | | (48), (50), (52), (55), (77), (79) are inconsistent by % 153.63/23.00 | | | | sub-proof #418. % 153.63/23.00 | | | | % 153.63/23.00 | | | Case 2: % 153.63/23.00 | | | | % 153.63/23.00 | | | | (80) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.63/23.00 | | | | % 153.63/23.00 | | | | BETA: splitting (80) gives: % 153.63/23.00 | | | | % 153.63/23.00 | | | | Case 1: % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | (81) all_56_10 = e1 % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | COMBINE_EQS: (64), (81) imply: % 153.63/23.00 | | | | | (82) e1 = e0 % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | REDUCE: (48), (82) imply: % 153.63/23.00 | | | | | (83) $false % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | CLOSE: (83) is inconsistent. % 153.63/23.00 | | | | | % 153.63/23.00 | | | | Case 2: % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | (84) all_56_11 = e1 | all_56_15 = e1 % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | BETA: splitting (84) gives: % 153.63/23.00 | | | | | % 153.63/23.00 | | | | | Case 1: % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | (85) all_56_11 = e1 % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | COMBINE_EQS: (21), (85) imply: % 153.63/23.00 | | | | | | (86) all_52_14 = e1 % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | SIMP: (86) implies: % 153.63/23.00 | | | | | | (87) all_52_14 = e1 % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | COMBINE_EQS: (13), (87) imply: % 153.63/23.00 | | | | | | (88) all_58_20 = e1 % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | REDUCE: (30), (87) imply: % 153.63/23.00 | | | | | | (89) ~ (all_52_12 = e1) % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | REDUCE: (53), (87) imply: % 153.63/23.00 | | | | | | (90) ~ (all_6_2 = e1) % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | SIMP: (90) implies: % 153.63/23.00 | | | | | | (91) ~ (all_6_2 = e1) % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | REDUCE: (47), (87) imply: % 153.63/23.00 | | | | | | (92) ~ (all_4_2 = e1) % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | BETA: splitting (51) gives: % 153.63/23.00 | | | | | | % 153.63/23.00 | | | | | | Case 1: % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | | (93) all_58_28 = e1 % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | | COMBINE_EQS: (2), (93) imply: % 153.63/23.00 | | | | | | | (94) e1 = e0 % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (94) are inconsistent by % 153.63/23.00 | | | | | | | sub-proof #229. % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | Case 2: % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | | (95) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | | BETA: splitting (95) gives: % 153.63/23.00 | | | | | | | % 153.63/23.00 | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | (96) all_58_29 = e1 % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | COMBINE_EQS: (29), (96) imply: % 153.63/23.00 | | | | | | | | (97) all_8_2 = e1 % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | REDUCE: (8), (97) imply: % 153.63/23.00 | | | | | | | | (98) ~ (all_52_4 = e1) % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | BETA: splitting (34) gives: % 153.63/23.00 | | | | | | | | % 153.63/23.00 | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | (99) all_56_0 = e1 % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | COMBINE_EQS: (15), (99) imply: % 153.63/23.00 | | | | | | | | | (100) e1 = e0 % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (100) are inconsistent % 153.63/23.00 | | | | | | | | | by sub-proof #229. % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | (101) ~ (all_56_0 = e1) % 153.63/23.00 | | | | | | | | | (102) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | REDUCE: (15), (101) imply: % 153.63/23.00 | | | | | | | | | (103) ~ (e1 = e0) % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | BETA: splitting (102) gives: % 153.63/23.00 | | | | | | | | | % 153.63/23.00 | | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | (104) all_56_1 = e1 % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | COMBINE_EQS: (22), (104) imply: % 153.63/23.00 | | | | | | | | | | (105) all_52_4 = e1 % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | REDUCE: (98), (105) imply: % 153.63/23.00 | | | | | | | | | | (106) $false % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | CLOSE: (106) is inconsistent. % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | (107) all_56_4 = e1 | all_56_9 = e1 % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | BETA: splitting (107) gives: % 153.63/23.00 | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | (108) all_56_4 = e1 % 153.63/23.00 | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | COMBINE_EQS: (7), (108) imply: % 153.63/23.00 | | | | | | | | | | | (109) all_52_8 = e1 % 153.63/23.00 | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | COMBINE_EQS: (43), (109) imply: % 153.63/23.00 | | | | | | | | | | | (110) all_58_4 = e1 % 153.63/23.00 | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | BETA: splitting (27) gives: % 153.63/23.00 | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | (111) all_58_31 = e0 % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | COMBINE_EQS: (1), (111) imply: % 153.63/23.00 | | | | | | | | | | | | (112) all_4_2 = e0 % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | REDUCE: (73), (112) imply: % 153.63/23.00 | | | | | | | | | | | | (113) $false % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | CLOSE: (113) is inconsistent. % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | (114) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 153.63/23.00 | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/23.00 | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.63/23.00 | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.63/23.00 | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.63/23.00 | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.63/23.00 | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.63/23.00 | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.63/23.00 | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.63/23.00 | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.63/23.00 | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.63/23.00 | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.63/23.00 | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.63/23.00 | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.63/23.00 | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.63/23.00 | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.63/23.00 | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.63/23.00 | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.63/23.00 | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.63/23.00 | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/23.00 | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.63/23.00 | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.63/23.00 | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.63/23.00 | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.63/23.00 | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.63/23.00 | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.63/23.00 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.63/23.00 | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.63/23.00 | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.63/23.00 | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.63/23.00 | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.63/23.00 | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.63/23.00 | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.63/23.00 | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.63/23.00 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.63/23.00 | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/23.00 | | | | | | | | | | | | e0) % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | BETA: splitting (114) gives: % 153.63/23.00 | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | (115) all_58_30 = e1 % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | COMBINE_EQS: (50), (115) imply: % 153.63/23.00 | | | | | | | | | | | | | (116) all_6_2 = e1 % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | REDUCE: (91), (116) imply: % 153.63/23.00 | | | | | | | | | | | | | (117) $false % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | (118) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 153.63/23.00 | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 153.63/23.00 | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.63/23.00 | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.63/23.00 | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 153.63/23.00 | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 153.63/23.00 | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 153.63/23.00 | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 153.63/23.00 | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.63/23.00 | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.63/23.00 | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 153.63/23.00 | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 153.63/23.00 | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 153.63/23.00 | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.63/23.00 | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/23.00 | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 153.63/23.00 | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.63/23.00 | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/23.00 | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.63/23.00 | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.63/23.00 | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/23.00 | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 153.63/23.00 | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 153.63/23.00 | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 153.63/23.00 | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 153.63/23.00 | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 153.63/23.00 | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 153.63/23.00 | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 153.63/23.00 | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 153.63/23.00 | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 153.63/23.00 | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 153.63/23.00 | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 153.63/23.00 | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 153.63/23.00 | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 153.63/23.00 | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 153.63/23.00 | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 153.63/23.00 | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 153.63/23.00 | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 153.63/23.00 | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 153.63/23.00 | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 153.63/23.00 | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 153.63/23.00 | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | BETA: splitting (118) gives: % 153.63/23.00 | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | (119) all_58_29 = e2 % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | REF_CLOSE: (31), (96), (119) are inconsistent by sub-proof % 153.63/23.00 | | | | | | | | | | | | | | #687. % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | (120) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 153.63/23.00 | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 153.63/23.00 | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 153.63/23.00 | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 153.63/23.00 | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 153.63/23.00 | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 153.63/23.00 | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 153.63/23.00 | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 153.63/23.00 | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 153.63/23.00 | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 153.63/23.00 | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.63/23.00 | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/23.00 | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 153.63/23.00 | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 153.63/23.00 | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 153.63/23.00 | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 153.63/23.00 | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.63/23.00 | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.63/23.00 | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.63/23.00 | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.63/23.00 | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.63/23.00 | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.63/23.00 | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.63/23.00 | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.63/23.00 | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.63/23.00 | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.63/23.00 | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/23.00 | | | | | | | | | | | | | | e0) % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | BETA: splitting (120) gives: % 153.63/23.00 | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | Case 1: % 153.63/23.00 | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | (121) all_58_28 = e3 % 153.63/23.00 | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | | REF_CLOSE: (2), (38), (121) are inconsistent by sub-proof % 153.63/23.00 | | | | | | | | | | | | | | | #689. % 153.63/23.00 | | | | | | | | | | | | | | | % 153.63/23.00 | | | | | | | | | | | | | | Case 2: % 153.63/23.00 | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | (122) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.63/23.01 | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.63/23.01 | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.63/23.01 | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.63/23.01 | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 153.63/23.01 | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 153.63/23.01 | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 153.63/23.01 | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 153.63/23.01 | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 153.63/23.01 | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 153.63/23.01 | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 153.63/23.01 | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 153.63/23.01 | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 153.63/23.01 | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.63/23.01 | | | | | | | | | | | | | | | e0) % 153.63/23.01 | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 153.63/23.01 | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | (123) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.63/23.01 | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.63/23.01 | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 153.63/23.01 | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.63/23.01 | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | | = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | (124) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (125) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e2) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (126) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (127) all_58_15 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (127) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (128) all_52_2 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | REDUCE: (20), (128) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (129) $false % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | CLOSE: (129) is inconsistent. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (130) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (131) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (132) all_58_22 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (54), (84), (85), (132) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (133) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (134) all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (134) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #227. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (135) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (136) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (137) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (138) all_58_13 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (67), (138) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #665. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (139) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (140) all_58_4 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (110), (140) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #647. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (141) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (142) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (143) all_58_22 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (54), (143) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #226. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (144) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (145) all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (145) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (146) e1 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (146) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | (147) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (148) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (149) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & e3 = e2) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (150) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (151) all_58_24 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (46), (151) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #643. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (152) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (153) e3 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (153) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (154) $false % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (155) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (156) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (157) all_58_22 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (54), (84), (85), (157) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (158) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (159) all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (159) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (160) e1 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (160) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (161) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (162) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (163) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (164) all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (48), (49), (84), (85), (164) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (165) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (166) all_58_22 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (54), (166) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #226. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (167) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (168) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (169) all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (169) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #227. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (170) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (171) all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (88), (171) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | (172) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.63/23.01 | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | (173) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (174) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (175) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (176) e3 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | REDUCE: (18), (176) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (177) $false % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (178) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (179) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (180) all_58_22 = e3 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (54), (180) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #226. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (181) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (182) all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (88), (182) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (183) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (184) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (185) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (186) all_58_22 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (54), (84), (85), (186) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (187) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (188) all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (48), (49), (84), (85), (188) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (189) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (190) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (191) all_58_22 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (191) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (192) e1 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (192) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (193) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (194) all_58_17 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (194) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | #227. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | (195) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 153.63/23.01 | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 153.63/23.01 | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (196) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (197) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (198) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (199) all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (48), (49), (84), (85), (199) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (200) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (201) all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (201) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (202) e1 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (202) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (203) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (204) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (205) all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (88), (205) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (206) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (207) all_58_17 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (207) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (208) e1 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (208) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (209) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.63/23.01 | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (210) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (211) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (212) all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (88), (212) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (213) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (214) all_58_26 = e1 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (48), (49), (84), (85), (214) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (215) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (216) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (217) e2 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (217) imply: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (218) $false % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (219) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | (220) all_58_20 = e0 % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (49), (84), (85), (88), (220) are % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 153.63/23.01 | | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | (221) all_56_9 = e1 % 153.63/23.01 | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | | REF_CLOSE: (28), (89), (221) are inconsistent by sub-proof % 153.63/23.01 | | | | | | | | | | | #486. % 153.63/23.01 | | | | | | | | | | | % 153.63/23.01 | | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | | % 153.63/23.01 | | | | | | | | | End of split % 153.63/23.01 | | | | | | | | | % 153.63/23.01 | | | | | | | | End of split % 153.63/23.01 | | | | | | | | % 153.63/23.01 | | | | | | | Case 2: % 153.63/23.01 | | | | | | | | % 153.63/23.01 | | | | | | | | (222) all_58_30 = e1 | all_58_31 = e1 % 153.63/23.01 | | | | | | | | % 153.63/23.01 | | | | | | | | REF_CLOSE: (1), (49), (50), (91), (222) are inconsistent by % 153.63/23.01 | | | | | | | | sub-proof #673. % 153.63/23.01 | | | | | | | | % 153.63/23.01 | | | | | | | End of split % 153.63/23.01 | | | | | | | % 153.63/23.01 | | | | | | End of split % 153.63/23.01 | | | | | | % 153.63/23.01 | | | | | Case 2: % 153.63/23.01 | | | | | | % 153.63/23.01 | | | | | | (223) all_56_15 = e1 % 153.63/23.01 | | | | | | % 153.63/23.01 | | | | | | REF_CLOSE: (4), (49), (223) are inconsistent by sub-proof #671. % 153.63/23.01 | | | | | | % 153.63/23.01 | | | | | End of split % 153.63/23.01 | | | | | % 153.63/23.01 | | | | End of split % 153.63/23.01 | | | | % 153.63/23.01 | | | End of split % 153.63/23.01 | | | % 153.63/23.01 | | End of split % 153.63/23.01 | | % 153.63/23.01 | End of split % 153.63/23.01 | % 153.63/23.01 End of proof % 153.63/23.01 % 153.63/23.01 Sub-proof #224 shows that the following formulas are inconsistent: % 153.63/23.01 ---------------------------------------------------------------- % 153.63/23.01 (1) all_56_15 = all_4_2 % 153.63/23.01 (2) all_58_20 = e0 % 153.63/23.01 (3) all_56_11 = e1 % 153.63/23.01 (4) all_56_11 = e1 | all_56_15 = e1 % 153.63/23.01 (5) ~ (e1 = e0) % 153.63/23.01 (6) all_58_20 = e1 % 153.63/23.01 (7) ~ (all_4_2 = e1) % 153.63/23.01 % 153.63/23.01 Begin of proof % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (2), (6) imply: % 153.63/23.01 | (8) e1 = e0 % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (3), (8) imply: % 153.63/23.01 | (9) all_56_11 = e0 % 153.63/23.01 | % 153.63/23.01 | REF_CLOSE: (1), (4), (5), (7), (9) are inconsistent by sub-proof #334. % 153.63/23.01 | % 153.63/23.01 End of proof % 153.63/23.01 % 153.63/23.01 Sub-proof #225 shows that the following formulas are inconsistent: % 153.63/23.01 ---------------------------------------------------------------- % 153.63/23.01 (1) all_56_15 = all_4_2 % 153.63/23.01 (2) all_56_11 = e1 % 153.63/23.01 (3) all_58_26 = e1 % 153.63/23.01 (4) all_58_26 = e0 % 153.63/23.01 (5) all_56_11 = e1 | all_56_15 = e1 % 153.63/23.01 (6) ~ (e1 = e0) % 153.63/23.01 (7) ~ (all_4_2 = e1) % 153.63/23.01 % 153.63/23.01 Begin of proof % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (3), (4) imply: % 153.63/23.01 | (8) e1 = e0 % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (2), (8) imply: % 153.63/23.01 | (9) all_56_11 = e0 % 153.63/23.01 | % 153.63/23.01 | REF_CLOSE: (1), (5), (6), (7), (9) are inconsistent by sub-proof #334. % 153.63/23.01 | % 153.63/23.01 End of proof % 153.63/23.01 % 153.63/23.01 Sub-proof #226 shows that the following formulas are inconsistent: % 153.63/23.01 ---------------------------------------------------------------- % 153.63/23.01 (1) all_58_22 = e3 % 153.63/23.01 (2) all_58_22 = e1 % 153.63/23.01 (3) ~ (e3 = e1) % 153.63/23.01 % 153.63/23.01 Begin of proof % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (1), (2) imply: % 153.63/23.01 | (4) e3 = e1 % 153.63/23.01 | % 153.63/23.01 | SIMP: (4) implies: % 153.63/23.01 | (5) e3 = e1 % 153.63/23.01 | % 153.63/23.01 | REDUCE: (3), (5) imply: % 153.63/23.01 | (6) $false % 153.63/23.01 | % 153.63/23.01 | CLOSE: (6) is inconsistent. % 153.63/23.01 | % 153.63/23.01 End of proof % 153.63/23.01 % 153.63/23.01 Sub-proof #227 shows that the following formulas are inconsistent: % 153.63/23.01 ---------------------------------------------------------------- % 153.63/23.01 (1) all_58_17 = e2 % 153.63/23.01 (2) all_58_17 = e0 % 153.63/23.01 (3) ~ (e2 = e0) % 153.63/23.01 % 153.63/23.01 Begin of proof % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (1), (2) imply: % 153.63/23.01 | (4) e2 = e0 % 153.63/23.01 | % 153.63/23.01 | SIMP: (4) implies: % 153.63/23.01 | (5) e2 = e0 % 153.63/23.01 | % 153.63/23.01 | REDUCE: (3), (5) imply: % 153.63/23.01 | (6) $false % 153.63/23.01 | % 153.63/23.01 | CLOSE: (6) is inconsistent. % 153.63/23.01 | % 153.63/23.01 End of proof % 153.63/23.01 % 153.63/23.01 Sub-proof #228 shows that the following formulas are inconsistent: % 153.63/23.01 ---------------------------------------------------------------- % 153.63/23.01 (1) all_56_15 = all_4_2 % 153.63/23.01 (2) all_58_22 = e0 % 153.63/23.01 (3) all_56_11 = e1 % 153.63/23.01 (4) all_56_11 = e1 | all_56_15 = e1 % 153.63/23.01 (5) ~ (e1 = e0) % 153.63/23.01 (6) ~ (all_4_2 = e1) % 153.63/23.01 (7) all_58_22 = e1 % 153.63/23.01 % 153.63/23.01 Begin of proof % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (2), (7) imply: % 153.63/23.01 | (8) e1 = e0 % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (3), (8) imply: % 153.63/23.01 | (9) all_56_11 = e0 % 153.63/23.01 | % 153.63/23.01 | REF_CLOSE: (1), (4), (5), (6), (9) are inconsistent by sub-proof #334. % 153.63/23.01 | % 153.63/23.01 End of proof % 153.63/23.01 % 153.63/23.01 Sub-proof #229 shows that the following formulas are inconsistent: % 153.63/23.01 ---------------------------------------------------------------- % 153.63/23.01 (1) all_56_15 = all_4_2 % 153.63/23.01 (2) all_56_11 = e1 % 153.63/23.01 (3) all_56_11 = e1 | all_56_15 = e1 % 153.63/23.01 (4) e1 = e0 % 153.63/23.01 (5) ~ (e1 = e0) % 153.63/23.01 (6) ~ (all_4_2 = e1) % 153.63/23.01 % 153.63/23.01 Begin of proof % 153.63/23.01 | % 153.63/23.01 | SIMP: (4) implies: % 153.63/23.01 | (7) e1 = e0 % 153.63/23.01 | % 153.63/23.01 | COMBINE_EQS: (2), (7) imply: % 153.63/23.01 | (8) all_56_11 = e0 % 153.63/23.01 | % 153.63/23.01 | REF_CLOSE: (1), (3), (5), (6), (8) are inconsistent by sub-proof #334. % 153.63/23.01 | % 153.63/23.02 End of proof % 153.63/23.02 % 153.63/23.02 Sub-proof #230 shows that the following formulas are inconsistent: % 153.63/23.02 ---------------------------------------------------------------- % 153.63/23.02 (1) all_56_12 = all_10_1 % 153.63/23.02 (2) all_56_12 = e0 % 153.63/23.02 (3) ~ (all_10_1 = e0) % 153.63/23.02 % 153.63/23.02 Begin of proof % 153.63/23.02 | % 153.63/23.02 | COMBINE_EQS: (1), (2) imply: % 153.63/23.02 | (4) all_10_1 = e0 % 153.63/23.02 | % 153.63/23.02 | SIMP: (4) implies: % 153.63/23.02 | (5) all_10_1 = e0 % 153.63/23.02 | % 153.63/23.02 | REDUCE: (3), (5) imply: % 153.63/23.02 | (6) $false % 153.63/23.02 | % 153.63/23.02 | CLOSE: (6) is inconsistent. % 153.63/23.02 | % 153.63/23.02 End of proof % 153.63/23.02 % 153.63/23.02 Sub-proof #231 shows that the following formulas are inconsistent: % 153.63/23.02 ---------------------------------------------------------------- % 153.63/23.02 (1) all_58_28 = e0 % 153.63/23.02 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/23.02 (3) all_54_5 = all_8_2 % 153.63/23.02 (4) ~ (e3 = e1) % 153.63/23.02 (5) all_54_5 = e0 % 153.63/23.02 (6) all_58_29 = all_8_2 % 153.63/23.02 (7) ~ (e2 = e1) % 153.63/23.02 (8) ~ (e3 = e0) % 153.63/23.02 (9) ~ (e2 = e0) % 153.63/23.02 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.02 (11) ~ (e1 = e0) % 153.63/23.02 (12) all_58_30 = all_6_2 % 153.63/23.02 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/23.02 (14) ~ (e3 = e2) % 153.63/23.02 % 153.63/23.02 Begin of proof % 153.63/23.02 | % 153.63/23.02 | COMBINE_EQS: (3), (5) imply: % 153.63/23.02 | (15) all_8_2 = e0 % 153.63/23.02 | % 153.63/23.02 | SIMP: (15) implies: % 153.63/23.02 | (16) all_8_2 = e0 % 153.63/23.02 | % 153.63/23.02 | COMBINE_EQS: (6), (16) imply: % 153.63/23.02 | (17) all_58_29 = e0 % 153.63/23.02 | % 153.63/23.02 | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (12), (13), (14), (17) % 153.63/23.02 | are inconsistent by sub-proof #483. % 153.63/23.02 | % 153.63/23.02 End of proof % 153.63/23.02 % 153.63/23.02 Sub-proof #232 shows that the following formulas are inconsistent: % 153.63/23.02 ---------------------------------------------------------------- % 153.63/23.02 (1) all_58_31 = all_4_2 % 153.63/23.02 (2) ~ (all_52_8 = all_52_9) % 153.63/23.02 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.63/23.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.63/23.02 (4) ~ (all_52_2 = all_52_3) % 153.63/23.02 (5) all_56_7 = all_52_6 % 153.63/23.02 (6) ~ (all_52_6 = all_6_2) % 153.63/23.02 (7) op(e1, all_6_2) = all_58_18 % 153.63/23.02 (8) op(all_10_2, all_10_1) = e0 % 153.63/23.02 (9) ~ (all_52_8 = all_10_2) % 153.63/23.02 (10) ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 153.63/23.02 (11) all_54_7 = all_52_13 % 153.63/23.02 (12) all_56_4 = all_52_8 % 153.63/23.02 (13) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.63/23.02 (14) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.63/23.02 (15) ~ (all_6_2 = e0) % 153.63/23.02 (16) ~ (all_52_4 = all_52_6) % 153.63/23.02 (17) op(e0, e1) = all_52_11 % 153.63/23.02 (18) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.63/23.02 (19) ~ (all_52_6 = all_52_7) % 153.63/23.02 (20) op(e2, e3) = all_52_1 % 153.63/23.02 (21) op(e0, all_52_3) = all_58_21 % 153.63/23.02 (22) ~ (all_52_2 = all_6_2) % 153.63/23.02 (23) op(e3, e3) = all_10_2 % 153.63/23.02 (24) op(e1, e2) = all_52_6 % 153.63/23.02 (25) ~ (all_52_13 = all_8_2) % 153.63/23.02 (26) ~ (e3 = e1) % 153.63/23.02 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 153.63/23.02 (28) ~ (all_52_1 = all_52_13) % 153.63/23.02 (29) all_56_5 = all_52_9 % 153.63/23.02 (30) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.63/23.02 (31) all_56_12 = all_52_3 % 153.63/23.02 (32) ~ (all_52_12 = e0) % 153.63/23.02 (33) all_56_11 = all_52_14 % 153.63/23.02 (34) all_56_1 = all_52_4 % 153.63/23.02 (35) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.63/23.02 (36) ~ (all_52_13 = e0) % 153.63/23.02 (37) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.63/23.02 (38) op(e1, e3) = all_52_2 % 153.63/23.02 (39) ~ (all_52_9 = all_52_11) % 153.63/23.02 (40) all_56_3 = all_8_2 % 153.63/23.02 (41) ~ (all_52_13 = all_52_14) % 153.63/23.02 (42) all_56_9 = all_52_12 % 153.63/23.02 (43) all_58_29 = all_8_2 % 153.63/23.02 (44) ~ (e2 = e1) % 153.63/23.02 (45) all_56_6 = all_52_2 % 153.63/23.02 (46) op(all_6_2, e1) = all_6_1 % 153.63/23.02 (47) op(e3, all_10_2) = all_58_0 % 153.63/23.02 (48) ~ (e3 = e0) % 153.63/23.02 (49) all_56_2 = all_52_1 % 153.63/23.02 (50) ~ (all_52_11 = e0) % 153.63/23.02 (51) op(e0, e3) = all_52_3 % 153.63/23.02 (52) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.63/23.02 (53) all_56_10 = all_52_13 % 153.63/23.02 (54) ~ (all_52_1 = all_52_3) % 153.63/23.02 (55) all_56_14 = all_52_11 % 153.63/23.02 (56) all_58_28 = all_10_2 % 153.63/23.02 (57) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.63/23.02 (58) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 153.63/23.02 (59) ~ (all_6_1 = e0) % 153.63/23.02 (60) op(all_8_2, e2) = all_8_1 % 153.63/23.02 (61) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.63/23.02 (62) ~ (e2 = e0) % 153.63/23.02 (63) ~ (all_52_2 = all_10_2) % 153.63/23.02 (64) all_56_0 = all_10_2 % 153.63/23.02 (65) all_58_31 = e0 % 153.63/23.02 (66) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 153.63/23.02 (67) ~ (all_52_3 = all_10_2) % 153.63/23.02 (68) all_56_8 = all_6_2 % 153.63/23.02 (69) op(e1, e1) = all_6_2 % 153.63/23.02 (70) ~ (all_52_1 = all_52_2) % 153.63/23.02 (71) op(e2, e0) = all_52_13 % 153.63/23.02 (72) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.63/23.02 (73) ~ (all_8_1 = e0) % 153.63/23.02 (74) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.02 (75) all_54_0 = all_10_2 % 153.63/23.02 (76) ~ (e1 = e0) % 153.63/23.02 (77) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.63/23.02 (78) ~ (all_52_14 = e0) % 153.63/23.02 (79) ~ (all_4_2 = e1) % 153.63/23.02 (80) op(e0, e2) = all_52_7 % 153.63/23.02 (81) all_58_30 = all_6_2 % 153.63/23.02 (82) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/23.02 (83) ~ (e3 = e2) % 153.63/23.02 (84) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.63/23.02 (85) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 153.63/23.02 (86) op(all_10_2, e3) = all_10_1 % 153.63/23.02 (87) all_54_12 = all_52_3 % 153.63/23.02 (88) op(e2, all_8_2) = all_58_9 % 153.63/23.02 (89) ~ (all_52_1 = all_10_2) % 153.63/23.02 % 153.63/23.02 Begin of proof % 153.63/23.02 | % 153.63/23.02 | BETA: splitting (57) gives: % 153.63/23.02 | % 153.63/23.02 | Case 1: % 153.63/23.02 | | % 153.63/23.02 | | (90) all_56_7 = e0 % 153.63/23.02 | | % 153.63/23.02 | | COMBINE_EQS: (5), (90) imply: % 153.63/23.02 | | (91) all_52_6 = e0 % 153.63/23.02 | | % 153.63/23.02 | | SIMP: (91) implies: % 153.63/23.02 | | (92) all_52_6 = e0 % 153.63/23.02 | | % 153.63/23.02 | | REDUCE: (16), (92) imply: % 153.63/23.02 | | (93) ~ (all_52_4 = e0) % 153.63/23.02 | | % 153.63/23.02 | | REDUCE: (19), (92) imply: % 153.63/23.02 | | (94) ~ (all_52_7 = e0) % 153.63/23.02 | | % 153.63/23.02 | | SIMP: (94) implies: % 153.63/23.02 | | (95) ~ (all_52_7 = e0) % 153.63/23.02 | | % 153.63/23.02 | | REDUCE: (6), (92) imply: % 153.63/23.02 | | (96) ~ (all_6_2 = e0) % 153.63/23.02 | | % 153.63/23.02 | | REDUCE: (24), (92) imply: % 153.63/23.02 | | (97) op(e1, e2) = e0 % 153.63/23.02 | | % 153.63/23.02 | | BETA: splitting (14) gives: % 153.63/23.02 | | % 153.63/23.02 | | Case 1: % 153.63/23.02 | | | % 153.63/23.02 | | | (98) all_56_2 = e0 % 153.63/23.02 | | | % 153.63/23.02 | | | COMBINE_EQS: (49), (98) imply: % 153.63/23.02 | | | (99) all_52_1 = e0 % 153.63/23.02 | | | % 153.63/23.02 | | | REDUCE: (70), (99) imply: % 153.63/23.02 | | | (100) ~ (all_52_2 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | SIMP: (100) implies: % 153.63/23.02 | | | (101) ~ (all_52_2 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | REDUCE: (54), (99) imply: % 153.63/23.02 | | | (102) ~ (all_52_3 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | SIMP: (102) implies: % 153.63/23.02 | | | (103) ~ (all_52_3 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | REDUCE: (28), (99) imply: % 153.63/23.02 | | | (104) ~ (all_52_13 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | REDUCE: (89), (99) imply: % 153.63/23.02 | | | (105) ~ (all_10_2 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | SIMP: (105) implies: % 153.63/23.02 | | | (106) ~ (all_10_2 = e0) % 153.63/23.02 | | | % 153.63/23.02 | | | REDUCE: (20), (99) imply: % 153.63/23.02 | | | (107) op(e2, e3) = e0 % 153.63/23.02 | | | % 153.63/23.02 | | | BETA: splitting (85) gives: % 153.63/23.02 | | | % 153.63/23.02 | | | Case 1: % 153.63/23.02 | | | | % 153.63/23.02 | | | | (108) all_54_7 = e0 % 153.63/23.02 | | | | % 153.63/23.02 | | | | COMBINE_EQS: (11), (108) imply: % 153.63/23.02 | | | | (109) all_52_13 = e0 % 153.63/23.02 | | | | % 153.63/23.02 | | | | REDUCE: (36), (109) imply: % 153.63/23.02 | | | | (110) $false % 153.63/23.02 | | | | % 153.63/23.02 | | | | CLOSE: (110) is inconsistent. % 153.63/23.02 | | | | % 153.63/23.02 | | | Case 2: % 153.63/23.02 | | | | % 153.63/23.02 | | | | (111) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 153.63/23.02 | | | | % 153.63/23.02 | | | | BETA: splitting (27) gives: % 153.63/23.02 | | | | % 153.63/23.02 | | | | Case 1: % 153.63/23.02 | | | | | % 153.63/23.02 | | | | | (112) all_54_0 = e0 % 153.63/23.02 | | | | | % 153.63/23.02 | | | | | REF_CLOSE: (75), (106), (112) are inconsistent by sub-proof #861. % 153.63/23.02 | | | | | % 153.63/23.02 | | | | Case 2: % 153.63/23.02 | | | | | % 153.63/23.02 | | | | | (113) ~ (all_54_0 = e0) % 153.63/23.02 | | | | | (114) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.63/23.02 | | | | | % 153.63/23.02 | | | | | BETA: splitting (61) gives: % 153.63/23.02 | | | | | % 153.63/23.02 | | | | | Case 1: % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | (115) all_56_12 = e1 % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | COMBINE_EQS: (31), (115) imply: % 153.63/23.02 | | | | | | (116) all_52_3 = e1 % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | SIMP: (116) implies: % 153.63/23.02 | | | | | | (117) all_52_3 = e1 % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | REDUCE: (4), (117) imply: % 153.63/23.02 | | | | | | (118) ~ (all_52_2 = e1) % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | REDUCE: (67), (117) imply: % 153.63/23.02 | | | | | | (119) ~ (all_10_2 = e1) % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | SIMP: (119) implies: % 153.63/23.02 | | | | | | (120) ~ (all_10_2 = e1) % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | BETA: splitting (58) gives: % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | Case 1: % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | (121) all_56_0 = e2 % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | COMBINE_EQS: (64), (121) imply: % 153.63/23.02 | | | | | | | (122) all_10_2 = e2 % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | SIMP: (122) implies: % 153.63/23.02 | | | | | | | (123) all_10_2 = e2 % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | COMBINE_EQS: (56), (123) imply: % 153.63/23.02 | | | | | | | (124) all_58_28 = e2 % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | REDUCE: (63), (123) imply: % 153.63/23.02 | | | | | | | (125) ~ (all_52_2 = e2) % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | REDUCE: (8), (123) imply: % 153.63/23.02 | | | | | | | (126) op(e2, all_10_1) = e0 % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | REDUCE: (86), (123) imply: % 153.63/23.02 | | | | | | | (127) op(e2, e3) = all_10_1 % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | BETA: splitting (37) gives: % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | | (128) all_56_0 = e3 % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | | REF_CLOSE: (83), (121), (128) are inconsistent by sub-proof % 153.63/23.02 | | | | | | | | #719. % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | | (129) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | | BETA: splitting (129) gives: % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | (130) all_56_2 = e3 % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | COMBINE_EQS: (98), (130) imply: % 153.63/23.02 | | | | | | | | | (131) e3 = e0 % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | REDUCE: (48), (131) imply: % 153.63/23.02 | | | | | | | | | (132) $false % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | CLOSE: (132) is inconsistent. % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | (133) all_56_6 = e3 | all_56_12 = e3 % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | BETA: splitting (133) gives: % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | (134) all_56_6 = e3 % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | COMBINE_EQS: (45), (134) imply: % 153.63/23.02 | | | | | | | | | | (135) all_52_2 = e3 % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | REDUCE: (22), (135) imply: % 153.63/23.02 | | | | | | | | | | (136) ~ (all_6_2 = e3) % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | SIMP: (136) implies: % 153.63/23.02 | | | | | | | | | | (137) ~ (all_6_2 = e3) % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | BETA: splitting (74) gives: % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | (138) all_58_28 = e3 % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | COMBINE_EQS: (124), (138) imply: % 153.63/23.02 | | | | | | | | | | | (139) e3 = e2 % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | REDUCE: (83), (139) imply: % 153.63/23.02 | | | | | | | | | | | (140) $false % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | CLOSE: (140) is inconsistent. % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | (141) ~ (all_58_28 = e3) % 153.63/23.02 | | | | | | | | | | | (142) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | REDUCE: (124), (141) imply: % 153.63/23.02 | | | | | | | | | | | (143) ~ (e3 = e2) % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | BETA: splitting (142) gives: % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | (144) all_58_29 = e3 % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | COMBINE_EQS: (43), (144) imply: % 153.63/23.02 | | | | | | | | | | | | (145) all_8_2 = e3 % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | SIMP: (145) implies: % 153.63/23.02 | | | | | | | | | | | | (146) all_8_2 = e3 % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | REDUCE: (25), (146) imply: % 153.63/23.02 | | | | | | | | | | | | (147) ~ (all_52_13 = e3) % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | REDUCE: (88), (146) imply: % 153.63/23.02 | | | | | | | | | | | | (148) op(e2, e3) = all_58_9 % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | BETA: splitting (82) gives: % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | (149) all_58_28 = e1 % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | REF_CLOSE: (44), (124), (149) are inconsistent by sub-proof % 153.63/23.02 | | | | | | | | | | | | | #856. % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | (150) ~ (all_58_28 = e1) % 153.63/23.02 | | | | | | | | | | | | | (151) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | BETA: splitting (151) gives: % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | (152) all_58_29 = e1 % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | REF_CLOSE: (26), (144), (152) are inconsistent by sub-proof % 153.63/23.02 | | | | | | | | | | | | | | #686. % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | (153) all_58_30 = e1 | all_58_31 = e1 % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | BETA: splitting (153) gives: % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | (154) all_58_30 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | COMBINE_EQS: (81), (154) imply: % 153.63/23.02 | | | | | | | | | | | | | | | (155) all_6_2 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | COMBINE_EQS: (68), (155) imply: % 153.63/23.02 | | | | | | | | | | | | | | | (156) all_56_8 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | REDUCE: (46), (155) imply: % 153.63/23.02 | | | | | | | | | | | | | | | (157) op(e1, e1) = all_6_1 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | REDUCE: (7), (155) imply: % 153.63/23.02 | | | | | | | | | | | | | | | (158) op(e1, e1) = all_58_18 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | REDUCE: (69), (155) imply: % 153.63/23.02 | | | | | | | | | | | | | | | (159) op(e1, e1) = e1 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | BETA: splitting (84) gives: % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | (160) all_56_6 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (160) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | (161) e3 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | REDUCE: (83), (161) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | (162) $false % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | (163) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | (164) all_56_7 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (164) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | (165) e2 = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | SIMP: (165) implies: % 153.63/23.02 | | | | | | | | | | | | | | | | | (166) e2 = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | REDUCE: (62), (166) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | (167) $false % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | (168) all_56_8 = e2 | all_56_11 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | (169) all_56_8 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (169) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | (170) e2 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | SIMP: (170) implies: % 153.63/23.02 | | | | | | | | | | | | | | | | | | (171) e2 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | REDUCE: (44), (171) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | (172) $false % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent. % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | (173) all_56_11 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (173) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | (174) all_52_14 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | REDUCE: (41), (174) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | (175) ~ (all_52_13 = e2) % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | Case 1: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (176) all_54_7 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (176) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (177) all_52_13 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | SIMP: (177) implies: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (178) all_52_13 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | REDUCE: (71), (178) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (179) op(e2, e0) = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_6_1, all_58_18, e1, e1, % 153.63/23.02 | | | | | | | | | | | | | | | | | | | simplifying with (157), (158) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (180) all_58_18 = all_6_1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_58_18, e1, e1, % 153.63/23.02 | | | | | | | | | | | | | | | | | | | simplifying with (158), (159) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (181) all_58_18 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_58_9, e3, e2, % 153.63/23.02 | | | | | | | | | | | | | | | | | | | simplifying with (107), (148) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (182) all_58_9 = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_10_1, all_58_9, e3, e2, % 153.63/23.02 | | | | | | | | | | | | | | | | | | | simplifying with (127), (148) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (183) all_58_9 = all_10_1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (183) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (184) all_10_1 = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (181) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (185) all_6_1 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (184) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (186) op(e2, e0) = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, e0, e0, e2, simplifying % 153.63/23.02 | | | | | | | | | | | | | | | | | | | with (179), (186) gives: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (187) e1 = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (187) imply: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (188) all_58_30 = e0 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (76), (79), (153), (188) are inconsistent by % 153.63/23.02 | | | | | | | | | | | | | | | | | | | sub-proof #711. % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | (189) all_54_7 = e3 | all_54_7 = e2 % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (147), (175), (189) are inconsistent by % 153.63/23.02 | | | | | | | | | | | | | | | | | | | sub-proof #602. % 153.63/23.02 | | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | (190) all_58_31 = e1 % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | | REF_CLOSE: (65), (76), (190) are inconsistent by sub-proof % 153.63/23.02 | | | | | | | | | | | | | | | #845. % 153.63/23.02 | | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | (191) all_58_30 = e3 | all_58_31 = e3 % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | | REF_CLOSE: (48), (65), (81), (137), (191) are inconsistent by % 153.63/23.02 | | | | | | | | | | | | sub-proof #768. % 153.63/23.02 | | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | Case 2: % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | (192) all_56_12 = e3 % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | COMBINE_EQS: (115), (192) imply: % 153.63/23.02 | | | | | | | | | | (193) e3 = e1 % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | REDUCE: (26), (193) imply: % 153.63/23.02 | | | | | | | | | | (194) $false % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | | CLOSE: (194) is inconsistent. % 153.63/23.02 | | | | | | | | | | % 153.63/23.02 | | | | | | | | | End of split % 153.63/23.02 | | | | | | | | | % 153.63/23.02 | | | | | | | | End of split % 153.63/23.02 | | | | | | | | % 153.63/23.02 | | | | | | | End of split % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | Case 2: % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | (195) ~ (all_56_0 = e2) % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | REDUCE: (64), (195) imply: % 153.63/23.02 | | | | | | | (196) ~ (all_10_2 = e2) % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | | REF_CLOSE: (3), (8), (23), (47), (64), (75), (77), (86), (106), % 153.63/23.02 | | | | | | | (114), (120), (196) are inconsistent by sub-proof #248. % 153.63/23.02 | | | | | | | % 153.63/23.02 | | | | | | End of split % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | Case 2: % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | (197) ~ (all_56_12 = e1) % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | REDUCE: (31), (197) imply: % 153.63/23.02 | | | | | | (198) ~ (all_52_3 = e1) % 153.63/23.02 | | | | | | % 153.63/23.02 | | | | | | BETA: splitting (18) gives: % 153.63/23.02 | | | | | | % 153.87/23.02 | | | | | | Case 1: % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | (199) all_56_0 = e1 % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | COMBINE_EQS: (64), (199) imply: % 153.87/23.02 | | | | | | | (200) all_10_2 = e1 % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | REDUCE: (8), (200) imply: % 153.87/23.02 | | | | | | | (201) op(e1, all_10_1) = e0 % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | REDUCE: (86), (200) imply: % 153.87/23.02 | | | | | | | (202) op(e1, e3) = all_10_1 % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | REF_CLOSE: (3), (10), (26), (37), (38), (44), (45), (48), (58), % 153.87/23.02 | | | | | | | (62), (83), (98), (101), (199), (200), (201), (202) are % 153.87/23.02 | | | | | | | inconsistent by sub-proof #242. % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | Case 2: % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | (203) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | BETA: splitting (203) gives: % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | | Case 1: % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | (204) all_56_2 = e1 % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | COMBINE_EQS: (98), (204) imply: % 153.87/23.02 | | | | | | | | (205) e1 = e0 % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | REDUCE: (76), (205) imply: % 153.87/23.02 | | | | | | | | (206) $false % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | CLOSE: (206) is inconsistent. % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | Case 2: % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | (207) all_56_6 = e1 | all_56_12 = e1 % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | BETA: splitting (207) gives: % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | | Case 1: % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | (208) all_56_6 = e1 % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | COMBINE_EQS: (45), (208) imply: % 153.87/23.02 | | | | | | | | | (209) all_52_2 = e1 % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | SIMP: (209) implies: % 153.87/23.02 | | | | | | | | | (210) all_52_2 = e1 % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | REDUCE: (63), (210) imply: % 153.87/23.02 | | | | | | | | | (211) ~ (all_10_2 = e1) % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | SIMP: (211) implies: % 153.87/23.02 | | | | | | | | | (212) ~ (all_10_2 = e1) % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | REDUCE: (22), (210) imply: % 153.87/23.02 | | | | | | | | | (213) ~ (all_6_2 = e1) % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | SIMP: (213) implies: % 153.87/23.02 | | | | | | | | | (214) ~ (all_6_2 = e1) % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | REF_CLOSE: (1), (3), (43), (56), (60), (73), (79), (81), (82), % 153.87/23.02 | | | | | | | | | (97), (212), (214) are inconsistent by sub-proof % 153.87/23.02 | | | | | | | | | #241. % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | Case 2: % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | (215) all_56_12 = e1 % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | | REF_CLOSE: (31), (198), (215) are inconsistent by sub-proof % 153.87/23.02 | | | | | | | | | #577. % 153.87/23.02 | | | | | | | | | % 153.87/23.02 | | | | | | | | End of split % 153.87/23.02 | | | | | | | | % 153.87/23.02 | | | | | | | End of split % 153.87/23.02 | | | | | | | % 153.87/23.02 | | | | | | End of split % 153.87/23.02 | | | | | | % 153.87/23.02 | | | | | End of split % 153.87/23.02 | | | | | % 153.87/23.02 | | | | End of split % 153.87/23.02 | | | | % 153.87/23.02 | | | End of split % 153.87/23.02 | | | % 153.87/23.02 | | Case 2: % 153.87/23.02 | | | % 153.87/23.02 | | | (216) ~ (all_56_2 = e0) % 153.87/23.02 | | | % 153.87/23.02 | | | REDUCE: (49), (216) imply: % 153.87/23.02 | | | (217) ~ (all_52_1 = e0) % 153.87/23.02 | | | % 153.87/23.02 | | | REF_CLOSE: (2), (3), (8), (9), (12), (13), (14), (15), (17), (21), (23), % 153.87/23.02 | | | (26), (29), (30), (31), (32), (34), (35), (36), (39), (40), % 153.87/23.02 | | | (42), (43), (44), (47), (48), (49), (50), (51), (52), (53), % 153.87/23.02 | | | (55), (56), (61), (62), (64), (65), (66), (67), (68), (72), % 153.87/23.02 | | | (74), (76), (77), (80), (81), (82), (83), (86), (87), (93), % 153.87/23.02 | | | (95), (217) are inconsistent by sub-proof #233. % 153.87/23.02 | | | % 153.87/23.02 | | End of split % 153.87/23.02 | | % 153.87/23.02 | Case 2: % 153.87/23.02 | | % 153.87/23.02 | | (218) all_56_8 = e0 | all_56_11 = e0 % 153.87/23.02 | | % 153.87/23.02 | | REF_CLOSE: (15), (33), (68), (78), (218) are inconsistent by sub-proof #763. % 153.87/23.02 | | % 153.87/23.02 | End of split % 153.87/23.02 | % 153.87/23.02 End of proof % 153.87/23.02 % 153.87/23.02 Sub-proof #233 shows that the following formulas are inconsistent: % 153.87/23.02 ---------------------------------------------------------------- % 153.87/23.02 (1) ~ (all_52_8 = all_52_9) % 153.87/23.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.02 (3) op(all_10_2, all_10_1) = e0 % 153.87/23.02 (4) ~ (all_52_8 = all_10_2) % 153.87/23.02 (5) all_56_4 = all_52_8 % 153.87/23.02 (6) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.02 (7) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.87/23.02 (8) ~ (all_6_2 = e0) % 153.87/23.02 (9) op(e0, e1) = all_52_11 % 153.87/23.02 (10) op(e0, all_52_3) = all_58_21 % 153.87/23.02 (11) op(e3, e3) = all_10_2 % 153.87/23.02 (12) ~ (e3 = e1) % 153.87/23.02 (13) all_56_5 = all_52_9 % 153.87/23.02 (14) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.87/23.02 (15) all_56_12 = all_52_3 % 153.87/23.02 (16) ~ (all_52_12 = e0) % 153.87/23.02 (17) all_56_1 = all_52_4 % 153.87/23.02 (18) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.87/23.03 (19) ~ (all_52_13 = e0) % 153.87/23.03 (20) ~ (all_52_9 = all_52_11) % 153.87/23.03 (21) all_56_3 = all_8_2 % 153.87/23.03 (22) all_56_9 = all_52_12 % 153.87/23.03 (23) all_58_29 = all_8_2 % 153.87/23.03 (24) ~ (e2 = e1) % 153.87/23.03 (25) ~ (all_52_4 = e0) % 153.87/23.03 (26) op(e3, all_10_2) = all_58_0 % 153.87/23.03 (27) ~ (e3 = e0) % 153.87/23.03 (28) all_56_2 = all_52_1 % 153.87/23.03 (29) ~ (all_52_11 = e0) % 153.87/23.03 (30) op(e0, e3) = all_52_3 % 153.87/23.03 (31) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.87/23.03 (32) all_56_10 = all_52_13 % 153.87/23.03 (33) all_56_14 = all_52_11 % 153.87/23.03 (34) all_58_28 = all_10_2 % 153.87/23.03 (35) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.87/23.03 (36) ~ (e2 = e0) % 153.87/23.03 (37) all_56_0 = all_10_2 % 153.87/23.03 (38) ~ (all_52_1 = e0) % 153.87/23.03 (39) all_58_31 = e0 % 153.87/23.03 (40) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 153.87/23.03 (41) ~ (all_52_3 = all_10_2) % 153.87/23.03 (42) all_56_8 = all_6_2 % 153.87/23.03 (43) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.87/23.03 (44) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.03 (45) ~ (all_52_7 = e0) % 153.87/23.03 (46) ~ (e1 = e0) % 153.87/23.03 (47) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.03 (48) op(e0, e2) = all_52_7 % 153.87/23.03 (49) all_58_30 = all_6_2 % 153.87/23.03 (50) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.03 (51) ~ (e3 = e2) % 153.87/23.03 (52) op(all_10_2, e3) = all_10_1 % 153.87/23.03 (53) all_54_12 = all_52_3 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (40) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (54) all_56_0 = e0 % 153.87/23.03 | | % 153.87/23.03 | | COMBINE_EQS: (37), (54) imply: % 153.87/23.03 | | (55) all_10_2 = e0 % 153.87/23.03 | | % 153.87/23.03 | | SIMP: (55) implies: % 153.87/23.03 | | (56) all_10_2 = e0 % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (41), (56) imply: % 153.87/23.03 | | (57) ~ (all_52_3 = e0) % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (4), (56) imply: % 153.87/23.03 | | (58) ~ (all_52_8 = e0) % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (3), (56) imply: % 153.87/23.03 | | (59) op(e0, all_10_1) = e0 % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (52), (56) imply: % 153.87/23.03 | | (60) op(e0, e3) = all_10_1 % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (2), (5), (8), (9), (10), (13), (15), (18), (20), (29), (30), % 153.87/23.03 | | (31), (33), (35), (42), (43), (45), (48), (53), (57), (58), (59), % 153.87/23.03 | | (60) are inconsistent by sub-proof #234. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (61) ~ (all_56_0 = e0) % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (37), (61) imply: % 153.87/23.03 | | (62) ~ (all_10_2 = e0) % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (11), (12), (13), (14), (16), (17), % 153.87/23.03 | | (19), (21), (22), (23), (24), (25), (26), (27), (28), (32), (34), % 153.87/23.03 | | (36), (37), (38), (39), (44), (46), (47), (49), (50), (51), (52), % 153.87/23.03 | | (62) are inconsistent by sub-proof #243. % 153.87/23.03 | | % 153.87/23.03 | End of split % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #234 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) op(e0, all_10_1) = e0 % 153.87/23.03 (3) all_56_4 = all_52_8 % 153.87/23.03 (4) ~ (all_6_2 = e0) % 153.87/23.03 (5) op(e0, e1) = all_52_11 % 153.87/23.03 (6) op(e0, all_52_3) = all_58_21 % 153.87/23.03 (7) ~ (all_52_3 = e0) % 153.87/23.03 (8) all_56_5 = all_52_9 % 153.87/23.03 (9) all_56_12 = all_52_3 % 153.87/23.03 (10) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.87/23.03 (11) op(e0, e3) = all_10_1 % 153.87/23.03 (12) ~ (all_52_9 = all_52_11) % 153.87/23.03 (13) ~ (all_52_11 = e0) % 153.87/23.03 (14) op(e0, e3) = all_52_3 % 153.87/23.03 (15) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.87/23.03 (16) all_56_14 = all_52_11 % 153.87/23.03 (17) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.87/23.03 (18) all_56_8 = all_6_2 % 153.87/23.03 (19) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.87/23.03 (20) ~ (all_52_7 = e0) % 153.87/23.03 (21) op(e0, e2) = all_52_7 % 153.87/23.03 (22) ~ (all_52_8 = e0) % 153.87/23.03 (23) all_54_12 = all_52_3 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (10) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (24) all_56_4 = e0 % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (3), (22), (24) are inconsistent by sub-proof #862. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (25) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.87/23.03 | | % 153.87/23.03 | | BETA: splitting (25) gives: % 153.87/23.03 | | % 153.87/23.03 | | Case 1: % 153.87/23.03 | | | % 153.87/23.03 | | | (26) all_56_5 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | COMBINE_EQS: (8), (26) imply: % 153.87/23.03 | | | (27) all_52_9 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | SIMP: (27) implies: % 153.87/23.03 | | | (28) all_52_9 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (12), (28) imply: % 153.87/23.03 | | | (29) ~ (all_52_11 = e0) % 153.87/23.03 | | | % 153.87/23.03 | | | GROUND_INST: instantiating (1) with all_52_3, all_10_1, e3, e0, % 153.87/23.03 | | | simplifying with (11), (14) gives: % 153.87/23.03 | | | (30) all_52_3 = all_10_1 % 153.87/23.03 | | | % 153.87/23.03 | | | COMBINE_EQS: (23), (30) imply: % 153.87/23.03 | | | (31) all_54_12 = all_10_1 % 153.87/23.03 | | | % 153.87/23.03 | | | COMBINE_EQS: (9), (30) imply: % 153.87/23.03 | | | (32) all_56_12 = all_10_1 % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (7), (30) imply: % 153.87/23.03 | | | (33) ~ (all_10_1 = e0) % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (6), (30) imply: % 153.87/23.03 | | | (34) op(e0, all_10_1) = all_58_21 % 153.87/23.03 | | | % 153.87/23.03 | | | GROUND_INST: instantiating (1) with e0, all_58_21, all_10_1, e0, % 153.87/23.03 | | | simplifying with (2), (34) gives: % 153.87/23.03 | | | (35) all_58_21 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | BETA: splitting (15) gives: % 153.87/23.03 | | | % 153.87/23.03 | | | Case 1: % 153.87/23.03 | | | | % 153.87/23.03 | | | | (36) all_54_12 = e0 % 153.87/23.03 | | | | % 153.87/23.03 | | | | REF_CLOSE: (31), (33), (36) are inconsistent by sub-proof #459. % 153.87/23.03 | | | | % 153.87/23.03 | | | Case 2: % 153.87/23.03 | | | | % 153.87/23.03 | | | | (37) ~ (all_54_12 = e0) % 153.87/23.03 | | | | (38) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.87/23.03 | | | | % 153.87/23.03 | | | | BETA: splitting (19) gives: % 153.87/23.03 | | | | % 153.87/23.03 | | | | Case 1: % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | (39) all_56_12 = e2 % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | REF_CLOSE: (1), (2), (20), (21), (32), (39) are inconsistent by % 153.87/23.03 | | | | | sub-proof #239. % 153.87/23.03 | | | | | % 153.87/23.03 | | | | Case 2: % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | (40) ~ (all_56_12 = e2) % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | REDUCE: (32), (40) imply: % 153.87/23.03 | | | | | (41) ~ (all_10_1 = e2) % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | REF_CLOSE: (1), (2), (5), (11), (13), (17), (31), (32), (33), (38), % 153.87/23.03 | | | | | (41) are inconsistent by sub-proof #235. % 153.87/23.03 | | | | | % 153.87/23.03 | | | | End of split % 153.87/23.03 | | | | % 153.87/23.03 | | | End of split % 153.87/23.03 | | | % 153.87/23.03 | | Case 2: % 153.87/23.03 | | | % 153.87/23.03 | | | (42) all_56_8 = e0 | all_56_14 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | REF_CLOSE: (4), (13), (16), (18), (42) are inconsistent by sub-proof #805. % 153.87/23.03 | | | % 153.87/23.03 | | End of split % 153.87/23.03 | | % 153.87/23.03 | End of split % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #235 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) ~ (all_10_1 = e0) % 153.87/23.03 (3) op(e0, all_10_1) = e0 % 153.87/23.03 (4) op(e0, e1) = all_52_11 % 153.87/23.03 (5) all_56_12 = all_10_1 % 153.87/23.03 (6) all_54_12 = all_10_1 % 153.87/23.03 (7) ~ (all_10_1 = e2) % 153.87/23.03 (8) op(e0, e3) = all_10_1 % 153.87/23.03 (9) ~ (all_52_11 = e0) % 153.87/23.03 (10) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.87/23.03 (11) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (10) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (12) all_56_12 = e1 % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (1), (3), (4), (5), (9), (12) are inconsistent by sub-proof #237. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (13) ~ (all_56_12 = e1) % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (5), (13) imply: % 153.87/23.03 | | (14) ~ (all_10_1 = e1) % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (11), (14) are inconsistent by % 153.87/23.03 | | sub-proof #236. % 153.87/23.03 | | % 153.87/23.03 | End of split % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #236 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) ~ (all_10_1 = e0) % 153.87/23.03 (3) op(e0, all_10_1) = e0 % 153.87/23.03 (4) all_54_12 = all_10_1 % 153.87/23.03 (5) ~ (all_10_1 = e2) % 153.87/23.03 (6) op(e0, e3) = all_10_1 % 153.87/23.03 (7) ~ (all_10_1 = e1) % 153.87/23.03 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (8) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (9) all_54_12 = e1 % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (4), (7), (9) are inconsistent by sub-proof #514. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (10) all_54_12 = e3 | all_54_12 = e2 % 153.87/23.03 | | % 153.87/23.03 | | BETA: splitting (10) gives: % 153.87/23.03 | | % 153.87/23.03 | | Case 1: % 153.87/23.03 | | | % 153.87/23.03 | | | (11) all_54_12 = e2 % 153.87/23.03 | | | % 153.87/23.03 | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #513. % 153.87/23.03 | | | % 153.87/23.03 | | Case 2: % 153.87/23.03 | | | % 153.87/23.03 | | | (12) all_54_12 = e3 % 153.87/23.03 | | | % 153.87/23.03 | | | COMBINE_EQS: (4), (12) imply: % 153.87/23.03 | | | (13) all_10_1 = e3 % 153.87/23.03 | | | % 153.87/23.03 | | | SIMP: (13) implies: % 153.87/23.03 | | | (14) all_10_1 = e3 % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (2), (14) imply: % 153.87/23.03 | | | (15) ~ (e3 = e0) % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (3), (14) imply: % 153.87/23.03 | | | (16) op(e0, e3) = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (6), (14) imply: % 153.87/23.03 | | | (17) op(e0, e3) = e3 % 153.87/23.03 | | | % 153.87/23.03 | | | GROUND_INST: instantiating (1) with e0, e3, e3, e0, simplifying with (16), % 153.87/23.03 | | | (17) gives: % 153.87/23.03 | | | (18) e3 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | REDUCE: (15), (18) imply: % 153.87/23.03 | | | (19) $false % 153.87/23.03 | | | % 153.87/23.03 | | | CLOSE: (19) is inconsistent. % 153.87/23.03 | | | % 153.87/23.03 | | End of split % 153.87/23.03 | | % 153.87/23.03 | End of split % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #237 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) op(e0, all_10_1) = e0 % 153.87/23.03 (3) op(e0, e1) = all_52_11 % 153.87/23.03 (4) all_56_12 = all_10_1 % 153.87/23.03 (5) all_56_12 = e1 % 153.87/23.03 (6) ~ (all_52_11 = e0) % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | COMBINE_EQS: (4), (5) imply: % 153.87/23.03 | (7) all_10_1 = e1 % 153.87/23.03 | % 153.87/23.03 | SIMP: (7) implies: % 153.87/23.03 | (8) all_10_1 = e1 % 153.87/23.03 | % 153.87/23.03 | REDUCE: (2), (8) imply: % 153.87/23.03 | (9) op(e0, e1) = e0 % 153.87/23.03 | % 153.87/23.03 | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #238. % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #238 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) op(e0, e1) = all_52_11 % 153.87/23.03 (3) op(e0, e1) = e0 % 153.87/23.03 (4) ~ (all_52_11 = e0) % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | GROUND_INST: instantiating (1) with all_52_11, e0, e1, e0, simplifying with % 153.87/23.03 | (2), (3) gives: % 153.87/23.03 | (5) all_52_11 = e0 % 153.87/23.03 | % 153.87/23.03 | REDUCE: (4), (5) imply: % 153.87/23.03 | (6) $false % 153.87/23.03 | % 153.87/23.03 | CLOSE: (6) is inconsistent. % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #239 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) op(e0, all_10_1) = e0 % 153.87/23.03 (3) all_56_12 = all_10_1 % 153.87/23.03 (4) all_56_12 = e2 % 153.87/23.03 (5) ~ (all_52_7 = e0) % 153.87/23.03 (6) op(e0, e2) = all_52_7 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | COMBINE_EQS: (3), (4) imply: % 153.87/23.03 | (7) all_10_1 = e2 % 153.87/23.03 | % 153.87/23.03 | SIMP: (7) implies: % 153.87/23.03 | (8) all_10_1 = e2 % 153.87/23.03 | % 153.87/23.03 | REDUCE: (2), (8) imply: % 153.87/23.03 | (9) op(e0, e2) = e0 % 153.87/23.03 | % 153.87/23.03 | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #240. % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #240 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) op(e0, e2) = all_52_7 % 153.87/23.03 (3) op(e0, e2) = e0 % 153.87/23.03 (4) ~ (all_52_7 = e0) % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | GROUND_INST: instantiating (1) with all_52_7, e0, e2, e0, simplifying with % 153.87/23.03 | (2), (3) gives: % 153.87/23.03 | (5) all_52_7 = e0 % 153.87/23.03 | % 153.87/23.03 | REDUCE: (4), (5) imply: % 153.87/23.03 | (6) $false % 153.87/23.03 | % 153.87/23.03 | CLOSE: (6) is inconsistent. % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #241 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) all_58_31 = all_4_2 % 153.87/23.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (3) ~ (all_10_2 = e1) % 153.87/23.03 (4) all_58_29 = all_8_2 % 153.87/23.03 (5) all_58_28 = all_10_2 % 153.87/23.03 (6) op(all_8_2, e2) = all_8_1 % 153.87/23.03 (7) ~ (all_8_1 = e0) % 153.87/23.03 (8) op(e1, e2) = e0 % 153.87/23.03 (9) ~ (all_6_2 = e1) % 153.87/23.03 (10) ~ (all_4_2 = e1) % 153.87/23.03 (11) all_58_30 = all_6_2 % 153.87/23.03 (12) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (12) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (13) all_58_28 = e1 % 153.87/23.03 | | % 153.87/23.03 | | COMBINE_EQS: (5), (13) imply: % 153.87/23.03 | | (14) all_10_2 = e1 % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (3), (14) imply: % 153.87/23.03 | | (15) $false % 153.87/23.03 | | % 153.87/23.03 | | CLOSE: (15) is inconsistent. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (16) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.03 | | % 153.87/23.03 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (16) are % 153.87/23.03 | | inconsistent by sub-proof #503. % 153.87/23.03 | | % 153.87/23.03 | End of split % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #242 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (2) ~ (all_52_2 = e0) % 153.87/23.03 (3) ~ (all_10_1 = e2) | ~ (all_10_2 = e1) % 153.87/23.03 (4) op(e1, all_10_1) = e0 % 153.87/23.03 (5) ~ (e3 = e1) % 153.87/23.03 (6) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.87/23.03 (7) op(e1, e3) = all_52_2 % 153.87/23.03 (8) all_56_0 = e1 % 153.87/23.03 (9) all_10_2 = e1 % 153.87/23.03 (10) ~ (e2 = e1) % 153.87/23.03 (11) all_56_6 = all_52_2 % 153.87/23.03 (12) all_56_2 = e0 % 153.87/23.03 (13) ~ (e3 = e0) % 153.87/23.03 (14) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 153.87/23.03 (15) ~ (e2 = e0) % 153.87/23.03 (16) op(e1, e3) = all_10_1 % 153.87/23.03 (17) ~ (e3 = e2) % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (3) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (18) ~ (all_10_2 = e1) % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (9), (18) imply: % 153.87/23.03 | | (19) $false % 153.87/23.03 | | % 153.87/23.03 | | CLOSE: (19) is inconsistent. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (20) ~ (all_10_1 = e2) % 153.87/23.03 | | % 153.87/23.03 | | GROUND_INST: instantiating (1) with all_52_2, all_10_1, e3, e1, simplifying % 153.87/23.03 | | with (7), (16) gives: % 153.87/23.03 | | (21) all_52_2 = all_10_1 % 153.87/23.03 | | % 153.87/23.03 | | COMBINE_EQS: (11), (21) imply: % 153.87/23.03 | | (22) all_56_6 = all_10_1 % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (2), (21) imply: % 153.87/23.03 | | (23) ~ (all_10_1 = e0) % 153.87/23.03 | | % 153.87/23.03 | | BETA: splitting (14) gives: % 153.87/23.03 | | % 153.87/23.03 | | Case 1: % 153.87/23.03 | | | % 153.87/23.03 | | | (24) all_56_0 = e2 % 153.87/23.03 | | | % 153.87/23.03 | | | REF_CLOSE: (8), (10), (24) are inconsistent by sub-proof #796. % 153.87/23.03 | | | % 153.87/23.03 | | Case 2: % 153.87/23.03 | | | % 153.87/23.03 | | | (25) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 153.87/23.03 | | | % 153.87/23.03 | | | BETA: splitting (25) gives: % 153.87/23.03 | | | % 153.87/23.03 | | | Case 1: % 153.87/23.03 | | | | % 153.87/23.03 | | | | (26) all_56_2 = e2 % 153.87/23.03 | | | | % 153.87/23.03 | | | | COMBINE_EQS: (12), (26) imply: % 153.87/23.03 | | | | (27) e2 = e0 % 153.87/23.03 | | | | % 153.87/23.03 | | | | REDUCE: (15), (27) imply: % 153.87/23.03 | | | | (28) $false % 153.87/23.03 | | | | % 153.87/23.03 | | | | CLOSE: (28) is inconsistent. % 153.87/23.03 | | | | % 153.87/23.03 | | | Case 2: % 153.87/23.03 | | | | % 153.87/23.03 | | | | (29) all_56_6 = e2 | all_56_12 = e2 % 153.87/23.03 | | | | % 153.87/23.03 | | | | BETA: splitting (29) gives: % 153.87/23.03 | | | | % 153.87/23.03 | | | | Case 1: % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | (30) all_56_6 = e2 % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | COMBINE_EQS: (22), (30) imply: % 153.87/23.03 | | | | | (31) all_10_1 = e2 % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | REDUCE: (20), (31) imply: % 153.87/23.03 | | | | | (32) $false % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | CLOSE: (32) is inconsistent. % 153.87/23.03 | | | | | % 153.87/23.03 | | | | Case 2: % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | (33) all_56_12 = e2 % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | BETA: splitting (6) gives: % 153.87/23.03 | | | | | % 153.87/23.03 | | | | | Case 1: % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | | (34) all_56_0 = e3 % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | | REF_CLOSE: (5), (8), (34) are inconsistent by sub-proof #569. % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | Case 2: % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | | (35) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | | BETA: splitting (35) gives: % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | | Case 1: % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | (36) all_56_2 = e3 % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | COMBINE_EQS: (12), (36) imply: % 153.87/23.03 | | | | | | | (37) e3 = e0 % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | REDUCE: (13), (37) imply: % 153.87/23.03 | | | | | | | (38) $false % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | CLOSE: (38) is inconsistent. % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | Case 2: % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | (39) all_56_6 = e3 | all_56_12 = e3 % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | BETA: splitting (39) gives: % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | | Case 1: % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | (40) all_56_6 = e3 % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | COMBINE_EQS: (22), (40) imply: % 153.87/23.03 | | | | | | | | (41) all_10_1 = e3 % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | REDUCE: (4), (41) imply: % 153.87/23.03 | | | | | | | | (42) op(e1, e3) = e0 % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | REF_CLOSE: (1), (16), (23), (42) are inconsistent by sub-proof % 153.87/23.03 | | | | | | | | #810. % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | Case 2: % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | (43) all_56_12 = e3 % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | COMBINE_EQS: (33), (43) imply: % 153.87/23.03 | | | | | | | | (44) e3 = e2 % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | REDUCE: (17), (44) imply: % 153.87/23.03 | | | | | | | | (45) $false % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | | CLOSE: (45) is inconsistent. % 153.87/23.03 | | | | | | | | % 153.87/23.03 | | | | | | | End of split % 153.87/23.03 | | | | | | | % 153.87/23.03 | | | | | | End of split % 153.87/23.03 | | | | | | % 153.87/23.03 | | | | | End of split % 153.87/23.03 | | | | | % 153.87/23.03 | | | | End of split % 153.87/23.03 | | | | % 153.87/23.03 | | | End of split % 153.87/23.03 | | | % 153.87/23.03 | | End of split % 153.87/23.03 | | % 153.87/23.03 | End of split % 153.87/23.03 | % 153.87/23.03 End of proof % 153.87/23.03 % 153.87/23.03 Sub-proof #243 shows that the following formulas are inconsistent: % 153.87/23.03 ---------------------------------------------------------------- % 153.87/23.03 (1) ~ (all_52_8 = all_52_9) % 153.87/23.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.03 (3) op(all_10_2, all_10_1) = e0 % 153.87/23.03 (4) all_56_4 = all_52_8 % 153.87/23.03 (5) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.03 (6) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.87/23.03 (7) ~ (all_10_2 = e0) % 153.87/23.03 (8) op(e3, e3) = all_10_2 % 153.87/23.03 (9) ~ (e3 = e1) % 153.87/23.03 (10) all_56_5 = all_52_9 % 153.87/23.03 (11) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.87/23.03 (12) ~ (all_52_12 = e0) % 153.87/23.03 (13) all_56_1 = all_52_4 % 153.87/23.03 (14) ~ (all_52_13 = e0) % 153.87/23.03 (15) all_56_3 = all_8_2 % 153.87/23.03 (16) all_56_9 = all_52_12 % 153.87/23.03 (17) all_58_29 = all_8_2 % 153.87/23.03 (18) ~ (e2 = e1) % 153.87/23.03 (19) ~ (all_52_4 = e0) % 153.87/23.03 (20) op(e3, all_10_2) = all_58_0 % 153.87/23.03 (21) ~ (e3 = e0) % 153.87/23.03 (22) all_56_2 = all_52_1 % 153.87/23.03 (23) all_56_10 = all_52_13 % 153.87/23.03 (24) all_58_28 = all_10_2 % 153.87/23.03 (25) ~ (e2 = e0) % 153.87/23.03 (26) all_56_0 = all_10_2 % 153.87/23.03 (27) ~ (all_52_1 = e0) % 153.87/23.03 (28) all_58_31 = e0 % 153.87/23.03 (29) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.03 (30) ~ (e1 = e0) % 153.87/23.03 (31) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.03 (32) all_58_30 = all_6_2 % 153.87/23.03 (33) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.03 (34) ~ (e3 = e2) % 153.87/23.03 (35) op(all_10_2, e3) = all_10_1 % 153.87/23.03 % 153.87/23.03 Begin of proof % 153.87/23.03 | % 153.87/23.03 | BETA: splitting (6) gives: % 153.87/23.03 | % 153.87/23.03 | Case 1: % 153.87/23.03 | | % 153.87/23.03 | | (36) all_56_2 = e0 % 153.87/23.03 | | % 153.87/23.03 | | COMBINE_EQS: (22), (36) imply: % 153.87/23.03 | | (37) all_52_1 = e0 % 153.87/23.03 | | % 153.87/23.03 | | REDUCE: (27), (37) imply: % 153.87/23.03 | | (38) $false % 153.87/23.03 | | % 153.87/23.03 | | CLOSE: (38) is inconsistent. % 153.87/23.03 | | % 153.87/23.03 | Case 2: % 153.87/23.03 | | % 153.87/23.03 | | (39) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 153.87/23.03 | | % 153.87/23.03 | | BETA: splitting (39) gives: % 153.87/23.03 | | % 153.87/23.03 | | Case 1: % 153.87/23.03 | | | % 153.87/23.03 | | | (40) all_56_3 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | COMBINE_EQS: (15), (40) imply: % 153.87/23.03 | | | (41) all_8_2 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | COMBINE_EQS: (17), (41) imply: % 153.87/23.03 | | | (42) all_58_29 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (18), (20), (21), (24), (25), % 153.87/23.03 | | | (26), (28), (29), (30), (31), (32), (33), (34), (35), (42) are % 153.87/23.03 | | | inconsistent by sub-proof #249. % 153.87/23.03 | | | % 153.87/23.03 | | Case 2: % 153.87/23.03 | | | % 153.87/23.03 | | | (43) all_56_5 = e0 | all_56_10 = e0 % 153.87/23.03 | | | % 153.87/23.03 | | | BETA: splitting (11) gives: % 153.87/23.03 | | | % 153.87/23.03 | | | Case 1: % 153.87/23.03 | | | | % 153.87/23.03 | | | | (44) all_56_0 = e0 % 153.87/23.03 | | | | % 153.87/23.03 | | | | REF_CLOSE: (7), (26), (44) are inconsistent by sub-proof #799. % 153.87/23.03 | | | | % 153.87/23.04 | | | Case 2: % 153.87/23.04 | | | | % 153.87/23.04 | | | | (45) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.87/23.04 | | | | % 153.87/23.04 | | | | BETA: splitting (45) gives: % 153.87/23.04 | | | | % 153.87/23.04 | | | | Case 1: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | (46) all_56_1 = e0 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | REF_CLOSE: (13), (19), (46) are inconsistent by sub-proof #244. % 153.87/23.04 | | | | | % 153.87/23.04 | | | | Case 2: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | (47) all_56_4 = e0 | all_56_9 = e0 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | BETA: splitting (47) gives: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | Case 1: % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | (48) all_56_4 = e0 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | COMBINE_EQS: (4), (48) imply: % 153.87/23.04 | | | | | | (49) all_52_8 = e0 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | REDUCE: (1), (49) imply: % 153.87/23.04 | | | | | | (50) ~ (all_52_9 = e0) % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | SIMP: (50) implies: % 153.87/23.04 | | | | | | (51) ~ (all_52_9 = e0) % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | REF_CLOSE: (10), (14), (23), (43), (51) are inconsistent by % 153.87/23.04 | | | | | | sub-proof #574. % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | Case 2: % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | (52) all_56_9 = e0 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | REF_CLOSE: (12), (16), (52) are inconsistent by sub-proof #521. % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | End of split % 153.87/23.04 | | | | | % 153.87/23.04 | | | | End of split % 153.87/23.04 | | | | % 153.87/23.04 | | | End of split % 153.87/23.04 | | | % 153.87/23.04 | | End of split % 153.87/23.04 | | % 153.87/23.04 | End of split % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #244 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) all_56_1 = all_52_4 % 153.87/23.04 (2) all_56_1 = e0 % 153.87/23.04 (3) ~ (all_52_4 = e0) % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | COMBINE_EQS: (1), (2) imply: % 153.87/23.04 | (4) all_52_4 = e0 % 153.87/23.04 | % 153.87/23.04 | SIMP: (4) implies: % 153.87/23.04 | (5) all_52_4 = e0 % 153.87/23.04 | % 153.87/23.04 | REDUCE: (3), (5) imply: % 153.87/23.04 | (6) $false % 153.87/23.04 | % 153.87/23.04 | CLOSE: (6) is inconsistent. % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #245 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.04 (2) op(all_10_2, all_10_1) = e0 % 153.87/23.04 (3) ~ (all_52_8 = all_10_2) % 153.87/23.04 (4) all_56_4 = all_52_8 % 153.87/23.04 (5) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.04 (6) ~ (all_52_8 = all_6_2) % 153.87/23.04 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.87/23.04 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 153.87/23.04 (9) ~ (all_10_2 = e0) % 153.87/23.04 (10) op(e3, e3) = all_10_2 % 153.87/23.04 (11) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 153.87/23.04 (12) ~ (all_52_13 = all_8_2) % 153.87/23.04 (13) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.87/23.04 (14) all_56_11 = all_52_14 % 153.87/23.04 (15) all_56_1 = e0 % 153.87/23.04 (16) ~ (all_52_1 = all_8_2) % 153.87/23.04 (17) all_56_3 = all_8_2 % 153.87/23.04 (18) all_58_29 = all_8_2 % 153.87/23.04 (19) all_58_14 = all_52_14 % 153.87/23.04 (20) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.87/23.04 (21) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.87/23.04 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 153.87/23.04 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 153.87/23.04 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 153.87/23.04 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 153.87/23.04 (all_58_27 = e0)) % 153.87/23.04 (22) ~ (all_10_2 = e2) % 153.87/23.04 (23) op(e3, all_10_2) = all_58_0 % 153.87/23.04 (24) ~ (e3 = e0) % 153.87/23.04 (25) all_56_2 = all_52_1 % 153.87/23.04 (26) all_56_10 = all_52_13 % 153.87/23.04 (27) all_56_5 = e0 % 153.87/23.04 (28) all_58_28 = all_10_2 % 153.87/23.04 (29) all_56_15 = e0 % 153.87/23.04 (30) all_56_0 = all_10_2 % 153.87/23.04 (31) ~ (all_52_1 = e0) % 153.87/23.04 (32) all_58_31 = e0 % 153.87/23.04 (33) all_58_27 = e0 % 153.87/23.04 (34) all_58_1 = e2 % 153.87/23.04 (35) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.04 (36) all_54_0 = all_10_2 % 153.87/23.04 (37) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.04 (38) all_58_10 = all_52_13 % 153.87/23.04 (39) ~ (all_52_8 = e0) % 153.87/23.04 (40) all_58_30 = all_6_2 % 153.87/23.04 (41) ~ (e3 = e2) % 153.87/23.04 (42) all_56_9 = e2 % 153.87/23.04 (43) op(all_10_2, e3) = all_10_1 % 153.87/23.04 (44) ~ (all_8_2 = e0) % 153.87/23.04 (45) all_54_4 = all_52_1 % 153.87/23.04 (46) ~ (all_52_1 = all_10_2) % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | BETA: splitting (20) gives: % 153.87/23.04 | % 153.87/23.04 | Case 1: % 153.87/23.04 | | % 153.87/23.04 | | (47) all_56_9 = e3 % 153.87/23.04 | | % 153.87/23.04 | | COMBINE_EQS: (42), (47) imply: % 153.87/23.04 | | (48) e3 = e2 % 153.87/23.04 | | % 153.87/23.04 | | REDUCE: (41), (48) imply: % 153.87/23.04 | | (49) $false % 153.87/23.04 | | % 153.87/23.04 | | CLOSE: (49) is inconsistent. % 153.87/23.04 | | % 153.87/23.04 | Case 2: % 153.87/23.04 | | % 153.87/23.04 | | (50) ~ (all_56_9 = e3) % 153.87/23.04 | | (51) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.87/23.04 | | % 153.87/23.04 | | REDUCE: (42), (50) imply: % 153.87/23.04 | | (52) ~ (e3 = e2) % 153.87/23.04 | | % 153.87/23.04 | | BETA: splitting (37) gives: % 153.87/23.04 | | % 153.87/23.04 | | Case 1: % 153.87/23.04 | | | % 153.87/23.04 | | | (53) all_56_0 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | COMBINE_EQS: (30), (53) imply: % 153.87/23.04 | | | (54) all_10_2 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | SIMP: (54) implies: % 153.87/23.04 | | | (55) all_10_2 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | REF_CLOSE: (1), (2), (9), (10), (23), (43), (55) are inconsistent by % 153.87/23.04 | | | sub-proof #251. % 153.87/23.04 | | | % 153.87/23.04 | | Case 2: % 153.87/23.04 | | | % 153.87/23.04 | | | (56) ~ (all_56_0 = e3) % 153.87/23.04 | | | (57) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | REDUCE: (30), (56) imply: % 153.87/23.04 | | | (58) ~ (all_10_2 = e3) % 153.87/23.04 | | | % 153.87/23.04 | | | BETA: splitting (7) gives: % 153.87/23.04 | | | % 153.87/23.04 | | | Case 1: % 153.87/23.04 | | | | % 153.87/23.04 | | | | (59) all_54_0 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | COMBINE_EQS: (36), (59) imply: % 153.87/23.04 | | | | (60) all_10_2 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | SIMP: (60) implies: % 153.87/23.04 | | | | (61) all_10_2 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | COMBINE_EQS: (28), (61) imply: % 153.87/23.04 | | | | (62) all_58_28 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | REDUCE: (46), (61) imply: % 153.87/23.04 | | | | (63) ~ (all_52_1 = e1) % 153.87/23.04 | | | | % 153.87/23.04 | | | | REDUCE: (3), (61) imply: % 153.87/23.04 | | | | (64) ~ (all_52_8 = e1) % 153.87/23.04 | | | | % 153.87/23.04 | | | | REDUCE: (9), (61) imply: % 153.87/23.04 | | | | (65) ~ (e1 = e0) % 153.87/23.04 | | | | % 153.87/23.04 | | | | BETA: splitting (57) gives: % 153.87/23.04 | | | | % 153.87/23.04 | | | | Case 1: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | (66) all_56_1 = e3 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | COMBINE_EQS: (15), (66) imply: % 153.87/23.04 | | | | | (67) e3 = e0 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | REDUCE: (24), (67) imply: % 153.87/23.04 | | | | | (68) $false % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | CLOSE: (68) is inconsistent. % 153.87/23.04 | | | | | % 153.87/23.04 | | | | Case 2: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | (69) all_56_4 = e3 | all_56_9 = e3 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | BETA: splitting (69) gives: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | Case 1: % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | (70) all_56_4 = e3 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | COMBINE_EQS: (4), (70) imply: % 153.87/23.04 | | | | | | (71) all_52_8 = e3 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | SIMP: (71) implies: % 153.87/23.04 | | | | | | (72) all_52_8 = e3 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | REDUCE: (6), (72) imply: % 153.87/23.04 | | | | | | (73) ~ (all_6_2 = e3) % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | SIMP: (73) implies: % 153.87/23.04 | | | | | | (74) ~ (all_6_2 = e3) % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | REDUCE: (64), (72) imply: % 153.87/23.04 | | | | | | (75) ~ (e3 = e1) % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | BETA: splitting (35) gives: % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | Case 1: % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | (76) all_58_28 = e3 % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | COMBINE_EQS: (62), (76) imply: % 153.87/23.04 | | | | | | | (77) e3 = e1 % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | REDUCE: (75), (77) imply: % 153.87/23.04 | | | | | | | (78) $false % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | CLOSE: (78) is inconsistent. % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | Case 2: % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | (79) ~ (all_58_28 = e3) % 153.87/23.04 | | | | | | | (80) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | REDUCE: (62), (79) imply: % 153.87/23.04 | | | | | | | (81) ~ (e3 = e1) % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | BETA: splitting (80) gives: % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | (82) all_58_29 = e3 % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | COMBINE_EQS: (18), (82) imply: % 153.87/23.04 | | | | | | | | (83) all_8_2 = e3 % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | SIMP: (83) implies: % 153.87/23.04 | | | | | | | | (84) all_8_2 = e3 % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | COMBINE_EQS: (17), (84) imply: % 153.87/23.04 | | | | | | | | (85) all_56_3 = e3 % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | REDUCE: (16), (84) imply: % 153.87/23.04 | | | | | | | | (86) ~ (all_52_1 = e3) % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | REDUCE: (12), (84) imply: % 153.87/23.04 | | | | | | | | (87) ~ (all_52_13 = e3) % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | BETA: splitting (11) gives: % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | (88) all_56_2 = e2 % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | COMBINE_EQS: (25), (88) imply: % 153.87/23.04 | | | | | | | | | (89) all_52_1 = e2 % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | SIMP: (89) implies: % 153.87/23.04 | | | | | | | | | (90) all_52_1 = e2 % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | REDUCE: (63), (90) imply: % 153.87/23.04 | | | | | | | | | (91) ~ (e2 = e1) % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | REDUCE: (31), (90) imply: % 153.87/23.04 | | | | | | | | | (92) ~ (e2 = e0) % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | BETA: splitting (13) gives: % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | (93) all_56_2 = e1 % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | REF_CLOSE: (88), (91), (93) are inconsistent by sub-proof % 153.87/23.04 | | | | | | | | | | #247. % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | (94) ~ (all_56_2 = e1) % 153.87/23.04 | | | | | | | | | | (95) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | BETA: splitting (95) gives: % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | (96) all_56_3 = e1 % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | REF_CLOSE: (75), (85), (96) are inconsistent by sub-proof % 153.87/23.04 | | | | | | | | | | | #449. % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | (97) all_56_5 = e1 | all_56_10 = e1 % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | BETA: splitting (51) gives: % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | (98) all_56_10 = e3 % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | REF_CLOSE: (26), (87), (98) are inconsistent by sub-proof % 153.87/23.04 | | | | | | | | | | | | #477. % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | (99) all_56_11 = e3 | all_56_15 = e3 % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | BETA: splitting (99) gives: % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | (100) all_56_11 = e3 % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | COMBINE_EQS: (14), (100) imply: % 153.87/23.04 | | | | | | | | | | | | | (101) all_52_14 = e3 % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | SIMP: (101) implies: % 153.87/23.04 | | | | | | | | | | | | | (102) all_52_14 = e3 % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | REF_CLOSE: (19), (21), (26), (27), (33), (34), (38), (65), % 153.87/23.04 | | | | | | | | | | | | | (97), (102) are inconsistent by sub-proof #246. % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | (103) all_56_15 = e3 % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | COMBINE_EQS: (29), (103) imply: % 153.87/23.04 | | | | | | | | | | | | | (104) e3 = e0 % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | COMBINE_EQS: (82), (104) imply: % 153.87/23.04 | | | | | | | | | | | | | (105) all_58_29 = e0 % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | BETA: splitting (5) gives: % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | Case 1: % 153.87/23.04 | | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | | (106) all_58_28 = e2 % 153.87/23.04 | | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | | REF_CLOSE: (62), (91), (106) are inconsistent by sub-proof % 153.87/23.04 | | | | | | | | | | | | | | #856. % 153.87/23.04 | | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | | (107) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.04 | | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | | REF_CLOSE: (24), (32), (41), (80), (92), (105), (107) are % 153.87/23.04 | | | | | | | | | | | | | | inconsistent by sub-proof #851. % 153.87/23.04 | | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | | End of split % 153.87/23.04 | | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | | End of split % 153.87/23.04 | | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | | End of split % 153.87/23.04 | | | | | | | | | | | % 153.87/23.04 | | | | | | | | | | End of split % 153.87/23.04 | | | | | | | | | | % 153.87/23.04 | | | | | | | | | End of split % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | (108) ~ (all_56_2 = e2) % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | REDUCE: (25), (108) imply: % 153.87/23.04 | | | | | | | | | (109) ~ (all_52_1 = e2) % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | | REF_CLOSE: (8), (45), (63), (86), (109) are inconsistent by % 153.87/23.04 | | | | | | | | | sub-proof #828. % 153.87/23.04 | | | | | | | | | % 153.87/23.04 | | | | | | | | End of split % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | Case 2: % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | (110) all_58_30 = e3 | all_58_31 = e3 % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | | REF_CLOSE: (24), (32), (40), (74), (110) are inconsistent by % 153.87/23.04 | | | | | | | | sub-proof #768. % 153.87/23.04 | | | | | | | | % 153.87/23.04 | | | | | | | End of split % 153.87/23.04 | | | | | | | % 153.87/23.04 | | | | | | End of split % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | Case 2: % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | (111) all_56_9 = e3 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | COMBINE_EQS: (42), (111) imply: % 153.87/23.04 | | | | | | (112) e3 = e2 % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | REDUCE: (41), (112) imply: % 153.87/23.04 | | | | | | (113) $false % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | | CLOSE: (113) is inconsistent. % 153.87/23.04 | | | | | | % 153.87/23.04 | | | | | End of split % 153.87/23.04 | | | | | % 153.87/23.04 | | | | End of split % 153.87/23.04 | | | | % 153.87/23.04 | | | Case 2: % 153.87/23.04 | | | | % 153.87/23.04 | | | | (114) all_54_0 = e3 | all_54_0 = e2 % 153.87/23.04 | | | | % 153.87/23.04 | | | | REF_CLOSE: (22), (36), (58), (114) are inconsistent by sub-proof #814. % 153.87/23.04 | | | | % 153.87/23.04 | | | End of split % 153.87/23.04 | | | % 153.87/23.04 | | End of split % 153.87/23.04 | | % 153.87/23.04 | End of split % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #246 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) all_56_5 = e1 | all_56_10 = e1 % 153.87/23.04 (2) all_58_14 = all_52_14 % 153.87/23.04 (3) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.87/23.04 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 153.87/23.04 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 153.87/23.04 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 153.87/23.04 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 153.87/23.04 (all_58_27 = e0)) % 153.87/23.04 (4) all_56_10 = all_52_13 % 153.87/23.04 (5) all_56_5 = e0 % 153.87/23.04 (6) all_52_14 = e3 % 153.87/23.04 (7) all_58_27 = e0 % 153.87/23.04 (8) all_58_1 = e2 % 153.87/23.04 (9) ~ (e1 = e0) % 153.87/23.04 (10) all_58_10 = all_52_13 % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | COMBINE_EQS: (2), (6) imply: % 153.87/23.04 | (11) all_58_14 = e3 % 153.87/23.04 | % 153.87/23.04 | BETA: splitting (3) gives: % 153.87/23.04 | % 153.87/23.04 | Case 1: % 153.87/23.04 | | % 153.87/23.04 | | (12) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.87/23.04 | | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 153.87/23.04 | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 153.87/23.04 | | % 153.87/23.04 | | BETA: splitting (12) gives: % 153.87/23.04 | | % 153.87/23.04 | | Case 1: % 153.87/23.04 | | | % 153.87/23.04 | | | (13) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.87/23.04 | | | (all_58_5 = e0) % 153.87/23.04 | | | % 153.87/23.04 | | | ALPHA: (13) implies: % 153.87/23.04 | | | (14) ~ (all_58_1 = e2) % 153.87/23.04 | | | % 153.87/23.04 | | | REDUCE: (8), (14) imply: % 153.87/23.04 | | | (15) $false % 153.87/23.04 | | | % 153.87/23.04 | | | CLOSE: (15) is inconsistent. % 153.87/23.04 | | | % 153.87/23.04 | | Case 2: % 153.87/23.04 | | | % 153.87/23.04 | | | (16) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 153.87/23.04 | | | (all_58_12 = e0) % 153.87/23.04 | | | % 153.87/23.04 | | | ALPHA: (16) implies: % 153.87/23.04 | | | (17) ~ (all_58_10 = e1) % 153.87/23.04 | | | % 153.87/23.04 | | | REDUCE: (10), (17) imply: % 153.87/23.04 | | | (18) ~ (all_52_13 = e1) % 153.87/23.04 | | | % 153.87/23.04 | | | REF_CLOSE: (1), (4), (5), (9), (18) are inconsistent by sub-proof #304. % 153.87/23.04 | | | % 153.87/23.04 | | End of split % 153.87/23.04 | | % 153.87/23.04 | Case 2: % 153.87/23.04 | | % 153.87/23.04 | | (19) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 153.87/23.04 | | ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & % 153.87/23.04 | | ~ (all_58_25 = e1) & ~ (all_58_27 = e0)) % 153.87/23.04 | | % 153.87/23.04 | | REF_CLOSE: (7), (11), (19) are inconsistent by sub-proof #779. % 153.87/23.04 | | % 153.87/23.04 | End of split % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #247 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) all_56_2 = e2 % 153.87/23.04 (2) all_56_2 = e1 % 153.87/23.04 (3) ~ (e2 = e1) % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | COMBINE_EQS: (1), (2) imply: % 153.87/23.04 | (4) e2 = e1 % 153.87/23.04 | % 153.87/23.04 | SIMP: (4) implies: % 153.87/23.04 | (5) e2 = e1 % 153.87/23.04 | % 153.87/23.04 | REDUCE: (3), (5) imply: % 153.87/23.04 | (6) $false % 153.87/23.04 | % 153.87/23.04 | CLOSE: (6) is inconsistent. % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #248 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.04 (2) op(all_10_2, all_10_1) = e0 % 153.87/23.04 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.87/23.04 (4) ~ (all_10_2 = e0) % 153.87/23.04 (5) op(e3, e3) = all_10_2 % 153.87/23.04 (6) ~ (all_10_2 = e1) % 153.87/23.04 (7) ~ (all_10_2 = e2) % 153.87/23.04 (8) op(e3, all_10_2) = all_58_0 % 153.87/23.04 (9) all_56_0 = all_10_2 % 153.87/23.04 (10) all_54_0 = all_10_2 % 153.87/23.04 (11) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.04 (12) op(all_10_2, e3) = all_10_1 % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | BETA: splitting (11) gives: % 153.87/23.04 | % 153.87/23.04 | Case 1: % 153.87/23.04 | | % 153.87/23.04 | | (13) all_56_0 = e3 % 153.87/23.04 | | % 153.87/23.04 | | COMBINE_EQS: (9), (13) imply: % 153.87/23.04 | | (14) all_10_2 = e3 % 153.87/23.04 | | % 153.87/23.04 | | SIMP: (14) implies: % 153.87/23.04 | | (15) all_10_2 = e3 % 153.87/23.04 | | % 153.87/23.04 | | REF_CLOSE: (1), (2), (4), (5), (8), (12), (15) are inconsistent by sub-proof % 153.87/23.04 | | #251. % 153.87/23.04 | | % 153.87/23.04 | Case 2: % 153.87/23.04 | | % 153.87/23.04 | | (16) ~ (all_56_0 = e3) % 153.87/23.04 | | % 153.87/23.04 | | REDUCE: (9), (16) imply: % 153.87/23.04 | | (17) ~ (all_10_2 = e3) % 153.87/23.04 | | % 153.87/23.04 | | REF_CLOSE: (3), (6), (7), (10), (17) are inconsistent by sub-proof #813. % 153.87/23.04 | | % 153.87/23.04 | End of split % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #249 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.04 (2) op(all_10_2, all_10_1) = e0 % 153.87/23.04 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.04 (4) ~ (all_10_2 = e0) % 153.87/23.04 (5) op(e3, e3) = all_10_2 % 153.87/23.04 (6) ~ (e3 = e1) % 153.87/23.04 (7) all_58_29 = e0 % 153.87/23.04 (8) ~ (e2 = e1) % 153.87/23.04 (9) op(e3, all_10_2) = all_58_0 % 153.87/23.04 (10) ~ (e3 = e0) % 153.87/23.04 (11) all_58_28 = all_10_2 % 153.87/23.04 (12) ~ (e2 = e0) % 153.87/23.04 (13) all_56_0 = all_10_2 % 153.87/23.04 (14) all_58_31 = e0 % 153.87/23.04 (15) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.04 (16) ~ (e1 = e0) % 153.87/23.04 (17) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.04 (18) all_58_30 = all_6_2 % 153.87/23.04 (19) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.04 (20) ~ (e3 = e2) % 153.87/23.04 (21) op(all_10_2, e3) = all_10_1 % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | BETA: splitting (19) gives: % 153.87/23.04 | % 153.87/23.04 | Case 1: % 153.87/23.04 | | % 153.87/23.04 | | (22) all_58_28 = e1 % 153.87/23.04 | | % 153.87/23.04 | | COMBINE_EQS: (11), (22) imply: % 153.87/23.04 | | (23) all_10_2 = e1 % 153.87/23.04 | | % 153.87/23.04 | | REF_CLOSE: (3), (6), (7), (8), (10), (12), (14), (15), (20), (22) are % 153.87/23.04 | | inconsistent by sub-proof #850. % 153.87/23.04 | | % 153.87/23.04 | Case 2: % 153.87/23.04 | | % 153.87/23.04 | | (24) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.04 | | % 153.87/23.04 | | BETA: splitting (24) gives: % 153.87/23.04 | | % 153.87/23.04 | | Case 1: % 153.87/23.04 | | | % 153.87/23.04 | | | (25) all_58_29 = e1 % 153.87/23.04 | | | % 153.87/23.04 | | | COMBINE_EQS: (7), (25) imply: % 153.87/23.04 | | | (26) e1 = e0 % 153.87/23.04 | | | % 153.87/23.04 | | | REDUCE: (16), (26) imply: % 153.87/23.04 | | | (27) $false % 153.87/23.04 | | | % 153.87/23.04 | | | CLOSE: (27) is inconsistent. % 153.87/23.04 | | | % 153.87/23.04 | | Case 2: % 153.87/23.04 | | | % 153.87/23.04 | | | (28) ~ (all_58_29 = e1) % 153.87/23.04 | | | (29) all_58_30 = e1 | all_58_31 = e1 % 153.87/23.04 | | | % 153.87/23.04 | | | REDUCE: (7), (28) imply: % 153.87/23.04 | | | (30) ~ (e1 = e0) % 153.87/23.04 | | | % 153.87/23.04 | | | BETA: splitting (29) gives: % 153.87/23.04 | | | % 153.87/23.04 | | | Case 1: % 153.87/23.04 | | | | % 153.87/23.04 | | | | (31) all_58_30 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | COMBINE_EQS: (18), (31) imply: % 153.87/23.04 | | | | (32) all_6_2 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | BETA: splitting (3) gives: % 153.87/23.04 | | | | % 153.87/23.04 | | | | Case 1: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | (33) all_58_28 = e2 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | COMBINE_EQS: (11), (33) imply: % 153.87/23.04 | | | | | (34) all_10_2 = e2 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | REF_CLOSE: (6), (7), (10), (14), (15), (20), (31), (33) are % 153.87/23.04 | | | | | inconsistent by sub-proof #847. % 153.87/23.04 | | | | | % 153.87/23.04 | | | | Case 2: % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | (35) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.04 | | | | | % 153.87/23.04 | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 153.87/23.04 | | | | | (13), (15), (17), (20), (21), (31), (35) are inconsistent % 153.87/23.04 | | | | | by sub-proof #250. % 153.87/23.04 | | | | | % 153.87/23.04 | | | | End of split % 153.87/23.04 | | | | % 153.87/23.04 | | | Case 2: % 153.87/23.04 | | | | % 153.87/23.04 | | | | (36) all_58_31 = e1 % 153.87/23.04 | | | | % 153.87/23.04 | | | | REF_CLOSE: (14), (16), (36) are inconsistent by sub-proof #845. % 153.87/23.04 | | | | % 153.87/23.04 | | | End of split % 153.87/23.04 | | | % 153.87/23.04 | | End of split % 153.87/23.04 | | % 153.87/23.04 | End of split % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #250 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.04 (2) op(all_10_2, all_10_1) = e0 % 153.87/23.04 (3) ~ (all_10_2 = e0) % 153.87/23.04 (4) op(e3, e3) = all_10_2 % 153.87/23.04 (5) ~ (e3 = e1) % 153.87/23.04 (6) all_58_29 = e0 % 153.87/23.04 (7) ~ (e2 = e1) % 153.87/23.04 (8) op(e3, all_10_2) = all_58_0 % 153.87/23.04 (9) ~ (e3 = e0) % 153.87/23.04 (10) all_58_28 = all_10_2 % 153.87/23.04 (11) all_58_30 = e1 % 153.87/23.04 (12) ~ (e2 = e0) % 153.87/23.04 (13) all_56_0 = all_10_2 % 153.87/23.04 (14) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.04 (15) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.04 (16) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.04 (17) ~ (e3 = e2) % 153.87/23.04 (18) op(all_10_2, e3) = all_10_1 % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | BETA: splitting (16) gives: % 153.87/23.04 | % 153.87/23.04 | Case 1: % 153.87/23.04 | | % 153.87/23.04 | | (19) all_56_0 = e3 % 153.87/23.04 | | % 153.87/23.04 | | COMBINE_EQS: (13), (19) imply: % 153.87/23.04 | | (20) all_10_2 = e3 % 153.87/23.04 | | % 153.87/23.04 | | SIMP: (20) implies: % 153.87/23.04 | | (21) all_10_2 = e3 % 153.87/23.04 | | % 153.87/23.04 | | REF_CLOSE: (1), (2), (3), (4), (8), (18), (21) are inconsistent by sub-proof % 153.87/23.04 | | #251. % 153.87/23.04 | | % 153.87/23.04 | Case 2: % 153.87/23.04 | | % 153.87/23.04 | | (22) ~ (all_56_0 = e3) % 153.87/23.04 | | % 153.87/23.04 | | REDUCE: (13), (22) imply: % 153.87/23.04 | | (23) ~ (all_10_2 = e3) % 153.87/23.04 | | % 153.87/23.04 | | BETA: splitting (15) gives: % 153.87/23.04 | | % 153.87/23.04 | | Case 1: % 153.87/23.04 | | | % 153.87/23.04 | | | (24) all_58_28 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | COMBINE_EQS: (10), (24) imply: % 153.87/23.04 | | | (25) all_10_2 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | REDUCE: (23), (25) imply: % 153.87/23.04 | | | (26) $false % 153.87/23.04 | | | % 153.87/23.04 | | | CLOSE: (26) is inconsistent. % 153.87/23.04 | | | % 153.87/23.04 | | Case 2: % 153.87/23.04 | | | % 153.87/23.04 | | | (27) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.04 | | | % 153.87/23.04 | | | REF_CLOSE: (5), (6), (7), (9), (11), (12), (14), (17), (27) are % 153.87/23.04 | | | inconsistent by sub-proof #661. % 153.87/23.04 | | | % 153.87/23.04 | | End of split % 153.87/23.04 | | % 153.87/23.04 | End of split % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #251 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.04 (2) op(all_10_2, all_10_1) = e0 % 153.87/23.04 (3) ~ (all_10_2 = e0) % 153.87/23.04 (4) op(e3, e3) = all_10_2 % 153.87/23.04 (5) all_10_2 = e3 % 153.87/23.04 (6) op(e3, all_10_2) = all_58_0 % 153.87/23.04 (7) op(all_10_2, e3) = all_10_1 % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | REDUCE: (3), (5) imply: % 153.87/23.04 | (8) ~ (e3 = e0) % 153.87/23.04 | % 153.87/23.04 | REDUCE: (2), (5) imply: % 153.87/23.04 | (9) op(e3, all_10_1) = e0 % 153.87/23.04 | % 153.87/23.04 | REDUCE: (5), (7) imply: % 153.87/23.04 | (10) op(e3, e3) = all_10_1 % 153.87/23.04 | % 153.87/23.04 | REDUCE: (5), (6) imply: % 153.87/23.04 | (11) op(e3, e3) = all_58_0 % 153.87/23.04 | % 153.87/23.04 | REDUCE: (4), (5) imply: % 153.87/23.04 | (12) op(e3, e3) = e3 % 153.87/23.04 | % 153.87/23.04 | REF_CLOSE: (1), (8), (9), (10), (11), (12) are inconsistent by sub-proof #252. % 153.87/23.04 | % 153.87/23.04 End of proof % 153.87/23.04 % 153.87/23.04 Sub-proof #252 shows that the following formulas are inconsistent: % 153.87/23.04 ---------------------------------------------------------------- % 153.87/23.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.04 (2) op(e3, e3) = all_58_0 % 153.87/23.04 (3) ~ (e3 = e0) % 153.87/23.04 (4) op(e3, e3) = e3 % 153.87/23.04 (5) op(e3, e3) = all_10_1 % 153.87/23.04 (6) op(e3, all_10_1) = e0 % 153.87/23.04 % 153.87/23.04 Begin of proof % 153.87/23.04 | % 153.87/23.04 | GROUND_INST: instantiating (1) with all_10_1, all_58_0, e3, e3, simplifying % 153.87/23.04 | with (2), (5) gives: % 153.87/23.04 | (7) all_58_0 = all_10_1 % 153.87/23.04 | % 153.87/23.05 | GROUND_INST: instantiating (1) with e3, all_58_0, e3, e3, simplifying with % 153.87/23.05 | (2), (4) gives: % 153.87/23.05 | (8) all_58_0 = e3 % 153.87/23.05 | % 153.87/23.05 | COMBINE_EQS: (7), (8) imply: % 153.87/23.05 | (9) all_10_1 = e3 % 153.87/23.05 | % 153.87/23.05 | SIMP: (9) implies: % 153.87/23.05 | (10) all_10_1 = e3 % 153.87/23.05 | % 153.87/23.05 | REDUCE: (6), (10) imply: % 153.87/23.05 | (11) op(e3, e3) = e0 % 153.87/23.05 | % 153.87/23.05 | GROUND_INST: instantiating (1) with e3, e0, e3, e3, simplifying with (4), (11) % 153.87/23.05 | gives: % 153.87/23.05 | (12) e3 = e0 % 153.87/23.05 | % 153.87/23.05 | REDUCE: (3), (12) imply: % 153.87/23.05 | (13) $false % 153.87/23.05 | % 153.87/23.05 | CLOSE: (13) is inconsistent. % 153.87/23.05 | % 153.87/23.05 End of proof % 153.87/23.05 % 153.87/23.05 Sub-proof #253 shows that the following formulas are inconsistent: % 153.87/23.05 ---------------------------------------------------------------- % 153.87/23.05 (1) all_56_6 = e1 % 153.87/23.05 (2) all_56_6 = e0 % 153.87/23.05 (3) ~ (e1 = e0) % 153.87/23.05 % 153.87/23.05 Begin of proof % 153.87/23.05 | % 153.87/23.05 | COMBINE_EQS: (1), (2) imply: % 153.87/23.05 | (4) e1 = e0 % 153.87/23.05 | % 153.87/23.05 | SIMP: (4) implies: % 153.87/23.05 | (5) e1 = e0 % 153.87/23.05 | % 153.87/23.05 | REDUCE: (3), (5) imply: % 153.87/23.05 | (6) $false % 153.87/23.05 | % 153.87/23.05 | CLOSE: (6) is inconsistent. % 153.87/23.05 | % 153.87/23.05 End of proof % 153.87/23.05 % 153.87/23.05 Sub-proof #254 shows that the following formulas are inconsistent: % 153.87/23.05 ---------------------------------------------------------------- % 153.87/23.05 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 153.87/23.05 (2) all_58_23 = all_8_0 % 153.87/23.05 (3) all_58_31 = all_4_2 % 153.87/23.05 (4) ~ (all_52_8 = all_52_9) % 153.87/23.05 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.87/23.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 153.87/23.05 (6) ~ (all_52_2 = all_52_3) % 153.87/23.05 (7) all_58_11 = all_52_9 % 153.87/23.05 (8) all_56_15 = all_4_2 % 153.87/23.05 (9) all_56_7 = all_52_6 % 153.87/23.05 (10) ~ (all_52_6 = all_6_2) % 153.87/23.05 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 153.87/23.05 (12) all_54_2 = all_52_8 % 153.87/23.05 (13) all_54_8 = all_52_2 % 153.87/23.05 (14) op(e1, all_6_2) = all_58_18 % 153.87/23.05 (15) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 153.87/23.05 (16) ~ (all_52_8 = all_10_2) % 153.87/23.05 (17) all_58_15 = all_52_2 % 153.87/23.05 (18) all_58_26 = all_52_11 % 153.87/23.05 (19) all_44_1 = all_4_1 % 153.87/23.05 (20) op(e1, all_52_14) = all_58_19 % 153.87/23.05 (21) all_56_3 = e0 % 153.87/23.05 (22) ~ (all_52_8 = all_52_11) % 153.87/23.05 (23) all_58_24 = all_8_1 % 153.87/23.05 (24) ~ (all_52_11 = all_4_2) % 153.87/23.05 (25) all_54_7 = all_52_13 % 153.87/23.05 (26) all_58_6 = all_52_12 % 153.87/23.05 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 153.87/23.05 (28) all_56_4 = all_52_8 % 153.87/23.05 (29) ~ (all_52_6 = all_8_1) % 153.87/23.05 (30) all_54_3 = all_52_12 % 153.87/23.05 (31) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.05 (32) all_54_1 = all_52_4 % 153.87/23.05 (33) op(e0, all_4_2) = all_58_27 % 153.87/23.05 (34) op(e0, e2) = all_8_1 % 153.87/23.05 (35) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 153.87/23.05 (36) ~ (all_52_4 = all_52_6) % 153.87/23.05 (37) ~ (all_44_0 = e3) | ~ (all_44_1 = e1) | ~ (all_44_2 = e2) % 153.87/23.05 (38) all_58_13 = all_52_13 % 153.87/23.05 (39) op(e0, e1) = all_52_11 % 153.87/23.05 (40) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 153.87/23.05 (41) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 153.87/23.05 (42) all_56_13 = all_8_1 % 153.87/23.05 (43) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 153.87/23.05 (44) all_54_11 = all_52_14 % 153.87/23.05 (45) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 153.87/23.05 (46) all_58_20 = all_52_14 % 153.87/23.05 (47) ~ (all_52_8 = all_6_2) % 153.87/23.05 (48) op(e2, e3) = all_52_1 % 153.87/23.05 (49) ~ (all_52_12 = all_52_13) % 153.87/23.05 (50) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 153.87/23.05 (51) all_54_10 = all_6_2 % 153.87/23.05 (52) ~ (all_52_6 = all_52_14) % 153.87/23.05 (53) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 153.87/23.05 (54) all_54_6 = all_52_9 % 153.87/23.05 (55) all_54_15 = all_4_2 % 153.87/23.05 (56) ~ (all_52_2 = all_6_2) % 153.87/23.05 (57) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 153.87/23.05 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 153.87/23.05 (58) ~ (all_26_0 = e2) | ~ (all_26_1 = e1) | ~ (all_26_2 = e3) % 153.87/23.05 (59) op(e3, e3) = all_10_2 % 153.87/23.05 (60) ~ (all_52_8 = all_52_12) % 153.87/23.05 (61) all_54_9 = all_52_6 % 153.87/23.05 (62) ~ (all_52_13 = all_4_2) % 153.87/23.05 (63) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 153.87/23.05 (64) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 153.87/23.05 (65) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 153.87/23.05 (66) ~ (e3 = e1) % 153.87/23.05 (67) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 153.87/23.05 (68) ~ (all_52_6 = e0) % 153.87/23.05 (69) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 153.87/23.05 (70) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 153.87/23.05 (71) ~ (all_4_0 = e1) % 153.87/23.05 (72) ~ (all_52_1 = all_52_13) % 153.87/23.05 (73) all_56_5 = all_52_9 % 153.87/23.05 (74) all_54_14 = all_52_11 % 153.87/23.05 (75) op(e0, all_8_1) = all_8_0 % 153.87/23.05 (76) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 153.87/23.05 (77) all_56_12 = all_52_3 % 153.87/23.05 (78) all_58_2 = all_52_4 % 153.87/23.05 (79) all_20_2 = all_4_2 % 153.87/23.05 (80) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 153.87/23.05 (81) all_56_11 = all_52_14 % 153.87/23.05 (82) all_56_1 = all_52_4 % 153.87/23.05 (83) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.87/23.05 (84) ~ (all_52_13 = e0) % 153.87/23.05 (85) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 153.87/23.05 (86) ~ (all_52_3 = all_4_2) % 153.87/23.05 (87) all_58_9 = all_52_13 % 153.87/23.05 (88) ~ (all_52_4 = all_8_1) % 153.87/23.05 (89) op(e1, e0) = all_52_14 % 153.87/23.05 (90) ~ (all_52_9 = all_52_11) % 153.87/23.05 (91) ~ (all_52_9 = e0) % 153.87/23.05 (92) ~ (all_52_13 = all_52_14) % 153.87/23.05 (93) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 153.87/23.05 (94) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 153.87/23.05 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 153.87/23.05 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 153.87/23.05 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 153.87/23.05 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 153.87/23.05 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 153.87/23.05 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 153.87/23.05 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 153.87/23.05 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 153.87/23.05 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 153.87/23.05 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 153.87/23.05 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 153.87/23.05 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 153.87/23.05 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 153.87/23.05 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 153.87/23.05 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 153.87/23.05 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 153.87/23.05 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 153.87/23.05 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 153.87/23.05 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 153.87/23.05 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 153.87/23.05 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 153.87/23.05 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 153.87/23.05 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 153.87/23.05 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 153.87/23.05 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 153.87/23.05 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 153.87/23.05 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 153.87/23.05 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 153.87/23.05 e0) % 153.87/23.05 (95) ~ (all_52_4 = all_52_8) % 153.87/23.05 (96) op(e1, all_52_2) = all_58_14 % 153.87/23.05 (97) all_58_29 = e0 % 153.87/23.05 (98) op(e2, e1) = all_52_9 % 153.87/23.05 (99) all_56_9 = all_52_12 % 153.87/23.05 (100) all_58_29 = all_8_2 % 153.87/23.05 (101) ~ (all_52_12 = all_52_14) % 153.87/23.05 (102) all_58_8 = all_52_1 % 153.87/23.05 (103) ~ (e2 = e1) % 153.87/23.05 (104) op(e3, e0) = all_52_12 % 153.87/23.05 (105) all_56_6 = all_52_2 % 153.87/23.05 (106) ~ (all_52_2 = all_52_6) % 153.87/23.05 (107) all_18_2 = all_6_2 % 153.87/23.05 (108) all_56_13 = all_52_7 % 153.87/23.05 (109) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 153.87/23.05 (110) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 153.87/23.05 (111) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 153.87/23.05 (112) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 153.87/23.05 (113) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 153.87/23.05 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 153.87/23.05 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 153.87/23.05 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 153.87/23.05 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 153.87/23.05 (all_58_27 = e0)) % 153.87/23.05 (114) ~ (all_52_9 = all_52_13) % 153.87/23.05 (115) ~ (all_52_11 = all_8_1) % 153.87/23.05 (116) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.87/23.05 (117) all_54_13 = all_8_1 % 153.87/23.05 (118) ~ (all_52_4 = e0) % 153.87/23.05 (119) op(e2, all_52_9) = all_58_10 % 153.87/23.05 (120) ~ (all_52_11 = all_6_2) % 153.87/23.05 (121) op(e3, all_10_2) = all_58_0 % 153.87/23.05 (122) all_44_2 = all_4_2 % 153.87/23.05 (123) ~ (e3 = e0) % 153.87/23.05 (124) all_56_2 = all_52_1 % 153.87/23.05 (125) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 153.87/23.05 (126) op(e3, all_52_12) = all_58_5 % 153.87/23.05 (127) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 153.87/23.05 (128) all_56_10 = all_52_13 % 153.87/23.05 (129) ~ (all_52_3 = all_8_1) % 153.87/23.05 (130) ~ (all_52_12 = all_10_2) % 153.87/23.05 (131) ~ (all_52_1 = all_52_3) % 153.87/23.05 (132) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 153.87/23.05 (133) all_56_14 = all_52_11 % 153.87/23.05 (134) all_58_28 = all_10_2 % 153.87/23.05 (135) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 153.87/23.05 (136) all_58_17 = all_52_6 % 153.87/23.05 (137) ~ (all_52_1 = all_52_9) % 153.87/23.05 (138) op(e3, e1) = all_52_8 % 153.87/23.05 (139) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 153.87/23.05 (140) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 153.87/23.05 (141) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.87/23.05 (142) all_14_0 = all_8_0 % 153.87/23.05 (143) ~ (e2 = e0) % 153.87/23.05 (144) ~ (all_52_9 = all_6_2) % 153.87/23.05 (145) ~ (all_8_1 = all_4_2) % 153.87/23.05 (146) ~ (all_52_2 = all_10_2) % 153.87/23.05 (147) all_56_0 = all_10_2 % 153.87/23.05 (148) op(e0, e0) = all_4_2 % 153.87/23.05 (149) ~ (all_52_1 = e0) % 153.87/23.05 (150) ~ (all_52_3 = all_52_11) % 153.87/23.05 (151) all_58_22 = all_52_3 % 153.87/23.05 (152) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 153.87/23.05 (153) ~ (all_52_12 = all_4_2) % 153.87/23.05 (154) ~ (all_52_3 = all_10_2) % 153.87/23.05 (155) all_56_8 = all_6_2 % 153.87/23.05 (156) op(e1, e1) = all_6_2 % 153.87/23.05 (157) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 153.87/23.05 (158) ~ (all_52_1 = all_52_2) % 153.87/23.05 (159) op(all_4_2, all_4_1) = all_4_0 % 153.87/23.05 (160) op(e2, e0) = all_52_13 % 153.87/23.05 (161) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 153.87/23.05 (162) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 153.87/23.05 (163) op(e2, all_52_13) = all_58_12 % 153.87/23.05 (164) all_58_4 = all_52_8 % 153.87/23.05 (165) ~ (all_8_1 = e0) % 153.87/23.05 (166) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 153.87/23.05 (167) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 153.87/23.05 (168) all_54_0 = all_10_2 % 153.87/23.05 (169) ~ (all_52_2 = all_52_14) % 153.87/23.05 (170) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.87/23.05 (171) all_14_1 = all_8_1 % 153.87/23.05 (172) ~ (all_52_7 = e0) % 153.87/23.05 (173) ~ (all_52_14 = all_4_2) % 153.87/23.05 (174) ~ (e1 = e0) % 153.87/23.05 (175) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 153.87/23.05 (176) all_26_1 = all_4_1 % 153.87/23.05 (177) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 153.87/23.05 (178) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 153.87/23.05 (179) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 153.87/23.05 (180) ~ (all_52_4 = all_10_2) % 153.87/23.05 (181) all_44_0 = all_4_0 % 153.87/23.05 (182) all_58_30 = all_6_2 % 153.87/23.05 (183) op(e2, all_52_1) = all_58_7 % 153.87/23.05 (184) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.05 (185) ~ (e3 = e2) % 153.87/23.05 (186) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 153.87/23.05 (187) ~ (all_52_14 = all_6_2) % 153.87/23.05 (188) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 153.87/23.05 (189) op(all_4_2, e0) = all_4_1 % 153.87/23.05 (190) ~ (all_52_4 = all_52_12) % 153.87/23.05 (191) all_54_12 = all_52_3 % 153.87/23.05 (192) all_54_4 = all_52_1 % 153.87/23.05 (193) ~ (all_52_1 = all_10_2) % 153.87/23.05 % 153.87/23.05 Begin of proof % 153.87/23.05 | % 153.87/23.05 | BETA: splitting (65) gives: % 153.87/23.05 | % 153.87/23.05 | Case 1: % 153.87/23.05 | | % 153.87/23.05 | | (194) ~ (all_18_2 = e0) % 153.87/23.05 | | % 153.87/23.05 | | REDUCE: (107), (194) imply: % 153.87/23.05 | | (195) ~ (all_6_2 = e0) % 153.87/23.05 | | % 153.87/23.05 | | BETA: splitting (139) gives: % 153.87/23.05 | | % 153.87/23.05 | | Case 1: % 153.87/23.05 | | | % 153.87/23.05 | | | (196) ~ (all_20_2 = e1) % 153.87/23.05 | | | % 153.87/23.05 | | | REDUCE: (79), (196) imply: % 153.87/23.05 | | | (197) ~ (all_4_2 = e1) % 153.87/23.05 | | | % 153.87/23.05 | | | BETA: splitting (58) gives: % 153.87/23.05 | | | % 153.87/23.05 | | | Case 1: % 153.87/23.05 | | | | % 153.87/23.05 | | | | (198) ~ (all_26_1 = e1) % 153.87/23.05 | | | | % 153.87/23.05 | | | | REDUCE: (176), (198) imply: % 153.87/23.05 | | | | (199) ~ (all_4_1 = e1) % 153.87/23.05 | | | | % 153.87/23.05 | | | | BETA: splitting (57) gives: % 153.87/23.05 | | | | % 153.87/23.05 | | | | Case 1: % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | (200) all_56_15 = e0 % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | COMBINE_EQS: (8), (200) imply: % 153.87/23.05 | | | | | (201) all_4_2 = e0 % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (143), (166), (174), % 153.87/23.05 | | | | | (182), (184), (185), (201) are inconsistent by sub-proof % 153.87/23.05 | | | | | #399. % 153.87/23.05 | | | | | % 153.87/23.05 | | | | Case 2: % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | (202) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 153.87/23.05 | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | ALPHA: (202) implies: % 153.87/23.05 | | | | | (203) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.87/23.05 | | | | | (204) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | BETA: splitting (27) gives: % 153.87/23.05 | | | | | % 153.87/23.05 | | | | | Case 1: % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | | (205) all_54_15 = e0 % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | | COMBINE_EQS: (55), (205) imply: % 153.87/23.05 | | | | | | (206) all_4_2 = e0 % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (143), (166), (174), % 153.87/23.05 | | | | | | (182), (184), (185), (206) are inconsistent by sub-proof % 153.87/23.05 | | | | | | #399. % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | Case 2: % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | | (207) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | | BETA: splitting (83) gives: % 153.87/23.05 | | | | | | % 153.87/23.05 | | | | | | Case 1: % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | (208) all_56_4 = e0 % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | COMBINE_EQS: (28), (208) imply: % 153.87/23.05 | | | | | | | (209) all_52_8 = e0 % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | COMBINE_EQS: (164), (209) imply: % 153.87/23.05 | | | | | | | (210) all_58_4 = e0 % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | REDUCE: (4), (209) imply: % 153.87/23.05 | | | | | | | (211) ~ (all_52_9 = e0) % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | REDUCE: (22), (209) imply: % 153.87/23.05 | | | | | | | (212) ~ (all_52_11 = e0) % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | SIMP: (212) implies: % 153.87/23.05 | | | | | | | (213) ~ (all_52_11 = e0) % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | REDUCE: (138), (209) imply: % 153.87/23.05 | | | | | | | (214) op(e3, e1) = e0 % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | BETA: splitting (203) gives: % 153.87/23.05 | | | | | | | % 153.87/23.05 | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | (215) all_56_12 = e0 % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | COMBINE_EQS: (77), (215) imply: % 153.87/23.05 | | | | | | | | (216) all_52_3 = e0 % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | SIMP: (216) implies: % 153.87/23.05 | | | | | | | | (217) all_52_3 = e0 % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | COMBINE_EQS: (151), (217) imply: % 153.87/23.05 | | | | | | | | (218) all_58_22 = e0 % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | REDUCE: (6), (217) imply: % 153.87/23.05 | | | | | | | | (219) ~ (all_52_2 = e0) % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | REDUCE: (129), (217) imply: % 153.87/23.05 | | | | | | | | (220) ~ (all_8_1 = e0) % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | BETA: splitting (170) gives: % 153.87/23.05 | | | | | | | | % 153.87/23.05 | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | (221) all_56_6 = e0 % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | COMBINE_EQS: (105), (221) imply: % 153.87/23.05 | | | | | | | | | (222) all_52_2 = e0 % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | REDUCE: (219), (222) imply: % 153.87/23.05 | | | | | | | | | (223) $false % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | CLOSE: (223) is inconsistent. % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | (224) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | BETA: splitting (224) gives: % 153.87/23.05 | | | | | | | | | % 153.87/23.05 | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | (225) all_56_7 = e0 % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | COMBINE_EQS: (9), (225) imply: % 153.87/23.05 | | | | | | | | | | (226) all_52_6 = e0 % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | REDUCE: (68), (226) imply: % 153.87/23.05 | | | | | | | | | | (227) $false % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | CLOSE: (227) is inconsistent. % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | (228) all_56_8 = e0 | all_56_11 = e0 % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | BETA: splitting (228) gives: % 153.87/23.05 | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | (229) all_56_8 = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (134), (143), % 153.87/23.05 | | | | | | | | | | | (155), (166), (174), (182), (184), (185), (197), % 153.87/23.05 | | | | | | | | | | | (229) are inconsistent by sub-proof #398. % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | (230) all_56_11 = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | COMBINE_EQS: (81), (230) imply: % 153.87/23.05 | | | | | | | | | | | (231) all_52_14 = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | SIMP: (231) implies: % 153.87/23.05 | | | | | | | | | | | (232) all_52_14 = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | COMBINE_EQS: (46), (232) imply: % 153.87/23.05 | | | | | | | | | | | (233) all_58_20 = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | REDUCE: (101), (232) imply: % 153.87/23.05 | | | | | | | | | | | (234) ~ (all_52_12 = e0) % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | REDUCE: (173), (232) imply: % 153.87/23.05 | | | | | | | | | | | (235) ~ (all_4_2 = e0) % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | SIMP: (235) implies: % 153.87/23.05 | | | | | | | | | | | (236) ~ (all_4_2 = e0) % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | REDUCE: (20), (232) imply: % 153.87/23.05 | | | | | | | | | | | (237) op(e1, e0) = all_58_19 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | REDUCE: (89), (232) imply: % 153.87/23.05 | | | | | | | | | | | (238) op(e1, e0) = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_58_19, e0, e1, % 153.87/23.05 | | | | | | | | | | | simplifying with (237), (238) gives: % 153.87/23.05 | | | | | | | | | | | (239) all_58_19 = e0 % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | BETA: splitting (43) gives: % 153.87/23.05 | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | (240) all_54_13 = e0 % 153.87/23.05 | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | REF_CLOSE: (117), (165), (240) are inconsistent by sub-proof % 153.87/23.05 | | | | | | | | | | | | #397. % 153.87/23.05 | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | (241) ~ (all_54_13 = e0) % 153.87/23.05 | | | | | | | | | | | | (242) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 153.87/23.05 | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | BETA: splitting (179) gives: % 153.87/23.05 | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | (243) all_54_6 = e0 % 153.87/23.05 | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | REF_CLOSE: (54), (91), (243) are inconsistent by sub-proof % 153.87/23.05 | | | | | | | | | | | | | #797. % 153.87/23.05 | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | (244) ~ (all_54_6 = e0) % 153.87/23.05 | | | | | | | | | | | | | (245) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 153.87/23.05 | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | BETA: splitting (67) gives: % 153.87/23.05 | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | (246) all_54_9 = e0 % 153.87/23.05 | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | REF_CLOSE: (61), (68), (246) are inconsistent by sub-proof % 153.87/23.05 | | | | | | | | | | | | | | #572. % 153.87/23.05 | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | (247) ~ (all_54_9 = e0) % 153.87/23.05 | | | | | | | | | | | | | | (248) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 153.87/23.05 | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | BETA: splitting (132) gives: % 153.87/23.05 | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | (249) all_54_14 = e0 % 153.87/23.05 | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | REF_CLOSE: (74), (213), (249) are inconsistent by sub-proof % 153.87/23.05 | | | | | | | | | | | | | | | #517. % 153.87/23.05 | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | (250) ~ (all_54_14 = e0) % 153.87/23.05 | | | | | | | | | | | | | | | (251) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 153.87/23.05 | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 153.87/23.05 | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | (252) all_54_8 = e0 % 153.87/23.05 | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (219), (252) are inconsistent by sub-proof % 153.87/23.05 | | | | | | | | | | | | | | | | #731. % 153.87/23.05 | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | (253) ~ (all_54_8 = e0) % 153.87/23.05 | | | | | | | | | | | | | | | | (254) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 153.87/23.05 | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 153.87/23.05 | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | (255) all_54_10 = e0 % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (255) imply: % 153.87/23.05 | | | | | | | | | | | | | | | | | (256) all_6_2 = e0 % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (134), (143), % 153.87/23.05 | | | | | | | | | | | | | | | | | (166), (174), (182), (184), (185), (197), (256) % 153.87/23.05 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #396. % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | (257) ~ (all_54_10 = e0) % 153.87/23.05 | | | | | | | | | | | | | | | | | (258) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 153.87/23.05 | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | (259) all_54_0 = e0 % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (134), (143), % 153.87/23.05 | | | | | | | | | | | | | | | | | | (166), (168), (174), (182), (184), (185), (259) % 153.87/23.05 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #395. % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | (260) ~ (all_54_0 = e0) % 153.87/23.05 | | | | | | | | | | | | | | | | | | (261) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | REDUCE: (168), (260) imply: % 153.87/23.05 | | | | | | | | | | | | | | | | | | (262) ~ (all_10_2 = e0) % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives: % 153.87/23.05 | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.05 | | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | | (263) all_54_3 = e0 % 153.87/23.05 | | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (234), (263) are inconsistent by sub-proof % 153.87/23.05 | | | | | | | | | | | | | | | | | | | #733. % 153.87/23.05 | | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.05 | | | | | | | | | | | | | | | | | | | % 153.87/23.05 | | | | | | | | | | | | | | | | | | | (264) ~ (all_54_3 = e0) % 153.87/23.05 | | | | | | | | | | | | | | | | | | | (265) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 153.87/23.05 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (13), (15), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (17), (18), (21), (23), (24), (26), (30), (31), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (32), (35), (36), (38), (39), (41), (42), (45), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (49), (50), (51), (54), (55), (56), (61), (62), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (63), (64), (66), (68), (69), (72), (73), (74), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (75), (78), (80), (82), (84), (88), (91), (93), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (94), (97), (98), (99), (102), (103), (105), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (106), (110), (111), (112), (113), (114), (115), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (116), (117), (118), (120), (123), (124), (125), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (126), (128), (130), (132), (133), (134), (136), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (137), (140), (142), (143), (144), (146), (147), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (149), (153), (155), (157), (158), (161), (165), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (166), (167), (168), (171), (174), (178), (180), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (182), (183), (184), (186), (190), (192), (193), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (195), (197), (207), (208), (210), (213), (214), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (215), (218), (219), (230), (233), (234), (236), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (239), (242), (245), (248), (251), (254), (258), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (261), (262), (265) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | | | | | | | | #333. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | End of split % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | (266) all_56_13 = e0 | all_56_14 = e0 % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | REF_CLOSE: (108), (133), (172), (213), (266) are inconsistent by % 153.87/23.06 | | | | | | | | sub-proof #609. % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | End of split % 153.87/23.06 | | | | | | | % 153.87/23.06 | | | | | | Case 2: % 153.87/23.06 | | | | | | | % 153.87/23.06 | | | | | | | (267) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 153.87/23.06 | | | | | | | % 153.87/23.06 | | | | | | | BETA: splitting (267) gives: % 153.87/23.06 | | | | | | | % 153.87/23.06 | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | (268) all_56_5 = e0 % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | COMBINE_EQS: (73), (268) imply: % 153.87/23.06 | | | | | | | | (269) all_52_9 = e0 % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | REDUCE: (91), (269) imply: % 153.87/23.06 | | | | | | | | (270) $false % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | CLOSE: (270) is inconsistent. % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | (271) all_56_8 = e0 | all_56_14 = e0 % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | BETA: splitting (271) gives: % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | (272) all_56_8 = e0 % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | COMBINE_EQS: (155), (272) imply: % 153.87/23.06 | | | | | | | | | (273) all_6_2 = e0 % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (134), (143), % 153.87/23.06 | | | | | | | | | (166), (174), (182), (184), (185), (197), (273) are % 153.87/23.06 | | | | | | | | | inconsistent by sub-proof #396. % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | (274) all_56_14 = e0 % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | COMBINE_EQS: (133), (274) imply: % 153.87/23.06 | | | | | | | | | (275) all_52_11 = e0 % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | SIMP: (275) implies: % 153.87/23.06 | | | | | | | | | (276) all_52_11 = e0 % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | COMBINE_EQS: (18), (276) imply: % 153.87/23.06 | | | | | | | | | (277) all_58_26 = e0 % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | REDUCE: (150), (276) imply: % 153.87/23.06 | | | | | | | | | (278) ~ (all_52_3 = e0) % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | REDUCE: (115), (276) imply: % 153.87/23.06 | | | | | | | | | (279) ~ (all_8_1 = e0) % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | BETA: splitting (152) gives: % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | (280) all_56_0 = e0 % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | COMBINE_EQS: (147), (280) imply: % 153.87/23.06 | | | | | | | | | | (281) all_10_2 = e0 % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | COMBINE_EQS: (134), (281) imply: % 153.87/23.06 | | | | | | | | | | (282) all_58_28 = e0 % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 153.87/23.06 | | | | | | | | | | (174), (182), (184), (185), (282) are inconsistent % 153.87/23.06 | | | | | | | | | | by sub-proof #483. % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | (283) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | BETA: splitting (283) gives: % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | (284) all_56_2 = e0 % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | COMBINE_EQS: (124), (284) imply: % 153.87/23.06 | | | | | | | | | | | (285) all_52_1 = e0 % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | REDUCE: (149), (285) imply: % 153.87/23.06 | | | | | | | | | | | (286) $false % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | CLOSE: (286) is inconsistent. % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | (287) all_56_6 = e0 | all_56_12 = e0 % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | BETA: splitting (287) gives: % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | (288) all_56_6 = e0 % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | COMBINE_EQS: (105), (288) imply: % 153.87/23.06 | | | | | | | | | | | | (289) all_52_2 = e0 % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | COMBINE_EQS: (17), (289) imply: % 153.87/23.06 | | | | | | | | | | | | (290) all_58_15 = e0 % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | REDUCE: (6), (289) imply: % 153.87/23.06 | | | | | | | | | | | | (291) ~ (all_52_3 = e0) % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | REDUCE: (106), (289) imply: % 153.87/23.06 | | | | | | | | | | | | (292) ~ (all_52_6 = e0) % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | REDUCE: (169), (289) imply: % 153.87/23.06 | | | | | | | | | | | | (293) ~ (all_52_14 = e0) % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | SIMP: (293) implies: % 153.87/23.06 | | | | | | | | | | | | (294) ~ (all_52_14 = e0) % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | REDUCE: (56), (289) imply: % 153.87/23.06 | | | | | | | | | | | | (295) ~ (all_6_2 = e0) % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | BETA: splitting (204) gives: % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | (296) all_56_9 = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | COMBINE_EQS: (99), (296) imply: % 153.87/23.06 | | | | | | | | | | | | | (297) all_52_12 = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | SIMP: (297) implies: % 153.87/23.06 | | | | | | | | | | | | | (298) all_52_12 = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | COMBINE_EQS: (26), (298) imply: % 153.87/23.06 | | | | | | | | | | | | | (299) all_58_6 = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | REDUCE: (60), (298) imply: % 153.87/23.06 | | | | | | | | | | | | | (300) ~ (all_52_8 = e0) % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | REDUCE: (49), (298) imply: % 153.87/23.06 | | | | | | | | | | | | | (301) ~ (all_52_13 = e0) % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | REDUCE: (153), (298) imply: % 153.87/23.06 | | | | | | | | | | | | | (302) ~ (all_4_2 = e0) % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | SIMP: (302) implies: % 153.87/23.06 | | | | | | | | | | | | | (303) ~ (all_4_2 = e0) % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | REDUCE: (126), (298) imply: % 153.87/23.06 | | | | | | | | | | | | | (304) op(e3, e0) = all_58_5 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | REDUCE: (104), (298) imply: % 153.87/23.06 | | | | | | | | | | | | | (305) op(e3, e0) = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_58_5, e0, e3, % 153.87/23.06 | | | | | | | | | | | | | simplifying with (304), (305) gives: % 153.87/23.06 | | | | | | | | | | | | | (306) all_58_5 = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | BETA: splitting (43) gives: % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | (307) all_54_13 = e0 % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | COMBINE_EQS: (117), (307) imply: % 153.87/23.06 | | | | | | | | | | | | | | (308) all_8_1 = e0 % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | REDUCE: (165), (308) imply: % 153.87/23.06 | | | | | | | | | | | | | | (309) $false % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | CLOSE: (309) is inconsistent. % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | (310) ~ (all_54_13 = e0) % 153.87/23.06 | | | | | | | | | | | | | | (311) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | BETA: splitting (116) gives: % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | (312) all_56_9 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | COMBINE_EQS: (296), (312) imply: % 153.87/23.06 | | | | | | | | | | | | | | | (313) e1 = e0 % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | REDUCE: (174), (313) imply: % 153.87/23.06 | | | | | | | | | | | | | | | (314) $false % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | CLOSE: (314) is inconsistent. % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | (315) ~ (all_56_9 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | (316) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | REDUCE: (296), (315) imply: % 153.87/23.06 | | | | | | | | | | | | | | | (317) ~ (e1 = e0) % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | (318) all_56_12 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (318) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | (319) all_52_3 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | SIMP: (319) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | (320) all_52_3 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | REDUCE: (131), (320) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | (321) ~ (all_52_1 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | REDUCE: (154), (320) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | (322) ~ (all_10_2 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | SIMP: (322) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | (323) ~ (all_10_2 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | REDUCE: (129), (320) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | (324) ~ (all_8_1 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | SIMP: (324) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | (325) ~ (all_8_1 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | REDUCE: (86), (320) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | (326) ~ (all_4_2 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | (327) all_58_28 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (327) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (328) all_10_2 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | REDUCE: (323), (328) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (329) $false % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | CLOSE: (329) is inconsistent. % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | (330) ~ (all_58_28 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | (331) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | BETA: splitting (331) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | (332) all_58_29 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (41), (56), (97), (105), (124), (147), (174), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (182), (195), (197), (318), (321), (323), (331), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (332) are inconsistent by sub-proof #332. % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | (333) all_58_30 = e1 | all_58_31 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (334) all_58_30 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (334) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (335) all_6_2 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | REDUCE: (187), (335) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (336) ~ (all_52_14 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | REDUCE: (14), (335) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (337) op(e1, e1) = all_58_18 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | REDUCE: (156), (335) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (338) op(e1, e1) = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | (339) all_56_10 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (339) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | (340) all_52_13 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | SIMP: (340) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | (341) all_52_13 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (341) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | (342) op(e2, e0) = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e1, all_58_18, e1, e1, % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | simplifying with (337), (338) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | (343) all_58_18 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | (344) all_54_4 = e0 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (192), (344) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | #859. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_54_4 = e0) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | (346) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | (347) all_54_0 = e0 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (134), (143), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | (166), (168), (182), (185), (333), (347) are % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #331. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | (348) ~ (all_54_0 = e0) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | (349) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (348) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_10_2 = e0) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | (351) all_56_0 = e3 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (351) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | (352) all_10_2 = e3 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (352) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | (353) all_10_2 = e3 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (353) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_28 = e3 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_28 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (355) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (356) e3 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (356) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (357) $false % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (358) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_29 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (143), (359) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | #706. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_58_30 = e2 | all_58_31 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_58_30 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (361) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) e2 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (362) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) $false % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (363) is inconsistent. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_31 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (364) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_4_2 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (365) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_4_2 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (366) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) op(e2, e0) = all_4_1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (199), (342), (367) are inconsistent by % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #586. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_56_0 = e3) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (368) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_10_2 = e3) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (370) all_54_0 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (323), (370) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | #841. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (371) ~ (all_54_0 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | (372) all_54_0 = e3 | all_54_0 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_54_0 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (373) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_10_2 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (374) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_10_2 = e2 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (375) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (376) ~ (all_52_1 = e2) % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (34), (42), (48), (75), (97), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (103), (113), (117), (124), (134), (135), (143), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (145), (147), (149), (162), (166), (167), (183), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (192), (193), (288), (306), (311), (318), (321), % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (323), (325), (334), (343), (346), (376) are % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_54_0 = e3 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (369), (377) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | #827. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | (378) all_56_11 = e1 | all_56_15 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (81), (197), (336), (378) are inconsistent by % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | sub-proof #579. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (379) all_58_31 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (379) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (380) all_4_2 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | REDUCE: (197), (380) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | | | (381) $false % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | | CLOSE: (381) is inconsistent. % 153.87/23.06 | | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | (382) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | BETA: splitting (382) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | (383) all_56_13 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (383) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (384) all_8_1 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | SIMP: (384) implies: % 153.87/23.06 | | | | | | | | | | | | | | | | | (385) all_8_1 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (385) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (386) all_58_24 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | REDUCE: (129), (385) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (387) ~ (all_52_3 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | REDUCE: (88), (385) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (388) ~ (all_52_4 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | REDUCE: (29), (385) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (389) ~ (all_52_6 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | REDUCE: (145), (385) imply: % 153.87/23.06 | | | | | | | | | | | | | | | | | (390) ~ (all_4_2 = e1) % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | Case 1: % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | (391) all_54_9 = e0 % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (68), (391) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | | | | | | | #572. % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | (392) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (16), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (21), (25), (28), (31), (32), (36), (38), (40), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (41), (44), (46), (47), (50), (51), (52), (53), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (54), (61), (63), (64), (68), (69), (70), (72), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (73), (77), (78), (82), (84), (85), (86), (91), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (92), (93), (94), (95), (97), (102), (103), (109), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (110), (112), (114), (118), (124), (125), (127), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (128), (131), (134), (135), (136), (137), (143), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (144), (147), (149), (151), (154), (157), (161), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (162), (164), (166), (167), (168), (173), (174), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (175), (177), (179), (180), (182), (184), (187), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (188), (191), (192), (193), (195), (197), (274), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (277), (278), (288), (290), (294), (296), (299), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (300), (303), (383), (386), (387), (388), (389), % 153.87/23.06 | | | | | | | | | | | | | | | | | | (392) are inconsistent by sub-proof #295. % 153.87/23.06 | | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | (393) all_56_14 = e1 | all_56_15 = e1 % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (174), (197), (274), (393) are inconsistent % 153.87/23.06 | | | | | | | | | | | | | | | | | by sub-proof #582. % 153.87/23.06 | | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | (394) all_56_10 = e0 | all_56_11 = e0 % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | | REF_CLOSE: (81), (84), (128), (294), (394) are inconsistent % 153.87/23.06 | | | | | | | | | | | | | by sub-proof #294. % 153.87/23.06 | | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | Case 2: % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | (395) all_56_12 = e0 % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | | REF_CLOSE: (77), (278), (395) are inconsistent by sub-proof % 153.87/23.06 | | | | | | | | | | | | #607. % 153.87/23.06 | | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | | % 153.87/23.06 | | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | | % 153.87/23.06 | | | | | | | | | End of split % 153.87/23.06 | | | | | | | | | % 153.87/23.06 | | | | | | | | End of split % 153.87/23.06 | | | | | | | | % 153.87/23.06 | | | | | | | End of split % 153.87/23.06 | | | | | | | % 153.87/23.06 | | | | | | End of split % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | End of split % 153.87/23.06 | | | | | % 153.87/23.06 | | | | End of split % 153.87/23.06 | | | | % 153.87/23.06 | | | Case 2: % 153.87/23.06 | | | | % 153.87/23.06 | | | | (396) all_26_1 = e1 % 153.87/23.06 | | | | % 153.87/23.06 | | | | COMBINE_EQS: (176), (396) imply: % 153.87/23.06 | | | | (397) all_4_1 = e1 % 153.87/23.06 | | | | % 153.87/23.06 | | | | COMBINE_EQS: (19), (397) imply: % 153.87/23.06 | | | | (398) all_44_1 = e1 % 153.87/23.06 | | | | % 153.87/23.06 | | | | REDUCE: (159), (397) imply: % 153.87/23.06 | | | | (399) op(all_4_2, e1) = all_4_0 % 153.87/23.06 | | | | % 153.87/23.06 | | | | REDUCE: (189), (397) imply: % 153.87/23.06 | | | | (400) op(all_4_2, e0) = e1 % 153.87/23.06 | | | | % 153.87/23.06 | | | | BETA: splitting (37) gives: % 153.87/23.06 | | | | % 153.87/23.06 | | | | Case 1: % 153.87/23.06 | | | | | % 153.87/23.06 | | | | | (401) ~ (all_44_1 = e1) % 153.87/23.06 | | | | | % 153.87/23.06 | | | | | REDUCE: (398), (401) imply: % 153.87/23.06 | | | | | (402) $false % 153.87/23.06 | | | | | % 153.87/23.06 | | | | | CLOSE: (402) is inconsistent. % 153.87/23.06 | | | | | % 153.87/23.06 | | | | Case 2: % 153.87/23.06 | | | | | % 153.87/23.06 | | | | | (403) ~ (all_44_0 = e3) | ~ (all_44_2 = e2) % 153.87/23.06 | | | | | % 153.87/23.06 | | | | | BETA: splitting (57) gives: % 153.87/23.06 | | | | | % 153.87/23.06 | | | | | Case 1: % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | (404) all_56_15 = e0 % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | REF_CLOSE: (5), (8), (33), (148), (197), (400), (404) are % 153.87/23.06 | | | | | | inconsistent by sub-proof #460. % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | Case 2: % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | (405) ~ (all_56_15 = e0) % 153.87/23.06 | | | | | | (406) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 153.87/23.06 | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | ALPHA: (406) implies: % 153.87/23.06 | | | | | | (407) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | REDUCE: (8), (405) imply: % 153.87/23.06 | | | | | | (408) ~ (all_4_2 = e0) % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | BETA: splitting (27) gives: % 153.87/23.06 | | | | | | % 153.87/23.06 | | | | | | Case 1: % 153.87/23.06 | | | | | | | % 154.00/23.06 | | | | | | | (409) all_54_15 = e0 % 154.00/23.06 | | | | | | | % 154.00/23.06 | | | | | | | REF_CLOSE: (55), (408), (409) are inconsistent by sub-proof #493. % 154.00/23.06 | | | | | | | % 154.00/23.06 | | | | | | Case 2: % 154.00/23.06 | | | | | | | % 154.00/23.06 | | | | | | | (410) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.00/23.06 | | | | | | | % 154.00/23.06 | | | | | | | BETA: splitting (76) gives: % 154.00/23.06 | | | | | | | % 154.00/23.06 | | | | | | | Case 1: % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | (411) all_56_0 = e0 % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | COMBINE_EQS: (147), (411) imply: % 154.00/23.06 | | | | | | | | (412) all_10_2 = e0 % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | COMBINE_EQS: (134), (412) imply: % 154.00/23.06 | | | | | | | | (413) all_58_28 = e0 % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), (174), % 154.00/23.06 | | | | | | | | (182), (184), (185), (413) are inconsistent by % 154.00/23.06 | | | | | | | | sub-proof #483. % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | Case 2: % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | (414) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | BETA: splitting (83) gives: % 154.00/23.06 | | | | | | | | % 154.00/23.06 | | | | | | | | Case 1: % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | (415) all_56_4 = e0 % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | COMBINE_EQS: (28), (415) imply: % 154.00/23.06 | | | | | | | | | (416) all_52_8 = e0 % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | COMBINE_EQS: (164), (416) imply: % 154.00/23.06 | | | | | | | | | (417) all_58_4 = e0 % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | REDUCE: (4), (416) imply: % 154.00/23.06 | | | | | | | | | (418) ~ (all_52_9 = e0) % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | REDUCE: (22), (416) imply: % 154.00/23.06 | | | | | | | | | (419) ~ (all_52_11 = e0) % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | SIMP: (419) implies: % 154.00/23.06 | | | | | | | | | (420) ~ (all_52_11 = e0) % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | REDUCE: (138), (416) imply: % 154.00/23.06 | | | | | | | | | (421) op(e3, e1) = e0 % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | BETA: splitting (407) gives: % 154.00/23.06 | | | | | | | | | % 154.00/23.06 | | | | | | | | | Case 1: % 154.00/23.06 | | | | | | | | | | % 154.00/23.06 | | | | | | | | | | (422) all_56_12 = e0 % 154.00/23.06 | | | | | | | | | | % 154.00/23.06 | | | | | | | | | | COMBINE_EQS: (77), (422) imply: % 154.00/23.06 | | | | | | | | | | (423) all_52_3 = e0 % 154.00/23.06 | | | | | | | | | | % 154.00/23.06 | | | | | | | | | | SIMP: (423) implies: % 154.00/23.06 | | | | | | | | | | (424) all_52_3 = e0 % 154.00/23.06 | | | | | | | | | | % 154.00/23.06 | | | | | | | | | | COMBINE_EQS: (151), (424) imply: % 154.00/23.06 | | | | | | | | | | (425) all_58_22 = e0 % 154.00/23.06 | | | | | | | | | | % 154.00/23.06 | | | | | | | | | | REDUCE: (6), (424) imply: % 154.00/23.06 | | | | | | | | | | (426) ~ (all_52_2 = e0) % 154.00/23.06 | | | | | | | | | | % 154.00/23.06 | | | | | | | | | | REDUCE: (129), (424) imply: % 154.00/23.06 | | | | | | | | | | (427) ~ (all_8_1 = e0) % 154.00/23.06 | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | BETA: splitting (170) gives: % 154.00/23.07 | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | (428) all_56_6 = e0 % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | COMBINE_EQS: (105), (428) imply: % 154.00/23.07 | | | | | | | | | | | (429) all_52_2 = e0 % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | REDUCE: (426), (429) imply: % 154.00/23.07 | | | | | | | | | | | (430) $false % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | CLOSE: (430) is inconsistent. % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | (431) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | BETA: splitting (431) gives: % 154.00/23.07 | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | (432) all_56_7 = e0 % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | COMBINE_EQS: (9), (432) imply: % 154.00/23.07 | | | | | | | | | | | | (433) all_52_6 = e0 % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | REDUCE: (68), (433) imply: % 154.00/23.07 | | | | | | | | | | | | (434) $false % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | CLOSE: (434) is inconsistent. % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | (435) all_56_8 = e0 | all_56_11 = e0 % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | BETA: splitting (435) gives: % 154.00/23.07 | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | (436) all_56_8 = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (134), (143), % 154.00/23.07 | | | | | | | | | | | | | (155), (166), (174), (182), (184), (185), (197), % 154.00/23.07 | | | | | | | | | | | | | (436) are inconsistent by sub-proof #398. % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | (437) all_56_11 = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | COMBINE_EQS: (81), (437) imply: % 154.00/23.07 | | | | | | | | | | | | | (438) all_52_14 = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | SIMP: (438) implies: % 154.00/23.07 | | | | | | | | | | | | | (439) all_52_14 = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | COMBINE_EQS: (46), (439) imply: % 154.00/23.07 | | | | | | | | | | | | | (440) all_58_20 = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | REDUCE: (101), (439) imply: % 154.00/23.07 | | | | | | | | | | | | | (441) ~ (all_52_12 = e0) % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | REDUCE: (187), (439) imply: % 154.00/23.07 | | | | | | | | | | | | | (442) ~ (all_6_2 = e0) % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | REDUCE: (173), (439) imply: % 154.00/23.07 | | | | | | | | | | | | | (443) ~ (all_4_2 = e0) % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | REDUCE: (20), (439) imply: % 154.00/23.07 | | | | | | | | | | | | | (444) op(e1, e0) = all_58_19 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | REDUCE: (89), (439) imply: % 154.00/23.07 | | | | | | | | | | | | | (445) op(e1, e0) = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_58_19, e0, e1, % 154.00/23.07 | | | | | | | | | | | | | simplifying with (444), (445) gives: % 154.00/23.07 | | | | | | | | | | | | | (446) all_58_19 = e0 % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | BETA: splitting (43) gives: % 154.00/23.07 | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | (447) all_54_13 = e0 % 154.00/23.07 | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | REF_CLOSE: (117), (165), (447) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | #397. % 154.00/23.07 | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | (448) ~ (all_54_13 = e0) % 154.00/23.07 | | | | | | | | | | | | | | (449) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.00/23.07 | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | BETA: splitting (179) gives: % 154.00/23.07 | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | (450) all_54_6 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | REF_CLOSE: (54), (91), (450) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | #797. % 154.00/23.07 | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | (451) ~ (all_54_6 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | (452) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 154.00/23.07 | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | (453) all_54_9 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | REF_CLOSE: (61), (68), (453) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | #572. % 154.00/23.07 | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | (454) ~ (all_54_9 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | (455) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | BETA: splitting (132) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | (456) all_54_14 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (420), (456) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | #517. % 154.00/23.07 | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | (457) ~ (all_54_14 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | (458) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | (459) all_54_8 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (426), (459) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | #731. % 154.00/23.07 | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | (460) ~ (all_54_8 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | (461) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | (462) all_54_0 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (134), (143), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | (166), (168), (174), (182), (184), (185), (462) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #395. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | (463) ~ (all_54_0 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | (464) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | REDUCE: (168), (463) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | (465) ~ (all_10_2 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | (466) all_54_3 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (441), (466) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | #733. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | (467) ~ (all_54_3 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | (468) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (469) all_56_9 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (9), (10), (21), (39), (41), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (42), (56), (62), (66), (69), (73), (74), (75), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (80), (82), (93), (97), (98), (99), (105), (111), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (113), (115), (123), (124), (126), (128), (130), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (132), (133), (134), (142), (147), (149), (153), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (167), (171), (182), (183), (184), (190), (195), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (420), (421), (422), (441), (446), (469) are % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #389. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | (470) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (471) all_56_10 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (471) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (472) all_52_13 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | SIMP: (472) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (473) all_52_13 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (473) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (474) all_58_13 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (473) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (475) ~ (all_52_1 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (473) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (476) ~ (all_52_9 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (473) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (477) ~ (all_52_12 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (473) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (478) ~ (all_4_2 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (473) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (479) op(e2, e1) = all_58_12 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_52_9, all_58_12, e1, % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (98), (479) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | (480) all_58_12 = all_52_9 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | (481) all_54_4 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (192), (481) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | #859. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | (482) ~ (all_54_4 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | (483) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | (484) all_54_1 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (118), (484) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | #798. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | (485) ~ (all_54_1 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | (486) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_56_2 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (487) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_52_1 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (488) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_52_9 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (489) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | (490) ~ (all_52_9 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (491) all_54_6 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (491) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_52_9 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (476), (492) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (493) $false % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (493) is inconsistent. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_54_6 = e3 | all_54_6 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (494) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_54_6 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (495) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_52_9 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (490), (496) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) $false % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (497) is inconsistent. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_54_6 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (498) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_52_9 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (499) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_58_11 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (499) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) ~ (all_6_2 = e3) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (501) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) ~ (all_6_2 = e3) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (499) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) op(e2, e1) = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_56_9 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (504) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_52_12 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (505) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_52_12 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (506) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_58_6 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (506) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) ~ (all_52_4 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (506) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) ~ (all_10_2 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (509) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) ~ (all_10_2 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (506) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) ~ (all_4_2 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) ~ (all_4_2 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_58_28 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (510), (513) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #388. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) ~ (all_58_28 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (515) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_58_29 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (516) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) e2 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (517) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) $false % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (518) is inconsistent. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_58_30 = e2 | all_58_31 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_54_15 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (197), (520) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #587. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) ~ (all_54_15 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_54_15 = e3 | all_54_15 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_54_15 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (512), (523) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_54_15 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (524) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_4_2 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (525) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_4_2 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (526) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_31 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (526) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) ~ (all_52_11 = e3) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (526) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) ~ (all_8_1 = e3) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (519) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_30 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (530) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_6_2 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (531) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_6_2 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (532) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) ~ (all_52_2 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (532) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) ~ (all_52_6 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (502), (532) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) ~ (e3 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_56_12 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (185), (422), (519), (527), (530), (536) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #293. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) ~ (all_56_12 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (422), (537) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) ~ (e2 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_58_28 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (540) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_10_2 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (541) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) ~ (all_52_2 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (180), (541) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) ~ (all_52_4 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (541) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ~ (e2 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_58_31 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (540), (545) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #850. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_56_13 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (547) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_8_1 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (548) implies: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_8_1 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (549) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_58_24 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (549) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) ~ (all_52_11 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_56_6 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (552) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) all_52_2 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (553) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) $false % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (554) is inconsistent. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) ~ (all_56_6 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_54_14 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (557) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_52_11 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (558) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_58_26 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_54_8 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (542), (560) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_54_8 = e3 | all_54_8 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_56_7 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (562) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_52_6 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (563) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_58_17 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_56_1 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (565) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_52_4 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (566) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_58_2 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_56_6 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (568) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_52_2 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (569) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_58_15 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_58_30 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503), (519), (571) are inconsistent by sub-proof % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #292. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) ~ (all_58_30 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (573) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_58_29 = e2 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (530), (540), (574) are inconsistent by % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #386. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) ~ (all_58_29 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_58_28 = e3 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (577) imply: % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) e3 = e1 % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (185), (527), (540), (578) are inconsistent % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #382. % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) ~ (all_58_28 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (579) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) ~ (e3 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (582) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (584) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (585) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_58_4 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (417), (540), (586) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #381. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (587) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (507), (530), (540), (588) are inconsistent % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #380. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (589) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_58_17 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (590) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503), (519), (530), (591) are inconsistent by % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #291. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (592) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_58_13 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (595) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503), (519), (530), (596) are inconsistent by % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #291. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (417), (530), (540), (567), (597) are % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #374. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (599) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_58_22 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_58_6 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (507), (601) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) e3 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (602) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) e3 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (600) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) e3 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (604) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) e3 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (603), (605) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) e2 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (606) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_58_30 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (540), (607) are inconsistent by sub-proof % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #701. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_58_11 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_58_2 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (567), (610) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) e3 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (500), (609) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) e3 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (612) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503), (519), (530), (613) are inconsistent by % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #291. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (614) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (417), (474), (500), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507), (530), (540), (567), (615) are inconsistent % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #370. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (617) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (618) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_58_20 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (440), (540), (619) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #369. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_58_22 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_58_15 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (570), (622) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) e3 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (621) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) e3 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (624) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) e3 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (540), (623), (625) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #371. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (417), (540), (559), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) are inconsistent by sub-proof #368. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (627) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (417), (474), (540), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559), (629) are inconsistent by sub-proof #367. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (630) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_58_13 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_58_6 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (507), (634) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) e2 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (633) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (636) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (637) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) e1 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (638) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_58_28 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (639) are inconsistent % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #483. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (640) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) all_58_20 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (440), (540), (641) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #369. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (507), (530), (540), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550), (564), (642) are inconsistent by sub-proof % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #365. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (643) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (644) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (645) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_58_20 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (440), (540), (647) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #369. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (648) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_58_13 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (649) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503), (519), (530), (650) are inconsistent by % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #291. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (651) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (540), (559), (652) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #363. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (654) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_58_30 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503), (519), (655) are inconsistent by sub-proof % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #292. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (182), (184), (185), (440), (474), (540), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559), (656) are inconsistent by sub-proof #362. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) ~ (all_56_6 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (657) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) ~ (all_52_2 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (561) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_54_8 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (533), (659) are inconsistent by sub-proof % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #787. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_54_8 = e3 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (658), (660) are inconsistent by sub-proof % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #786. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) ~ (all_56_1 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (661) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) ~ (all_52_4 = e3) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (486), (508), (543), (662) are inconsistent % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) ~ (all_56_7 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (663) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) ~ (all_52_6 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (36), (61), (455), (486), (508), (534), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543), (664) are inconsistent by sub-proof #421. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_54_14 = e3 | all_54_14 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (528), (551), (665) are inconsistent by % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #358. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) ~ (all_56_13 = e2) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (666) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) ~ (all_8_1 = e2) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (449) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_54_13 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (668) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_8_1 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (669) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_8_1 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (670) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) ~ (all_52_6 = e1) % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (36), (61), (455), (486), (508), (534), % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543), (671) are inconsistent by sub-proof #421. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_54_13 = e3 | all_54_13 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (529), (667), (672) are inconsistent by % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (97), (103), (174), (527), (530), (673) are % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #357. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_58_31 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (527), (674) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) e3 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (675) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) $false % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (676) is inconsistent. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (677) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_56_10 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (471), (678) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) e2 = e1 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (679) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) $false % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (680) is inconsistent. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_56_11 = e2 | all_56_15 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (681) gives: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_56_11 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (437), (682) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) e2 = e0 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (683) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) $false % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (684) is inconsistent. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_56_15 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (685) imply: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_4_2 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (686) implies: % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) all_4_2 = e2 % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (122), (181), (399), (403), (503), (687) are % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #570. % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (688) ~ (all_56_2 = e2) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (10), (13), (17), (18), (21), (23), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (24), (26), (30), (31), (32), (35), (36), (41), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (42), (45), (50), (51), (56), (68), (73), (78), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (82), (88), (91), (93), (94), (97), (99), (102), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (103), (105), (106), (111), (112), (115), (117), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (118), (120), (124), (125), (130), (133), (134), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (136), (143), (144), (146), (147), (153), (155), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (158), (161), (165), (166), (168), (180), (182), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (184), (186), (190), (192), (193), (195), (197), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (408), (415), (417), (420), (422), (425), (426), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (437), (440), (441), (449), (464), (465), (468), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (471), (474), (475), (476), (483), (688), (689) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #335. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | (690) all_56_11 = e1 | all_56_15 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (174), (197), (437), (690) are inconsistent % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #334. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | (691) all_56_13 = e0 | all_56_14 = e0 % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | REF_CLOSE: (108), (133), (172), (420), (691) are inconsistent % 154.00/23.09 | | | | | | | | | | by sub-proof #609. % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | % 154.00/23.09 | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | % 154.00/23.09 | | | | | | | | | (692) ~ (all_56_4 = e0) % 154.00/23.09 | | | | | | | | | (693) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 154.00/23.09 | | | | | | | | | % 154.00/23.09 | | | | | | | | | REDUCE: (28), (692) imply: % 154.00/23.09 | | | | | | | | | (694) ~ (all_52_8 = e0) % 154.00/23.09 | | | | | | | | | % 154.00/23.09 | | | | | | | | | BETA: splitting (693) gives: % 154.00/23.09 | | | | | | | | | % 154.00/23.09 | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | (695) all_56_5 = e0 % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | COMBINE_EQS: (73), (695) imply: % 154.00/23.09 | | | | | | | | | | (696) all_52_9 = e0 % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | REDUCE: (91), (696) imply: % 154.00/23.09 | | | | | | | | | | (697) $false % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | CLOSE: (697) is inconsistent. % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | (698) all_56_8 = e0 | all_56_14 = e0 % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | BETA: splitting (414) gives: % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | (699) all_56_1 = e0 % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | COMBINE_EQS: (82), (699) imply: % 154.00/23.09 | | | | | | | | | | | (700) all_52_4 = e0 % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | REDUCE: (118), (700) imply: % 154.00/23.09 | | | | | | | | | | | (701) $false % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | CLOSE: (701) is inconsistent. % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | (702) all_56_4 = e0 | all_56_9 = e0 % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | BETA: splitting (702) gives: % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | (703) all_56_4 = e0 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | COMBINE_EQS: (28), (703) imply: % 154.00/23.09 | | | | | | | | | | | | (704) all_52_8 = e0 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | REDUCE: (694), (704) imply: % 154.00/23.09 | | | | | | | | | | | | (705) $false % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | CLOSE: (705) is inconsistent. % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | (706) all_56_9 = e0 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | COMBINE_EQS: (99), (706) imply: % 154.00/23.09 | | | | | | | | | | | | (707) all_52_12 = e0 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | COMBINE_EQS: (26), (707) imply: % 154.00/23.09 | | | | | | | | | | | | (708) all_58_6 = e0 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | REDUCE: (49), (707) imply: % 154.00/23.09 | | | | | | | | | | | | (709) ~ (all_52_13 = e0) % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | REDUCE: (101), (707) imply: % 154.00/23.09 | | | | | | | | | | | | (710) ~ (all_52_14 = e0) % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | SIMP: (710) implies: % 154.00/23.09 | | | | | | | | | | | | (711) ~ (all_52_14 = e0) % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | REDUCE: (126), (707) imply: % 154.00/23.09 | | | | | | | | | | | | (712) op(e3, e0) = all_58_5 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | REDUCE: (104), (707) imply: % 154.00/23.09 | | | | | | | | | | | | (713) op(e3, e0) = e0 % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | BETA: splitting (170) gives: % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | (714) all_56_6 = e0 % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | COMBINE_EQS: (105), (714) imply: % 154.00/23.09 | | | | | | | | | | | | | (715) all_52_2 = e0 % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | COMBINE_EQS: (17), (715) imply: % 154.00/23.09 | | | | | | | | | | | | | (716) all_58_15 = e0 % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | REDUCE: (106), (715) imply: % 154.00/23.09 | | | | | | | | | | | | | (717) ~ (all_52_6 = e0) % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | BETA: splitting (698) gives: % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | (718) all_56_8 = e0 % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | REF_CLOSE: (3), (31), (66), (97), (103), (123), (134), (143), % 154.00/23.09 | | | | | | | | | | | | | | (155), (166), (174), (182), (184), (185), (197), % 154.00/23.09 | | | | | | | | | | | | | | (718) are inconsistent by sub-proof #398. % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | (719) all_56_14 = e0 % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | COMBINE_EQS: (133), (719) imply: % 154.00/23.09 | | | | | | | | | | | | | | (720) all_52_11 = e0 % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | SIMP: (720) implies: % 154.00/23.09 | | | | | | | | | | | | | | (721) all_52_11 = e0 % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | COMBINE_EQS: (18), (721) imply: % 154.00/23.09 | | | | | | | | | | | | | | (722) all_58_26 = e0 % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | REDUCE: (150), (721) imply: % 154.00/23.09 | | | | | | | | | | | | | | (723) ~ (all_52_3 = e0) % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | REDUCE: (115), (721) imply: % 154.00/23.09 | | | | | | | | | | | | | | (724) ~ (all_8_1 = e0) % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | REDUCE: (120), (721) imply: % 154.00/23.09 | | | | | | | | | | | | | | (725) ~ (all_6_2 = e0) % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | REDUCE: (24), (721) imply: % 154.00/23.09 | | | | | | | | | | | | | | (726) ~ (all_4_2 = e0) % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_58_5, e0, e3, % 154.00/23.09 | | | | | | | | | | | | | | simplifying with (712), (713) gives: % 154.00/23.09 | | | | | | | | | | | | | | (727) all_58_5 = e0 % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | BETA: splitting (116) gives: % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | (728) all_56_9 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | COMBINE_EQS: (706), (728) imply: % 154.00/23.09 | | | | | | | | | | | | | | | (729) e1 = e0 % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | REDUCE: (174), (729) imply: % 154.00/23.09 | | | | | | | | | | | | | | | (730) $false % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | CLOSE: (730) is inconsistent. % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | (731) ~ (all_56_9 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | (732) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | REDUCE: (706), (731) imply: % 154.00/23.09 | | | | | | | | | | | | | | | (733) ~ (e1 = e0) % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | (734) all_54_9 = e0 % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | REF_CLOSE: (61), (68), (734) are inconsistent by sub-proof % 154.00/23.09 | | | | | | | | | | | | | | | | #572. % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | (735) ~ (all_54_9 = e0) % 154.00/23.09 | | | | | | | | | | | | | | | | (736) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | (737) all_56_12 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (737) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | (738) all_52_3 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | SIMP: (738) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | (739) all_52_3 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | REDUCE: (131), (739) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | (740) ~ (all_52_1 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | REDUCE: (154), (739) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | (741) ~ (all_10_2 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | SIMP: (741) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | (742) ~ (all_10_2 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | REDUCE: (86), (739) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | (743) ~ (all_4_2 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | (744) all_58_28 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (744) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (745) all_10_2 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REDUCE: (742), (745) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (746) $false % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | CLOSE: (746) is inconsistent. % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | (747) ~ (all_58_28 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | (748) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | BETA: splitting (748) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | (749) all_58_29 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (41), (56), (97), (105), (124), (147), (174), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | (182), (195), (197), (737), (740), (742), (748), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | (749) are inconsistent by sub-proof #332. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | (750) all_58_30 = e1 | all_58_31 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | (751) all_58_30 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (751) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | (752) all_6_2 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (752) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | (753) ~ (all_52_14 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (732) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | (754) all_56_10 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (754) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | (755) all_52_13 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | SIMP: (755) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | (756) all_52_13 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (756) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | (757) ~ (all_52_9 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (756) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | (758) ~ (all_52_14 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | (759) all_54_0 = e0 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (134), (143), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | (166), (168), (182), (185), (750), (759) are % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #331. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | (760) ~ (all_54_0 = e0) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | (761) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (760) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | (762) ~ (all_10_2 = e0) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | (763) all_54_11 = e0 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (711), (763) are inconsistent by sub-proof % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | #743. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | (764) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (765) all_56_2 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (765) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (766) all_52_1 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (766) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (767) ~ (all_10_2 = e3) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (767) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (768) ~ (all_10_2 = e3) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (44), (66), (97), (123), (134), (135), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (147), (166), (168), (173), (174), (185), (197), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (400), (713), (742), (750), (751), (753), (761), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (764), (768) are inconsistent by sub-proof #288. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | (769) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_56_3 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (770) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (771) e3 = e0 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (771) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (772) e3 = e0 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (772) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (773) $false % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (773) is inconsistent. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (774) ~ (all_56_3 = e3) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_56_5 = e3 | all_56_10 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (774) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | (776) ~ (e3 = e0) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_56_0 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (777) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_10_2 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (778) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_10_2 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (779) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_28 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_56_0 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (777), (781) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) e3 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (782) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) e3 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (780), (783) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_58_28 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (44), (66), (97), (123), (166), (173), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (185), (197), (400), (713), (750), (751), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (753), (764), (784) are inconsistent by sub-proof % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | #289. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_56_2 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (786) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_52_1 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (787) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) ~ (all_52_9 = e2) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (788) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ~ (all_52_9 = e2) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (775) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_56_5 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (790) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) all_52_9 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (791) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) op(e2, e1) = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_58_28 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (44), (66), (97), (123), (166), (173), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (185), (197), (400), (713), (750), (751), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753), (764), (793) are inconsistent by sub-proof % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #289. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_58_29 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (143), (795) are inconsistent by sub-proof % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #706. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) all_58_30 = e2 | all_58_31 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (103), (122), (181), (399), (403), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751), (792), (796) are inconsistent by sub-proof % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #292. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_56_10 = e3 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (754), (797) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) e3 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (798) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) $false % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (799) is inconsistent. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_56_6 = e2 | all_56_12 = e2 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (143), (714), (737), (800) are inconsistent % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #327. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (801) ~ (all_56_0 = e3) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (801) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (802) ~ (all_10_2 = e3) % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (44), (66), (97), (123), (134), (135), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (147), (166), (168), (173), (174), (185), (197), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (400), (713), (742), (750), (751), (753), (761), % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (764), (802) are inconsistent by sub-proof #288. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | (803) all_56_11 = e1 | all_56_15 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (81), (197), (753), (803) are inconsistent by % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | sub-proof #579. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | (804) all_58_31 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (804) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | (805) all_4_2 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (805) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | (806) $false % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | CLOSE: (806) is inconsistent. % 154.00/23.09 | | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | (807) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | BETA: splitting (807) gives: % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | (808) all_56_13 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (808) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (809) all_8_1 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | SIMP: (809) implies: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (810) all_8_1 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (810) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (811) all_58_24 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REDUCE: (129), (810) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (812) ~ (all_52_3 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REDUCE: (88), (810) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (813) ~ (all_52_4 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REDUCE: (29), (810) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (814) ~ (all_52_6 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REDUCE: (145), (810) imply: % 154.00/23.09 | | | | | | | | | | | | | | | | | | (815) ~ (all_4_2 = e1) % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (16), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (21), (25), (28), (31), (32), (36), (38), (40), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (41), (44), (46), (47), (50), (51), (52), (53), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (54), (61), (63), (64), (68), (69), (70), (72), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (73), (77), (78), (82), (84), (85), (86), (91), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (92), (93), (94), (95), (97), (102), (103), (109), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (110), (112), (114), (118), (124), (125), (127), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (128), (131), (134), (135), (136), (137), (143), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (144), (147), (149), (151), (154), (157), (161), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (162), (164), (166), (167), (168), (173), (174), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (175), (177), (179), (180), (182), (184), (187), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (188), (191), (192), (193), (195), (197), (408), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (694), (706), (708), (711), (714), (716), (719), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (722), (723), (736), (808), (811), (812), (813), % 154.00/23.09 | | | | | | | | | | | | | | | | | | (814) are inconsistent by sub-proof #295. % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | (816) all_56_14 = e1 | all_56_15 = e1 % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (174), (197), (719), (816) are inconsistent % 154.00/23.09 | | | | | | | | | | | | | | | | | | by sub-proof #582. % 154.00/23.09 | | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | Case 2: % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | (817) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | | REF_CLOSE: (9), (68), (81), (155), (195), (711), (817) are % 154.00/23.09 | | | | | | | | | | | | | inconsistent by sub-proof #287. % 154.00/23.09 | | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | | % 154.00/23.09 | | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | | % 154.00/23.09 | | | | | | | | | End of split % 154.00/23.09 | | | | | | | | | % 154.00/23.09 | | | | | | | | End of split % 154.00/23.09 | | | | | | | | % 154.00/23.09 | | | | | | | End of split % 154.00/23.09 | | | | | | | % 154.00/23.09 | | | | | | End of split % 154.00/23.09 | | | | | | % 154.00/23.09 | | | | | End of split % 154.00/23.09 | | | | | % 154.00/23.09 | | | | End of split % 154.00/23.09 | | | | % 154.00/23.09 | | | End of split % 154.00/23.09 | | | % 154.00/23.09 | | Case 2: % 154.00/23.09 | | | % 154.00/23.09 | | | (818) all_20_2 = e1 % 154.00/23.09 | | | % 154.00/23.09 | | | COMBINE_EQS: (79), (818) imply: % 154.00/23.09 | | | (819) all_4_2 = e1 % 154.00/23.09 | | | % 154.00/23.09 | | | SIMP: (819) implies: % 154.00/23.09 | | | (820) all_4_2 = e1 % 154.00/23.09 | | | % 154.00/23.09 | | | COMBINE_EQS: (8), (820) imply: % 154.00/23.09 | | | (821) all_56_15 = e1 % 154.00/23.09 | | | % 154.00/23.09 | | | COMBINE_EQS: (3), (820) imply: % 154.00/23.09 | | | (822) all_58_31 = e1 % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (86), (820) imply: % 154.00/23.09 | | | (823) ~ (all_52_3 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (24), (820) imply: % 154.00/23.09 | | | (824) ~ (all_52_11 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (153), (820) imply: % 154.00/23.09 | | | (825) ~ (all_52_12 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (62), (820) imply: % 154.00/23.09 | | | (826) ~ (all_52_13 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (173), (820) imply: % 154.00/23.09 | | | (827) ~ (all_52_14 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (145), (820) imply: % 154.00/23.09 | | | (828) ~ (all_8_1 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (159), (820) imply: % 154.00/23.09 | | | (829) op(e1, all_4_1) = all_4_0 % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (189), (820) imply: % 154.00/23.09 | | | (830) op(e1, e0) = all_4_1 % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (33), (820) imply: % 154.00/23.09 | | | (831) op(e0, e1) = all_58_27 % 154.00/23.09 | | | % 154.00/23.09 | | | GROUND_INST: instantiating (5) with all_52_11, all_58_27, e1, e0, % 154.00/23.09 | | | simplifying with (39), (831) gives: % 154.00/23.09 | | | (832) all_58_27 = all_52_11 % 154.00/23.09 | | | % 154.00/23.09 | | | GROUND_INST: instantiating (5) with all_52_14, all_4_1, e0, e1, % 154.00/23.09 | | | simplifying with (89), (830) gives: % 154.00/23.09 | | | (833) all_52_14 = all_4_1 % 154.00/23.09 | | | % 154.00/23.09 | | | COMBINE_EQS: (44), (833) imply: % 154.00/23.09 | | | (834) all_54_11 = all_4_1 % 154.00/23.09 | | | % 154.00/23.09 | | | COMBINE_EQS: (81), (833) imply: % 154.00/23.09 | | | (835) all_56_11 = all_4_1 % 154.00/23.09 | | | % 154.00/23.09 | | | COMBINE_EQS: (46), (833) imply: % 154.00/23.09 | | | (836) all_58_20 = all_4_1 % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (169), (833) imply: % 154.00/23.09 | | | (837) ~ (all_52_2 = all_4_1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (52), (833) imply: % 154.00/23.09 | | | (838) ~ (all_52_6 = all_4_1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (101), (833) imply: % 154.00/23.09 | | | (839) ~ (all_52_12 = all_4_1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (92), (833) imply: % 154.00/23.09 | | | (840) ~ (all_52_13 = all_4_1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (187), (833) imply: % 154.00/23.09 | | | (841) ~ (all_6_2 = all_4_1) % 154.00/23.09 | | | % 154.00/23.09 | | | SIMP: (841) implies: % 154.00/23.09 | | | (842) ~ (all_6_2 = all_4_1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (827), (833) imply: % 154.00/23.09 | | | (843) ~ (all_4_1 = e1) % 154.00/23.09 | | | % 154.00/23.09 | | | REDUCE: (20), (833) imply: % 154.00/23.09 | | | (844) op(e1, all_4_1) = all_58_19 % 154.00/23.09 | | | % 154.00/23.09 | | | GROUND_INST: instantiating (5) with all_4_0, all_58_19, all_4_1, e1, % 154.00/23.09 | | | simplifying with (829), (844) gives: % 154.00/23.09 | | | (845) all_58_19 = all_4_0 % 154.00/23.09 | | | % 154.00/23.09 | | | BETA: splitting (188) gives: % 154.00/23.09 | | | % 154.00/23.09 | | | Case 1: % 154.00/23.09 | | | | % 154.00/23.09 | | | | (846) all_54_7 = e0 % 154.00/23.09 | | | | % 154.00/23.09 | | | | COMBINE_EQS: (25), (846) imply: % 154.00/23.09 | | | | (847) all_52_13 = e0 % 154.00/23.09 | | | | % 154.00/23.09 | | | | REDUCE: (84), (847) imply: % 154.00/23.09 | | | | (848) $false % 154.00/23.09 | | | | % 154.00/23.09 | | | | CLOSE: (848) is inconsistent. % 154.00/23.09 | | | | % 154.00/23.09 | | | Case 2: % 154.00/23.09 | | | | % 154.00/23.09 | | | | (849) ~ (all_54_7 = e0) % 154.00/23.09 | | | | (850) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.00/23.09 | | | | % 154.00/23.10 | | | | BETA: splitting (76) gives: % 154.00/23.10 | | | | % 154.00/23.10 | | | | Case 1: % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | (851) all_56_0 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | COMBINE_EQS: (147), (851) imply: % 154.00/23.10 | | | | | (852) all_10_2 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | COMBINE_EQS: (134), (852) imply: % 154.00/23.10 | | | | | (853) all_58_28 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), (182), (185), % 154.00/23.10 | | | | | (822), (853) are inconsistent by sub-proof #653. % 154.00/23.10 | | | | | % 154.00/23.10 | | | | Case 2: % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | (854) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | BETA: splitting (83) gives: % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | Case 1: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | (855) all_56_4 = e0 % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | COMBINE_EQS: (28), (855) imply: % 154.00/23.10 | | | | | | (856) all_52_8 = e0 % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | COMBINE_EQS: (164), (856) imply: % 154.00/23.10 | | | | | | (857) all_58_4 = e0 % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | REDUCE: (4), (856) imply: % 154.00/23.10 | | | | | | (858) ~ (all_52_9 = e0) % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | REDUCE: (22), (856) imply: % 154.00/23.10 | | | | | | (859) ~ (all_52_11 = e0) % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | SIMP: (859) implies: % 154.00/23.10 | | | | | | (860) ~ (all_52_11 = e0) % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | BETA: splitting (57) gives: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | Case 1: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | (861) all_56_15 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | COMBINE_EQS: (821), (861) imply: % 154.00/23.10 | | | | | | | (862) e1 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | SIMP: (862) implies: % 154.00/23.10 | | | | | | | (863) e1 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | COMBINE_EQS: (822), (863) imply: % 154.00/23.10 | | | | | | | (864) all_58_31 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (143), (166), (174), % 154.00/23.10 | | | | | | | (182), (184), (185), (864) are inconsistent by % 154.00/23.10 | | | | | | | sub-proof #844. % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | Case 2: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | (865) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.00/23.10 | | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | ALPHA: (865) implies: % 154.00/23.10 | | | | | | | (866) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | BETA: splitting (866) gives: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | (867) all_56_12 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | COMBINE_EQS: (77), (867) imply: % 154.00/23.10 | | | | | | | | (868) all_52_3 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | SIMP: (868) implies: % 154.00/23.10 | | | | | | | | (869) all_52_3 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | COMBINE_EQS: (151), (869) imply: % 154.00/23.10 | | | | | | | | (870) all_58_22 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REDUCE: (6), (869) imply: % 154.00/23.10 | | | | | | | | (871) ~ (all_52_2 = e0) % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | BETA: splitting (170) gives: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | (872) all_56_6 = e0 % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | COMBINE_EQS: (105), (872) imply: % 154.00/23.10 | | | | | | | | | (873) all_52_2 = e0 % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | REDUCE: (871), (873) imply: % 154.00/23.10 | | | | | | | | | (874) $false % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | CLOSE: (874) is inconsistent. % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | (875) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | BETA: splitting (875) gives: % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | (876) all_56_7 = e0 % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | COMBINE_EQS: (9), (876) imply: % 154.00/23.10 | | | | | | | | | | (877) all_52_6 = e0 % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | REDUCE: (68), (877) imply: % 154.00/23.10 | | | | | | | | | | (878) $false % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | CLOSE: (878) is inconsistent. % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | (879) all_56_8 = e0 | all_56_11 = e0 % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | BETA: splitting (879) gives: % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | (880) all_56_8 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | COMBINE_EQS: (155), (880) imply: % 154.00/23.10 | | | | | | | | | | | (881) all_6_2 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | SIMP: (881) implies: % 154.00/23.10 | | | | | | | | | | | (882) all_6_2 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | COMBINE_EQS: (182), (882) imply: % 154.00/23.10 | | | | | | | | | | | (883) all_58_30 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REF_CLOSE: (31), (66), (97), (103), (123), (134), (143), % 154.00/23.10 | | | | | | | | | | | (166), (185), (822), (883) are inconsistent by % 154.00/23.10 | | | | | | | | | | | sub-proof #692. % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | (884) all_56_11 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | COMBINE_EQS: (835), (884) imply: % 154.00/23.10 | | | | | | | | | | | (885) all_4_1 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | SIMP: (885) implies: % 154.00/23.10 | | | | | | | | | | | (886) all_4_1 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | COMBINE_EQS: (836), (886) imply: % 154.00/23.10 | | | | | | | | | | | (887) all_58_20 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REDUCE: (839), (886) imply: % 154.00/23.10 | | | | | | | | | | | (888) ~ (all_52_12 = e0) % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REDUCE: (829), (886) imply: % 154.00/23.10 | | | | | | | | | | | (889) op(e1, e0) = all_4_0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REDUCE: (830), (886) imply: % 154.00/23.10 | | | | | | | | | | | (890) op(e1, e0) = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_4_0, e0, e1, % 154.00/23.10 | | | | | | | | | | | simplifying with (889), (890) gives: % 154.00/23.10 | | | | | | | | | | | (891) all_4_0 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | COMBINE_EQS: (845), (891) imply: % 154.00/23.10 | | | | | | | | | | | (892) all_58_19 = e0 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REDUCE: (71), (891) imply: % 154.00/23.10 | | | | | | | | | | | (893) ~ (e1 = e0) % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (10), (17), (18), (21), (26), % 154.00/23.10 | | | | | | | | | | | (31), (34), (41), (42), (50), (59), (66), (68), % 154.00/23.10 | | | | | | | | | | | (69), (73), (75), (78), (82), (91), (94), (97), % 154.00/23.10 | | | | | | | | | | | (98), (103), (105), (106), (111), (113), (114), % 154.00/23.10 | | | | | | | | | | | (118), (119), (121), (123), (124), (128), (133), % 154.00/23.10 | | | | | | | | | | | (134), (136), (137), (143), (147), (155), (157), % 154.00/23.10 | | | | | | | | | | | (166), (174), (182), (184), (185), (195), (822), % 154.00/23.10 | | | | | | | | | | | (824), (826), (828), (855), (857), (860), (867), % 154.00/23.10 | | | | | | | | | | | (870), (871), (887), (888), (892) are inconsistent % 154.00/23.10 | | | | | | | | | | | by sub-proof #270. % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | End of split % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | End of split % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | End of split % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | (894) all_56_13 = e0 | all_56_14 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REF_CLOSE: (108), (133), (172), (860), (894) are inconsistent by % 154.00/23.10 | | | | | | | | sub-proof #609. % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | End of split % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | End of split % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | Case 2: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | (895) ~ (all_56_4 = e0) % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | REDUCE: (28), (895) imply: % 154.00/23.10 | | | | | | (896) ~ (all_52_8 = e0) % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | BETA: splitting (854) gives: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | Case 1: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | (897) all_56_1 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | COMBINE_EQS: (82), (897) imply: % 154.00/23.10 | | | | | | | (898) all_52_4 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | REDUCE: (118), (898) imply: % 154.00/23.10 | | | | | | | (899) $false % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | CLOSE: (899) is inconsistent. % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | Case 2: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | (900) all_56_4 = e0 | all_56_9 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | BETA: splitting (170) gives: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | (901) all_56_6 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | COMBINE_EQS: (105), (901) imply: % 154.00/23.10 | | | | | | | | (902) all_52_2 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | COMBINE_EQS: (17), (902) imply: % 154.00/23.10 | | | | | | | | (903) all_58_15 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REDUCE: (6), (902) imply: % 154.00/23.10 | | | | | | | | (904) ~ (all_52_3 = e0) % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | SIMP: (904) implies: % 154.00/23.10 | | | | | | | | (905) ~ (all_52_3 = e0) % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REDUCE: (106), (902) imply: % 154.00/23.10 | | | | | | | | (906) ~ (all_52_6 = e0) % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REDUCE: (837), (902) imply: % 154.00/23.10 | | | | | | | | (907) ~ (all_4_1 = e0) % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | SIMP: (907) implies: % 154.00/23.10 | | | | | | | | (908) ~ (all_4_1 = e0) % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REDUCE: (96), (902) imply: % 154.00/23.10 | | | | | | | | (909) op(e1, e0) = all_58_14 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REF_CLOSE: (5), (7), (12), (15), (16), (18), (21), (23), (25), % 154.00/23.10 | | | | | | | | (26), (28), (29), (31), (32), (36), (38), (40), (42), % 154.00/23.10 | | | | | | | | (47), (49), (50), (53), (54), (57), (60), (61), (64), % 154.00/23.10 | | | | | | | | (67), (68), (69), (72), (73), (77), (78), (82), (84), % 154.00/23.10 | | | | | | | | (87), (90), (94), (95), (97), (99), (100), (102), % 154.00/23.10 | | | | | | | | (103), (104), (110), (113), (114), (115), (120), % 154.00/23.10 | | | | | | | | (124), (126), (127), (128), (129), (131), (133), % 154.00/23.10 | | | | | | | | (134), (136), (137), (143), (144), (149), (150), % 154.00/23.10 | | | | | | | | (151), (154), (161), (162), (164), (165), (166), % 154.00/23.10 | | | | | | | | (167), (174), (177), (179), (180), (182), (190), % 154.00/23.10 | | | | | | | | (191), (192), (193), (821), (822), (823), (825), % 154.00/23.10 | | | | | | | | (826), (828), (830), (832), (834), (835), (836), % 154.00/23.10 | | | | | | | | (838), (839), (840), (842), (843), (850), (903), % 154.00/23.10 | | | | | | | | (905), (908), (909) are inconsistent by sub-proof % 154.00/23.10 | | | | | | | | #255. % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | (910) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REF_CLOSE: (9), (28), (68), (81), (99), (101), (155), (195), % 154.00/23.10 | | | | | | | | (896), (900), (910) are inconsistent by sub-proof % 154.00/23.10 | | | | | | | | #482. % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | End of split % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | End of split % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | End of split % 154.00/23.10 | | | | | % 154.00/23.10 | | | | End of split % 154.00/23.10 | | | | % 154.00/23.10 | | | End of split % 154.00/23.10 | | | % 154.00/23.10 | | End of split % 154.00/23.10 | | % 154.00/23.10 | Case 2: % 154.00/23.10 | | % 154.00/23.10 | | (911) all_18_2 = e0 % 154.00/23.10 | | % 154.00/23.10 | | COMBINE_EQS: (107), (911) imply: % 154.00/23.10 | | (912) all_6_2 = e0 % 154.00/23.10 | | % 154.00/23.10 | | COMBINE_EQS: (182), (912) imply: % 154.00/23.10 | | (913) all_58_30 = e0 % 154.00/23.10 | | % 154.00/23.10 | | REF_CLOSE: (3), (31), (66), (79), (97), (103), (123), (134), (139), (143), % 154.00/23.10 | | (166), (174), (184), (185), (913) are inconsistent by sub-proof % 154.00/23.10 | | #691. % 154.00/23.10 | | % 154.00/23.10 | End of split % 154.00/23.10 | % 154.00/23.10 End of proof % 154.00/23.10 % 154.00/23.10 Sub-proof #255 shows that the following formulas are inconsistent: % 154.00/23.10 ---------------------------------------------------------------- % 154.00/23.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.00/23.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.00/23.10 (2) all_58_11 = all_52_9 % 154.00/23.10 (3) all_54_2 = all_52_8 % 154.00/23.10 (4) ~ (all_52_13 = e1) % 154.00/23.10 (5) all_58_31 = e1 % 154.00/23.10 (6) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.00/23.10 (7) ~ (all_52_8 = all_10_2) % 154.00/23.10 (8) all_58_26 = all_52_11 % 154.00/23.10 (9) all_56_3 = e0 % 154.00/23.10 (10) all_58_24 = all_8_1 % 154.00/23.10 (11) all_54_7 = all_52_13 % 154.00/23.10 (12) all_58_6 = all_52_12 % 154.00/23.10 (13) all_56_4 = all_52_8 % 154.00/23.10 (14) ~ (all_52_6 = all_8_1) % 154.00/23.10 (15) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.10 (16) all_54_1 = all_52_4 % 154.00/23.10 (17) ~ (all_52_4 = all_52_6) % 154.00/23.10 (18) all_54_11 = all_4_1 % 154.00/23.10 (19) all_58_13 = all_52_13 % 154.00/23.10 (20) all_56_11 = all_4_1 % 154.00/23.10 (21) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.00/23.10 (22) all_56_13 = all_8_1 % 154.00/23.10 (23) ~ (all_6_2 = all_4_1) % 154.00/23.10 (24) ~ (all_52_8 = all_6_2) % 154.00/23.10 (25) ~ (all_52_3 = e1) % 154.00/23.10 (26) ~ (all_52_12 = all_52_13) % 154.00/23.10 (27) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.00/23.10 (28) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 154.00/23.10 (29) all_54_6 = all_52_9 % 154.00/23.10 (30) all_58_27 = all_52_11 % 154.00/23.10 (31) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.00/23.10 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 154.00/23.10 (32) ~ (all_52_8 = all_52_12) % 154.00/23.10 (33) all_54_9 = all_52_6 % 154.00/23.10 (34) ~ (all_52_3 = e0) % 154.00/23.10 (35) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.00/23.10 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 154.00/23.10 (37) ~ (all_52_6 = e0) % 154.00/23.10 (38) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.00/23.10 (39) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.00/23.10 (40) ~ (all_52_1 = all_52_13) % 154.00/23.10 (41) all_56_5 = all_52_9 % 154.00/23.10 (42) all_56_12 = all_52_3 % 154.00/23.10 (43) all_58_2 = all_52_4 % 154.00/23.10 (44) all_56_1 = all_52_4 % 154.00/23.10 (45) ~ (all_52_13 = e0) % 154.00/23.10 (46) all_58_20 = all_4_1 % 154.00/23.10 (47) all_58_9 = all_52_13 % 154.00/23.10 (48) ~ (all_52_9 = all_52_11) % 154.00/23.10 (49) ~ (all_52_6 = all_4_1) % 154.00/23.10 (50) ~ (all_52_12 = all_4_1) % 154.00/23.10 (51) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.00/23.10 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.00/23.10 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.00/23.10 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.00/23.10 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.00/23.10 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.00/23.10 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.00/23.10 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.00/23.10 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.00/23.10 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.00/23.10 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.00/23.10 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.00/23.10 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.10 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.10 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.10 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.10 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.10 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.00/23.10 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.10 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.00/23.10 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.10 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.00/23.10 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.00/23.10 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.00/23.10 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.00/23.10 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.00/23.10 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.00/23.10 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.00/23.10 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.10 e0) % 154.00/23.10 (52) ~ (all_52_4 = all_52_8) % 154.00/23.10 (53) all_58_29 = e0 % 154.00/23.10 (54) all_56_9 = all_52_12 % 154.00/23.10 (55) all_58_29 = all_8_2 % 154.00/23.10 (56) all_58_8 = all_52_1 % 154.00/23.10 (57) ~ (e2 = e1) % 154.00/23.10 (58) op(e3, e0) = all_52_12 % 154.00/23.10 (59) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.00/23.10 (60) ~ (all_4_1 = e1) % 154.00/23.10 (61) all_58_15 = e0 % 154.00/23.10 (62) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.00/23.10 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.00/23.10 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.00/23.10 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.00/23.10 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.00/23.10 (all_58_27 = e0)) % 154.00/23.10 (63) ~ (all_52_9 = all_52_13) % 154.00/23.10 (64) ~ (all_52_11 = all_8_1) % 154.00/23.10 (65) ~ (all_52_11 = all_6_2) % 154.00/23.10 (66) all_56_2 = all_52_1 % 154.00/23.10 (67) op(e3, all_52_12) = all_58_5 % 154.00/23.10 (68) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 154.00/23.10 (69) all_56_10 = all_52_13 % 154.00/23.10 (70) ~ (all_52_3 = all_8_1) % 154.00/23.10 (71) ~ (all_52_1 = all_52_3) % 154.00/23.10 (72) ~ (all_52_12 = e1) % 154.00/23.10 (73) all_56_14 = all_52_11 % 154.00/23.10 (74) all_58_28 = all_10_2 % 154.00/23.10 (75) all_58_17 = all_52_6 % 154.00/23.10 (76) ~ (all_52_1 = all_52_9) % 154.00/23.10 (77) ~ (e2 = e0) % 154.00/23.10 (78) ~ (all_52_9 = all_6_2) % 154.00/23.10 (79) ~ (all_52_1 = e0) % 154.00/23.10 (80) ~ (all_52_3 = all_52_11) % 154.00/23.10 (81) all_58_22 = all_52_3 % 154.00/23.10 (82) ~ (all_52_3 = all_10_2) % 154.00/23.10 (83) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.00/23.10 (84) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.00/23.10 (85) all_58_4 = all_52_8 % 154.00/23.10 (86) ~ (all_8_1 = e0) % 154.00/23.10 (87) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.00/23.10 (88) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.00/23.10 (89) ~ (all_52_13 = all_4_1) % 154.00/23.10 (90) ~ (all_8_1 = e1) % 154.00/23.10 (91) ~ (e1 = e0) % 154.00/23.10 (92) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 154.00/23.10 (93) op(e1, e0) = all_58_14 % 154.00/23.10 (94) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 154.00/23.10 (95) ~ (all_52_4 = all_10_2) % 154.00/23.10 (96) all_58_30 = all_6_2 % 154.00/23.10 (97) ~ (all_4_1 = e0) % 154.00/23.10 (98) all_56_15 = e1 % 154.00/23.10 (99) ~ (all_52_4 = all_52_12) % 154.00/23.10 (100) all_54_12 = all_52_3 % 154.00/23.10 (101) all_54_4 = all_52_1 % 154.00/23.10 (102) op(e1, e0) = all_4_1 % 154.00/23.10 (103) ~ (all_52_1 = all_10_2) % 154.00/23.10 % 154.00/23.10 Begin of proof % 154.00/23.10 | % 154.00/23.10 | BETA: splitting (31) gives: % 154.00/23.10 | % 154.00/23.10 | Case 1: % 154.00/23.10 | | % 154.00/23.10 | | (104) all_56_15 = e0 % 154.00/23.10 | | % 154.00/23.10 | | REF_CLOSE: (91), (98), (104) are inconsistent by sub-proof #550. % 154.00/23.10 | | % 154.00/23.10 | Case 2: % 154.00/23.10 | | % 154.00/23.10 | | (105) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 = e0 % 154.00/23.10 | | | all_56_13 = e0 | all_56_14 = e0) % 154.00/23.10 | | % 154.00/23.10 | | ALPHA: (105) implies: % 154.00/23.10 | | (106) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 154.00/23.10 | | (107) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 154.00/23.10 | | % 154.00/23.10 | | BETA: splitting (106) gives: % 154.00/23.10 | | % 154.00/23.10 | | Case 1: % 154.00/23.10 | | | % 154.00/23.10 | | | (108) all_56_12 = e0 % 154.00/23.10 | | | % 154.00/23.10 | | | REF_CLOSE: (34), (42), (108) are inconsistent by sub-proof #607. % 154.00/23.10 | | | % 154.00/23.10 | | Case 2: % 154.00/23.10 | | | % 154.00/23.10 | | | (109) all_56_13 = e0 | all_56_14 = e0 % 154.00/23.10 | | | % 154.00/23.10 | | | BETA: splitting (109) gives: % 154.00/23.10 | | | % 154.00/23.10 | | | Case 1: % 154.00/23.10 | | | | % 154.00/23.10 | | | | (110) all_56_13 = e0 % 154.00/23.10 | | | | % 154.00/23.10 | | | | REF_CLOSE: (22), (86), (110) are inconsistent by sub-proof #269. % 154.00/23.10 | | | | % 154.00/23.10 | | | Case 2: % 154.00/23.10 | | | | % 154.00/23.10 | | | | (111) all_56_14 = e0 % 154.00/23.10 | | | | % 154.00/23.10 | | | | COMBINE_EQS: (73), (111) imply: % 154.00/23.10 | | | | (112) all_52_11 = e0 % 154.00/23.10 | | | | % 154.00/23.10 | | | | SIMP: (112) implies: % 154.00/23.10 | | | | (113) all_52_11 = e0 % 154.00/23.10 | | | | % 154.00/23.10 | | | | COMBINE_EQS: (30), (113) imply: % 154.00/23.10 | | | | (114) all_58_27 = e0 % 154.00/23.10 | | | | % 154.00/23.10 | | | | COMBINE_EQS: (8), (113) imply: % 154.00/23.10 | | | | (115) all_58_26 = e0 % 154.00/23.10 | | | | % 154.00/23.10 | | | | REDUCE: (48), (113) imply: % 154.00/23.10 | | | | (116) ~ (all_52_9 = e0) % 154.00/23.10 | | | | % 154.00/23.10 | | | | REDUCE: (64), (113) imply: % 154.00/23.10 | | | | (117) ~ (all_8_1 = e0) % 154.00/23.10 | | | | % 154.00/23.10 | | | | REDUCE: (65), (113) imply: % 154.00/23.10 | | | | (118) ~ (all_6_2 = e0) % 154.00/23.10 | | | | % 154.00/23.10 | | | | SIMP: (118) implies: % 154.00/23.10 | | | | (119) ~ (all_6_2 = e0) % 154.00/23.10 | | | | % 154.00/23.10 | | | | BETA: splitting (107) gives: % 154.00/23.10 | | | | % 154.00/23.10 | | | | Case 1: % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | (120) all_56_9 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | COMBINE_EQS: (54), (120) imply: % 154.00/23.10 | | | | | (121) all_52_12 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | SIMP: (121) implies: % 154.00/23.10 | | | | | (122) all_52_12 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | COMBINE_EQS: (12), (122) imply: % 154.00/23.10 | | | | | (123) all_58_6 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (99), (122) imply: % 154.00/23.10 | | | | | (124) ~ (all_52_4 = e0) % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (32), (122) imply: % 154.00/23.10 | | | | | (125) ~ (all_52_8 = e0) % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (26), (122) imply: % 154.00/23.10 | | | | | (126) ~ (all_52_13 = e0) % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (50), (122) imply: % 154.00/23.10 | | | | | (127) ~ (all_4_1 = e0) % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (72), (122) imply: % 154.00/23.10 | | | | | (128) ~ (e1 = e0) % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (67), (122) imply: % 154.00/23.10 | | | | | (129) op(e3, e0) = all_58_5 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | REDUCE: (58), (122) imply: % 154.00/23.10 | | | | | (130) op(e3, e0) = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | GROUND_INST: instantiating (1) with all_4_1, all_58_14, e0, e1, % 154.00/23.10 | | | | | simplifying with (93), (102) gives: % 154.00/23.10 | | | | | (131) all_58_14 = all_4_1 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | GROUND_INST: instantiating (1) with e0, all_58_5, e0, e3, simplifying % 154.00/23.10 | | | | | with (129), (130) gives: % 154.00/23.10 | | | | | (132) all_58_5 = e0 % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | BETA: splitting (68) gives: % 154.00/23.10 | | | | | % 154.00/23.10 | | | | | Case 1: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | (133) all_54_12 = e0 % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | REF_CLOSE: (34), (100), (133) are inconsistent by sub-proof #762. % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | Case 2: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | (134) ~ (all_54_12 = e0) % 154.00/23.10 | | | | | | (135) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | BETA: splitting (28) gives: % 154.00/23.10 | | | | | | % 154.00/23.10 | | | | | | Case 1: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | (136) all_54_11 = e0 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | REF_CLOSE: (18), (97), (136) are inconsistent by sub-proof #551. % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | Case 2: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | (137) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | BETA: splitting (36) gives: % 154.00/23.10 | | | | | | | % 154.00/23.10 | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | (138) all_54_9 = e0 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | REF_CLOSE: (33), (37), (138) are inconsistent by sub-proof #572. % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | (139) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | BETA: splitting (83) gives: % 154.00/23.10 | | | | | | | | % 154.00/23.10 | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | (140) all_54_1 = e0 % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | REF_CLOSE: (16), (124), (140) are inconsistent by sub-proof % 154.00/23.10 | | | | | | | | | #798. % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | (141) ~ (all_54_1 = e0) % 154.00/23.10 | | | | | | | | | (142) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | BETA: splitting (59) gives: % 154.00/23.10 | | | | | | | | | % 154.00/23.10 | | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | (143) all_54_4 = e0 % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | REF_CLOSE: (79), (101), (143) are inconsistent by sub-proof % 154.00/23.10 | | | | | | | | | | #859. % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | (144) ~ (all_54_4 = e0) % 154.00/23.10 | | | | | | | | | | (145) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | BETA: splitting (84) gives: % 154.00/23.10 | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | (146) all_56_12 = e2 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | COMBINE_EQS: (42), (146) imply: % 154.00/23.10 | | | | | | | | | | | (147) all_52_3 = e2 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | SIMP: (147) implies: % 154.00/23.10 | | | | | | | | | | | (148) all_52_3 = e2 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | REDUCE: (82), (148) imply: % 154.00/23.10 | | | | | | | | | | | (149) ~ (all_10_2 = e2) % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | SIMP: (149) implies: % 154.00/23.10 | | | | | | | | | | | (150) ~ (all_10_2 = e2) % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | BETA: splitting (15) gives: % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | (151) all_58_28 = e2 % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | REF_CLOSE: (74), (150), (151) are inconsistent by sub-proof % 154.00/23.10 | | | | | | | | | | | | #388. % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | (152) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (18), (23), (39), (47), (53), % 154.00/23.10 | | | | | | | | | | | | (57), (60), (62), (69), (77), (89), (96), (114), % 154.00/23.10 | | | | | | | | | | | | (119), (120), (131), (132), (137), (152) are % 154.00/23.10 | | | | | | | | | | | | inconsistent by sub-proof #268. % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | End of split % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | Case 2: % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | (153) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | BETA: splitting (153) gives: % 154.00/23.10 | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | Case 1: % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | (154) all_56_13 = e2 % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | COMBINE_EQS: (22), (154) imply: % 154.00/23.10 | | | | | | | | | | | | (155) all_8_1 = e2 % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | SIMP: (155) implies: % 154.00/23.10 | | | | | | | | | | | | (156) all_8_1 = e2 % 154.00/23.10 | | | | | | | | | | | | % 154.00/23.10 | | | | | | | | | | | | COMBINE_EQS: (10), (156) imply: % 154.00/23.11 | | | | | | | | | | | | (157) all_58_24 = e2 % 154.00/23.11 | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | REDUCE: (70), (156) imply: % 154.00/23.11 | | | | | | | | | | | | (158) ~ (all_52_3 = e2) % 154.00/23.11 | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | REDUCE: (14), (156) imply: % 154.00/23.11 | | | | | | | | | | | | (159) ~ (all_52_6 = e2) % 154.00/23.11 | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | BETA: splitting (135) gives: % 154.00/23.11 | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | (160) all_54_12 = e1 % 154.00/23.11 | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | REF_CLOSE: (25), (100), (160) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | #558. % 154.00/23.11 | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | (161) ~ (all_54_12 = e1) % 154.00/23.11 | | | | | | | | | | | | | (162) all_54_12 = e3 | all_54_12 = e2 % 154.00/23.11 | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | BETA: splitting (162) gives: % 154.00/23.11 | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | (163) all_54_12 = e2 % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | REF_CLOSE: (100), (158), (163) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | #749. % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | (164) all_54_12 = e3 % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | COMBINE_EQS: (100), (164) imply: % 154.00/23.11 | | | | | | | | | | | | | | (165) all_52_3 = e3 % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | SIMP: (165) implies: % 154.00/23.11 | | | | | | | | | | | | | | (166) all_52_3 = e3 % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | COMBINE_EQS: (81), (166) imply: % 154.00/23.11 | | | | | | | | | | | | | | (167) all_58_22 = e3 % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | REDUCE: (71), (166) imply: % 154.00/23.11 | | | | | | | | | | | | | | (168) ~ (all_52_1 = e3) % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | REDUCE: (82), (166) imply: % 154.00/23.11 | | | | | | | | | | | | | | (169) ~ (all_10_2 = e3) % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | SIMP: (169) implies: % 154.00/23.11 | | | | | | | | | | | | | | (170) ~ (all_10_2 = e3) % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | REDUCE: (25), (166) imply: % 154.00/23.11 | | | | | | | | | | | | | | (171) ~ (e3 = e1) % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | REDUCE: (34), (166) imply: % 154.00/23.11 | | | | | | | | | | | | | | (172) ~ (e3 = e0) % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | BETA: splitting (87) gives: % 154.00/23.11 | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | (173) all_58_28 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | REF_CLOSE: (74), (170), (173) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | #783. % 154.00/23.11 | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | (174) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 154.00/23.11 | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | (175) all_58_29 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (175) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | (176) e3 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | REDUCE: (172), (176) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | (177) $false % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent. % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | (178) all_58_30 = e3 | all_58_31 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | BETA: splitting (178) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | (179) all_58_30 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (179) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | (180) all_6_2 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | SIMP: (180) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | (181) all_6_2 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | REDUCE: (24), (181) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | (182) ~ (all_52_8 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | REDUCE: (78), (181) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | (183) ~ (all_52_9 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | REDUCE: (23), (181) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | (184) ~ (all_4_1 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | SIMP: (184) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | (185) ~ (all_4_1 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | BETA: splitting (15) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | (186) all_58_28 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (186) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | (187) all_10_2 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | SIMP: (187) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | (188) all_10_2 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | REDUCE: (103), (188) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | (189) ~ (all_52_1 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | REDUCE: (95), (188) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | (190) ~ (all_52_4 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | REDUCE: (7), (188) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | (191) ~ (all_52_8 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (192) all_56_1 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (192) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (193) all_52_4 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | SIMP: (193) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (194) all_52_4 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (194) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (195) all_58_2 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | REDUCE: (17), (194) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (196) ~ (all_52_6 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | SIMP: (196) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (197) ~ (all_52_6 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | REDUCE: (52), (194) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | (198) ~ (all_52_8 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | (199) all_56_4 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (199) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | (200) all_52_8 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | SIMP: (200) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | (201) all_52_8 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (201) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | (202) $false % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | (203) ~ (all_56_4 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | (204) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | (205) all_58_31 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (91), (205) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | #845. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | (206) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | (207) all_54_2 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (125), (207) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | #860. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | (208) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_2 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (209) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_8 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | (211) all_52_8 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (211) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_4 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | (213) all_54_6 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (116), (213) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | #797. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | (214) ~ (all_54_6 = e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | (215) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_54_9 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (216) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_52_6 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (217) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_52_6 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (218) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_17 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (218) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_4_1 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_56_2 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (221) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_52_1 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_52_1 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (223) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_58_8 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (223) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (225) ~ (all_52_9 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (225) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_52_9 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (223) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_52_13 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (223) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (e3 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_56_2 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (229) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) e3 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (230) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) $false % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_56_2 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_54_11 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (60), (234) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #545. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_11 = e3 | all_54_11 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_54_11 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (236) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_4_1 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (237) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_4_1 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (238) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_20 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_56_3 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (240) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) e3 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (241) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_30 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (172), (178), (242) are inconsistent % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #694. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_56_5 = e3 | all_56_10 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_56_5 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (183), (244) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #267. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_56_10 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (245) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_52_13 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (246) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_58_13 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_56_5 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (248) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_52_9 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_52_9 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (250) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_58_11 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (250) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (e3 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) ~ (e3 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_30 = e1 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (179), (254) are inconsistent by sub-proof % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #290. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) ~ (all_58_30 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_29 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (257) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e2 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (258) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) $false % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) ~ (all_58_29 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (260) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) ~ (e2 = e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_28 = e3 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (263) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) e3 = e2 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (264) imply: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) $false % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) ~ (all_58_28 = e3) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_58_15 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_8 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (273) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (171), (172), (178), (179), (272), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) are inconsistent by sub-proof #266. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (277) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (172), (178), (179), (278) are % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #265. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (219), (279) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #264. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_13 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_8 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (284) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (283) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (285), (286) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_15 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_4 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_2 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (290) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (289) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (288) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (293), (294) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (293) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (297) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (294), (298) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_8 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_6 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_2 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (303) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (302) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (301) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (306) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (308) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (306), (308) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_11 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (251), (311) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_13 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_8 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_58_2 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (318) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (317) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (316) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (319), (321) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (322) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (323) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (321), (323) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (224), (325) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #261. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (328) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (172), (178), (179), (329) are % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #265. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_58_15 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_11 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_58_4 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (333) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (332) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (331) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (335), (337), (338) are % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #260. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_58_20 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_58_15 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_58_4 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (344) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (345) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (343) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (342) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (346), (347), (349) are % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #260. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_6 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (351) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (172), (178), (179), (352) are % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #265. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_58_15 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (355) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (356) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) $false % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (358) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_15 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (359) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (360) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) $false % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (361) is inconsistent. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (364) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) e3 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_15 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (171), (172), (178), (179), (366), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) are inconsistent by sub-proof #266. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (369) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_58_24 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_13 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (371) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (370) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (372), (373) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_20 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_58_6 = e3 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (376) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (377) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (375) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (379) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (378), (380) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (382) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_58_13 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (385) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (384) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (387) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (388) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (389) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (388), (390) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_58_26 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_58_20 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (394) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (395) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (393) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (397) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (392) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (399) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (396), (400) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (398), (401) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (402) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (403) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_58_22 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (404) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (172), (178), (179), (405) are % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #265. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (406) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_58_24 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_58_17 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_58_13 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (409) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) e3 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (408) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (407) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (411), (412) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) e1 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (410), (412) are inconsistent % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (417) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_58_26 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (115), (418) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #343. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (419) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_58_11 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (251), (420) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_58_20 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_58_11 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (424) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (425) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (423) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (426), (427) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (428) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_58_11 = e1 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (251), (429) are inconsistent by sub-proof % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (431) gives: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_58_20 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_58_13 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (434) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) e3 = e2 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (433) imply: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (436) implies: % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) e2 = e0 % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (435), (437) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) e3 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (437), (438) are inconsistent % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (439) implies: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_58_24 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_58_13 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (441) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) e3 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (440) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) e2 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (442), (443) are inconsistent % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_58_24 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_58_13 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (447) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) e3 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (446) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) e2 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (55), (57), (77), (171), (172), (174), % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (186), (253), (448), (449) are inconsistent % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #262. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) e1 = e0 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (451) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) $false % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (452) is inconsistent. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) ~ (all_56_5 = e2) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (453) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) ~ (all_52_9 = e2) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (183), (215), (226), (454) are inconsistent % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #771. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_54_11 = e3 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (185), (455) are inconsistent by sub-proof % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #544. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (456) ~ (all_56_2 = e1) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (456) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (457) ~ (all_52_1 = e1) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (145), (168), (189), (457) are inconsistent % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #828. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_54_9 = e3 | all_54_9 = e2 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (159), (197), (458) are inconsistent by % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #559. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | (459) all_54_2 = e3 | all_54_2 = e2 % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (182), (191), (459) are inconsistent by % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #555. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | (460) ~ (all_56_1 = e3) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | REDUCE: (44), (460) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | | | (461) ~ (all_52_4 = e3) % 154.00/23.13 | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (16), (27), (52), (92), (125), (142), % 154.00/23.13 | | | | | | | | | | | | | | | | | | | (182), (190), (191), (461) are inconsistent by % 154.00/23.13 | | | | | | | | | | | | | | | | | | | sub-proof #257. % 154.00/23.13 | | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | (462) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.13 | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (18), (23), (39), (47), (53), % 154.00/23.13 | | | | | | | | | | | | | | | | | | (57), (60), (62), (69), (77), (89), (96), (114), % 154.00/23.13 | | | | | | | | | | | | | | | | | | (119), (120), (131), (132), (137), (462) are % 154.00/23.13 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #268. % 154.00/23.13 | | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | (463) all_58_31 = e3 % 154.00/23.13 | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (463) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | (464) e3 = e1 % 154.00/23.13 | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | REDUCE: (171), (464) imply: % 154.00/23.13 | | | | | | | | | | | | | | | | | (465) $false % 154.00/23.13 | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent. % 154.00/23.13 | | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | (466) all_56_14 = e2 | all_56_15 = e2 % 154.00/23.13 | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | | REF_CLOSE: (57), (77), (98), (111), (466) are inconsistent by % 154.00/23.13 | | | | | | | | | | | | sub-proof #256. % 154.00/23.13 | | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | | % 154.00/23.13 | | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | | % 154.00/23.13 | | | | | | | | | End of split % 154.00/23.13 | | | | | | | | | % 154.00/23.13 | | | | | | | | End of split % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | End of split % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | End of split % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | End of split % 154.00/23.13 | | | | | % 154.00/23.13 | | | | Case 2: % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | (467) all_56_10 = e0 | all_56_11 = e0 % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | REF_CLOSE: (20), (45), (69), (97), (467) are inconsistent by sub-proof % 154.00/23.13 | | | | | #524. % 154.00/23.13 | | | | | % 154.00/23.13 | | | | End of split % 154.00/23.13 | | | | % 154.00/23.13 | | | End of split % 154.00/23.13 | | | % 154.00/23.13 | | End of split % 154.00/23.13 | | % 154.00/23.13 | End of split % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #256 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_56_14 = e0 % 154.00/23.13 (2) all_56_14 = e2 | all_56_15 = e2 % 154.00/23.13 (3) ~ (e2 = e1) % 154.00/23.13 (4) ~ (e2 = e0) % 154.00/23.13 (5) all_56_15 = e1 % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | BETA: splitting (2) gives: % 154.00/23.13 | % 154.00/23.13 | Case 1: % 154.00/23.13 | | % 154.00/23.13 | | (6) all_56_14 = e2 % 154.00/23.13 | | % 154.00/23.13 | | COMBINE_EQS: (1), (6) imply: % 154.00/23.13 | | (7) e2 = e0 % 154.00/23.13 | | % 154.00/23.13 | | REDUCE: (4), (7) imply: % 154.00/23.13 | | (8) $false % 154.00/23.13 | | % 154.00/23.13 | | CLOSE: (8) is inconsistent. % 154.00/23.13 | | % 154.00/23.13 | Case 2: % 154.00/23.13 | | % 154.00/23.13 | | (9) all_56_15 = e2 % 154.00/23.13 | | % 154.00/23.13 | | COMBINE_EQS: (5), (9) imply: % 154.00/23.13 | | (10) e2 = e1 % 154.00/23.13 | | % 154.00/23.13 | | REDUCE: (3), (10) imply: % 154.00/23.13 | | (11) $false % 154.00/23.13 | | % 154.00/23.13 | | CLOSE: (11) is inconsistent. % 154.00/23.13 | | % 154.00/23.13 | End of split % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #257 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) ~ (all_52_8 = e2) % 154.00/23.13 (2) all_54_2 = all_52_8 % 154.00/23.13 (3) all_56_4 = all_52_8 % 154.00/23.13 (4) all_54_1 = all_52_4 % 154.00/23.13 (5) ~ (all_52_4 = e3) % 154.00/23.13 (6) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.00/23.13 (7) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.00/23.13 (8) ~ (all_52_8 = e3) % 154.00/23.13 (9) ~ (all_52_4 = e2) % 154.00/23.13 (10) ~ (all_52_4 = all_52_8) % 154.00/23.13 (11) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 154.00/23.13 (12) ~ (all_52_8 = e0) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | BETA: splitting (11) gives: % 154.00/23.13 | % 154.00/23.13 | Case 1: % 154.00/23.13 | | % 154.00/23.13 | | (13) all_54_2 = e0 % 154.00/23.13 | | % 154.00/23.13 | | REF_CLOSE: (2), (12), (13) are inconsistent by sub-proof #860. % 154.00/23.13 | | % 154.00/23.13 | Case 2: % 154.00/23.13 | | % 154.00/23.13 | | (14) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.00/23.13 | | % 154.00/23.13 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (14) are % 154.00/23.13 | | inconsistent by sub-proof #258. % 154.00/23.13 | | % 154.00/23.13 | End of split % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #258 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) ~ (all_52_8 = e2) % 154.00/23.13 (2) all_54_2 = all_52_8 % 154.00/23.13 (3) all_56_4 = all_52_8 % 154.00/23.13 (4) all_54_1 = all_52_4 % 154.00/23.13 (5) ~ (all_52_4 = e3) % 154.00/23.13 (6) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.00/23.13 (7) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.00/23.13 (8) ~ (all_52_8 = e3) % 154.00/23.13 (9) ~ (all_52_4 = e2) % 154.00/23.13 (10) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.00/23.13 (11) ~ (all_52_4 = all_52_8) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | BETA: splitting (7) gives: % 154.00/23.13 | % 154.00/23.13 | Case 1: % 154.00/23.13 | | % 154.00/23.13 | | (12) all_56_4 = e1 % 154.00/23.13 | | % 154.00/23.13 | | COMBINE_EQS: (3), (12) imply: % 154.00/23.13 | | (13) all_52_8 = e1 % 154.00/23.13 | | % 154.00/23.13 | | SIMP: (13) implies: % 154.00/23.13 | | (14) all_52_8 = e1 % 154.00/23.13 | | % 154.00/23.13 | | REDUCE: (11), (14) imply: % 154.00/23.13 | | (15) ~ (all_52_4 = e1) % 154.00/23.13 | | % 154.00/23.13 | | REF_CLOSE: (4), (5), (6), (9), (15) are inconsistent by sub-proof #738. % 154.00/23.13 | | % 154.00/23.13 | Case 2: % 154.00/23.13 | | % 154.00/23.13 | | (16) ~ (all_56_4 = e1) % 154.00/23.13 | | % 154.00/23.13 | | REDUCE: (3), (16) imply: % 154.00/23.13 | | (17) ~ (all_52_8 = e1) % 154.00/23.13 | | % 154.00/23.13 | | REF_CLOSE: (1), (2), (8), (10), (17) are inconsistent by sub-proof #554. % 154.00/23.13 | | % 154.00/23.13 | End of split % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #259 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) e2 = e0 % 154.00/23.13 (2) e2 = e1 % 154.00/23.13 (3) ~ (e1 = e0) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | SIMP: (1) implies: % 154.00/23.13 | (4) e2 = e0 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (2), (4) imply: % 154.00/23.13 | (5) e1 = e0 % 154.00/23.13 | % 154.00/23.13 | REDUCE: (3), (5) imply: % 154.00/23.13 | (6) $false % 154.00/23.13 | % 154.00/23.13 | CLOSE: (6) is inconsistent. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #260 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_31 = e1 % 154.00/23.13 (2) all_58_30 = e3 % 154.00/23.13 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.13 (4) ~ (e3 = e1) % 154.00/23.13 (5) e3 = e1 % 154.00/23.13 (6) all_58_29 = all_8_2 % 154.00/23.13 (7) ~ (e2 = e1) % 154.00/23.13 (8) e2 = e1 % 154.00/23.13 (9) ~ (e3 = e0) % 154.00/23.13 (10) e3 = e0 % 154.00/23.13 (11) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.00/23.13 (12) ~ (e2 = e0) % 154.00/23.13 (13) all_58_28 = e2 % 154.00/23.13 (14) ~ (e3 = e2) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (5), (10) imply: % 154.00/23.13 | (15) e1 = e0 % 154.00/23.13 | % 154.00/23.13 | SIMP: (15) implies: % 154.00/23.13 | (16) e1 = e0 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (8), (16) imply: % 154.00/23.13 | (17) e2 = e0 % 154.00/23.13 | % 154.00/23.13 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), % 154.00/23.13 | (17) are inconsistent by sub-proof #262. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #261 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.00/23.13 (2) all_58_8 = e1 % 154.00/23.13 (3) ~ (e2 = e1) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | ALPHA: (1) implies: % 154.00/23.13 | (4) all_58_8 = e2 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (2), (4) imply: % 154.00/23.13 | (5) e2 = e1 % 154.00/23.13 | % 154.00/23.13 | REDUCE: (3), (5) imply: % 154.00/23.13 | (6) $false % 154.00/23.13 | % 154.00/23.13 | CLOSE: (6) is inconsistent. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #262 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_31 = e1 % 154.00/23.13 (2) all_58_30 = e3 % 154.00/23.13 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.13 (4) ~ (e3 = e1) % 154.00/23.13 (5) all_58_29 = all_8_2 % 154.00/23.13 (6) ~ (e2 = e1) % 154.00/23.13 (7) ~ (e3 = e0) % 154.00/23.13 (8) e3 = e0 % 154.00/23.13 (9) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.00/23.13 (10) ~ (e2 = e0) % 154.00/23.13 (11) e2 = e0 % 154.00/23.13 (12) all_58_28 = e2 % 154.00/23.13 (13) ~ (e3 = e2) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (2), (8) imply: % 154.00/23.13 | (14) all_58_30 = e0 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (11), (12) imply: % 154.00/23.13 | (15) all_58_28 = e0 % 154.00/23.13 | % 154.00/23.13 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (13), (14), (15) are % 154.00/23.13 | inconsistent by sub-proof #681. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #263 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) e3 = e2 % 154.00/23.13 (2) e3 = e1 % 154.00/23.13 (3) ~ (e2 = e1) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (1), (2) imply: % 154.00/23.13 | (4) e2 = e1 % 154.00/23.13 | % 154.00/23.13 | SIMP: (4) implies: % 154.00/23.13 | (5) e2 = e1 % 154.00/23.13 | % 154.00/23.13 | REDUCE: (3), (5) imply: % 154.00/23.13 | (6) $false % 154.00/23.13 | % 154.00/23.13 | CLOSE: (6) is inconsistent. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #264 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2 % 154.00/23.13 (2) all_58_17 = e1 % 154.00/23.13 (3) ~ (e2 = e1) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | ALPHA: (1) implies: % 154.00/23.13 | (4) all_58_17 = e2 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (2), (4) imply: % 154.00/23.13 | (5) e2 = e1 % 154.00/23.13 | % 154.00/23.13 | REDUCE: (3), (5) imply: % 154.00/23.13 | (6) $false % 154.00/23.13 | % 154.00/23.13 | CLOSE: (6) is inconsistent. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #265 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_31 = e1 % 154.00/23.13 (2) all_58_30 = e3 % 154.00/23.13 (3) ~ (e3 = e1) % 154.00/23.13 (4) ~ (e3 = e0) % 154.00/23.13 (5) e3 = e0 % 154.00/23.13 (6) all_58_30 = e3 | all_58_31 = e3 % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | SIMP: (5) implies: % 154.00/23.13 | (7) e3 = e0 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (2), (7) imply: % 154.00/23.13 | (8) all_58_30 = e0 % 154.00/23.13 | % 154.00/23.13 | REF_CLOSE: (1), (3), (4), (6), (8) are inconsistent by sub-proof #694. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #266 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_31 = e1 % 154.00/23.13 (2) all_58_15 = e1 % 154.00/23.13 (3) all_58_30 = e3 % 154.00/23.13 (4) ~ (e3 = e1) % 154.00/23.13 (5) e3 = e1 % 154.00/23.13 (6) all_58_15 = e0 % 154.00/23.13 (7) ~ (e3 = e0) % 154.00/23.13 (8) all_58_30 = e3 | all_58_31 = e3 % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (2), (6) imply: % 154.00/23.13 | (9) e1 = e0 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (5), (9) imply: % 154.00/23.13 | (10) e3 = e0 % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (3), (10) imply: % 154.00/23.13 | (11) all_58_30 = e0 % 154.00/23.13 | % 154.00/23.13 | REF_CLOSE: (1), (4), (7), (8), (11) are inconsistent by sub-proof #694. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #267 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_56_5 = all_52_9 % 154.00/23.13 (2) all_56_5 = e3 % 154.00/23.13 (3) ~ (all_52_9 = e3) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (1), (2) imply: % 154.00/23.13 | (4) all_52_9 = e3 % 154.00/23.13 | % 154.00/23.13 | SIMP: (4) implies: % 154.00/23.13 | (5) all_52_9 = e3 % 154.00/23.13 | % 154.00/23.13 | REDUCE: (3), (5) imply: % 154.00/23.13 | (6) $false % 154.00/23.13 | % 154.00/23.13 | CLOSE: (6) is inconsistent. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #268 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) ~ (all_52_13 = e1) % 154.00/23.13 (2) all_58_31 = e1 % 154.00/23.13 (3) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.00/23.13 (4) all_54_7 = all_52_13 % 154.00/23.13 (5) ~ (all_6_2 = e0) % 154.00/23.13 (6) all_54_11 = all_4_1 % 154.00/23.13 (7) all_58_14 = all_4_1 % 154.00/23.13 (8) all_58_5 = e0 % 154.00/23.13 (9) ~ (all_6_2 = all_4_1) % 154.00/23.13 (10) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.00/23.13 (11) all_58_9 = all_52_13 % 154.00/23.13 (12) all_58_29 = e0 % 154.00/23.13 (13) ~ (e2 = e1) % 154.00/23.13 (14) ~ (all_4_1 = e1) % 154.00/23.13 (15) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.00/23.13 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.00/23.13 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.00/23.13 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.00/23.13 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.00/23.13 (all_58_27 = e0)) % 154.00/23.13 (16) all_56_10 = all_52_13 % 154.00/23.13 (17) all_56_9 = e0 % 154.00/23.13 (18) ~ (e2 = e0) % 154.00/23.13 (19) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.13 (20) all_58_27 = e0 % 154.00/23.13 (21) ~ (all_52_13 = all_4_1) % 154.00/23.13 (22) all_58_30 = all_6_2 % 154.00/23.13 (23) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | BETA: splitting (19) gives: % 154.00/23.13 | % 154.00/23.13 | Case 1: % 154.00/23.13 | | % 154.00/23.13 | | (24) all_58_29 = e2 % 154.00/23.13 | | % 154.00/23.13 | | COMBINE_EQS: (12), (24) imply: % 154.00/23.13 | | (25) e2 = e0 % 154.00/23.13 | | % 154.00/23.13 | | REDUCE: (18), (25) imply: % 154.00/23.13 | | (26) $false % 154.00/23.13 | | % 154.00/23.13 | | CLOSE: (26) is inconsistent. % 154.00/23.13 | | % 154.00/23.13 | Case 2: % 154.00/23.13 | | % 154.00/23.13 | | (27) all_58_30 = e2 | all_58_31 = e2 % 154.00/23.13 | | % 154.00/23.13 | | BETA: splitting (27) gives: % 154.00/23.13 | | % 154.00/23.13 | | Case 1: % 154.00/23.13 | | | % 154.00/23.13 | | | (28) all_58_30 = e2 % 154.00/23.13 | | | % 154.00/23.13 | | | COMBINE_EQS: (22), (28) imply: % 154.00/23.13 | | | (29) all_6_2 = e2 % 154.00/23.13 | | | % 154.00/23.13 | | | SIMP: (29) implies: % 154.00/23.13 | | | (30) all_6_2 = e2 % 154.00/23.13 | | | % 154.00/23.13 | | | REDUCE: (9), (30) imply: % 154.00/23.13 | | | (31) ~ (all_4_1 = e2) % 154.00/23.13 | | | % 154.00/23.13 | | | SIMP: (31) implies: % 154.00/23.13 | | | (32) ~ (all_4_1 = e2) % 154.00/23.13 | | | % 154.00/23.13 | | | BETA: splitting (23) gives: % 154.00/23.13 | | | % 154.00/23.13 | | | Case 1: % 154.00/23.13 | | | | % 154.00/23.13 | | | | (33) all_54_11 = e1 % 154.00/23.13 | | | | % 154.00/23.13 | | | | REF_CLOSE: (6), (14), (33) are inconsistent by sub-proof #545. % 154.00/23.13 | | | | % 154.00/23.13 | | | Case 2: % 154.00/23.13 | | | | % 154.00/23.13 | | | | (34) all_54_11 = e3 | all_54_11 = e2 % 154.00/23.13 | | | | % 154.00/23.13 | | | | BETA: splitting (3) gives: % 154.00/23.13 | | | | % 154.00/23.13 | | | | Case 1: % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | (35) all_56_9 = e2 % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | COMBINE_EQS: (17), (35) imply: % 154.00/23.13 | | | | | (36) e2 = e0 % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | COMBINE_EQS: (28), (36) imply: % 154.00/23.13 | | | | | (37) all_58_30 = e0 % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | REF_CLOSE: (2), (13), (18), (27), (37) are inconsistent by sub-proof % 154.00/23.13 | | | | | #675. % 154.00/23.13 | | | | | % 154.00/23.13 | | | | Case 2: % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | (38) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | BETA: splitting (38) gives: % 154.00/23.13 | | | | | % 154.00/23.13 | | | | | Case 1: % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | (39) all_56_10 = e2 % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | COMBINE_EQS: (16), (39) imply: % 154.00/23.13 | | | | | | (40) all_52_13 = e2 % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | SIMP: (40) implies: % 154.00/23.13 | | | | | | (41) all_52_13 = e2 % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | COMBINE_EQS: (11), (41) imply: % 154.00/23.13 | | | | | | (42) all_58_9 = e2 % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | BETA: splitting (34) gives: % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | Case 1: % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | (43) all_54_11 = e2 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | REF_CLOSE: (6), (32), (43) are inconsistent by sub-proof #453. % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | Case 2: % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | (44) all_54_11 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | COMBINE_EQS: (6), (44) imply: % 154.00/23.13 | | | | | | | (45) all_4_1 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | SIMP: (45) implies: % 154.00/23.13 | | | | | | | (46) all_4_1 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | COMBINE_EQS: (7), (46) imply: % 154.00/23.13 | | | | | | | (47) all_58_14 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | BETA: splitting (15) gives: % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | Case 1: % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | | (48) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 % 154.00/23.13 | | | | | | | | = e1) & ~ (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & % 154.00/23.13 | | | | | | | | ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 154.00/23.13 | | | | | | | | (all_58_12 = e0)) % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | | REF_CLOSE: (8), (42), (48) are inconsistent by sub-proof #584. % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | Case 2: % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | | (49) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.00/23.13 | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.00/23.13 | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 % 154.00/23.13 | | | | | | | | = e1) & ~ (all_58_27 = e0)) % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | | REF_CLOSE: (20), (47), (49) are inconsistent by sub-proof #779. % 154.00/23.13 | | | | | | | | % 154.00/23.13 | | | | | | | End of split % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | End of split % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | Case 2: % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | (50) ~ (all_56_10 = e2) % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | REDUCE: (16), (50) imply: % 154.00/23.13 | | | | | | (51) ~ (all_52_13 = e2) % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | BETA: splitting (34) gives: % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | | Case 1: % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | (52) all_54_11 = e2 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | REF_CLOSE: (6), (32), (52) are inconsistent by sub-proof #453. % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | Case 2: % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | (53) all_54_11 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | COMBINE_EQS: (6), (53) imply: % 154.00/23.13 | | | | | | | (54) all_4_1 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | SIMP: (54) implies: % 154.00/23.13 | | | | | | | (55) all_4_1 = e3 % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | REDUCE: (21), (55) imply: % 154.00/23.13 | | | | | | | (56) ~ (all_52_13 = e3) % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | | REF_CLOSE: (1), (4), (10), (51), (56) are inconsistent by % 154.00/23.13 | | | | | | | sub-proof #601. % 154.00/23.13 | | | | | | | % 154.00/23.13 | | | | | | End of split % 154.00/23.13 | | | | | | % 154.00/23.13 | | | | | End of split % 154.00/23.13 | | | | | % 154.00/23.13 | | | | End of split % 154.00/23.13 | | | | % 154.00/23.13 | | | End of split % 154.00/23.13 | | | % 154.00/23.13 | | Case 2: % 154.00/23.13 | | | % 154.00/23.13 | | | (57) all_58_31 = e2 % 154.00/23.13 | | | % 154.00/23.13 | | | COMBINE_EQS: (2), (57) imply: % 154.00/23.13 | | | (58) e2 = e1 % 154.00/23.13 | | | % 154.00/23.13 | | | REDUCE: (13), (58) imply: % 154.00/23.13 | | | (59) $false % 154.00/23.13 | | | % 154.00/23.13 | | | CLOSE: (59) is inconsistent. % 154.00/23.13 | | | % 154.00/23.13 | | End of split % 154.00/23.13 | | % 154.00/23.13 | End of split % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #269 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_56_13 = all_8_1 % 154.00/23.13 (2) all_56_13 = e0 % 154.00/23.13 (3) ~ (all_8_1 = e0) % 154.00/23.13 % 154.00/23.13 Begin of proof % 154.00/23.13 | % 154.00/23.13 | COMBINE_EQS: (1), (2) imply: % 154.00/23.13 | (4) all_8_1 = e0 % 154.00/23.13 | % 154.00/23.13 | SIMP: (4) implies: % 154.00/23.13 | (5) all_8_1 = e0 % 154.00/23.13 | % 154.00/23.13 | REDUCE: (3), (5) imply: % 154.00/23.13 | (6) $false % 154.00/23.13 | % 154.00/23.13 | CLOSE: (6) is inconsistent. % 154.00/23.13 | % 154.00/23.13 End of proof % 154.00/23.13 % 154.00/23.13 Sub-proof #270 shows that the following formulas are inconsistent: % 154.00/23.13 ---------------------------------------------------------------- % 154.00/23.13 (1) all_58_23 = all_8_0 % 154.00/23.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.00/23.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.00/23.13 (3) all_58_11 = all_52_9 % 154.00/23.13 (4) all_56_7 = all_52_6 % 154.00/23.13 (5) ~ (all_52_6 = all_6_2) % 154.00/23.13 (6) all_58_22 = e0 % 154.00/23.13 (7) ~ (all_52_2 = e0) % 154.00/23.13 (8) ~ (all_52_13 = e1) % 154.00/23.13 (9) all_58_31 = e1 % 154.00/23.13 (10) all_58_15 = all_52_2 % 154.00/23.13 (11) all_58_26 = all_52_11 % 154.00/23.13 (12) all_56_3 = e0 % 154.00/23.13 (13) all_58_6 = all_52_12 % 154.00/23.13 (14) all_58_4 = e0 % 154.00/23.13 (15) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.00/23.13 (16) op(e0, e2) = all_8_1 % 154.00/23.13 (17) ~ (all_6_2 = e0) % 154.00/23.13 (18) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.00/23.13 (19) all_56_13 = all_8_1 % 154.00/23.13 (20) all_58_20 = e0 % 154.00/23.13 (21) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.00/23.13 (22) op(e3, e3) = all_10_2 % 154.00/23.13 (23) all_58_19 = e0 % 154.00/23.13 (24) ~ (e3 = e1) % 154.00/23.13 (25) ~ (all_52_6 = e0) % 154.00/23.13 (26) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.00/23.13 (27) all_56_5 = all_52_9 % 154.00/23.13 (28) op(e0, all_8_1) = all_8_0 % 154.00/23.13 (29) ~ (all_52_12 = e0) % 154.00/23.13 (30) all_58_2 = all_52_4 % 154.00/23.13 (31) all_56_1 = all_52_4 % 154.00/23.13 (32) ~ (all_52_9 = e0) % 154.00/23.13 (33) ~ (all_52_11 = e1) % 154.00/23.13 (34) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.00/23.13 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.00/23.13 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.00/23.13 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.00/23.13 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.00/23.14 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.00/23.14 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.00/23.14 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.00/23.14 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.00/23.14 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.00/23.14 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.00/23.14 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.00/23.14 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.00/23.14 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.00/23.14 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.14 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.00/23.14 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.00/23.14 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.00/23.14 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.00/23.14 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.00/23.14 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.00/23.14 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.00/23.14 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.00/23.14 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.00/23.14 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.00/23.14 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.00/23.14 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.00/23.14 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.00/23.14 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.00/23.14 e0) % 154.00/23.14 (35) all_58_29 = e0 % 154.00/23.14 (36) op(e2, e1) = all_52_9 % 154.00/23.14 (37) ~ (e2 = e1) % 154.00/23.14 (38) all_56_6 = all_52_2 % 154.00/23.14 (39) ~ (all_52_2 = all_52_6) % 154.00/23.14 (40) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.00/23.14 (41) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.00/23.14 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.00/23.14 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.00/23.14 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.00/23.14 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.00/23.14 (all_58_27 = e0)) % 154.00/23.14 (42) ~ (all_52_9 = all_52_13) % 154.00/23.14 (43) ~ (all_52_4 = e0) % 154.00/23.14 (44) op(e2, all_52_9) = all_58_10 % 154.00/23.14 (45) op(e3, all_10_2) = all_58_0 % 154.00/23.14 (46) ~ (e3 = e0) % 154.00/23.14 (47) all_56_2 = all_52_1 % 154.00/23.14 (48) all_56_4 = e0 % 154.00/23.14 (49) ~ (all_52_11 = e0) % 154.00/23.14 (50) all_56_10 = all_52_13 % 154.00/23.14 (51) all_56_14 = all_52_11 % 154.00/23.14 (52) all_58_28 = all_10_2 % 154.00/23.14 (53) all_58_17 = all_52_6 % 154.00/23.14 (54) ~ (all_52_1 = all_52_9) % 154.00/23.14 (55) ~ (e2 = e0) % 154.00/23.14 (56) all_56_12 = e0 % 154.00/23.14 (57) all_56_0 = all_10_2 % 154.00/23.14 (58) all_56_8 = all_6_2 % 154.00/23.14 (59) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.00/23.14 (60) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.00/23.14 (61) ~ (all_8_1 = e1) % 154.00/23.14 (62) ~ (e1 = e0) % 154.00/23.14 (63) all_58_30 = all_6_2 % 154.00/23.14 (64) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.00/23.14 (65) ~ (e3 = e2) % 154.00/23.14 % 154.00/23.14 Begin of proof % 154.00/23.14 | % 154.00/23.14 | BETA: splitting (40) gives: % 154.00/23.14 | % 154.00/23.14 | Case 1: % 154.00/23.14 | | % 154.00/23.14 | | (66) all_56_1 = e1 % 154.00/23.14 | | % 154.00/23.14 | | COMBINE_EQS: (31), (66) imply: % 154.00/23.14 | | (67) all_52_4 = e1 % 154.00/23.14 | | % 154.00/23.14 | | COMBINE_EQS: (30), (67) imply: % 154.00/23.14 | | (68) all_58_2 = e1 % 154.00/23.14 | | % 154.00/23.14 | | BETA: splitting (21) gives: % 154.00/23.14 | | % 154.00/23.14 | | Case 1: % 154.00/23.14 | | | % 154.00/23.14 | | | (69) all_56_4 = e1 % 154.00/23.14 | | | % 154.00/23.14 | | | REF_CLOSE: (9), (15), (24), (35), (37), (46), (48), (55), (60), (62), % 154.00/23.14 | | | (63), (64), (65), (69) are inconsistent by sub-proof #286. % 154.00/23.14 | | | % 154.00/23.14 | | Case 2: % 154.00/23.14 | | | % 154.00/23.14 | | | (70) ~ (all_56_4 = e1) % 154.00/23.14 | | | (71) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.00/23.14 | | | % 154.00/23.14 | | | REDUCE: (48), (70) imply: % 154.00/23.14 | | | (72) ~ (e1 = e0) % 154.00/23.14 | | | % 154.00/23.14 | | | BETA: splitting (26) gives: % 154.00/23.14 | | | % 154.00/23.14 | | | Case 1: % 154.00/23.14 | | | | % 154.00/23.14 | | | | (73) all_56_2 = e1 % 154.00/23.14 | | | | % 154.00/23.14 | | | | COMBINE_EQS: (47), (73) imply: % 154.00/23.14 | | | | (74) all_52_1 = e1 % 154.00/23.14 | | | | % 154.00/23.14 | | | | SIMP: (74) implies: % 154.00/23.14 | | | | (75) all_52_1 = e1 % 154.00/23.14 | | | | % 154.00/23.14 | | | | REDUCE: (54), (75) imply: % 154.00/23.14 | | | | (76) ~ (all_52_9 = e1) % 154.00/23.14 | | | | % 154.00/23.14 | | | | SIMP: (76) implies: % 154.00/23.14 | | | | (77) ~ (all_52_9 = e1) % 154.00/23.14 | | | | % 154.00/23.14 | | | | BETA: splitting (71) gives: % 154.00/23.14 | | | | % 154.00/23.14 | | | | Case 1: % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | (78) all_56_5 = e1 % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | REF_CLOSE: (27), (77), (78) are inconsistent by sub-proof #285. % 154.00/23.14 | | | | | % 154.00/23.14 | | | | Case 2: % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | (79) all_56_8 = e1 | all_56_14 = e1 % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | REF_CLOSE: (9), (15), (24), (33), (35), (37), (46), (51), (52), (55), % 154.00/23.14 | | | | | (58), (60), (63), (65), (79) are inconsistent by sub-proof % 154.00/23.14 | | | | | #282. % 154.00/23.14 | | | | | % 154.00/23.14 | | | | End of split % 154.00/23.14 | | | | % 154.00/23.14 | | | Case 2: % 154.00/23.14 | | | | % 154.00/23.14 | | | | (80) ~ (all_56_2 = e1) % 154.00/23.14 | | | | (81) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.00/23.14 | | | | % 154.00/23.14 | | | | REDUCE: (47), (80) imply: % 154.00/23.14 | | | | (82) ~ (all_52_1 = e1) % 154.00/23.14 | | | | % 154.00/23.14 | | | | BETA: splitting (18) gives: % 154.00/23.14 | | | | % 154.00/23.14 | | | | Case 1: % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | (83) all_56_0 = e1 % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | REF_CLOSE: (9), (15), (24), (35), (37), (46), (52), (55), (57), (60), % 154.00/23.14 | | | | | (63), (65), (83) are inconsistent by sub-proof #281. % 154.00/23.14 | | | | | % 154.00/23.14 | | | | Case 2: % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | (84) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | BETA: splitting (84) gives: % 154.00/23.14 | | | | | % 154.00/23.14 | | | | | Case 1: % 154.00/23.14 | | | | | | % 154.00/23.14 | | | | | | (85) all_56_2 = e1 % 154.00/23.14 | | | | | | % 154.00/23.14 | | | | | | REF_CLOSE: (47), (82), (85) are inconsistent by sub-proof #450. % 154.00/23.14 | | | | | | % 154.00/23.14 | | | | | Case 2: % 154.00/23.14 | | | | | | % 154.00/23.14 | | | | | | (86) all_56_6 = e1 | all_56_12 = e1 % 154.00/23.14 | | | | | | % 154.00/23.14 | | | | | | BETA: splitting (81) gives: % 154.00/23.14 | | | | | | % 154.00/23.14 | | | | | | Case 1: % 154.00/23.14 | | | | | | | % 154.00/23.14 | | | | | | | (87) all_56_3 = e1 % 154.00/23.14 | | | | | | | % 154.00/23.14 | | | | | | | REF_CLOSE: (9), (12), (15), (24), (35), (37), (46), (55), (60), % 154.00/23.14 | | | | | | | (62), (63), (64), (65), (87) are inconsistent by % 154.00/23.14 | | | | | | | sub-proof #280. % 154.00/23.14 | | | | | | | % 154.00/23.14 | | | | | | Case 2: % 154.00/23.14 | | | | | | | % 154.00/23.14 | | | | | | | (88) all_56_5 = e1 | all_56_10 = e1 % 154.00/23.14 | | | | | | | % 154.00/23.14 | | | | | | | BETA: splitting (88) gives: % 154.00/23.14 | | | | | | | % 154.00/23.14 | | | | | | | Case 1: % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | (89) all_56_5 = e1 % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | COMBINE_EQS: (27), (89) imply: % 154.00/23.14 | | | | | | | | (90) all_52_9 = e1 % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | SIMP: (90) implies: % 154.00/23.14 | | | | | | | | (91) all_52_9 = e1 % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | COMBINE_EQS: (3), (91) imply: % 154.00/23.14 | | | | | | | | (92) all_58_11 = e1 % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | REDUCE: (42), (91) imply: % 154.00/23.14 | | | | | | | | (93) ~ (all_52_13 = e1) % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | REDUCE: (44), (91) imply: % 154.00/23.14 | | | | | | | | (94) op(e2, e1) = all_58_10 % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | REDUCE: (36), (91) imply: % 154.00/23.14 | | | | | | | | (95) op(e2, e1) = e1 % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | BETA: splitting (86) gives: % 154.00/23.14 | | | | | | | | % 154.00/23.14 | | | | | | | | Case 1: % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | (96) all_56_6 = e1 % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | COMBINE_EQS: (38), (96) imply: % 154.00/23.14 | | | | | | | | | (97) all_52_2 = e1 % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | SIMP: (97) implies: % 154.00/23.14 | | | | | | | | | (98) all_52_2 = e1 % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | COMBINE_EQS: (10), (98) imply: % 154.00/23.14 | | | | | | | | | (99) all_58_15 = e1 % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | REDUCE: (39), (98) imply: % 154.00/23.14 | | | | | | | | | (100) ~ (all_52_6 = e1) % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | SIMP: (100) implies: % 154.00/23.14 | | | | | | | | | (101) ~ (all_52_6 = e1) % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | BETA: splitting (34) gives: % 154.00/23.14 | | | | | | | | | % 154.00/23.14 | | | | | | | | | Case 1: % 154.00/23.14 | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | (102) all_58_31 = e0 % 154.00/23.14 | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | REF_CLOSE: (15), (24), (35), (37), (46), (55), (60), (62), % 154.00/23.14 | | | | | | | | | | (63), (64), (65), (102) are inconsistent by % 154.00/23.14 | | | | | | | | | | sub-proof #844. % 154.00/23.14 | | | | | | | | | | % 154.00/23.14 | | | | | | | | | Case 2: % 154.00/23.14 | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | (103) ~ (all_58_31 = e0) % 154.00/23.14 | | | | | | | | | | (104) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.00/23.14 | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.00/23.14 | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.00/23.14 | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.00/23.14 | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = % 154.00/23.14 | | | | | | | | | | e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 % 154.00/23.14 | | | | | | | | | | = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 154.00/23.14 | | | | | | | | | | all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.00/23.14 | | | | | | | | | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.00/23.14 | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.00/23.14 | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.00/23.14 | | | | | | | | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.00/23.14 | | | | | | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.00/23.14 | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.00/23.14 | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.00/23.14 | | | | | | | | | | & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 154.00/23.14 | | | | | | | | | | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 % 154.00/23.14 | | | | | | | | | | = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.00/23.14 | | | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 % 154.00/23.14 | | | | | | | | | | & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = % 154.00/23.14 | | | | | | | | | | e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 % 154.00/23.14 | | | | | | | | | | = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 154.00/23.14 | | | | | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.00/23.14 | | | | | | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) % 154.00/23.14 | | | | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 % 154.00/23.14 | | | | | | | | | | & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.00/23.14 | | | | | | | | | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 % 154.00/23.14 | | | | | | | | | | = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.00/23.14 | | | | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 % 154.00/23.14 | | | | | | | | | | & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.00/23.14 | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.00/23.14 | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.00/23.14 | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.00/23.14 | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.00/23.14 | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.00/23.14 | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.00/23.14 | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.00/23.14 | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.00/23.14 | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.00/23.14 | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.00/23.14 | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.00/23.14 | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | BETA: splitting (104) gives: % 154.00/23.14 | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | Case 1: % 154.00/23.14 | | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | | (105) all_58_30 = e1 % 154.00/23.14 | | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | | REF_CLOSE: (9), (15), (24), (35), (37), (46), (52), (55), % 154.00/23.14 | | | | | | | | | | | (60), (65), (105) are inconsistent by sub-proof % 154.00/23.14 | | | | | | | | | | | #283. % 154.00/23.14 | | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | Case 2: % 154.00/23.14 | | | | | | | | | | | % 154.00/23.14 | | | | | | | | | | | (106) ~ (all_58_30 = e1) % 154.12/23.14 | | | | | | | | | | | (107) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.12/23.14 | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.12/23.14 | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.12/23.14 | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.12/23.14 | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.12/23.14 | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.12/23.14 | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.12/23.14 | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.12/23.14 | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.12/23.14 | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.12/23.14 | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.12/23.14 | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.12/23.14 | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.12/23.14 | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.12/23.14 | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.12/23.14 | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.12/23.14 | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.12/23.14 | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.12/23.14 | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.12/23.14 | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.12/23.14 | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.12/23.14 | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.12/23.14 | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.12/23.14 | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.12/23.14 | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.12/23.14 | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.12/23.14 | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.12/23.14 | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.12/23.14 | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.12/23.14 | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.12/23.14 | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.12/23.14 | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.12/23.14 | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.12/23.14 | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.12/23.14 | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.12/23.14 | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.12/23.14 | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.12/23.14 | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.12/23.14 | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.12/23.14 | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.12/23.14 | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.12/23.14 | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.12/23.14 | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | REDUCE: (63), (106) imply: % 154.12/23.14 | | | | | | | | | | | (108) ~ (all_6_2 = e1) % 154.12/23.14 | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | BETA: splitting (107) gives: % 154.12/23.14 | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | (109) all_58_29 = e2 % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | REF_CLOSE: (35), (55), (109) are inconsistent by sub-proof % 154.12/23.14 | | | | | | | | | | | | #706. % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | (110) ~ (all_58_29 = e2) % 154.12/23.14 | | | | | | | | | | | | (111) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.12/23.14 | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.12/23.14 | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.12/23.14 | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.12/23.14 | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.12/23.14 | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.12/23.14 | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.12/23.14 | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.12/23.14 | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.12/23.14 | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.12/23.14 | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.12/23.14 | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.12/23.14 | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.12/23.14 | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.12/23.14 | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.12/23.14 | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.12/23.14 | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.12/23.14 | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.12/23.14 | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.12/23.14 | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.12/23.14 | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.12/23.14 | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.12/23.14 | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.12/23.14 | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.12/23.14 | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.12/23.14 | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.12/23.14 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.12/23.14 | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.12/23.14 | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.12/23.14 | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.12/23.14 | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.12/23.14 | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.12/23.14 | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.12/23.14 | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.12/23.14 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.12/23.14 | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.12/23.14 | | | | | | | | | | | | e0) % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | REDUCE: (35), (110) imply: % 154.12/23.14 | | | | | | | | | | | | (112) ~ (e2 = e0) % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | BETA: splitting (111) gives: % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | (113) all_58_28 = e3 % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | COMBINE_EQS: (52), (113) imply: % 154.12/23.14 | | | | | | | | | | | | | (114) all_10_2 = e3 % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | REDUCE: (45), (114) imply: % 154.12/23.14 | | | | | | | | | | | | | (115) op(e3, e3) = all_58_0 % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | REDUCE: (22), (114) imply: % 154.12/23.14 | | | | | | | | | | | | | (116) op(e3, e3) = e3 % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | BETA: splitting (15) gives: % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | (117) all_58_28 = e2 % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | COMBINE_EQS: (113), (117) imply: % 154.12/23.14 | | | | | | | | | | | | | | (118) e3 = e2 % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | REDUCE: (65), (118) imply: % 154.12/23.14 | | | | | | | | | | | | | | (119) $false % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | CLOSE: (119) is inconsistent. % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | (120) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | BETA: splitting (120) gives: % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | (121) all_58_29 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | REF_CLOSE: (35), (55), (121) are inconsistent by sub-proof % 154.12/23.14 | | | | | | | | | | | | | | | #706. % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | (122) all_58_30 = e2 | all_58_31 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | (123) all_58_30 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (123) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | (124) all_6_2 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | REDUCE: (5), (124) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | (125) ~ (all_52_6 = e2) % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | (126) all_56_1 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (126) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | (127) e2 = e1 % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | SIMP: (127) implies: % 154.12/23.14 | | | | | | | | | | | | | | | | | (128) e2 = e1 % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (128) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | (129) all_58_30 = e1 % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (122), (129) are inconsistent by % 154.12/23.14 | | | | | | | | | | | | | | | | | sub-proof #448. % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | (130) ~ (all_56_1 = e2) % 154.12/23.14 | | | | | | | | | | | | | | | | | (131) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | REDUCE: (66), (130) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | (132) ~ (e2 = e1) % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | (133) all_56_3 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (133) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | (134) e2 = e0 % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | SIMP: (134) implies: % 154.12/23.14 | | | | | | | | | | | | | | | | | | (135) e2 = e0 % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (135) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | (136) all_58_30 = e0 % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (55), (122), (136) are inconsistent by % 154.12/23.14 | | | | | | | | | | | | | | | | | | sub-proof #675. % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | (137) all_56_7 = e2 | all_56_13 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (138) all_56_7 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (125), (138) are inconsistent by sub-proof % 154.12/23.14 | | | | | | | | | | | | | | | | | | | #279. % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (139) all_56_13 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (139) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (140) all_8_1 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | SIMP: (140) implies: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (141) all_8_1 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | REDUCE: (28), (141) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (142) op(e0, e2) = all_8_0 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | REDUCE: (16), (141) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (143) op(e0, e2) = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e2, all_8_0, e2, e0, % 154.12/23.14 | | | | | | | | | | | | | | | | | | | simplifying with (142), (143) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (144) all_8_0 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e1, all_58_10, e1, e2, % 154.12/23.14 | | | | | | | | | | | | | | | | | | | simplifying with (94), (95) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (145) all_58_10 = e1 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (2) with e3, all_58_0, e3, e3, % 154.12/23.14 | | | | | | | | | | | | | | | | | | | simplifying with (115), (116) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (146) all_58_0 = e3 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (144) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | (147) all_58_23 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (148) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (149) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0) % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (150) ~ (all_58_0 = e3) % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (150) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (151) $false % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (152) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0) % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (153) ~ (all_58_10 = e1) % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (153) imply: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | (154) $false % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent. % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (155) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (147), (155) are inconsistent by sub-proof % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | #478. % 154.12/23.14 | | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | (156) all_58_31 = e2 % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (156) are inconsistent by sub-proof % 154.12/23.14 | | | | | | | | | | | | | | | | #697. % 154.12/23.14 | | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | (157) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.12/23.14 | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.12/23.14 | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.12/23.14 | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.12/23.14 | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.12/23.14 | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.12/23.14 | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.12/23.14 | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.12/23.14 | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.12/23.14 | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.12/23.14 | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.12/23.14 | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.12/23.14 | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.12/23.14 | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.12/23.14 | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.12/23.14 | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.12/23.14 | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.12/23.14 | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.12/23.14 | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.12/23.14 | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.12/23.14 | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.12/23.14 | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.12/23.14 | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.12/23.14 | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.12/23.14 | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.12/23.14 | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.12/23.14 | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.12/23.14 | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.12/23.14 | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.12/23.14 | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.12/23.14 | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.12/23.14 | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.12/23.14 | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.12/23.14 | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.12/23.14 | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.12/23.14 | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.12/23.14 | | | | | | | | | | | | | e0) % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (11), (13), (14), (20), (24), (29), % 154.12/23.14 | | | | | | | | | | | | | (37), (46), (49), (50), (53), (55), (62), (68), % 154.12/23.14 | | | | | | | | | | | | | (88), (89), (92), (99), (101), (157) are % 154.12/23.14 | | | | | | | | | | | | | inconsistent by sub-proof #272. % 154.12/23.14 | | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | | % 154.12/23.14 | | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | | % 154.12/23.14 | | | | | | | | | End of split % 154.12/23.14 | | | | | | | | | % 154.12/23.14 | | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | | % 154.12/23.14 | | | | | | | | | (158) all_56_12 = e1 % 154.12/23.14 | | | | | | | | | % 154.12/23.14 | | | | | | | | | COMBINE_EQS: (56), (158) imply: % 154.12/23.14 | | | | | | | | | (159) e1 = e0 % 154.12/23.14 | | | | | | | | | % 154.12/23.14 | | | | | | | | | COMBINE_EQS: (9), (159) imply: % 154.12/23.14 | | | | | | | | | (160) all_58_31 = e0 % 154.12/23.14 | | | | | | | | | % 154.12/23.14 | | | | | | | | | REF_CLOSE: (15), (24), (35), (37), (46), (55), (60), (62), % 154.12/23.14 | | | | | | | | | (63), (64), (65), (160) are inconsistent by % 154.12/23.14 | | | | | | | | | sub-proof #844. % 154.12/23.14 | | | | | | | | | % 154.12/23.14 | | | | | | | | End of split % 154.12/23.14 | | | | | | | | % 154.12/23.14 | | | | | | | Case 2: % 154.12/23.14 | | | | | | | | % 154.12/23.14 | | | | | | | | (161) all_56_10 = e1 % 154.12/23.14 | | | | | | | | % 154.12/23.14 | | | | | | | | REF_CLOSE: (8), (50), (161) are inconsistent by sub-proof #606. % 154.12/23.14 | | | | | | | | % 154.12/23.14 | | | | | | | End of split % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | End of split % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | End of split % 154.12/23.14 | | | | | % 154.12/23.14 | | | | End of split % 154.12/23.14 | | | | % 154.12/23.14 | | | End of split % 154.12/23.14 | | | % 154.12/23.14 | | End of split % 154.12/23.14 | | % 154.12/23.14 | Case 2: % 154.12/23.14 | | % 154.12/23.14 | | (162) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.12/23.14 | | % 154.12/23.14 | | BETA: splitting (162) gives: % 154.12/23.14 | | % 154.12/23.14 | | Case 1: % 154.12/23.14 | | | % 154.12/23.14 | | | (163) all_56_3 = e1 % 154.12/23.14 | | | % 154.12/23.14 | | | REF_CLOSE: (9), (12), (15), (24), (35), (37), (46), (55), (60), (62), % 154.12/23.14 | | | (63), (64), (65), (163) are inconsistent by sub-proof #280. % 154.12/23.14 | | | % 154.12/23.14 | | Case 2: % 154.12/23.14 | | | % 154.12/23.14 | | | (164) all_56_7 = e1 | all_56_13 = e1 % 154.12/23.14 | | | % 154.12/23.14 | | | BETA: splitting (164) gives: % 154.12/23.14 | | | % 154.12/23.14 | | | Case 1: % 154.12/23.14 | | | | % 154.12/23.14 | | | | (165) all_56_7 = e1 % 154.12/23.14 | | | | % 154.12/23.14 | | | | COMBINE_EQS: (4), (165) imply: % 154.12/23.14 | | | | (166) all_52_6 = e1 % 154.12/23.14 | | | | % 154.12/23.14 | | | | SIMP: (166) implies: % 154.12/23.14 | | | | (167) all_52_6 = e1 % 154.12/23.14 | | | | % 154.12/23.14 | | | | REDUCE: (39), (167) imply: % 154.12/23.14 | | | | (168) ~ (all_52_2 = e1) % 154.12/23.14 | | | | % 154.12/23.14 | | | | BETA: splitting (21) gives: % 154.12/23.14 | | | | % 154.12/23.14 | | | | Case 1: % 154.12/23.14 | | | | | % 154.12/23.14 | | | | | (169) all_56_4 = e1 % 154.12/23.14 | | | | | % 154.12/23.14 | | | | | REF_CLOSE: (9), (15), (24), (35), (37), (46), (48), (55), (60), (62), % 154.12/23.14 | | | | | (63), (64), (65), (169) are inconsistent by sub-proof #286. % 154.12/23.14 | | | | | % 154.12/23.14 | | | | Case 2: % 154.12/23.14 | | | | | % 154.12/23.14 | | | | | (170) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.12/23.14 | | | | | % 154.12/23.14 | | | | | BETA: splitting (170) gives: % 154.12/23.14 | | | | | % 154.12/23.14 | | | | | Case 1: % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | (171) all_56_5 = e1 % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | COMBINE_EQS: (27), (171) imply: % 154.12/23.14 | | | | | | (172) all_52_9 = e1 % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | SIMP: (172) implies: % 154.12/23.14 | | | | | | (173) all_52_9 = e1 % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | REDUCE: (54), (173) imply: % 154.12/23.14 | | | | | | (174) ~ (all_52_1 = e1) % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | BETA: splitting (18) gives: % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | Case 1: % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | | (175) all_56_0 = e1 % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | | REF_CLOSE: (9), (15), (24), (35), (37), (46), (52), (55), (57), % 154.12/23.14 | | | | | | | (60), (63), (65), (175) are inconsistent by sub-proof % 154.12/23.14 | | | | | | | #281. % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | Case 2: % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | | (176) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | | REF_CLOSE: (38), (47), (56), (62), (168), (174), (176) are % 154.12/23.14 | | | | | | | inconsistent by sub-proof #637. % 154.12/23.14 | | | | | | | % 154.12/23.14 | | | | | | End of split % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | Case 2: % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | (177) all_56_8 = e1 | all_56_14 = e1 % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | | REF_CLOSE: (9), (15), (24), (33), (35), (37), (46), (51), (52), % 154.12/23.14 | | | | | | (55), (58), (60), (63), (65), (177) are inconsistent by % 154.12/23.14 | | | | | | sub-proof #282. % 154.12/23.14 | | | | | | % 154.12/23.14 | | | | | End of split % 154.12/23.14 | | | | | % 154.12/23.14 | | | | End of split % 154.12/23.14 | | | | % 154.12/23.14 | | | Case 2: % 154.12/23.14 | | | | % 154.12/23.14 | | | | (178) all_56_13 = e1 % 154.12/23.14 | | | | % 154.12/23.14 | | | | REF_CLOSE: (19), (61), (178) are inconsistent by sub-proof #271. % 154.12/23.14 | | | | % 154.12/23.14 | | | End of split % 154.12/23.14 | | | % 154.12/23.14 | | End of split % 154.12/23.14 | | % 154.12/23.14 | End of split % 154.12/23.14 | % 154.12/23.14 End of proof % 154.12/23.14 % 154.12/23.14 Sub-proof #271 shows that the following formulas are inconsistent: % 154.12/23.14 ---------------------------------------------------------------- % 154.12/23.14 (1) all_56_13 = all_8_1 % 154.12/23.14 (2) all_56_13 = e1 % 154.12/23.14 (3) ~ (all_8_1 = e1) % 154.12/23.14 % 154.12/23.14 Begin of proof % 154.12/23.14 | % 154.12/23.14 | COMBINE_EQS: (1), (2) imply: % 154.12/23.14 | (4) all_8_1 = e1 % 154.12/23.14 | % 154.12/23.14 | SIMP: (4) implies: % 154.12/23.14 | (5) all_8_1 = e1 % 154.12/23.14 | % 154.12/23.14 | REDUCE: (3), (5) imply: % 154.12/23.14 | (6) $false % 154.12/23.14 | % 154.12/23.14 | CLOSE: (6) is inconsistent. % 154.12/23.14 | % 154.12/23.14 End of proof % 154.12/23.14 % 154.12/23.14 Sub-proof #272 shows that the following formulas are inconsistent: % 154.12/23.14 ---------------------------------------------------------------- % 154.12/23.14 (1) all_58_22 = e0 % 154.12/23.14 (2) ~ (all_52_13 = e1) % 154.12/23.14 (3) all_58_26 = all_52_11 % 154.12/23.14 (4) all_58_6 = all_52_12 % 154.12/23.14 (5) all_58_4 = e0 % 154.12/23.14 (6) all_58_15 = e1 % 154.12/23.14 (7) all_58_20 = e0 % 154.12/23.14 (8) ~ (all_52_6 = e1) % 154.12/23.14 (9) all_56_5 = e1 | all_56_10 = e1 % 154.12/23.14 (10) ~ (e3 = e1) % 154.12/23.14 (11) all_58_11 = e1 % 154.12/23.14 (12) ~ (all_52_12 = e0) % 154.12/23.14 (13) ~ (e2 = e1) % 154.12/23.14 (14) ~ (e3 = e0) % 154.12/23.14 (15) ~ (all_52_11 = e0) % 154.12/23.14 (16) all_56_5 = e1 % 154.12/23.14 (17) all_56_10 = all_52_13 % 154.12/23.14 (18) all_58_17 = all_52_6 % 154.12/23.14 (19) ~ (e2 = e0) % 154.12/23.14 (20) all_58_2 = e1 % 154.12/23.14 (21) ~ (e1 = e0) % 154.12/23.15 (22) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.12/23.15 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.12/23.15 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.12/23.15 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.12/23.15 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.12/23.15 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.12/23.15 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.12/23.15 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.12/23.15 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.12/23.15 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.12/23.15 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.12/23.15 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.12/23.15 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.12/23.15 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.12/23.15 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.12/23.15 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.12/23.15 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.12/23.15 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.12/23.15 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.12/23.15 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.12/23.15 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.12/23.15 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.12/23.15 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.12/23.15 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.12/23.15 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.12/23.15 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.12/23.15 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.12/23.15 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.12/23.15 e0) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | BETA: splitting (22) gives: % 154.12/23.15 | % 154.12/23.15 | Case 1: % 154.12/23.15 | | % 154.12/23.15 | | (23) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.12/23.15 | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.12/23.15 | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.12/23.15 | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.12/23.15 | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.12/23.15 | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.12/23.15 | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.12/23.15 | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.12/23.15 | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.12/23.15 | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 154.12/23.15 | | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 154.12/23.15 | | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 % 154.12/23.15 | | = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 154.12/23.15 | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.12/23.15 | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.12/23.15 | | % 154.12/23.15 | | BETA: splitting (23) gives: % 154.12/23.15 | | % 154.12/23.15 | | Case 1: % 154.12/23.15 | | | % 154.12/23.15 | | | (24) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.12/23.15 | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.12/23.15 | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) % 154.12/23.15 | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = % 154.12/23.15 | | | e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 % 154.12/23.15 | | | = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.12/23.15 | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = % 154.12/23.15 | | | e1 & all_58_17 = e1) % 154.12/23.15 | | | % 154.12/23.15 | | | BETA: splitting (24) gives: % 154.12/23.15 | | | % 154.12/23.15 | | | Case 1: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (25) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.12/23.15 | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.12/23.15 | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.12/23.15 | | | | all_58_17 = e2) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (25) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (26) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1 % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | ALPHA: (26) implies: % 154.12/23.15 | | | | | (27) all_58_4 = e1 % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | REF_CLOSE: (2), (5), (9), (16), (17), (21), (27) are inconsistent by % 154.12/23.15 | | | | | sub-proof #278. % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (28) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.12/23.15 | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.12/23.15 | | | | | all_58_17 = e2) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (28) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (29) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.12/23.15 | | | | | | e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (29) implies: % 154.12/23.15 | | | | | | (30) all_58_2 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (10), (20), (30) are inconsistent by sub-proof #277. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (31) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = % 154.12/23.15 | | | | | | e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (31) implies: % 154.12/23.15 | | | | | | (32) all_58_11 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (11), (13), (32) are inconsistent by sub-proof #276. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | Case 2: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (33) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = % 154.12/23.15 | | | | e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.12/23.15 | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = % 154.12/23.15 | | | | e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.12/23.15 | | | | all_58_11 = e1 & all_58_17 = e1) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (33) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (34) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = % 154.12/23.15 | | | | | e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.12/23.15 | | | | | all_58_15 = e3) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (34) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (35) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = % 154.12/23.15 | | | | | | e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (35) implies: % 154.12/23.15 | | | | | | (36) all_58_2 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (10), (20), (36) are inconsistent by sub-proof #277. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (37) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.12/23.15 | | | | | | e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (37) implies: % 154.12/23.15 | | | | | | (38) all_58_15 = e3 % 154.12/23.15 | | | | | | (39) all_58_4 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (5), (39) imply: % 154.12/23.15 | | | | | | (40) e3 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | SIMP: (40) implies: % 154.12/23.15 | | | | | | (41) e3 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (6), (38) imply: % 154.12/23.15 | | | | | | (42) e3 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (41), (42) imply: % 154.12/23.15 | | | | | | (43) e1 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (16), (43) imply: % 154.12/23.15 | | | | | | (44) all_56_5 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (9), (17), (21), (44) are inconsistent by sub-proof % 154.12/23.15 | | | | | | #304. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (45) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.12/23.15 | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.12/23.15 | | | | | all_58_17 = e1) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (45) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (46) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.12/23.15 | | | | | | e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (46) implies: % 154.12/23.15 | | | | | | (47) all_58_2 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (13), (20), (47) are inconsistent by sub-proof #275. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (48) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = % 154.12/23.15 | | | | | | e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (48) implies: % 154.12/23.15 | | | | | | (49) all_58_2 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (13), (20), (49) are inconsistent by sub-proof #275. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | End of split % 154.12/23.15 | | | % 154.12/23.15 | | Case 2: % 154.12/23.15 | | | % 154.12/23.15 | | | (50) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.12/23.15 | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.12/23.15 | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.12/23.15 | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.12/23.15 | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) % 154.12/23.15 | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 154.12/23.15 | | | e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.12/23.15 | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = % 154.12/23.15 | | | e0 & all_58_26 = e0) % 154.12/23.15 | | | % 154.12/23.15 | | | BETA: splitting (50) gives: % 154.12/23.15 | | | % 154.12/23.15 | | | Case 1: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (51) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.12/23.15 | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = % 154.12/23.15 | | | | e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.12/23.15 | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = % 154.12/23.15 | | | | e1) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (51) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (52) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.12/23.15 | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (52) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (53) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.12/23.15 | | | | | | e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (53) implies: % 154.12/23.15 | | | | | | (54) all_58_2 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (13), (20), (54) are inconsistent by sub-proof #275. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (55) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (55) implies: % 154.12/23.15 | | | | | | (56) all_58_2 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (13), (20), (56) are inconsistent by sub-proof #275. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (57) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = % 154.12/23.15 | | | | | e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.12/23.15 | | | | | all_58_17 = e1) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (57) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (58) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = % 154.12/23.15 | | | | | | e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (58) implies: % 154.12/23.15 | | | | | | (59) all_58_15 = e3 % 154.12/23.15 | | | | | | (60) all_58_4 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (5), (60) imply: % 154.12/23.15 | | | | | | (61) e3 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | SIMP: (61) implies: % 154.12/23.15 | | | | | | (62) e3 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (6), (59) imply: % 154.12/23.15 | | | | | | (63) e3 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | SIMP: (63) implies: % 154.12/23.15 | | | | | | (64) e3 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (62), (64) imply: % 154.12/23.15 | | | | | | (65) e1 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (16), (65) imply: % 154.12/23.15 | | | | | | (66) all_56_5 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (9), (17), (21), (66) are inconsistent by sub-proof % 154.12/23.15 | | | | | | #304. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (67) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.12/23.15 | | | | | | = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (67) implies: % 154.12/23.15 | | | | | | (68) all_58_15 = e3 % 154.12/23.15 | | | | | | (69) all_58_4 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (5), (6), (9), (16), (17), (21), (68), (69) are % 154.12/23.15 | | | | | | inconsistent by sub-proof #274. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | Case 2: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (70) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.12/23.15 | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.12/23.15 | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 % 154.12/23.15 | | | | = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.12/23.15 | | | | all_58_20 = e0 & all_58_26 = e0) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (70) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (71) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.12/23.15 | | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.12/23.15 | | | | | all_58_22 = e3) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (71) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (72) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 % 154.12/23.15 | | | | | | = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (72) implies: % 154.12/23.15 | | | | | | (73) all_58_15 = e3 % 154.12/23.15 | | | | | | (74) all_58_4 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (5), (6), (9), (16), (17), (21), (73), (74) are % 154.12/23.15 | | | | | | inconsistent by sub-proof #274. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (75) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 154.12/23.15 | | | | | | e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (75) implies: % 154.12/23.15 | | | | | | (76) all_58_4 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (5), (9), (16), (17), (21), (76) are inconsistent by % 154.12/23.15 | | | | | | sub-proof #278. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (77) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = % 154.12/23.15 | | | | | e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.12/23.15 | | | | | all_58_26 = e0) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (77) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (78) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.12/23.15 | | | | | | = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (78) implies: % 154.12/23.15 | | | | | | (79) all_58_4 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (5), (9), (16), (17), (21), (79) are inconsistent by % 154.12/23.15 | | | | | | sub-proof #278. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (80) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.12/23.15 | | | | | | = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (80) implies: % 154.12/23.15 | | | | | | (81) all_58_4 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (5), (9), (16), (17), (21), (81) are inconsistent by % 154.12/23.15 | | | | | | sub-proof #278. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | End of split % 154.12/23.15 | | | % 154.12/23.15 | | End of split % 154.12/23.15 | | % 154.12/23.15 | Case 2: % 154.12/23.15 | | % 154.12/23.15 | | (82) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.12/23.15 | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 % 154.12/23.15 | | & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.12/23.15 | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 % 154.12/23.15 | | = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.12/23.15 | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & % 154.12/23.15 | | all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.12/23.15 | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.12/23.15 | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.12/23.15 | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 154.12/23.15 | | e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = % 154.12/23.15 | | e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.12/23.15 | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.12/23.15 | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.12/23.15 | | all_58_26 = e0 & e1 = e0) % 154.12/23.15 | | % 154.12/23.15 | | BETA: splitting (82) gives: % 154.12/23.15 | | % 154.12/23.15 | | Case 1: % 154.12/23.15 | | | % 154.12/23.15 | | | (83) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.12/23.15 | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.12/23.15 | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.12/23.15 | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) % 154.12/23.15 | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = % 154.12/23.15 | | | e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 154.12/23.15 | | | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.12/23.15 | | | % 154.12/23.15 | | | BETA: splitting (83) gives: % 154.12/23.15 | | | % 154.12/23.15 | | | Case 1: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (84) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.12/23.15 | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 % 154.12/23.15 | | | | = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (84) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (85) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | ALPHA: (85) implies: % 154.12/23.15 | | | | | (86) all_58_4 = e1 % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | REF_CLOSE: (2), (5), (9), (16), (17), (21), (86) are inconsistent by % 154.12/23.15 | | | | | sub-proof #278. % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (87) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.12/23.15 | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.12/23.15 | | | | | all_58_26 = e0) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (87) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (88) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 % 154.12/23.15 | | | | | | = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (88) implies: % 154.12/23.15 | | | | | | (89) all_58_22 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (1), (14), (89) are inconsistent by sub-proof #299. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (90) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.12/23.15 | | | | | | = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (90) implies: % 154.12/23.15 | | | | | | (91) all_58_22 = e3 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (1), (14), (91) are inconsistent by sub-proof #299. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | Case 2: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (92) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = % 154.12/23.15 | | | | e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.12/23.15 | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.12/23.15 | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.12/23.15 | | | | e0) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (92) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (93) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = % 154.12/23.15 | | | | | e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.12/23.15 | | | | | all_58_26 = e1) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (93) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (94) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.12/23.15 | | | | | | = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (94) implies: % 154.12/23.15 | | | | | | (95) all_58_6 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (4), (95) imply: % 154.12/23.15 | | | | | | (96) all_52_12 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REDUCE: (12), (96) imply: % 154.12/23.15 | | | | | | (97) $false % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | CLOSE: (97) is inconsistent. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (98) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.12/23.15 | | | | | | = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (98) implies: % 154.12/23.15 | | | | | | (99) all_58_20 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (7), (9), (16), (17), (21), (99) are inconsistent by % 154.12/23.15 | | | | | | sub-proof #300. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (100) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.12/23.15 | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (100) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (101) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (101) implies: % 154.12/23.15 | | | | | | (102) e3 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REDUCE: (14), (102) imply: % 154.12/23.15 | | | | | | (103) $false % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | CLOSE: (103) is inconsistent. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (104) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.12/23.15 | | | | | | all_58_24 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (104) implies: % 154.12/23.15 | | | | | | (105) all_58_11 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (11), (13), (105) are inconsistent by sub-proof #276. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | End of split % 154.12/23.15 | | | % 154.12/23.15 | | Case 2: % 154.12/23.15 | | | % 154.12/23.15 | | | (106) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = % 154.12/23.15 | | | e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.12/23.15 | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 % 154.12/23.15 | | | = e0 & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 % 154.12/23.15 | | | = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.12/23.15 | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 % 154.12/23.15 | | | = e0 & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 % 154.12/23.15 | | | = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.12/23.15 | | | % 154.12/23.15 | | | BETA: splitting (106) gives: % 154.12/23.15 | | | % 154.12/23.15 | | | Case 1: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (107) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = % 154.12/23.15 | | | | e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.12/23.15 | | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.12/23.15 | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 154.12/23.15 | | | | all_58_17 = e1 & e2 = e1) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (107) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (108) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.12/23.15 | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.12/23.15 | | | | | all_58_24 = e2) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (108) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (109) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.12/23.15 | | | | | | all_58_26 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (109) implies: % 154.12/23.15 | | | | | | (110) all_58_20 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (7), (110) imply: % 154.12/23.15 | | | | | | (111) e1 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (16), (111) imply: % 154.12/23.15 | | | | | | (112) all_56_5 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (9), (17), (21), (112) are inconsistent by sub-proof % 154.12/23.15 | | | | | | #304. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (113) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.12/23.15 | | | | | | all_58_24 = e2 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (113) implies: % 154.12/23.15 | | | | | | (114) all_58_17 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (18), (114) imply: % 154.12/23.15 | | | | | | (115) all_52_6 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REDUCE: (8), (115) imply: % 154.12/23.15 | | | | | | (116) $false % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | CLOSE: (116) is inconsistent. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (117) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.12/23.15 | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (117) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (118) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.12/23.15 | | | | | | all_58_26 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (118) implies: % 154.12/23.15 | | | | | | (119) all_58_26 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (3), (15), (119) are inconsistent by sub-proof #273. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (120) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (120) implies: % 154.12/23.15 | | | | | | (121) e2 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REDUCE: (13), (121) imply: % 154.12/23.15 | | | | | | (122) $false % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | CLOSE: (122) is inconsistent. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | Case 2: % 154.12/23.15 | | | | % 154.12/23.15 | | | | (123) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.12/23.15 | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.12/23.15 | | | | all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) % 154.12/23.15 | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.12/23.15 | | | | % 154.12/23.15 | | | | BETA: splitting (123) gives: % 154.12/23.15 | | | | % 154.12/23.15 | | | | Case 1: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (124) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 % 154.12/23.15 | | | | | = e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.12/23.15 | | | | | all_58_26 = e1) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (124) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (125) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.12/23.15 | | | | | | all_58_26 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (125) implies: % 154.12/23.15 | | | | | | (126) all_58_26 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (3), (15), (126) are inconsistent by sub-proof #273. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (127) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.12/23.15 | | | | | | all_58_26 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (127) implies: % 154.12/23.15 | | | | | | (128) all_58_20 = e1 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (7), (9), (16), (17), (21), (128) are inconsistent % 154.12/23.15 | | | | | | by sub-proof #300. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | Case 2: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | (129) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.12/23.15 | | | | | & all_58_26 = e0 & e1 = e0) % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | BETA: splitting (129) gives: % 154.12/23.15 | | | | | % 154.12/23.15 | | | | | Case 1: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (130) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (130) implies: % 154.12/23.15 | | | | | | (131) e2 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REDUCE: (19), (131) imply: % 154.12/23.15 | | | | | | (132) $false % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | CLOSE: (132) is inconsistent. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | Case 2: % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | (133) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | ALPHA: (133) implies: % 154.12/23.15 | | | | | | (134) e1 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | COMBINE_EQS: (16), (134) imply: % 154.12/23.15 | | | | | | (135) all_56_5 = e0 % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | | REF_CLOSE: (2), (9), (17), (21), (135) are inconsistent by sub-proof % 154.12/23.15 | | | | | | #304. % 154.12/23.15 | | | | | | % 154.12/23.15 | | | | | End of split % 154.12/23.15 | | | | | % 154.12/23.15 | | | | End of split % 154.12/23.15 | | | | % 154.12/23.15 | | | End of split % 154.12/23.15 | | | % 154.12/23.15 | | End of split % 154.12/23.15 | | % 154.12/23.15 | End of split % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #273 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_26 = all_52_11 % 154.12/23.15 (2) all_58_26 = e0 % 154.12/23.15 (3) ~ (all_52_11 = e0) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (2) imply: % 154.12/23.15 | (4) all_52_11 = e0 % 154.12/23.15 | % 154.12/23.15 | SIMP: (4) implies: % 154.12/23.15 | (5) all_52_11 = e0 % 154.12/23.15 | % 154.12/23.15 | REDUCE: (3), (5) imply: % 154.12/23.15 | (6) $false % 154.12/23.15 | % 154.12/23.15 | CLOSE: (6) is inconsistent. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #274 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_4 = e3 % 154.12/23.15 (2) ~ (all_52_13 = e1) % 154.12/23.15 (3) all_58_4 = e0 % 154.12/23.15 (4) all_58_15 = e1 % 154.12/23.15 (5) all_56_5 = e1 | all_56_10 = e1 % 154.12/23.15 (6) all_56_5 = e1 % 154.12/23.15 (7) all_56_10 = all_52_13 % 154.12/23.15 (8) all_58_15 = e3 % 154.12/23.15 (9) ~ (e1 = e0) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (3) imply: % 154.12/23.15 | (10) e3 = e0 % 154.12/23.15 | % 154.12/23.15 | SIMP: (10) implies: % 154.12/23.15 | (11) e3 = e0 % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (4), (8) imply: % 154.12/23.15 | (12) e3 = e1 % 154.12/23.15 | % 154.12/23.15 | SIMP: (12) implies: % 154.12/23.15 | (13) e3 = e1 % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (11), (13) imply: % 154.12/23.15 | (14) e1 = e0 % 154.12/23.15 | % 154.12/23.15 | SIMP: (14) implies: % 154.12/23.15 | (15) e1 = e0 % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (6), (15) imply: % 154.12/23.15 | (16) all_56_5 = e0 % 154.12/23.15 | % 154.12/23.15 | REF_CLOSE: (2), (5), (7), (9), (16) are inconsistent by sub-proof #304. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #275 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_2 = e2 % 154.12/23.15 (2) all_58_2 = e1 % 154.12/23.15 (3) ~ (e2 = e1) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (2) imply: % 154.12/23.15 | (4) e2 = e1 % 154.12/23.15 | % 154.12/23.15 | SIMP: (4) implies: % 154.12/23.15 | (5) e2 = e1 % 154.12/23.15 | % 154.12/23.15 | REDUCE: (3), (5) imply: % 154.12/23.15 | (6) $false % 154.12/23.15 | % 154.12/23.15 | CLOSE: (6) is inconsistent. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #276 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_11 = e2 % 154.12/23.15 (2) all_58_11 = e1 % 154.12/23.15 (3) ~ (e2 = e1) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (2) imply: % 154.12/23.15 | (4) e2 = e1 % 154.12/23.15 | % 154.12/23.15 | SIMP: (4) implies: % 154.12/23.15 | (5) e2 = e1 % 154.12/23.15 | % 154.12/23.15 | REDUCE: (3), (5) imply: % 154.12/23.15 | (6) $false % 154.12/23.15 | % 154.12/23.15 | CLOSE: (6) is inconsistent. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #277 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_2 = e3 % 154.12/23.15 (2) all_58_2 = e1 % 154.12/23.15 (3) ~ (e3 = e1) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (2) imply: % 154.12/23.15 | (4) e3 = e1 % 154.12/23.15 | % 154.12/23.15 | SIMP: (4) implies: % 154.12/23.15 | (5) e3 = e1 % 154.12/23.15 | % 154.12/23.15 | REDUCE: (3), (5) imply: % 154.12/23.15 | (6) $false % 154.12/23.15 | % 154.12/23.15 | CLOSE: (6) is inconsistent. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #278 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) ~ (all_52_13 = e1) % 154.12/23.15 (2) all_58_4 = e0 % 154.12/23.15 (3) all_56_5 = e1 | all_56_10 = e1 % 154.12/23.15 (4) all_58_4 = e1 % 154.12/23.15 (5) all_56_5 = e1 % 154.12/23.15 (6) all_56_10 = all_52_13 % 154.12/23.15 (7) ~ (e1 = e0) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (2), (4) imply: % 154.12/23.15 | (8) e1 = e0 % 154.12/23.15 | % 154.12/23.15 | SIMP: (8) implies: % 154.12/23.15 | (9) e1 = e0 % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (5), (9) imply: % 154.12/23.15 | (10) all_56_5 = e0 % 154.12/23.15 | % 154.12/23.15 | REF_CLOSE: (1), (3), (6), (7), (10) are inconsistent by sub-proof #304. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #279 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_56_7 = all_52_6 % 154.12/23.15 (2) all_56_7 = e2 % 154.12/23.15 (3) ~ (all_52_6 = e2) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (2) imply: % 154.12/23.15 | (4) all_52_6 = e2 % 154.12/23.15 | % 154.12/23.15 | SIMP: (4) implies: % 154.12/23.15 | (5) all_52_6 = e2 % 154.12/23.15 | % 154.12/23.15 | REDUCE: (3), (5) imply: % 154.12/23.15 | (6) $false % 154.12/23.15 | % 154.12/23.15 | CLOSE: (6) is inconsistent. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #280 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_31 = e1 % 154.12/23.15 (2) all_56_3 = e0 % 154.12/23.15 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.15 (4) ~ (e3 = e1) % 154.12/23.15 (5) all_58_29 = e0 % 154.12/23.15 (6) ~ (e2 = e1) % 154.12/23.15 (7) all_56_3 = e1 % 154.12/23.15 (8) ~ (e3 = e0) % 154.12/23.15 (9) ~ (e2 = e0) % 154.12/23.15 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.15 (11) ~ (e1 = e0) % 154.12/23.15 (12) all_58_30 = all_6_2 % 154.12/23.15 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.12/23.15 (14) ~ (e3 = e2) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (2), (7) imply: % 154.12/23.15 | (15) e1 = e0 % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (1), (15) imply: % 154.12/23.15 | (16) all_58_31 = e0 % 154.12/23.15 | % 154.12/23.15 | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14), (16) % 154.12/23.15 | are inconsistent by sub-proof #844. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #281 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_31 = e1 % 154.12/23.15 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.15 (3) ~ (e3 = e1) % 154.12/23.15 (4) all_56_0 = e1 % 154.12/23.15 (5) all_58_29 = e0 % 154.12/23.15 (6) ~ (e2 = e1) % 154.12/23.15 (7) ~ (e3 = e0) % 154.12/23.15 (8) all_58_28 = all_10_2 % 154.12/23.15 (9) ~ (e2 = e0) % 154.12/23.15 (10) all_56_0 = all_10_2 % 154.12/23.15 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.15 (12) all_58_30 = all_6_2 % 154.12/23.15 (13) ~ (e3 = e2) % 154.12/23.15 % 154.12/23.15 Begin of proof % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (4), (10) imply: % 154.12/23.15 | (14) all_10_2 = e1 % 154.12/23.15 | % 154.12/23.15 | COMBINE_EQS: (8), (14) imply: % 154.12/23.15 | (15) all_58_28 = e1 % 154.12/23.15 | % 154.12/23.15 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (12), (13), (15) are % 154.12/23.15 | inconsistent by sub-proof #383. % 154.12/23.15 | % 154.12/23.15 End of proof % 154.12/23.15 % 154.12/23.15 Sub-proof #282 shows that the following formulas are inconsistent: % 154.12/23.15 ---------------------------------------------------------------- % 154.12/23.15 (1) all_58_31 = e1 % 154.12/23.16 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (3) ~ (e3 = e1) % 154.12/23.16 (4) ~ (all_52_11 = e1) % 154.12/23.16 (5) all_58_29 = e0 % 154.12/23.16 (6) ~ (e2 = e1) % 154.12/23.16 (7) ~ (e3 = e0) % 154.12/23.16 (8) all_56_14 = all_52_11 % 154.12/23.16 (9) all_58_28 = all_10_2 % 154.12/23.16 (10) ~ (e2 = e0) % 154.12/23.16 (11) all_56_8 = all_6_2 % 154.12/23.16 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (13) all_56_8 = e1 | all_56_14 = e1 % 154.12/23.16 (14) all_58_30 = all_6_2 % 154.12/23.16 (15) ~ (e3 = e2) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (13) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (16) all_56_8 = e1 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (11), (16) imply: % 154.12/23.16 | | (17) all_6_2 = e1 % 154.12/23.16 | | % 154.12/23.16 | | SIMP: (17) implies: % 154.12/23.16 | | (18) all_6_2 = e1 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (14), (18) imply: % 154.12/23.16 | | (19) all_58_30 = e1 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (12), (15), (19) are % 154.12/23.16 | | inconsistent by sub-proof #283. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (20) all_56_14 = e1 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (4), (8), (20) are inconsistent by sub-proof #811. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #283 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = e1 % 154.12/23.16 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (3) ~ (e3 = e1) % 154.12/23.16 (4) all_58_29 = e0 % 154.12/23.16 (5) ~ (e2 = e1) % 154.12/23.16 (6) ~ (e3 = e0) % 154.12/23.16 (7) all_58_28 = all_10_2 % 154.12/23.16 (8) all_58_30 = e1 % 154.12/23.16 (9) ~ (e2 = e0) % 154.12/23.16 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (11) ~ (e3 = e2) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (10) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (12) all_58_28 = e3 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (7), (12) imply: % 154.12/23.16 | | (13) all_10_2 = e3 % 154.12/23.16 | | % 154.12/23.16 | | BETA: splitting (2) gives: % 154.12/23.16 | | % 154.12/23.16 | | Case 1: % 154.12/23.16 | | | % 154.12/23.16 | | | (14) all_58_28 = e2 % 154.12/23.16 | | | % 154.12/23.16 | | | COMBINE_EQS: (12), (14) imply: % 154.12/23.16 | | | (15) e3 = e2 % 154.12/23.16 | | | % 154.12/23.16 | | | REDUCE: (11), (15) imply: % 154.12/23.16 | | | (16) $false % 154.12/23.16 | | | % 154.12/23.16 | | | CLOSE: (16) is inconsistent. % 154.12/23.16 | | | % 154.12/23.16 | | Case 2: % 154.12/23.16 | | | % 154.12/23.16 | | | (17) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 | | | % 154.12/23.16 | | | REF_CLOSE: (1), (4), (5), (8), (9), (17) are inconsistent by sub-proof % 154.12/23.16 | | | #379. % 154.12/23.16 | | | % 154.12/23.16 | | End of split % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (18) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (1), (3), (4), (6), (8), (18) are inconsistent by sub-proof #284. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #284 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = e1 % 154.12/23.16 (2) ~ (e3 = e1) % 154.12/23.16 (3) all_58_29 = e0 % 154.12/23.16 (4) ~ (e3 = e0) % 154.12/23.16 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (6) all_58_30 = e1 % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (5) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (7) all_58_29 = e3 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (3), (7) imply: % 154.12/23.16 | | (8) e3 = e0 % 154.12/23.16 | | % 154.12/23.16 | | REDUCE: (4), (8) imply: % 154.12/23.16 | | (9) $false % 154.12/23.16 | | % 154.12/23.16 | | CLOSE: (9) is inconsistent. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (10) all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #498. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #285 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_56_5 = all_52_9 % 154.12/23.16 (2) all_56_5 = e1 % 154.12/23.16 (3) ~ (all_52_9 = e1) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (1), (2) imply: % 154.12/23.16 | (4) all_52_9 = e1 % 154.12/23.16 | % 154.12/23.16 | SIMP: (4) implies: % 154.12/23.16 | (5) all_52_9 = e1 % 154.12/23.16 | % 154.12/23.16 | REDUCE: (3), (5) imply: % 154.12/23.16 | (6) $false % 154.12/23.16 | % 154.12/23.16 | CLOSE: (6) is inconsistent. % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #286 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = e1 % 154.12/23.16 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (3) ~ (e3 = e1) % 154.12/23.16 (4) all_58_29 = e0 % 154.12/23.16 (5) ~ (e2 = e1) % 154.12/23.16 (6) ~ (e3 = e0) % 154.12/23.16 (7) all_56_4 = e0 % 154.12/23.16 (8) ~ (e2 = e0) % 154.12/23.16 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (10) ~ (e1 = e0) % 154.12/23.16 (11) all_58_30 = all_6_2 % 154.12/23.16 (12) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.12/23.16 (13) ~ (e3 = e2) % 154.12/23.16 (14) all_56_4 = e1 % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (7), (14) imply: % 154.12/23.16 | (15) e1 = e0 % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (1), (15) imply: % 154.12/23.16 | (16) all_58_31 = e0 % 154.12/23.16 | % 154.12/23.16 | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16) are % 154.12/23.16 | inconsistent by sub-proof #844. % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #287 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_56_7 = all_52_6 % 154.12/23.16 (2) ~ (all_6_2 = e0) % 154.12/23.16 (3) ~ (all_52_6 = e0) % 154.12/23.16 (4) all_56_11 = all_52_14 % 154.12/23.16 (5) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.12/23.16 (6) all_56_8 = all_6_2 % 154.12/23.16 (7) ~ (all_52_14 = e0) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (5) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (8) all_56_7 = e0 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (1), (8) imply: % 154.12/23.16 | | (9) all_52_6 = e0 % 154.12/23.16 | | % 154.12/23.16 | | REDUCE: (3), (9) imply: % 154.12/23.16 | | (10) $false % 154.12/23.16 | | % 154.12/23.16 | | CLOSE: (10) is inconsistent. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (11) all_56_8 = e0 | all_56_11 = e0 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (2), (4), (6), (7), (11) are inconsistent by sub-proof #763. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #288 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = all_4_2 % 154.12/23.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.12/23.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.12/23.16 (3) all_54_11 = all_52_14 % 154.12/23.16 (4) ~ (all_52_14 = e1) % 154.12/23.16 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.12/23.16 (6) ~ (all_10_2 = e3) % 154.12/23.16 (7) ~ (e3 = e1) % 154.12/23.16 (8) op(all_4_2, e0) = e1 % 154.12/23.16 (9) ~ (all_10_2 = e1) % 154.12/23.16 (10) all_58_29 = e0 % 154.12/23.16 (11) ~ (e3 = e0) % 154.12/23.16 (12) all_58_28 = all_10_2 % 154.12/23.16 (13) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.12/23.16 (14) all_58_30 = e1 % 154.12/23.16 (15) all_56_0 = all_10_2 % 154.12/23.16 (16) all_58_30 = e1 | all_58_31 = e1 % 154.12/23.16 (17) op(e3, e0) = e0 % 154.12/23.16 (18) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (19) all_54_0 = all_10_2 % 154.12/23.16 (20) ~ (all_52_14 = all_4_2) % 154.12/23.16 (21) ~ (e1 = e0) % 154.12/23.16 (22) ~ (all_4_2 = e1) % 154.12/23.16 (23) ~ (e3 = e2) % 154.12/23.16 (24) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (13) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (25) all_56_0 = e2 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (15), (25) imply: % 154.12/23.16 | | (26) all_10_2 = e2 % 154.12/23.16 | | % 154.12/23.16 | | SIMP: (26) implies: % 154.12/23.16 | | (27) all_10_2 = e2 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (12), (27) imply: % 154.12/23.16 | | (28) all_58_28 = e2 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (14), (16), (17), (18), % 154.12/23.16 | | (20), (21), (22), (23), (24), (28) are inconsistent by sub-proof % 154.12/23.16 | | #289. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (29) ~ (all_56_0 = e2) % 154.12/23.16 | | % 154.12/23.16 | | REDUCE: (15), (29) imply: % 154.12/23.16 | | (30) ~ (all_10_2 = e2) % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (5), (6), (9), (19), (30) are inconsistent by sub-proof #813. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #289 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = all_4_2 % 154.12/23.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.12/23.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.12/23.16 (3) all_54_11 = all_52_14 % 154.12/23.16 (4) ~ (all_52_14 = e1) % 154.12/23.16 (5) ~ (e3 = e1) % 154.12/23.16 (6) op(all_4_2, e0) = e1 % 154.12/23.16 (7) all_58_29 = e0 % 154.12/23.16 (8) ~ (e3 = e0) % 154.12/23.16 (9) all_58_30 = e1 % 154.12/23.16 (10) all_58_30 = e1 | all_58_31 = e1 % 154.12/23.16 (11) all_58_28 = e2 % 154.12/23.16 (12) op(e3, e0) = e0 % 154.12/23.16 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (14) ~ (all_52_14 = all_4_2) % 154.12/23.16 (15) ~ (e1 = e0) % 154.12/23.16 (16) ~ (all_4_2 = e1) % 154.12/23.16 (17) ~ (e3 = e2) % 154.12/23.16 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (13) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (19) all_58_28 = e3 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (11), (17), (19) are inconsistent by sub-proof #849. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (20) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 | | % 154.12/23.16 | | BETA: splitting (20) gives: % 154.12/23.16 | | % 154.12/23.16 | | Case 1: % 154.12/23.16 | | | % 154.12/23.16 | | | (21) all_58_29 = e3 % 154.12/23.16 | | | % 154.12/23.16 | | | REF_CLOSE: (7), (8), (21) are inconsistent by sub-proof #707. % 154.12/23.16 | | | % 154.12/23.16 | | Case 2: % 154.12/23.16 | | | % 154.12/23.16 | | | (22) all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 | | | % 154.12/23.16 | | | BETA: splitting (22) gives: % 154.12/23.16 | | | % 154.12/23.16 | | | Case 1: % 154.12/23.16 | | | | % 154.12/23.16 | | | | (23) all_58_30 = e3 % 154.12/23.16 | | | | % 154.12/23.16 | | | | REF_CLOSE: (5), (9), (23) are inconsistent by sub-proof #290. % 154.12/23.16 | | | | % 154.12/23.16 | | | Case 2: % 154.12/23.16 | | | | % 154.12/23.16 | | | | (24) all_58_31 = e3 % 154.12/23.16 | | | | % 154.12/23.16 | | | | COMBINE_EQS: (1), (24) imply: % 154.12/23.16 | | | | (25) all_4_2 = e3 % 154.12/23.16 | | | | % 154.12/23.16 | | | | SIMP: (25) implies: % 154.12/23.16 | | | | (26) all_4_2 = e3 % 154.12/23.16 | | | | % 154.12/23.16 | | | | REDUCE: (14), (26) imply: % 154.12/23.16 | | | | (27) ~ (all_52_14 = e3) % 154.12/23.16 | | | | % 154.12/23.16 | | | | REDUCE: (6), (26) imply: % 154.12/23.16 | | | | (28) op(e3, e0) = e1 % 154.12/23.16 | | | | % 154.12/23.16 | | | | BETA: splitting (18) gives: % 154.12/23.16 | | | | % 154.12/23.16 | | | | Case 1: % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | (29) all_54_11 = e1 % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | COMBINE_EQS: (3), (29) imply: % 154.12/23.16 | | | | | (30) all_52_14 = e1 % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | REDUCE: (4), (30) imply: % 154.12/23.16 | | | | | (31) $false % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | CLOSE: (31) is inconsistent. % 154.12/23.16 | | | | | % 154.12/23.16 | | | | Case 2: % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | (32) all_54_11 = e3 | all_54_11 = e2 % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | BETA: splitting (32) gives: % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | Case 1: % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | GROUND_INST: instantiating (2) with e0, e1, e0, e3, simplifying with % 154.12/23.16 | | | | | | (12), (28) gives: % 154.12/23.16 | | | | | | (33) e1 = e0 % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | COMBINE_EQS: (9), (33) imply: % 154.12/23.16 | | | | | | (34) all_58_30 = e0 % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | REF_CLOSE: (1), (10), (15), (16), (34) are inconsistent by sub-proof % 154.12/23.16 | | | | | | #711. % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | Case 2: % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | (35) all_54_11 = e3 % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | REF_CLOSE: (3), (27), (35) are inconsistent by sub-proof #776. % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | End of split % 154.12/23.16 | | | | | % 154.12/23.16 | | | | End of split % 154.12/23.16 | | | | % 154.12/23.16 | | | End of split % 154.12/23.16 | | | % 154.12/23.16 | | End of split % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #290 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_30 = e3 % 154.12/23.16 (2) all_58_30 = e1 % 154.12/23.16 (3) ~ (e3 = e1) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (1), (2) imply: % 154.12/23.16 | (4) e3 = e1 % 154.12/23.16 | % 154.12/23.16 | SIMP: (4) implies: % 154.12/23.16 | (5) e3 = e1 % 154.12/23.16 | % 154.12/23.16 | REDUCE: (3), (5) imply: % 154.12/23.16 | (6) $false % 154.12/23.16 | % 154.12/23.16 | CLOSE: (6) is inconsistent. % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #291 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = all_4_2 % 154.12/23.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.12/23.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.12/23.16 (3) ~ (all_44_0 = e3) | ~ (all_44_2 = e2) % 154.12/23.16 (4) e2 = e1 % 154.12/23.16 (5) all_58_30 = e2 % 154.12/23.16 (6) ~ (e2 = e1) % 154.12/23.16 (7) op(e2, e1) = e3 % 154.12/23.16 (8) all_44_2 = all_4_2 % 154.12/23.16 (9) all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (10) op(all_4_2, e1) = all_4_0 % 154.12/23.16 (11) all_44_0 = all_4_0 % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | SIMP: (4) implies: % 154.12/23.16 | (12) e2 = e1 % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (5), (12) imply: % 154.12/23.16 | (13) all_58_30 = e1 % 154.12/23.16 | % 154.12/23.16 | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (13) are % 154.12/23.16 | inconsistent by sub-proof #292. % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #292 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_58_31 = all_4_2 % 154.12/23.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.12/23.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.12/23.16 (3) ~ (all_44_0 = e3) | ~ (all_44_2 = e2) % 154.12/23.16 (4) ~ (e2 = e1) % 154.12/23.16 (5) op(e2, e1) = e3 % 154.12/23.16 (6) all_44_2 = all_4_2 % 154.12/23.16 (7) all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (8) all_58_30 = e1 % 154.12/23.16 (9) op(all_4_2, e1) = all_4_0 % 154.12/23.16 (10) all_44_0 = all_4_0 % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (7) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (11) all_58_30 = e2 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #500. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (12) all_58_31 = e2 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (1), (12) imply: % 154.12/23.16 | | (13) all_4_2 = e2 % 154.12/23.16 | | % 154.12/23.16 | | SIMP: (13) implies: % 154.12/23.16 | | (14) all_4_2 = e2 % 154.12/23.16 | | % 154.12/23.16 | | REF_CLOSE: (2), (3), (5), (6), (9), (10), (14) are inconsistent by sub-proof % 154.12/23.16 | | #570. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #293 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_56_12 = e2 % 154.12/23.16 (2) all_58_30 = e2 % 154.12/23.16 (3) all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (4) all_58_31 = e3 % 154.12/23.16 (5) ~ (e2 = e0) % 154.12/23.16 (6) all_56_12 = e0 % 154.12/23.16 (7) ~ (e3 = e2) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (1), (6) imply: % 154.12/23.16 | (8) e2 = e0 % 154.12/23.16 | % 154.12/23.16 | COMBINE_EQS: (2), (8) imply: % 154.12/23.16 | (9) all_58_30 = e0 % 154.12/23.16 | % 154.12/23.16 | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #705. % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #294 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_56_10 = e0 | all_56_11 = e0 % 154.12/23.16 (2) all_56_11 = all_52_14 % 154.12/23.16 (3) ~ (all_52_13 = e0) % 154.12/23.16 (4) all_56_10 = all_52_13 % 154.12/23.16 (5) ~ (all_52_14 = e0) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (1) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (6) all_56_10 = e0 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (4), (6) imply: % 154.12/23.16 | | (7) all_52_13 = e0 % 154.12/23.16 | | % 154.12/23.16 | | REDUCE: (3), (7) imply: % 154.12/23.16 | | (8) $false % 154.12/23.16 | | % 154.12/23.16 | | CLOSE: (8) is inconsistent. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (9) all_56_11 = e0 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (2), (9) imply: % 154.12/23.16 | | (10) all_52_14 = e0 % 154.12/23.16 | | % 154.12/23.16 | | REDUCE: (5), (10) imply: % 154.12/23.16 | | (11) $false % 154.12/23.16 | | % 154.12/23.16 | | CLOSE: (11) is inconsistent. % 154.12/23.16 | | % 154.12/23.16 | End of split % 154.12/23.16 | % 154.12/23.16 End of proof % 154.12/23.16 % 154.12/23.16 Sub-proof #295 shows that the following formulas are inconsistent: % 154.12/23.16 ---------------------------------------------------------------- % 154.12/23.16 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 154.12/23.16 (2) all_58_31 = all_4_2 % 154.12/23.16 (3) ~ (all_52_8 = all_52_9) % 154.12/23.16 (4) all_56_14 = e0 % 154.12/23.16 (5) all_58_11 = all_52_9 % 154.12/23.16 (6) all_56_15 = all_4_2 % 154.12/23.16 (7) all_56_7 = all_52_6 % 154.12/23.16 (8) ~ (all_52_6 = all_6_2) % 154.12/23.16 (9) all_54_2 = all_52_8 % 154.12/23.16 (10) ~ (all_52_8 = all_10_2) % 154.12/23.16 (11) all_56_3 = e0 % 154.12/23.16 (12) all_54_7 = all_52_13 % 154.12/23.16 (13) all_56_4 = all_52_8 % 154.12/23.16 (14) all_56_6 = e0 % 154.12/23.16 (15) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.16 (16) all_54_1 = all_52_4 % 154.12/23.16 (17) ~ (all_6_2 = e0) % 154.12/23.16 (18) ~ (all_52_4 = all_52_6) % 154.12/23.16 (19) all_58_13 = all_52_13 % 154.12/23.16 (20) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.12/23.16 (21) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.12/23.16 (22) all_54_11 = all_52_14 % 154.12/23.16 (23) all_56_13 = e1 % 154.12/23.16 (24) all_58_20 = all_52_14 % 154.12/23.16 (25) ~ (all_52_6 = e1) % 154.12/23.16 (26) ~ (all_52_8 = all_6_2) % 154.12/23.16 (27) ~ (all_52_3 = e1) % 154.12/23.16 (28) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.12/23.16 (29) all_54_10 = all_6_2 % 154.12/23.16 (30) ~ (all_52_6 = all_52_14) % 154.12/23.16 (31) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 154.12/23.16 (32) all_54_6 = all_52_9 % 154.12/23.16 (33) all_54_9 = all_52_6 % 154.12/23.16 (34) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.12/23.16 (35) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.12/23.16 (36) ~ (all_52_3 = e0) % 154.12/23.16 (37) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.12/23.16 (38) ~ (all_52_6 = e0) % 154.12/23.16 (39) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.12/23.16 (40) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 154.12/23.16 (41) all_58_6 = e0 % 154.12/23.16 (42) ~ (all_52_1 = all_52_13) % 154.12/23.16 (43) all_56_5 = all_52_9 % 154.12/23.16 (44) all_56_12 = all_52_3 % 154.12/23.16 (45) all_58_2 = all_52_4 % 154.12/23.16 (46) all_56_1 = all_52_4 % 154.12/23.16 (47) ~ (all_52_13 = e0) % 154.12/23.16 (48) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 154.12/23.16 (49) ~ (all_52_3 = all_4_2) % 154.12/23.16 (50) ~ (all_52_9 = e0) % 154.12/23.16 (51) ~ (all_52_13 = all_52_14) % 154.12/23.16 (52) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.12/23.16 (53) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.12/23.16 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.12/23.16 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.12/23.16 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.12/23.16 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.12/23.16 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.12/23.16 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.12/23.16 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.12/23.16 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.12/23.16 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.12/23.16 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.12/23.16 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.12/23.16 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.12/23.16 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.12/23.16 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.12/23.16 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.12/23.16 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.12/23.16 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.12/23.16 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.12/23.16 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.12/23.16 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.12/23.16 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.12/23.16 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.12/23.16 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.12/23.16 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.12/23.16 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.12/23.16 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.12/23.16 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.12/23.16 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.12/23.16 e0) % 154.12/23.16 (54) ~ (all_52_4 = all_52_8) % 154.12/23.16 (55) all_58_29 = e0 % 154.12/23.16 (56) ~ (all_52_4 = e1) % 154.12/23.16 (57) all_58_8 = all_52_1 % 154.12/23.16 (58) ~ (e2 = e1) % 154.12/23.16 (59) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.12/23.16 (60) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.12/23.16 (61) all_58_26 = e0 % 154.12/23.16 (62) all_58_15 = e0 % 154.12/23.16 (63) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.12/23.16 (64) ~ (all_52_9 = all_52_13) % 154.12/23.16 (65) ~ (all_52_4 = e0) % 154.12/23.16 (66) all_56_2 = all_52_1 % 154.12/23.16 (67) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 154.12/23.16 (68) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 154.12/23.16 (69) all_56_10 = all_52_13 % 154.12/23.16 (70) ~ (all_52_1 = all_52_3) % 154.12/23.16 (71) all_58_28 = all_10_2 % 154.12/23.16 (72) all_56_9 = e0 % 154.12/23.16 (73) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.12/23.16 (74) all_58_17 = all_52_6 % 154.12/23.16 (75) ~ (all_52_1 = all_52_9) % 154.12/23.16 (76) ~ (e2 = e0) % 154.12/23.16 (77) ~ (all_4_2 = e0) % 154.12/23.16 (78) ~ (all_52_9 = all_6_2) % 154.12/23.16 (79) all_56_0 = all_10_2 % 154.12/23.16 (80) ~ (all_52_1 = e0) % 154.12/23.16 (81) all_58_22 = all_52_3 % 154.12/23.16 (82) ~ (all_52_3 = all_10_2) % 154.12/23.16 (83) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.12/23.16 (84) all_58_24 = e1 % 154.12/23.16 (85) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.12/23.16 (86) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.12/23.16 (87) all_58_4 = all_52_8 % 154.12/23.16 (88) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.16 (89) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.12/23.16 (90) all_54_0 = all_10_2 % 154.12/23.16 (91) ~ (all_52_14 = all_4_2) % 154.12/23.16 (92) ~ (e1 = e0) % 154.12/23.16 (93) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 154.12/23.16 (94) ~ (all_52_14 = e0) % 154.12/23.16 (95) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 154.12/23.16 (96) ~ (all_4_2 = e1) % 154.12/23.16 (97) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 154.12/23.16 (98) ~ (all_52_8 = e0) % 154.12/23.16 (99) ~ (all_52_4 = all_10_2) % 154.12/23.16 (100) all_58_30 = all_6_2 % 154.12/23.16 (101) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.12/23.16 (102) ~ (all_52_14 = all_6_2) % 154.12/23.16 (103) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 154.12/23.16 (104) all_54_12 = all_52_3 % 154.12/23.16 (105) all_54_4 = all_52_1 % 154.12/23.16 (106) ~ (all_52_1 = all_10_2) % 154.12/23.16 % 154.12/23.16 Begin of proof % 154.12/23.16 | % 154.12/23.16 | BETA: splitting (68) gives: % 154.12/23.16 | % 154.12/23.16 | Case 1: % 154.12/23.16 | | % 154.12/23.16 | | (107) all_54_12 = e0 % 154.12/23.16 | | % 154.12/23.16 | | COMBINE_EQS: (104), (107) imply: % 154.12/23.16 | | (108) all_52_3 = e0 % 154.12/23.16 | | % 154.12/23.16 | | REDUCE: (36), (108) imply: % 154.12/23.16 | | (109) $false % 154.12/23.16 | | % 154.12/23.16 | | CLOSE: (109) is inconsistent. % 154.12/23.16 | | % 154.12/23.16 | Case 2: % 154.12/23.16 | | % 154.12/23.16 | | (110) ~ (all_54_12 = e0) % 154.12/23.16 | | (111) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.12/23.16 | | % 154.12/23.16 | | BETA: splitting (85) gives: % 154.12/23.16 | | % 154.12/23.16 | | Case 1: % 154.12/23.16 | | | % 154.12/23.16 | | | (112) all_54_1 = e0 % 154.12/23.16 | | | % 154.12/23.16 | | | REF_CLOSE: (16), (65), (112) are inconsistent by sub-proof #798. % 154.12/23.16 | | | % 154.12/23.16 | | Case 2: % 154.12/23.16 | | | % 154.12/23.16 | | | (113) ~ (all_54_1 = e0) % 154.12/23.16 | | | (114) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.12/23.16 | | | % 154.12/23.16 | | | BETA: splitting (60) gives: % 154.12/23.16 | | | % 154.12/23.16 | | | Case 1: % 154.12/23.16 | | | | % 154.12/23.16 | | | | (115) all_54_4 = e0 % 154.12/23.16 | | | | % 154.12/23.16 | | | | COMBINE_EQS: (105), (115) imply: % 154.12/23.16 | | | | (116) all_52_1 = e0 % 154.12/23.16 | | | | % 154.12/23.16 | | | | REDUCE: (80), (116) imply: % 154.12/23.16 | | | | (117) $false % 154.12/23.16 | | | | % 154.12/23.16 | | | | CLOSE: (117) is inconsistent. % 154.12/23.16 | | | | % 154.12/23.16 | | | Case 2: % 154.12/23.16 | | | | % 154.12/23.16 | | | | (118) ~ (all_54_4 = e0) % 154.12/23.16 | | | | (119) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.12/23.16 | | | | % 154.12/23.16 | | | | BETA: splitting (83) gives: % 154.12/23.16 | | | | % 154.12/23.16 | | | | Case 1: % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | (120) all_56_1 = e2 % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | COMBINE_EQS: (46), (120) imply: % 154.12/23.16 | | | | | (121) all_52_4 = e2 % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | COMBINE_EQS: (45), (121) imply: % 154.12/23.16 | | | | | (122) all_58_2 = e2 % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | REDUCE: (18), (121) imply: % 154.12/23.16 | | | | | (123) ~ (all_52_6 = e2) % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | SIMP: (123) implies: % 154.12/23.16 | | | | | (124) ~ (all_52_6 = e2) % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | REDUCE: (54), (121) imply: % 154.12/23.16 | | | | | (125) ~ (all_52_8 = e2) % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | SIMP: (125) implies: % 154.12/23.16 | | | | | (126) ~ (all_52_8 = e2) % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | REDUCE: (99), (121) imply: % 154.12/23.16 | | | | | (127) ~ (all_10_2 = e2) % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | SIMP: (127) implies: % 154.12/23.16 | | | | | (128) ~ (all_10_2 = e2) % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | BETA: splitting (35) gives: % 154.12/23.16 | | | | | % 154.12/23.16 | | | | | Case 1: % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | (129) all_54_9 = e1 % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | | REF_CLOSE: (25), (33), (129) are inconsistent by sub-proof #622. % 154.12/23.16 | | | | | | % 154.12/23.16 | | | | | Case 2: % 154.12/23.16 | | | | | | % 154.12/23.17 | | | | | | (130) ~ (all_54_9 = e1) % 154.12/23.17 | | | | | | (131) all_54_9 = e3 | all_54_9 = e2 % 154.12/23.17 | | | | | | % 154.12/23.17 | | | | | | BETA: splitting (131) gives: % 154.12/23.17 | | | | | | % 154.12/23.17 | | | | | | Case 1: % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | (132) all_54_9 = e2 % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | REF_CLOSE: (33), (124), (132) are inconsistent by sub-proof #621. % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | Case 2: % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | (133) all_54_9 = e3 % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | COMBINE_EQS: (33), (133) imply: % 154.12/23.17 | | | | | | | (134) all_52_6 = e3 % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | SIMP: (134) implies: % 154.12/23.17 | | | | | | | (135) all_52_6 = e3 % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | COMBINE_EQS: (74), (135) imply: % 154.12/23.17 | | | | | | | (136) all_58_17 = e3 % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | REDUCE: (30), (135) imply: % 154.12/23.17 | | | | | | | (137) ~ (all_52_14 = e3) % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | SIMP: (137) implies: % 154.12/23.17 | | | | | | | (138) ~ (all_52_14 = e3) % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | REDUCE: (124), (135) imply: % 154.12/23.17 | | | | | | | (139) ~ (e3 = e2) % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | REDUCE: (25), (135) imply: % 154.12/23.17 | | | | | | | (140) ~ (e3 = e1) % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | REDUCE: (38), (135) imply: % 154.12/23.17 | | | | | | | (141) ~ (e3 = e0) % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | BETA: splitting (31) gives: % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | | (142) all_54_11 = e0 % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | | REF_CLOSE: (22), (94), (142) are inconsistent by sub-proof #743. % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | | (143) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | | BETA: splitting (67) gives: % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | (144) all_54_10 = e0 % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | COMBINE_EQS: (29), (144) imply: % 154.12/23.17 | | | | | | | | | (145) all_6_2 = e0 % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | COMBINE_EQS: (100), (145) imply: % 154.12/23.17 | | | | | | | | | (146) all_58_30 = e0 % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | REF_CLOSE: (2), (15), (55), (58), (71), (76), (88), (92), % 154.12/23.17 | | | | | | | | | (96), (101), (139), (140), (141), (146) are % 154.12/23.17 | | | | | | | | | inconsistent by sub-proof #698. % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | (147) ~ (all_54_10 = e0) % 154.12/23.17 | | | | | | | | | (148) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | BETA: splitting (40) gives: % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | (149) all_54_0 = e0 % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | COMBINE_EQS: (90), (149) imply: % 154.12/23.17 | | | | | | | | | | (150) all_10_2 = e0 % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | COMBINE_EQS: (71), (150) imply: % 154.12/23.17 | | | | | | | | | | (151) all_58_28 = e0 % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | REF_CLOSE: (15), (55), (58), (76), (88), (92), (100), (101), % 154.12/23.17 | | | | | | | | | | (139), (140), (141), (151) are inconsistent by % 154.12/23.17 | | | | | | | | | | sub-proof #483. % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | (152) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | BETA: splitting (95) gives: % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | (153) all_54_2 = e0 % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | COMBINE_EQS: (9), (153) imply: % 154.12/23.17 | | | | | | | | | | | (154) all_52_8 = e0 % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | REDUCE: (98), (154) imply: % 154.12/23.17 | | | | | | | | | | | (155) $false % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | CLOSE: (155) is inconsistent. % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | (156) ~ (all_54_2 = e0) % 154.12/23.17 | | | | | | | | | | | (157) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | BETA: splitting (73) gives: % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | (158) all_56_0 = e2 % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | COMBINE_EQS: (79), (158) imply: % 154.12/23.17 | | | | | | | | | | | | (159) all_10_2 = e2 % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | REDUCE: (128), (159) imply: % 154.12/23.17 | | | | | | | | | | | | (160) $false % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | (161) ~ (all_56_0 = e2) % 154.12/23.17 | | | | | | | | | | | | (162) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | BETA: splitting (52) gives: % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | (163) all_56_12 = e3 % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | COMBINE_EQS: (44), (163) imply: % 154.12/23.17 | | | | | | | | | | | | | (164) all_52_3 = e3 % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | SIMP: (164) implies: % 154.12/23.17 | | | | | | | | | | | | | (165) all_52_3 = e3 % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | REDUCE: (82), (165) imply: % 154.12/23.17 | | | | | | | | | | | | | (166) ~ (all_10_2 = e3) % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | SIMP: (166) implies: % 154.12/23.17 | | | | | | | | | | | | | (167) ~ (all_10_2 = e3) % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | BETA: splitting (93) gives: % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | (168) all_56_0 = e3 % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | COMBINE_EQS: (79), (168) imply: % 154.12/23.17 | | | | | | | | | | | | | | (169) all_10_2 = e3 % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | REDUCE: (167), (169) imply: % 154.12/23.17 | | | | | | | | | | | | | | (170) $false % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | (171) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | BETA: splitting (171) gives: % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | (172) all_56_1 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | REF_CLOSE: (120), (139), (172) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | #568. % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | (173) all_56_4 = e3 | all_56_9 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | (174) all_56_4 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (174) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (175) all_52_8 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | SIMP: (175) implies: % 154.12/23.17 | | | | | | | | | | | | | | | | (176) all_52_8 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (176) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (177) all_58_4 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | REDUCE: (3), (176) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (178) ~ (all_52_9 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | SIMP: (178) implies: % 154.12/23.17 | | | | | | | | | | | | | | | | (179) ~ (all_52_9 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | REDUCE: (26), (176) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (180) ~ (all_6_2 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | SIMP: (180) implies: % 154.12/23.17 | | | | | | | | | | | | | | | | (181) ~ (all_6_2 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | (182) all_56_0 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (182) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | (183) all_10_2 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (183) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | (184) all_58_28 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | REDUCE: (106), (183) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | (185) ~ (all_52_1 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | REDUCE: (167), (183) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | (186) ~ (e3 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | REDUCE: (128), (183) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | (187) ~ (e2 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | (188) all_58_28 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (184), (188) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | | #857. % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | (189) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (11), (14), (15), (19), (20), (22), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (24), (27), (28), (29), (32), (34), (36), (41), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (42), (43), (44), (47), (49), (50), (53), (55), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (57), (58), (61), (62), (64), (66), (69), (70), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (75), (76), (78), (80), (81), (84), (86), (88), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (89), (97), (100), (101), (102), (104), (105), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (111), (119), (122), (136), (138), (139), (141), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (143), (148), (162), (174), (177), (179), (181), % 154.12/23.17 | | | | | | | | | | | | | | | | | | (184), (185), (189) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | | #307. % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | (190) ~ (all_56_0 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | REDUCE: (79), (190) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | (191) ~ (all_10_2 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (128), (152), (167), (191) are inconsistent % 154.12/23.17 | | | | | | | | | | | | | | | | | by sub-proof #813. % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | (192) ~ (all_56_4 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | REDUCE: (13), (192) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (193) ~ (all_52_8 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (72), (141), (173), (193) are inconsistent % 154.12/23.17 | | | | | | | | | | | | | | | | by sub-proof #751. % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | (194) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | BETA: splitting (194) gives: % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | (195) all_56_13 = e3 % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | COMBINE_EQS: (23), (195) imply: % 154.12/23.17 | | | | | | | | | | | | | | (196) e3 = e1 % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | REDUCE: (140), (196) imply: % 154.12/23.17 | | | | | | | | | | | | | | (197) $false % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | (198) all_56_14 = e3 | all_56_15 = e3 % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | BETA: splitting (198) gives: % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | (199) all_56_14 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | COMBINE_EQS: (4), (199) imply: % 154.12/23.17 | | | | | | | | | | | | | | | (200) e3 = e0 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | REDUCE: (141), (200) imply: % 154.12/23.17 | | | | | | | | | | | | | | | (201) $false % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent. % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | (202) all_56_15 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | COMBINE_EQS: (6), (202) imply: % 154.12/23.17 | | | | | | | | | | | | | | | (203) all_4_2 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | COMBINE_EQS: (2), (203) imply: % 154.12/23.17 | | | | | | | | | | | | | | | (204) all_58_31 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | BETA: splitting (15) gives: % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | (205) all_58_28 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (205) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (206) all_10_2 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | REDUCE: (128), (206) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | (207) $false % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent. % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | (208) ~ (all_58_28 = e2) % 154.12/23.17 | | | | | | | | | | | | | | | | (209) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | (210) all_58_29 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (76), (210) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | #706. % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | (211) all_58_30 = e2 | all_58_31 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | (212) all_58_30 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (212) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | (213) all_6_2 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | (214) all_58_28 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (214) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | (215) all_10_2 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | REDUCE: (106), (215) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | (216) ~ (all_52_1 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | REDUCE: (10), (215) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | (217) ~ (all_52_8 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | REDUCE: (128), (215) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | (218) ~ (e2 = e1) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | (219) all_54_2 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (217), (219) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | #819. % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | (220) all_54_2 = e3 | all_54_2 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | (221) all_58_28 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (214), (221) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | #857. % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | (222) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (223) all_54_2 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (126), (223) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | #556. % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (224) all_54_2 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (224) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (225) all_52_8 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | SIMP: (225) implies: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (226) all_52_8 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (226) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (227) all_56_4 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (226) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (228) all_58_4 = e3 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (226) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_52_9 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | SIMP: (229) implies: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_52_9 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (226) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_6_2 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | SIMP: (231) implies: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_6_2 = e3) % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (11), (14), (15), (19), (20), (22), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (24), (27), (28), (29), (32), (34), (36), (41), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (42), (43), (44), (47), (49), (50), (53), (55), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (57), (58), (61), (62), (64), (66), (69), (70), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (75), (76), (78), (80), (81), (84), (86), (88), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (89), (97), (100), (101), (102), (104), (105), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (111), (119), (122), (136), (138), (139), (141), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (143), (148), (162), (214), (216), (222), (227), % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | (228), (230), (232) are inconsistent by sub-proof % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | #307. % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | (233) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (58), (92), (140), (204), (212), (233) are % 154.12/23.17 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #357. % 154.12/23.17 | | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | Case 2: % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | (234) all_58_31 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (234) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | (235) e3 = e2 % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | REDUCE: (139), (235) imply: % 154.12/23.17 | | | | | | | | | | | | | | | | | | (236) $false % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 154.12/23.17 | | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | | % 154.12/23.17 | | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | | % 154.12/23.17 | | | | | | | | | End of split % 154.12/23.17 | | | | | | | | | % 154.12/23.17 | | | | | | | | End of split % 154.12/23.17 | | | | | | | | % 154.12/23.17 | | | | | | | End of split % 154.12/23.17 | | | | | | | % 154.12/23.17 | | | | | | End of split % 154.12/23.17 | | | | | | % 154.12/23.17 | | | | | End of split % 154.12/23.17 | | | | | % 154.12/23.17 | | | | Case 2: % 154.12/23.17 | | | | | % 154.12/23.17 | | | | | (237) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.12/23.17 | | | | | % 154.12/23.17 | | | | | BETA: splitting (114) gives: % 154.12/23.17 | | | | | % 154.12/23.17 | | | | | Case 1: % 154.12/23.17 | | | | | | % 154.12/23.17 | | | | | | (238) all_54_1 = e1 % 154.12/23.17 | | | | | | % 154.12/23.17 | | | | | | REF_CLOSE: (16), (56), (238) are inconsistent by sub-proof #741. % 154.12/23.17 | | | | | | % 154.12/23.17 | | | | | Case 2: % 154.12/23.17 | | | | | | % 154.17/23.17 | | | | | | (239) ~ (all_54_1 = e1) % 154.17/23.17 | | | | | | (240) all_54_1 = e3 | all_54_1 = e2 % 154.17/23.17 | | | | | | % 154.17/23.17 | | | | | | BETA: splitting (237) gives: % 154.17/23.17 | | | | | | % 154.17/23.17 | | | | | | Case 1: % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | (241) all_56_3 = e2 % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | COMBINE_EQS: (11), (241) imply: % 154.17/23.17 | | | | | | | (242) e2 = e0 % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | SIMP: (242) implies: % 154.17/23.17 | | | | | | | (243) e2 = e0 % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | REDUCE: (76), (243) imply: % 154.17/23.17 | | | | | | | (244) $false % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | CLOSE: (244) is inconsistent. % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | Case 2: % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | (245) all_56_7 = e2 | all_56_13 = e2 % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | BETA: splitting (245) gives: % 154.17/23.17 | | | | | | | % 154.17/23.17 | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | (246) all_56_7 = e2 % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | COMBINE_EQS: (7), (246) imply: % 154.17/23.17 | | | | | | | | (247) all_52_6 = e2 % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | SIMP: (247) implies: % 154.17/23.17 | | | | | | | | (248) all_52_6 = e2 % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | COMBINE_EQS: (74), (248) imply: % 154.17/23.17 | | | | | | | | (249) all_58_17 = e2 % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | REDUCE: (18), (248) imply: % 154.17/23.17 | | | | | | | | (250) ~ (all_52_4 = e2) % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | REDUCE: (8), (248) imply: % 154.17/23.17 | | | | | | | | (251) ~ (all_6_2 = e2) % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | SIMP: (251) implies: % 154.17/23.17 | | | | | | | | (252) ~ (all_6_2 = e2) % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | BETA: splitting (37) gives: % 154.17/23.17 | | | | | | | | % 154.17/23.17 | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | (253) all_56_1 = e3 % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | COMBINE_EQS: (46), (253) imply: % 154.17/23.17 | | | | | | | | | (254) all_52_4 = e3 % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | COMBINE_EQS: (45), (254) imply: % 154.17/23.17 | | | | | | | | | (255) all_58_2 = e3 % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | REDUCE: (99), (254) imply: % 154.17/23.17 | | | | | | | | | (256) ~ (all_10_2 = e3) % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | SIMP: (256) implies: % 154.17/23.17 | | | | | | | | | (257) ~ (all_10_2 = e3) % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | REDUCE: (250), (254) imply: % 154.17/23.17 | | | | | | | | | (258) ~ (e3 = e2) % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | REDUCE: (56), (254) imply: % 154.17/23.17 | | | | | | | | | (259) ~ (e3 = e1) % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | REDUCE: (65), (254) imply: % 154.17/23.17 | | | | | | | | | (260) ~ (e3 = e0) % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | BETA: splitting (31) gives: % 154.17/23.17 | | | | | | | | | % 154.17/23.17 | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | (261) all_54_11 = e0 % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | COMBINE_EQS: (22), (261) imply: % 154.17/23.17 | | | | | | | | | | (262) all_52_14 = e0 % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | REDUCE: (94), (262) imply: % 154.17/23.17 | | | | | | | | | | (263) $false % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | CLOSE: (263) is inconsistent. % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | (264) ~ (all_54_11 = e0) % 154.17/23.17 | | | | | | | | | | (265) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | BETA: splitting (40) gives: % 154.17/23.17 | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | (266) all_54_0 = e0 % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | REF_CLOSE: (15), (55), (58), (71), (76), (88), (90), (92), % 154.17/23.17 | | | | | | | | | | | (100), (101), (258), (259), (260), (266) are % 154.17/23.17 | | | | | | | | | | | inconsistent by sub-proof #395. % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | (267) ~ (all_54_0 = e0) % 154.17/23.17 | | | | | | | | | | | (268) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | REDUCE: (90), (267) imply: % 154.17/23.17 | | | | | | | | | | | (269) ~ (all_10_2 = e0) % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | BETA: splitting (52) gives: % 154.17/23.17 | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | (270) all_56_12 = e3 % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | COMBINE_EQS: (44), (270) imply: % 154.17/23.17 | | | | | | | | | | | | (271) all_52_3 = e3 % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | SIMP: (271) implies: % 154.17/23.17 | | | | | | | | | | | | (272) all_52_3 = e3 % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | COMBINE_EQS: (81), (272) imply: % 154.17/23.17 | | | | | | | | | | | | (273) all_58_22 = e3 % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | REDUCE: (70), (272) imply: % 154.17/23.17 | | | | | | | | | | | | (274) ~ (all_52_1 = e3) % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | REDUCE: (49), (272) imply: % 154.17/23.17 | | | | | | | | | | | | (275) ~ (all_4_2 = e3) % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | SIMP: (275) implies: % 154.17/23.17 | | | | | | | | | | | | (276) ~ (all_4_2 = e3) % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | BETA: splitting (86) gives: % 154.17/23.17 | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | (277) all_56_12 = e2 % 154.17/23.17 | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | REF_CLOSE: (258), (270), (277) are inconsistent by sub-proof % 154.17/23.17 | | | | | | | | | | | | | #588. % 154.17/23.17 | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | (278) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.17/23.17 | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | BETA: splitting (278) gives: % 154.17/23.17 | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | (279) all_56_13 = e2 % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | COMBINE_EQS: (23), (279) imply: % 154.17/23.17 | | | | | | | | | | | | | | (280) e2 = e1 % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | REDUCE: (58), (280) imply: % 154.17/23.17 | | | | | | | | | | | | | | (281) $false % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | (282) all_56_14 = e2 | all_56_15 = e2 % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | BETA: splitting (88) gives: % 154.17/23.17 | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | (283) all_58_28 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (283) imply: % 154.17/23.17 | | | | | | | | | | | | | | | (284) all_10_2 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | REDUCE: (257), (284) imply: % 154.17/23.17 | | | | | | | | | | | | | | | (285) $false % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent. % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | (286) ~ (all_58_28 = e3) % 154.17/23.17 | | | | | | | | | | | | | | | (287) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 154.17/23.17 | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | (288) all_56_14 = e2 % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (288) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | (289) e2 = e0 % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | REDUCE: (76), (289) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | (290) $false % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | (291) all_56_15 = e2 % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (291) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | (292) all_4_2 = e2 % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | SIMP: (292) implies: % 154.17/23.17 | | | | | | | | | | | | | | | | (293) all_4_2 = e2 % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (293) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | (294) all_58_31 = e2 % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | REDUCE: (91), (293) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | (295) ~ (all_52_14 = e2) % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | REDUCE: (276), (293) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | (296) ~ (e3 = e2) % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 154.17/23.17 | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | (297) all_58_29 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (260), (297) are inconsistent by sub-proof % 154.17/23.17 | | | | | | | | | | | | | | | | | #707. % 154.17/23.17 | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | (298) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 154.17/23.17 | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | (299) all_58_30 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (299) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | (300) all_6_2 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | REDUCE: (26), (300) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | (301) ~ (all_52_8 = e3) % 154.17/23.17 | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | REDUCE: (102), (300) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | (302) ~ (all_52_14 = e3) % 154.17/23.17 | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 154.17/23.17 | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | (303) all_58_28 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (303) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | (304) all_10_2 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (305) all_56_9 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (305) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (306) e3 = e0 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (306) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (307) all_58_30 = e0 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (55), (58), (76), (258), (260), (287), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (303), (307) are inconsistent by sub-proof #702. % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (308) ~ (all_56_9 = e3) % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (309) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (308) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | (310) ~ (e3 = e0) % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (311) all_54_11 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (311) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (312) all_52_14 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (313) all_52_14 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (313) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (314) all_58_20 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (313) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (315) ~ (all_52_13 = e1) % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (313) imply: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (316) ~ (e3 = e1) % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (10), (11), (12), (13), (15), (19), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (20), (34), (39), (41), (42), (43), (47), (50), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (53), (55), (57), (61), (62), (64), (66), (69), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (71), (76), (84), (87), (88), (90), (92), (95), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (98), (100), (101), (103), (105), (106), (119), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (249), (255), (257), (258), (259), (260), (268), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (269), (273), (274), (294), (298), (299), (301), % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (309), (314), (315) are inconsistent by sub-proof % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | #296. % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | (317) all_54_11 = e3 | all_54_11 = e2 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (295), (302), (317) are inconsistent by % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | sub-proof #775. % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.17 | | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.17 | | | | | | | | | | | | | | | | | | | (318) ~ (all_58_28 = e1) % 154.17/23.17 | | | | | | | | | | | | | | | | | | | (319) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.17 | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (55), (71), (88), (90), (92), (100), (257), % 154.17/23.18 | | | | | | | | | | | | | | | | | | | (259), (260), (268), (269), (294), (298), (318), % 154.17/23.18 | | | | | | | | | | | | | | | | | | | (319) are inconsistent by sub-proof #297. % 154.17/23.18 | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | (320) all_58_31 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (294), (320) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | | | | | | | | | #585. % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | (321) ~ (all_56_12 = e3) % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | REDUCE: (44), (321) imply: % 154.17/23.18 | | | | | | | | | | | | (322) ~ (all_52_3 = e3) % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | BETA: splitting (48) gives: % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | (323) all_56_0 = e3 % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | COMBINE_EQS: (79), (323) imply: % 154.17/23.18 | | | | | | | | | | | | | (324) all_10_2 = e3 % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | REDUCE: (257), (324) imply: % 154.17/23.18 | | | | | | | | | | | | | (325) $false % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | CLOSE: (325) is inconsistent. % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | (326) ~ (all_56_0 = e3) % 154.17/23.18 | | | | | | | | | | | | | (327) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | BETA: splitting (327) gives: % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | (328) all_56_2 = e3 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | COMBINE_EQS: (66), (328) imply: % 154.17/23.18 | | | | | | | | | | | | | | (329) all_52_1 = e3 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | REDUCE: (70), (329) imply: % 154.17/23.18 | | | | | | | | | | | | | | (330) ~ (all_52_3 = e3) % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | BETA: splitting (21) gives: % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | (331) all_56_0 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | COMBINE_EQS: (79), (331) imply: % 154.17/23.18 | | | | | | | | | | | | | | | (332) all_10_2 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (332) imply: % 154.17/23.18 | | | | | | | | | | | | | | | (333) all_58_28 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | BETA: splitting (15) gives: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | (334) all_58_28 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | REF_CLOSE: (58), (333), (334) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | | | | | | | #856. % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | (335) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | (336) all_58_29 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (76), (336) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | | | | | | | | #706. % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | (337) all_58_30 = e2 | all_58_31 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | BETA: splitting (337) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | (338) all_58_30 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (338) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | (339) all_6_2 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | REDUCE: (252), (339) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | (340) $false % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | (341) all_58_31 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (341) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | (342) all_4_2 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | REDUCE: (49), (342) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | (343) ~ (all_52_3 = e2) % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (104), (111), (322), (343) are inconsistent % 154.17/23.18 | | | | | | | | | | | | | | | | | | by sub-proof #557. % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | (344) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | BETA: splitting (344) gives: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | (345) all_56_2 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (345) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | (346) e3 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | REDUCE: (259), (346) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | (347) $false % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | CLOSE: (347) is inconsistent. % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | (348) all_56_6 = e1 | all_56_12 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (27), (44), (92), (348) are inconsistent by % 154.17/23.18 | | | | | | | | | | | | | | | | sub-proof #807. % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | (349) ~ (all_56_2 = e3) % 154.17/23.18 | | | | | | | | | | | | | | (350) all_56_6 = e3 | all_56_12 = e3 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | REF_CLOSE: (14), (44), (66), (70), (82), (90), (104), (105), % 154.17/23.18 | | | | | | | | | | | | | | (106), (111), (119), (257), (259), (260), (268), % 154.17/23.18 | | | | | | | | | | | | | | (322), (349), (350) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | | | | | #744. % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | End of split % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | (351) ~ (all_56_1 = e3) % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | REDUCE: (46), (351) imply: % 154.17/23.18 | | | | | | | | | (352) ~ (all_52_4 = e3) % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | REF_CLOSE: (16), (240), (250), (352) are inconsistent by % 154.17/23.18 | | | | | | | | | sub-proof #722. % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | End of split % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | (353) all_56_13 = e2 % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | COMBINE_EQS: (23), (353) imply: % 154.17/23.18 | | | | | | | | (354) e2 = e1 % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | REDUCE: (58), (354) imply: % 154.17/23.18 | | | | | | | | (355) $false % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | CLOSE: (355) is inconsistent. % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | End of split % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | End of split % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | End of split % 154.17/23.18 | | | | | % 154.17/23.18 | | | | End of split % 154.17/23.18 | | | | % 154.17/23.18 | | | End of split % 154.17/23.18 | | | % 154.17/23.18 | | End of split % 154.17/23.18 | | % 154.17/23.18 | End of split % 154.17/23.18 | % 154.17/23.18 End of proof % 154.17/23.18 % 154.17/23.18 Sub-proof #296 shows that the following formulas are inconsistent: % 154.17/23.18 ---------------------------------------------------------------- % 154.17/23.18 (1) ~ (all_52_8 = all_52_9) % 154.17/23.18 (2) all_58_11 = all_52_9 % 154.17/23.18 (3) all_58_31 = e2 % 154.17/23.18 (4) all_54_2 = all_52_8 % 154.17/23.18 (5) ~ (all_52_13 = e1) % 154.17/23.18 (6) ~ (all_52_8 = all_10_2) % 154.17/23.18 (7) all_56_3 = e0 % 154.17/23.18 (8) all_54_7 = all_52_13 % 154.17/23.18 (9) ~ (all_52_1 = e3) % 154.17/23.18 (10) all_56_4 = all_52_8 % 154.17/23.18 (11) all_58_30 = e3 % 154.17/23.18 (12) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.18 (13) all_58_13 = all_52_13 % 154.17/23.18 (14) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.17/23.18 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.17/23.18 (16) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.17/23.18 (17) ~ (all_10_2 = e0) % 154.17/23.18 (18) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.17/23.18 (19) ~ (all_10_2 = e3) % 154.17/23.18 (20) ~ (e3 = e1) % 154.17/23.18 (21) ~ (all_52_8 = e3) % 154.17/23.18 (22) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.17/23.18 (23) all_58_6 = e0 % 154.17/23.18 (24) ~ (all_52_1 = all_52_13) % 154.17/23.18 (25) all_56_5 = all_52_9 % 154.17/23.18 (26) ~ (all_52_13 = e0) % 154.17/23.18 (27) ~ (all_52_9 = e0) % 154.17/23.18 (28) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.17/23.18 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.17/23.18 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.17/23.18 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.17/23.18 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.17/23.18 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.17/23.18 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.17/23.18 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.17/23.18 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.17/23.18 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.17/23.18 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.17/23.18 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.17/23.18 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.17/23.18 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.18 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.18 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.18 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.18 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.17/23.18 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.18 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.18 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.18 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.17/23.18 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.18 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.18 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.18 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.17/23.18 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.17/23.18 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.17/23.18 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.17/23.18 e0) % 154.17/23.18 (29) all_58_29 = e0 % 154.17/23.18 (30) all_58_8 = all_52_1 % 154.17/23.18 (31) all_58_26 = e0 % 154.17/23.18 (32) all_58_15 = e0 % 154.17/23.18 (33) ~ (all_52_9 = all_52_13) % 154.17/23.18 (34) ~ (e3 = e0) % 154.17/23.18 (35) all_56_2 = all_52_1 % 154.17/23.18 (36) all_56_10 = all_52_13 % 154.17/23.18 (37) all_58_28 = all_10_2 % 154.17/23.18 (38) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.18 (39) ~ (e2 = e0) % 154.17/23.18 (40) all_58_2 = e3 % 154.17/23.18 (41) all_58_24 = e1 % 154.17/23.18 (42) all_58_17 = e2 % 154.17/23.18 (43) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.17/23.18 (44) all_58_4 = all_52_8 % 154.17/23.18 (45) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.18 (46) all_54_0 = all_10_2 % 154.17/23.18 (47) ~ (e1 = e0) % 154.17/23.18 (48) all_58_20 = e1 % 154.17/23.18 (49) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 154.17/23.18 (50) ~ (all_52_8 = e0) % 154.17/23.18 (51) all_58_30 = all_6_2 % 154.17/23.18 (52) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.18 (53) ~ (e3 = e2) % 154.17/23.18 (54) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 154.17/23.18 (55) all_58_22 = e3 % 154.17/23.18 (56) all_54_4 = all_52_1 % 154.17/23.18 (57) ~ (all_52_1 = all_10_2) % 154.17/23.18 % 154.17/23.18 Begin of proof % 154.17/23.18 | % 154.17/23.18 | BETA: splitting (54) gives: % 154.17/23.18 | % 154.17/23.18 | Case 1: % 154.17/23.18 | | % 154.17/23.18 | | (58) all_54_7 = e0 % 154.17/23.18 | | % 154.17/23.18 | | COMBINE_EQS: (8), (58) imply: % 154.17/23.18 | | (59) all_52_13 = e0 % 154.17/23.18 | | % 154.17/23.18 | | REDUCE: (26), (59) imply: % 154.17/23.18 | | (60) $false % 154.17/23.18 | | % 154.17/23.18 | | CLOSE: (60) is inconsistent. % 154.17/23.18 | | % 154.17/23.18 | Case 2: % 154.17/23.18 | | % 154.17/23.18 | | (61) ~ (all_54_7 = e0) % 154.17/23.18 | | (62) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.17/23.18 | | % 154.17/23.18 | | BETA: splitting (52) gives: % 154.17/23.18 | | % 154.17/23.18 | | Case 1: % 154.17/23.18 | | | % 154.17/23.18 | | | (63) all_58_28 = e1 % 154.17/23.18 | | | % 154.17/23.18 | | | COMBINE_EQS: (37), (63) imply: % 154.17/23.18 | | | (64) all_10_2 = e1 % 154.17/23.18 | | | % 154.17/23.18 | | | REDUCE: (57), (64) imply: % 154.17/23.18 | | | (65) ~ (all_52_1 = e1) % 154.17/23.18 | | | % 154.17/23.18 | | | REDUCE: (6), (64) imply: % 154.17/23.18 | | | (66) ~ (all_52_8 = e1) % 154.17/23.18 | | | % 154.17/23.18 | | | REDUCE: (19), (64) imply: % 154.17/23.18 | | | (67) ~ (e3 = e1) % 154.17/23.18 | | | % 154.17/23.18 | | | BETA: splitting (49) gives: % 154.17/23.18 | | | % 154.17/23.18 | | | Case 1: % 154.17/23.18 | | | | % 154.17/23.18 | | | | (68) all_54_2 = e0 % 154.17/23.18 | | | | % 154.17/23.18 | | | | REF_CLOSE: (4), (50), (68) are inconsistent by sub-proof #860. % 154.17/23.18 | | | | % 154.17/23.18 | | | Case 2: % 154.17/23.18 | | | | % 154.17/23.18 | | | | (69) ~ (all_54_2 = e0) % 154.17/23.18 | | | | (70) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.17/23.18 | | | | % 154.17/23.18 | | | | BETA: splitting (28) gives: % 154.17/23.18 | | | | % 154.17/23.18 | | | | Case 1: % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | (71) all_58_31 = e0 % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | COMBINE_EQS: (3), (71) imply: % 154.17/23.18 | | | | | (72) e2 = e0 % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | REDUCE: (39), (72) imply: % 154.17/23.18 | | | | | (73) $false % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | CLOSE: (73) is inconsistent. % 154.17/23.18 | | | | | % 154.17/23.18 | | | | Case 2: % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | (74) ~ (all_58_31 = e0) % 154.17/23.18 | | | | | (75) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = % 154.17/23.18 | | | | | e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.17/23.18 | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.17/23.18 | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.17/23.18 | | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 % 154.17/23.18 | | | | | = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.17/23.18 | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 % 154.17/23.18 | | | | | = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.18 | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 % 154.17/23.18 | | | | | = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.17/23.18 | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.17/23.18 | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 % 154.17/23.18 | | | | | = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.17/23.18 | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.17/23.18 | | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.17/23.18 | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.18 | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 154.17/23.18 | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.18 | | | | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.17/23.18 | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.17/23.18 | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = % 154.17/23.18 | | | | | e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.18 | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.17/23.18 | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.17/23.18 | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 % 154.17/23.18 | | | | | & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 154.17/23.18 | | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.18 | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.17/23.18 | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.17/23.18 | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.17/23.18 | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.17/23.18 | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.17/23.18 | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.17/23.18 | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 % 154.17/23.18 | | | | | & e1 = e0) % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | BETA: splitting (75) gives: % 154.17/23.18 | | | | | % 154.17/23.18 | | | | | Case 1: % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | | (76) all_58_30 = e1 % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | | REF_CLOSE: (3), (20), (29), (34), (45), (53), (63), (76) are % 154.17/23.18 | | | | | | inconsistent by sub-proof #355. % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | Case 2: % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | | (77) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 % 154.17/23.18 | | | | | | = e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 154.17/23.18 | | | | | | all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.17/23.18 | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.18 | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.18 | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.17/23.18 | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.17/23.18 | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.17/23.18 | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.17/23.18 | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.18 | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 154.17/23.18 | | | | | | e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.17/23.18 | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.17/23.18 | | | | | | all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & % 154.17/23.18 | | | | | | all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.18 | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.18 | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.17/23.18 | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.18 | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 154.17/23.18 | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = % 154.17/23.18 | | | | | | e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & % 154.17/23.18 | | | | | | all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.17/23.18 | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.17/23.18 | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.18 | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.17/23.18 | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.17/23.18 | | | | | | all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.17/23.18 | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.17/23.18 | | | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.18 | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.17/23.18 | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.17/23.18 | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.17/23.18 | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.17/23.18 | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.17/23.18 | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.17/23.18 | | | | | | e0 & e1 = e0) % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | | BETA: splitting (77) gives: % 154.17/23.18 | | | | | | % 154.17/23.18 | | | | | | Case 1: % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | (78) all_58_29 = e2 % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | COMBINE_EQS: (29), (78) imply: % 154.17/23.18 | | | | | | | (79) e2 = e0 % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | REDUCE: (39), (79) imply: % 154.17/23.18 | | | | | | | (80) $false % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | CLOSE: (80) is inconsistent. % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | Case 2: % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | (81) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 % 154.17/23.18 | | | | | | | = e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.18 | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.17/23.18 | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.17/23.18 | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.18 | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.17/23.18 | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.17/23.18 | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.17/23.18 | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.17/23.18 | | | | | | | all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.17/23.18 | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.17/23.18 | | | | | | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.17/23.18 | | | | | | | e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 154.17/23.18 | | | | | | | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.17/23.18 | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.18 | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.17/23.18 | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.17/23.18 | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.17/23.18 | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.17/23.18 | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.17/23.18 | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.18 | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.17/23.18 | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & % 154.17/23.18 | | | | | | | all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.17/23.18 | | | | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.18 | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.17/23.18 | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.18 | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.17/23.18 | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.17/23.18 | | | | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.18 | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.17/23.18 | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 % 154.17/23.18 | | | | | | | = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = % 154.17/23.18 | | | | | | | e2 & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 % 154.17/23.18 | | | | | | | & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.17/23.18 | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 % 154.17/23.18 | | | | | | | = e0 & e1 = e0) % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | BETA: splitting (22) gives: % 154.17/23.18 | | | | | | | % 154.17/23.18 | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | (82) all_56_2 = e1 % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | COMBINE_EQS: (35), (82) imply: % 154.17/23.18 | | | | | | | | (83) all_52_1 = e1 % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | REDUCE: (65), (83) imply: % 154.17/23.18 | | | | | | | | (84) $false % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | CLOSE: (84) is inconsistent. % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | (85) ~ (all_56_2 = e1) % 154.17/23.18 | | | | | | | | (86) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | BETA: splitting (16) gives: % 154.17/23.18 | | | | | | | | % 154.17/23.18 | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | (87) all_54_4 = e1 % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | REF_CLOSE: (56), (65), (87) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | #832. % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | (88) all_54_4 = e3 | all_54_4 = e2 % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | BETA: splitting (70) gives: % 154.17/23.18 | | | | | | | | | % 154.17/23.18 | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | (89) all_54_2 = e1 % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | REF_CLOSE: (4), (66), (89) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | #819. % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | (90) all_54_2 = e3 | all_54_2 = e2 % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | BETA: splitting (86) gives: % 154.17/23.18 | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | (91) all_56_3 = e1 % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | REF_CLOSE: (7), (47), (91) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | | #306. % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | (92) all_56_5 = e1 | all_56_10 = e1 % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | BETA: splitting (92) gives: % 154.17/23.18 | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | (93) all_56_5 = e1 % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | COMBINE_EQS: (25), (93) imply: % 154.17/23.18 | | | | | | | | | | | | (94) all_52_9 = e1 % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | COMBINE_EQS: (2), (94) imply: % 154.17/23.18 | | | | | | | | | | | | (95) all_58_11 = e1 % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | REDUCE: (33), (94) imply: % 154.17/23.18 | | | | | | | | | | | | (96) ~ (all_52_13 = e1) % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | BETA: splitting (18) gives: % 154.17/23.18 | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | (97) all_56_2 = e2 % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | COMBINE_EQS: (35), (97) imply: % 154.17/23.18 | | | | | | | | | | | | | (98) all_52_1 = e2 % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | COMBINE_EQS: (30), (98) imply: % 154.17/23.18 | | | | | | | | | | | | | (99) all_58_8 = e2 % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | REDUCE: (24), (98) imply: % 154.17/23.18 | | | | | | | | | | | | | (100) ~ (all_52_13 = e2) % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | SIMP: (100) implies: % 154.17/23.18 | | | | | | | | | | | | | (101) ~ (all_52_13 = e2) % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | BETA: splitting (14) gives: % 154.17/23.18 | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | (102) all_56_4 = e2 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | COMBINE_EQS: (10), (102) imply: % 154.17/23.18 | | | | | | | | | | | | | | (103) all_52_8 = e2 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | SIMP: (103) implies: % 154.17/23.18 | | | | | | | | | | | | | | (104) all_52_8 = e2 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | COMBINE_EQS: (44), (104) imply: % 154.17/23.18 | | | | | | | | | | | | | | (105) all_58_4 = e2 % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | REDUCE: (66), (104) imply: % 154.17/23.18 | | | | | | | | | | | | | | (106) ~ (e2 = e1) % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | BETA: splitting (62) gives: % 154.17/23.18 | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | (107) all_54_7 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (107) are inconsistent by sub-proof % 154.17/23.18 | | | | | | | | | | | | | | | #605. % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | (108) ~ (all_54_7 = e1) % 154.17/23.18 | | | | | | | | | | | | | | | (109) all_54_7 = e3 | all_54_7 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 154.17/23.18 | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | (110) all_56_10 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (110) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | (111) all_52_13 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | SIMP: (111) implies: % 154.17/23.18 | | | | | | | | | | | | | | | | (112) all_52_13 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (112) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | (113) all_58_13 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | (114) all_58_28 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (114) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | (115) e3 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (115) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | (116) all_58_30 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (20), (29), (34), (45), (53), (63), (116) are % 154.17/23.18 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #355. % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | (117) ~ (all_58_28 = e3) % 154.17/23.18 | | | | | | | | | | | | | | | | | (118) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.18 | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.17/23.18 | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.17/23.18 | | | | | | | | | | | | | | | | | e0) % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | (119) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.18 | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.17/23.18 | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.18 | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.18 | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.18 | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.18 | | | | | | | | | | | | | | | | | | = e0) % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | (120) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.18 | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | (121) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | = e2) % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | (122) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | (123) all_58_15 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (123) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | (124) e1 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (124) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | (125) all_56_5 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (125) are inconsistent by % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | (126) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (127) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (128) all_58_22 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (129) all_58_8 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (129) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (130) e3 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (128) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (131) e3 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | SIMP: (131) implies: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (132) e3 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (132) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (133) e2 = e0 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (133) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (134) $false % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (134) is inconsistent. % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (135) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (136) all_58_11 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (137) all_58_8 = e3 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (137) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (138) e3 = e2 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (136) imply: % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | (139) e2 = e1 % 154.17/23.18 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (139) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (140) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (20), (29), (34), (45), (53), (63), % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (138), (140) are inconsistent by sub-proof #303. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (141) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (142) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (143) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (144) all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (145) all_58_13 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (145) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (146) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (146) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (147) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (144) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (148) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (20), (29), (34), (45), (53), (63), % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (147), (148) are inconsistent by sub-proof #303. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (149) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (150) all_58_15 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (151) all_58_4 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (151) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (152) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (150) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (153) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (153) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (154) e2 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (154) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (155) $false % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (156) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (157) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (158) all_58_6 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (159) all_58_2 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (159) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (160) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (158) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (161) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (161) are inconsistent by sub-proof % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | #302. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (162) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (163) all_58_17 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (164) all_58_2 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (164) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (165) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (163) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (166) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (166) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (167) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (20), (29), (34), (45), (53), (63), % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (165), (167) are inconsistent by sub-proof #303. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (168) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (169) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (170) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (171) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (172) all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (41), (47), (92), (93), (172) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #301. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (173) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (174) all_58_2 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (174) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (175) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (175) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (176) all_58_30 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (38), (53), (176) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #476. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (177) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (178) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (179) all_58_22 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (180) all_58_4 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (180) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (181) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (179) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (182) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (182) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (183) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (181), (183) are inconsistent by sub-proof % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | #302. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (184) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (185) all_58_17 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (186) all_58_15 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (187) all_58_4 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (187) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (188) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (186) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (189) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (185) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (190) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (190) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (191) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (189) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (192) e2 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (192) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (193) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (193) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (194) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (194) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (195) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (196) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (197) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (198) all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (198) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (199) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (199) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (200) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (200) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (201) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (202) all_58_15 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (202) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (203) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (203) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (204) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (204) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (205) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (206) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (207) all_58_15 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (207) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (208) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (208) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (209) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (209) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (210) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (211) all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (48), (92), (93), (211) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (212) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.17/23.19 | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (213) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (214) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (215) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (216) all_58_15 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (216) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (217) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (217) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (218) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (218) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (219) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (220) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (221) all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (41), (47), (92), (93), (221) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #301. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (222) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (223) all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (48), (92), (93), (223) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (224) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (225) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (226) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (227) all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (228) all_58_22 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (229) all_58_13 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (229) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (230) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (231) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (228) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (232) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (233) e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (227) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (234) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (233) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (235) e2 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (236) e2 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (234), (236) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (237) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (237) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (238) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (238) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (239) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (240) all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (240) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (241) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (241) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (242) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (242) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (243) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (244) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (245) all_58_22 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (55), (245) are inconsistent by sub-proof % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | #299. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (246) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (247) all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (247) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (248) e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (248) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (249) all_56_5 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (92), (249) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #304. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (250) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.17/23.19 | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (251) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (252) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (253) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (254) all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (31), (36), (47), (92), (93), (254) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (255) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (256) all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (257) all_58_13 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (257) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (258) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (258) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (259) e3 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (256) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (260) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (260) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (261) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (20), (29), (34), (45), (53), (63), % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (259), (261) are inconsistent by sub-proof #303. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (262) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (263) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (264) all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (48), (92), (93), (264) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (265) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (266) all_58_17 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (266) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (267) e2 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (20), (29), (34), (39), (45), (51), % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (53), (63), (106), (267) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #354. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (268) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (269) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (270) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (271) all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (48), (92), (93), (271) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (272) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (273) all_58_26 = e1 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (31), (36), (47), (92), (93), (273) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (274) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (275) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (276) all_58_24 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (41), (47), (92), (93), (276) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #301. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (277) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies: % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | (278) all_58_20 = e0 % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (47), (48), (92), (93), (278) are % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #300. % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | (279) ~ (all_56_10 = e3) % 154.17/23.19 | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | REDUCE: (36), (279) imply: % 154.17/23.19 | | | | | | | | | | | | | | | | (280) ~ (all_52_13 = e3) % 154.17/23.19 | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (101), (109), (280) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | | | | sub-proof #511. % 154.17/23.19 | | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | (281) ~ (all_56_4 = e2) % 154.17/23.19 | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | REDUCE: (10), (281) imply: % 154.17/23.19 | | | | | | | | | | | | | | (282) ~ (all_52_8 = e2) % 154.17/23.19 | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | BETA: splitting (90) gives: % 154.17/23.19 | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | Case 1: % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | (283) all_54_2 = e2 % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | REF_CLOSE: (4), (282), (283) are inconsistent by sub-proof % 154.17/23.19 | | | | | | | | | | | | | | | #556. % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | (284) all_54_2 = e3 % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (284) are inconsistent by sub-proof % 154.17/23.19 | | | | | | | | | | | | | | | #816. % 154.17/23.19 | | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | (285) ~ (all_56_2 = e2) % 154.17/23.19 | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | REDUCE: (35), (285) imply: % 154.17/23.19 | | | | | | | | | | | | | (286) ~ (all_52_1 = e2) % 154.17/23.19 | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | | REF_CLOSE: (9), (56), (88), (286) are inconsistent by % 154.17/23.19 | | | | | | | | | | | | | sub-proof #329. % 154.17/23.19 | | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | Case 2: % 154.17/23.19 | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | (287) all_56_10 = e1 % 154.17/23.19 | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | | REF_CLOSE: (5), (36), (287) are inconsistent by sub-proof % 154.17/23.19 | | | | | | | | | | | | #606. % 154.17/23.19 | | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | | % 154.17/23.19 | | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | | % 154.17/23.19 | | | | | | | | | End of split % 154.17/23.19 | | | | | | | | | % 154.17/23.19 | | | | | | | | End of split % 154.17/23.19 | | | | | | | | % 154.17/23.19 | | | | | | | End of split % 154.17/23.19 | | | | | | | % 154.17/23.19 | | | | | | End of split % 154.17/23.19 | | | | | | % 154.17/23.19 | | | | | End of split % 154.17/23.19 | | | | | % 154.17/23.19 | | | | End of split % 154.17/23.19 | | | | % 154.17/23.19 | | | End of split % 154.17/23.19 | | | % 154.17/23.19 | | Case 2: % 154.17/23.19 | | | % 154.17/23.19 | | | (288) ~ (all_58_28 = e1) % 154.17/23.19 | | | (289) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.19 | | | % 154.17/23.19 | | | REF_CLOSE: (3), (12), (15), (17), (19), (20), (29), (34), (37), (38), % 154.17/23.19 | | | (45), (46), (47), (51), (288), (289) are inconsistent by % 154.17/23.19 | | | sub-proof #297. % 154.17/23.19 | | | % 154.17/23.19 | | End of split % 154.17/23.19 | | % 154.17/23.19 | End of split % 154.17/23.19 | % 154.17/23.19 End of proof % 154.17/23.19 % 154.17/23.19 Sub-proof #297 shows that the following formulas are inconsistent: % 154.17/23.19 ---------------------------------------------------------------- % 154.17/23.19 (1) all_58_31 = e2 % 154.17/23.19 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.19 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.17/23.19 (4) ~ (all_10_2 = e0) % 154.17/23.19 (5) ~ (all_10_2 = e3) % 154.17/23.19 (6) ~ (e3 = e1) % 154.17/23.19 (7) ~ (all_58_28 = e1) % 154.17/23.19 (8) all_58_29 = e0 % 154.17/23.19 (9) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.19 (10) ~ (e3 = e0) % 154.17/23.19 (11) all_58_28 = all_10_2 % 154.17/23.19 (12) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.19 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.19 (14) all_54_0 = all_10_2 % 154.17/23.19 (15) ~ (e1 = e0) % 154.17/23.19 (16) all_58_30 = all_6_2 % 154.17/23.19 % 154.17/23.19 Begin of proof % 154.17/23.19 | % 154.17/23.19 | REDUCE: (7), (11) imply: % 154.17/23.19 | (17) ~ (all_10_2 = e1) % 154.17/23.19 | % 154.17/23.19 | BETA: splitting (3) gives: % 154.17/23.19 | % 154.17/23.19 | Case 1: % 154.17/23.19 | | % 154.17/23.19 | | (18) all_54_0 = e1 % 154.17/23.19 | | % 154.17/23.19 | | REF_CLOSE: (14), (17), (18) are inconsistent by sub-proof #841. % 154.17/23.19 | | % 154.17/23.19 | Case 2: % 154.17/23.19 | | % 154.17/23.19 | | (19) ~ (all_54_0 = e1) % 154.17/23.19 | | (20) all_54_0 = e3 | all_54_0 = e2 % 154.17/23.19 | | % 154.17/23.19 | | BETA: splitting (9) gives: % 154.17/23.19 | | % 154.17/23.19 | | Case 1: % 154.17/23.19 | | | % 154.17/23.19 | | | (21) all_58_29 = e1 % 154.17/23.19 | | | % 154.17/23.19 | | | REF_CLOSE: (8), (15), (21) are inconsistent by sub-proof #700. % 154.17/23.19 | | | % 154.17/23.19 | | Case 2: % 154.17/23.19 | | | % 154.17/23.19 | | | (22) all_58_30 = e1 | all_58_31 = e1 % 154.17/23.19 | | | % 154.17/23.19 | | | BETA: splitting (20) gives: % 154.17/23.19 | | | % 154.17/23.19 | | | Case 1: % 154.17/23.19 | | | | % 154.17/23.19 | | | | (23) all_54_0 = e2 % 154.17/23.19 | | | | % 154.17/23.19 | | | | COMBINE_EQS: (14), (23) imply: % 154.17/23.19 | | | | (24) all_10_2 = e2 % 154.17/23.19 | | | | % 154.17/23.19 | | | | SIMP: (24) implies: % 154.17/23.19 | | | | (25) all_10_2 = e2 % 154.17/23.19 | | | | % 154.17/23.19 | | | | COMBINE_EQS: (11), (25) imply: % 154.17/23.19 | | | | (26) all_58_28 = e2 % 154.17/23.19 | | | | % 154.17/23.19 | | | | REDUCE: (5), (25) imply: % 154.17/23.19 | | | | (27) ~ (e3 = e2) % 154.17/23.19 | | | | % 154.17/23.19 | | | | SIMP: (27) implies: % 154.17/23.19 | | | | (28) ~ (e3 = e2) % 154.17/23.19 | | | | % 154.17/23.19 | | | | REDUCE: (17), (25) imply: % 154.17/23.19 | | | | (29) ~ (e2 = e1) % 154.17/23.19 | | | | % 154.17/23.19 | | | | REDUCE: (4), (25) imply: % 154.17/23.19 | | | | (30) ~ (e2 = e0) % 154.17/23.19 | | | | % 154.17/23.19 | | | | BETA: splitting (22) gives: % 154.17/23.19 | | | | % 154.17/23.19 | | | | Case 1: % 154.17/23.19 | | | | | % 154.17/23.19 | | | | | (31) all_58_30 = e1 % 154.17/23.19 | | | | | % 154.17/23.19 | | | | | REF_CLOSE: (1), (6), (12), (28), (31) are inconsistent by sub-proof % 154.17/23.19 | | | | | #664. % 154.17/23.19 | | | | | % 154.17/23.19 | | | | Case 2: % 154.17/23.19 | | | | | % 154.17/23.19 | | | | | (32) all_58_31 = e1 % 154.17/23.19 | | | | | % 154.17/23.19 | | | | | COMBINE_EQS: (1), (32) imply: % 154.17/23.19 | | | | | (33) e2 = e1 % 154.17/23.19 | | | | | % 154.17/23.19 | | | | | COMBINE_EQS: (26), (33) imply: % 154.17/23.19 | | | | | (34) all_58_28 = e1 % 154.17/23.19 | | | | | % 154.17/23.19 | | | | | REF_CLOSE: (2), (6), (8), (10), (13), (16), (28), (29), (30), (32), % 154.17/23.19 | | | | | (34) are inconsistent by sub-proof #383. % 154.17/23.19 | | | | | % 154.17/23.19 | | | | End of split % 154.17/23.19 | | | | % 154.17/23.19 | | | Case 2: % 154.17/23.19 | | | | % 154.17/23.19 | | | | (35) all_54_0 = e3 % 154.17/23.19 | | | | % 154.17/23.19 | | | | REF_CLOSE: (5), (14), (35) are inconsistent by sub-proof #827. % 154.17/23.19 | | | | % 154.17/23.19 | | | End of split % 154.17/23.19 | | | % 154.17/23.19 | | End of split % 154.17/23.19 | | % 154.17/23.19 | End of split % 154.17/23.19 | % 154.17/23.19 End of proof % 154.17/23.19 % 154.17/23.19 Sub-proof #298 shows that the following formulas are inconsistent: % 154.17/23.19 ---------------------------------------------------------------- % 154.17/23.19 (1) ~ (all_52_13 = e1) % 154.17/23.19 (2) all_56_5 = e1 | all_56_10 = e1 % 154.17/23.19 (3) all_58_26 = e1 % 154.17/23.19 (4) all_58_26 = e0 % 154.17/23.19 (5) all_56_5 = e1 % 154.17/23.19 (6) all_56_10 = all_52_13 % 154.17/23.19 (7) ~ (e1 = e0) % 154.17/23.19 % 154.17/23.19 Begin of proof % 154.17/23.19 | % 154.17/23.19 | COMBINE_EQS: (3), (4) imply: % 154.17/23.19 | (8) e1 = e0 % 154.17/23.19 | % 154.17/23.19 | SIMP: (8) implies: % 154.17/23.19 | (9) e1 = e0 % 154.17/23.19 | % 154.17/23.19 | COMBINE_EQS: (5), (9) imply: % 154.17/23.19 | (10) all_56_5 = e0 % 154.17/23.19 | % 154.17/23.19 | REF_CLOSE: (1), (2), (6), (7), (10) are inconsistent by sub-proof #304. % 154.17/23.19 | % 154.17/23.19 End of proof % 154.17/23.19 % 154.17/23.19 Sub-proof #299 shows that the following formulas are inconsistent: % 154.17/23.19 ---------------------------------------------------------------- % 154.17/23.19 (1) all_58_22 = e3 % 154.17/23.19 (2) all_58_22 = e0 % 154.17/23.19 (3) ~ (e3 = e0) % 154.17/23.19 % 154.17/23.19 Begin of proof % 154.17/23.19 | % 154.17/23.19 | COMBINE_EQS: (1), (2) imply: % 154.17/23.19 | (4) e3 = e0 % 154.17/23.19 | % 154.17/23.19 | SIMP: (4) implies: % 154.17/23.19 | (5) e3 = e0 % 154.17/23.19 | % 154.17/23.19 | REDUCE: (3), (5) imply: % 154.17/23.19 | (6) $false % 154.17/23.19 | % 154.17/23.19 | CLOSE: (6) is inconsistent. % 154.17/23.19 | % 154.17/23.19 End of proof % 154.17/23.19 % 154.17/23.19 Sub-proof #300 shows that the following formulas are inconsistent: % 154.17/23.19 ---------------------------------------------------------------- % 154.17/23.19 (1) ~ (all_52_13 = e1) % 154.17/23.20 (2) all_58_20 = e0 % 154.17/23.20 (3) all_56_5 = e1 | all_56_10 = e1 % 154.17/23.20 (4) all_56_5 = e1 % 154.17/23.20 (5) all_56_10 = all_52_13 % 154.17/23.20 (6) ~ (e1 = e0) % 154.17/23.20 (7) all_58_20 = e1 % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (2), (7) imply: % 154.17/23.20 | (8) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | SIMP: (8) implies: % 154.17/23.20 | (9) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (4), (9) imply: % 154.17/23.20 | (10) all_56_5 = e0 % 154.17/23.20 | % 154.17/23.20 | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #304. % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #301 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) ~ (all_52_13 = e1) % 154.17/23.20 (2) all_56_5 = e1 | all_56_10 = e1 % 154.17/23.20 (3) all_58_24 = e0 % 154.17/23.20 (4) all_56_5 = e1 % 154.17/23.20 (5) all_56_10 = all_52_13 % 154.17/23.20 (6) all_58_24 = e1 % 154.17/23.20 (7) ~ (e1 = e0) % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (3), (6) imply: % 154.17/23.20 | (8) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | SIMP: (8) implies: % 154.17/23.20 | (9) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (4), (9) imply: % 154.17/23.20 | (10) all_56_5 = e0 % 154.17/23.20 | % 154.17/23.20 | REF_CLOSE: (1), (2), (5), (7), (10) are inconsistent by sub-proof #304. % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #302 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) e3 = e2 % 154.17/23.20 (2) e3 = e0 % 154.17/23.20 (3) ~ (e2 = e0) % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (1), (2) imply: % 154.17/23.20 | (4) e2 = e0 % 154.17/23.20 | % 154.17/23.20 | SIMP: (4) implies: % 154.17/23.20 | (5) e2 = e0 % 154.17/23.20 | % 154.17/23.20 | REDUCE: (3), (5) imply: % 154.17/23.20 | (6) $false % 154.17/23.20 | % 154.17/23.20 | CLOSE: (6) is inconsistent. % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #303 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) all_58_31 = e2 % 154.17/23.20 (2) all_58_30 = e3 % 154.17/23.20 (3) ~ (e3 = e1) % 154.17/23.20 (4) all_58_28 = e1 % 154.17/23.20 (5) all_58_29 = e0 % 154.17/23.20 (6) e2 = e1 % 154.17/23.20 (7) ~ (e3 = e0) % 154.17/23.20 (8) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.20 (9) ~ (e3 = e2) % 154.17/23.20 (10) e3 = e2 % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (6), (10) imply: % 154.17/23.20 | (11) e3 = e1 % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (2), (11) imply: % 154.17/23.20 | (12) all_58_30 = e1 % 154.17/23.20 | % 154.17/23.20 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (12) are inconsistent by % 154.17/23.20 | sub-proof #355. % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #304 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) ~ (all_52_13 = e1) % 154.17/23.20 (2) all_56_5 = e1 | all_56_10 = e1 % 154.17/23.20 (3) all_56_10 = all_52_13 % 154.17/23.20 (4) all_56_5 = e0 % 154.17/23.20 (5) ~ (e1 = e0) % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | BETA: splitting (2) gives: % 154.17/23.20 | % 154.17/23.20 | Case 1: % 154.17/23.20 | | % 154.17/23.20 | | (6) all_56_5 = e1 % 154.17/23.20 | | % 154.17/23.20 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #305. % 154.17/23.20 | | % 154.17/23.20 | Case 2: % 154.17/23.20 | | % 154.17/23.20 | | (7) all_56_10 = e1 % 154.17/23.20 | | % 154.17/23.20 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #606. % 154.17/23.20 | | % 154.17/23.20 | End of split % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #305 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) all_56_5 = e1 % 154.17/23.20 (2) all_56_5 = e0 % 154.17/23.20 (3) ~ (e1 = e0) % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (1), (2) imply: % 154.17/23.20 | (4) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | SIMP: (4) implies: % 154.17/23.20 | (5) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | REDUCE: (3), (5) imply: % 154.17/23.20 | (6) $false % 154.17/23.20 | % 154.17/23.20 | CLOSE: (6) is inconsistent. % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #306 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) all_56_3 = e1 % 154.17/23.20 (2) all_56_3 = e0 % 154.17/23.20 (3) ~ (e1 = e0) % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | COMBINE_EQS: (1), (2) imply: % 154.17/23.20 | (4) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | SIMP: (4) implies: % 154.17/23.20 | (5) e1 = e0 % 154.17/23.20 | % 154.17/23.20 | REDUCE: (3), (5) imply: % 154.17/23.20 | (6) $false % 154.17/23.20 | % 154.17/23.20 | CLOSE: (6) is inconsistent. % 154.17/23.20 | % 154.17/23.20 End of proof % 154.17/23.20 % 154.17/23.20 Sub-proof #307 shows that the following formulas are inconsistent: % 154.17/23.20 ---------------------------------------------------------------- % 154.17/23.20 (1) all_58_31 = all_4_2 % 154.17/23.20 (2) ~ (all_52_1 = e1) % 154.17/23.20 (3) all_58_11 = all_52_9 % 154.17/23.20 (4) all_58_2 = e2 % 154.17/23.20 (5) all_58_4 = e3 % 154.17/23.20 (6) all_58_17 = e3 % 154.17/23.20 (7) all_56_3 = e0 % 154.17/23.20 (8) all_56_6 = e0 % 154.17/23.20 (9) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.20 (10) all_58_13 = all_52_13 % 154.17/23.20 (11) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.17/23.20 (12) all_54_11 = all_52_14 % 154.17/23.20 (13) all_58_20 = all_52_14 % 154.17/23.20 (14) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.17/23.20 (15) ~ (all_52_3 = e1) % 154.17/23.20 (16) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.17/23.20 (17) all_54_10 = all_6_2 % 154.17/23.20 (18) all_54_6 = all_52_9 % 154.17/23.20 (19) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.17/23.20 (20) ~ (all_52_3 = e0) % 154.17/23.20 (21) all_58_6 = e0 % 154.17/23.20 (22) ~ (all_52_1 = all_52_13) % 154.17/23.20 (23) all_56_5 = all_52_9 % 154.17/23.20 (24) all_56_12 = all_52_3 % 154.17/23.20 (25) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.17/23.20 (26) ~ (all_52_9 = e3) % 154.17/23.20 (27) ~ (all_52_13 = e0) % 154.17/23.20 (28) ~ (all_52_3 = all_4_2) % 154.17/23.20 (29) all_58_28 = e1 % 154.17/23.20 (30) ~ (all_52_9 = e0) % 154.17/23.20 (31) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.17/23.20 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.17/23.20 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.17/23.20 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.17/23.20 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.17/23.20 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.17/23.20 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.17/23.20 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.17/23.20 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.17/23.20 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.17/23.20 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.17/23.20 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.17/23.20 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.17/23.20 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.20 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.20 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.20 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.20 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.17/23.20 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.20 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.20 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.20 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.17/23.20 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.20 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.20 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.20 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.17/23.20 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.17/23.20 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.17/23.20 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.17/23.20 e0) % 154.17/23.20 (32) all_58_29 = e0 % 154.17/23.20 (33) all_58_8 = all_52_1 % 154.17/23.20 (34) ~ (e2 = e1) % 154.17/23.20 (35) all_58_26 = e0 % 154.17/23.20 (36) all_58_15 = e0 % 154.17/23.20 (37) ~ (all_52_9 = all_52_13) % 154.17/23.20 (38) ~ (e3 = e0) % 154.17/23.20 (39) all_56_2 = all_52_1 % 154.17/23.20 (40) all_56_10 = all_52_13 % 154.17/23.20 (41) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.17/23.20 (42) all_56_4 = e3 % 154.17/23.20 (43) ~ (all_52_1 = all_52_3) % 154.17/23.20 (44) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.20 (45) ~ (all_52_1 = all_52_9) % 154.17/23.20 (46) ~ (e2 = e0) % 154.17/23.20 (47) ~ (all_52_9 = all_6_2) % 154.17/23.20 (48) ~ (all_6_2 = e3) % 154.17/23.20 (49) ~ (all_52_1 = e0) % 154.17/23.20 (50) ~ (all_52_14 = e3) % 154.17/23.20 (51) all_58_22 = all_52_3 % 154.17/23.20 (52) all_58_24 = e1 % 154.17/23.20 (53) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.17/23.20 (54) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.20 (55) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.17/23.20 (56) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 154.17/23.20 (57) all_58_30 = all_6_2 % 154.17/23.20 (58) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.20 (59) ~ (e3 = e2) % 154.17/23.20 (60) ~ (all_52_14 = all_6_2) % 154.17/23.20 (61) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.17/23.20 (62) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.17/23.20 (63) all_54_12 = all_52_3 % 154.17/23.20 (64) all_54_4 = all_52_1 % 154.17/23.20 % 154.17/23.20 Begin of proof % 154.17/23.20 | % 154.17/23.20 | BETA: splitting (31) gives: % 154.17/23.20 | % 154.17/23.20 | Case 1: % 154.17/23.20 | | % 154.17/23.20 | | (65) all_58_31 = e0 % 154.17/23.20 | | % 154.17/23.20 | | BETA: splitting (9) gives: % 154.17/23.20 | | % 154.17/23.20 | | Case 1: % 154.17/23.20 | | | % 154.17/23.20 | | | (66) all_58_28 = e2 % 154.17/23.20 | | | % 154.17/23.20 | | | REF_CLOSE: (29), (34), (66) are inconsistent by sub-proof #856. % 154.17/23.20 | | | % 154.17/23.20 | | Case 2: % 154.17/23.20 | | | % 154.17/23.20 | | | (67) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.20 | | | % 154.17/23.20 | | | REF_CLOSE: (32), (38), (44), (46), (59), (65), (67) are inconsistent by % 154.17/23.20 | | | sub-proof #851. % 154.17/23.20 | | | % 154.17/23.20 | | End of split % 154.17/23.20 | | % 154.17/23.20 | Case 2: % 154.17/23.20 | | % 154.17/23.20 | | (68) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = e3 & % 154.17/23.20 | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 154.17/23.20 | | all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.17/23.20 | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 % 154.17/23.20 | | & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.20 | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.17/23.20 | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.17/23.20 | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 % 154.17/23.20 | | = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.17/23.20 | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.17/23.20 | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 154.17/23.20 | | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 154.17/23.20 | | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 % 154.17/23.20 | | = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 154.17/23.20 | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.17/23.20 | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.20 | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.17/23.20 | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 % 154.17/23.20 | | & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.17/23.20 | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 % 154.17/23.20 | | = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.20 | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & % 154.17/23.20 | | all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.17/23.20 | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.20 | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.17/23.20 | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 154.17/23.20 | | e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = % 154.17/23.20 | | e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.17/23.20 | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.17/23.20 | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.17/23.20 | | all_58_26 = e0 & e1 = e0) % 154.17/23.20 | | % 154.17/23.20 | | BETA: splitting (68) gives: % 154.17/23.20 | | % 154.17/23.20 | | Case 1: % 154.17/23.20 | | | % 154.17/23.20 | | | (69) all_58_30 = e1 % 154.17/23.20 | | | % 154.17/23.20 | | | COMBINE_EQS: (57), (69) imply: % 154.17/23.20 | | | (70) all_6_2 = e1 % 154.17/23.20 | | | % 154.17/23.20 | | | REDUCE: (47), (70) imply: % 154.17/23.20 | | | (71) ~ (all_52_9 = e1) % 154.17/23.20 | | | % 154.17/23.20 | | | BETA: splitting (56) gives: % 154.17/23.20 | | | % 154.17/23.20 | | | Case 1: % 154.17/23.20 | | | | % 154.17/23.20 | | | | (72) all_54_6 = e0 % 154.17/23.20 | | | | % 154.17/23.20 | | | | REF_CLOSE: (18), (30), (72) are inconsistent by sub-proof #797. % 154.17/23.20 | | | | % 154.17/23.20 | | | Case 2: % 154.17/23.20 | | | | % 154.17/23.20 | | | | (73) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.17/23.20 | | | | % 154.17/23.20 | | | | BETA: splitting (11) gives: % 154.17/23.20 | | | | % 154.17/23.20 | | | | Case 1: % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | (74) all_56_4 = e2 % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | COMBINE_EQS: (42), (74) imply: % 154.17/23.20 | | | | | (75) e3 = e2 % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | REDUCE: (59), (75) imply: % 154.17/23.20 | | | | | (76) $false % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | CLOSE: (76) is inconsistent. % 154.17/23.20 | | | | | % 154.17/23.20 | | | | Case 2: % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | (77) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | BETA: splitting (77) gives: % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | Case 1: % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | (78) all_56_5 = e2 % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | COMBINE_EQS: (23), (78) imply: % 154.17/23.20 | | | | | | (79) all_52_9 = e2 % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | REDUCE: (45), (79) imply: % 154.17/23.20 | | | | | | (80) ~ (all_52_1 = e2) % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | BETA: splitting (14) gives: % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | Case 1: % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | (81) all_54_4 = e1 % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | REF_CLOSE: (2), (64), (81) are inconsistent by sub-proof #832. % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | Case 2: % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | (82) ~ (all_54_4 = e1) % 154.17/23.20 | | | | | | | (83) all_54_4 = e3 | all_54_4 = e2 % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | BETA: splitting (83) gives: % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | (84) all_54_4 = e2 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | REF_CLOSE: (64), (80), (84) are inconsistent by sub-proof #831. % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | (85) all_54_4 = e3 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | COMBINE_EQS: (64), (85) imply: % 154.17/23.20 | | | | | | | | (86) all_52_1 = e3 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | SIMP: (86) implies: % 154.17/23.20 | | | | | | | | (87) all_52_1 = e3 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | REDUCE: (43), (87) imply: % 154.17/23.20 | | | | | | | | (88) ~ (all_52_3 = e3) % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | SIMP: (88) implies: % 154.17/23.20 | | | | | | | | (89) ~ (all_52_3 = e3) % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | REDUCE: (2), (87) imply: % 154.17/23.20 | | | | | | | | (90) ~ (e3 = e1) % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | BETA: splitting (53) gives: % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | (91) all_56_12 = e2 % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | COMBINE_EQS: (24), (91) imply: % 154.17/23.20 | | | | | | | | | (92) all_52_3 = e2 % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | SIMP: (92) implies: % 154.17/23.20 | | | | | | | | | (93) all_52_3 = e2 % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | REDUCE: (89), (93) imply: % 154.17/23.20 | | | | | | | | | (94) ~ (e3 = e2) % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | REF_CLOSE: (8), (9), (29), (32), (34), (38), (39), (41), (44), % 154.17/23.20 | | | | | | | | | (46), (59), (69), (80), (90), (91) are inconsistent % 154.17/23.20 | | | | | | | | | by sub-proof #324. % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | (95) ~ (all_56_12 = e2) % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | REDUCE: (24), (95) imply: % 154.17/23.20 | | | | | | | | | (96) ~ (all_52_3 = e2) % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | REF_CLOSE: (15), (62), (63), (89), (96) are inconsistent by % 154.17/23.20 | | | | | | | | | sub-proof #557. % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | End of split % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | End of split % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | End of split % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | Case 2: % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | (97) ~ (all_56_5 = e2) % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | REDUCE: (23), (97) imply: % 154.17/23.20 | | | | | | (98) ~ (all_52_9 = e2) % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | REF_CLOSE: (18), (26), (71), (73), (98) are inconsistent by % 154.17/23.20 | | | | | | sub-proof #771. % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | End of split % 154.17/23.20 | | | | | % 154.17/23.20 | | | | End of split % 154.17/23.20 | | | | % 154.17/23.20 | | | End of split % 154.17/23.20 | | | % 154.17/23.20 | | Case 2: % 154.17/23.20 | | | % 154.17/23.20 | | | (99) ~ (all_58_30 = e1) % 154.17/23.20 | | | (100) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 = e1 % 154.17/23.20 | | | & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = % 154.17/23.20 | | | e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.17/23.20 | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.17/23.20 | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.17/23.20 | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) % 154.17/23.20 | | | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.17/23.20 | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.17/23.20 | | | all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = % 154.17/23.20 | | | e0 & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 154.17/23.20 | | | e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.17/23.20 | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = % 154.17/23.20 | | | e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.20 | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = % 154.17/23.20 | | | e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.17/23.20 | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.20 | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.20 | | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.17/23.20 | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.17/23.20 | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.17/23.20 | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = % 154.17/23.20 | | | e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.20 | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.20 | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.17/23.20 | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.17/23.20 | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 % 154.17/23.20 | | | = e1 & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.17/23.20 | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.20 | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 % 154.17/23.20 | | | = e2 & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.17/23.20 | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.17/23.20 | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.17/23.20 | | | % 154.17/23.20 | | | REDUCE: (57), (99) imply: % 154.17/23.20 | | | (101) ~ (all_6_2 = e1) % 154.17/23.20 | | | % 154.17/23.20 | | | BETA: splitting (25) gives: % 154.17/23.20 | | | % 154.17/23.20 | | | Case 1: % 154.17/23.20 | | | | % 154.17/23.20 | | | | (102) all_54_10 = e1 % 154.17/23.20 | | | | % 154.17/23.20 | | | | COMBINE_EQS: (17), (102) imply: % 154.17/23.20 | | | | (103) all_6_2 = e1 % 154.17/23.20 | | | | % 154.17/23.20 | | | | REDUCE: (101), (103) imply: % 154.17/23.20 | | | | (104) $false % 154.17/23.20 | | | | % 154.17/23.20 | | | | CLOSE: (104) is inconsistent. % 154.17/23.20 | | | | % 154.17/23.20 | | | Case 2: % 154.17/23.20 | | | | % 154.17/23.20 | | | | (105) all_54_10 = e3 | all_54_10 = e2 % 154.17/23.20 | | | | % 154.17/23.20 | | | | BETA: splitting (105) gives: % 154.17/23.20 | | | | % 154.17/23.20 | | | | Case 1: % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | (106) all_54_10 = e2 % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | COMBINE_EQS: (17), (106) imply: % 154.17/23.20 | | | | | (107) all_6_2 = e2 % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | COMBINE_EQS: (57), (107) imply: % 154.17/23.20 | | | | | (108) all_58_30 = e2 % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | REDUCE: (47), (107) imply: % 154.17/23.20 | | | | | (109) ~ (all_52_9 = e2) % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | REDUCE: (60), (107) imply: % 154.17/23.20 | | | | | (110) ~ (all_52_14 = e2) % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | REDUCE: (48), (107) imply: % 154.17/23.20 | | | | | (111) ~ (e3 = e2) % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | BETA: splitting (56) gives: % 154.17/23.20 | | | | | % 154.17/23.20 | | | | | Case 1: % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | (112) all_54_6 = e0 % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | REF_CLOSE: (18), (30), (112) are inconsistent by sub-proof #797. % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | Case 2: % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | (113) ~ (all_54_6 = e0) % 154.17/23.20 | | | | | | (114) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | BETA: splitting (44) gives: % 154.17/23.20 | | | | | | % 154.17/23.20 | | | | | | Case 1: % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | (115) all_58_29 = e3 % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | REF_CLOSE: (32), (38), (115) are inconsistent by sub-proof #707. % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | Case 2: % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | (116) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | BETA: splitting (61) gives: % 154.17/23.20 | | | | | | | % 154.17/23.20 | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | (117) all_54_11 = e1 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | COMBINE_EQS: (12), (117) imply: % 154.17/23.20 | | | | | | | | (118) all_52_14 = e1 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | SIMP: (118) implies: % 154.17/23.20 | | | | | | | | (119) all_52_14 = e1 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | COMBINE_EQS: (13), (119) imply: % 154.17/23.20 | | | | | | | | (120) all_58_20 = e1 % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | REDUCE: (50), (119) imply: % 154.17/23.20 | | | | | | | | (121) ~ (e3 = e1) % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | SIMP: (121) implies: % 154.17/23.20 | | | | | | | | (122) ~ (e3 = e1) % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | BETA: splitting (16) gives: % 154.17/23.20 | | | | | | | | % 154.17/23.20 | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | (123) all_56_4 = e1 % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | COMBINE_EQS: (42), (123) imply: % 154.17/23.20 | | | | | | | | | (124) e3 = e1 % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | REDUCE: (122), (124) imply: % 154.17/23.20 | | | | | | | | | (125) $false % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | CLOSE: (125) is inconsistent. % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | (126) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | BETA: splitting (126) gives: % 154.17/23.20 | | | | | | | | | % 154.17/23.20 | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | (127) all_56_5 = e1 % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | COMBINE_EQS: (23), (127) imply: % 154.17/23.20 | | | | | | | | | | (128) all_52_9 = e1 % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | COMBINE_EQS: (3), (128) imply: % 154.17/23.20 | | | | | | | | | | (129) all_58_11 = e1 % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | REDUCE: (37), (128) imply: % 154.17/23.20 | | | | | | | | | | (130) ~ (all_52_13 = e1) % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | SIMP: (130) implies: % 154.17/23.20 | | | | | | | | | | (131) ~ (all_52_13 = e1) % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | REDUCE: (30), (128) imply: % 154.17/23.20 | | | | | | | | | | (132) ~ (e1 = e0) % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | BETA: splitting (116) gives: % 154.17/23.20 | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | (133) all_58_30 = e3 % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | REF_CLOSE: (59), (108), (133) are inconsistent by sub-proof % 154.17/23.20 | | | | | | | | | | | #659. % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | (134) all_58_31 = e3 % 154.17/23.20 | | | | | | | | | | | (135) ~ (all_58_30 = e3) % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | COMBINE_EQS: (1), (134) imply: % 154.17/23.20 | | | | | | | | | | | (136) all_4_2 = e3 % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | REDUCE: (28), (136) imply: % 154.17/23.20 | | | | | | | | | | | (137) ~ (all_52_3 = e3) % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | BETA: splitting (55) gives: % 154.17/23.20 | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | (138) all_56_2 = e3 % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | COMBINE_EQS: (39), (138) imply: % 154.17/23.20 | | | | | | | | | | | | (139) all_52_1 = e3 % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | COMBINE_EQS: (33), (139) imply: % 154.17/23.20 | | | | | | | | | | | | (140) all_58_8 = e3 % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | REDUCE: (43), (139) imply: % 154.17/23.20 | | | | | | | | | | | | (141) ~ (all_52_3 = e3) % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | REDUCE: (22), (139) imply: % 154.17/23.20 | | | | | | | | | | | | (142) ~ (all_52_13 = e3) % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | SIMP: (142) implies: % 154.17/23.20 | | | | | | | | | | | | (143) ~ (all_52_13 = e3) % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | BETA: splitting (19) gives: % 154.17/23.20 | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | (144) all_56_2 = e2 % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | COMBINE_EQS: (138), (144) imply: % 154.17/23.20 | | | | | | | | | | | | | (145) e3 = e2 % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | REF_CLOSE: (17), (25), (48), (57), (59), (116), (122), (134), % 154.17/23.20 | | | | | | | | | | | | | (145) are inconsistent by sub-proof #323. % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | (146) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | BETA: splitting (53) gives: % 154.17/23.20 | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | (147) all_56_12 = e2 % 154.17/23.20 | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | COMBINE_EQS: (24), (147) imply: % 154.17/23.20 | | | | | | | | | | | | | | (148) all_52_3 = e2 % 154.17/23.20 | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | SIMP: (148) implies: % 154.17/23.20 | | | | | | | | | | | | | | (149) all_52_3 = e2 % 154.17/23.20 | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | COMBINE_EQS: (51), (149) imply: % 154.17/23.20 | | | | | | | | | | | | | | (150) all_58_22 = e2 % 154.17/23.20 | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | BETA: splitting (146) gives: % 154.17/23.20 | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | (151) all_56_3 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | COMBINE_EQS: (7), (151) imply: % 154.17/23.20 | | | | | | | | | | | | | | | (152) e2 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | COMBINE_EQS: (108), (152) imply: % 154.17/23.20 | | | | | | | | | | | | | | | (153) all_58_30 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (116), % 154.17/23.20 | | | | | | | | | | | | | | | (153) are inconsistent by sub-proof #322. % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | (154) all_56_5 = e2 | all_56_10 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 154.17/23.20 | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | (155) all_56_5 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (155) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | (156) e2 = e1 % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | REDUCE: (34), (156) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | (157) $false % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | (158) all_56_10 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (158) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | (159) all_52_13 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | SIMP: (159) implies: % 154.17/23.20 | | | | | | | | | | | | | | | | (160) all_52_13 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (160) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | (161) all_58_13 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 154.17/23.20 | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | (162) all_58_29 = e2 % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (162) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | | (163) e2 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (163) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | | (164) all_58_30 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (116), % 154.17/23.20 | | | | | | | | | | | | | | | | | (164) are inconsistent by sub-proof #322. % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | (165) ~ (all_58_29 = e2) % 154.17/23.20 | | | | | | | | | | | | | | | | | (166) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.17/23.20 | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.17/23.20 | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.17/23.20 | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.17/23.20 | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.17/23.20 | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.20 | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.17/23.20 | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.17/23.20 | | | | | | | | | | | | | | | | | e0) % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | REDUCE: (32), (165) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | | (167) ~ (e2 = e0) % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 154.17/23.20 | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | (168) all_58_28 = e3 % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (168) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | | | (169) e3 = e1 % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (169) imply: % 154.17/23.20 | | | | | | | | | | | | | | | | | | (170) all_58_31 = e1 % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (44), (46), (57), % 154.17/23.20 | | | | | | | | | | | | | | | | | | (59), (122), (170) are inconsistent by sub-proof % 154.17/23.20 | | | | | | | | | | | | | | | | | | #384. % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | (171) ~ (all_58_28 = e3) % 154.17/23.20 | | | | | | | | | | | | | | | | | | (172) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.20 | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.17/23.20 | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | e0) % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives: % 154.17/23.20 | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.20 | | | | | | | | | | | | | | | | | | | % 154.17/23.20 | | | | | | | | | | | | | | | | | | | (173) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.20 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.17/23.20 | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.20 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.17/23.20 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.20 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.20 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.17/23.20 | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.20 | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (174) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (175) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e2) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (176) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (36), (38), (46), (54), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (57), (58), (59), (122), (132), (176) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #321. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (177) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (178) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (179) all_58_22 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (108), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (116), (150), (179) are inconsistent by sub-proof % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | #320. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (180) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_17 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (182) all_58_11 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (182) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (183) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (183) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (184) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (181) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (185) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (186) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (186) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (187) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (116), (122), (134), (184), (187) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (188) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (189) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (190) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_2 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (192) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (193) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (193) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (194) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (191) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (195) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (195) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (196) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (116), (122), (134), (195), (196) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (197) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_15 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (199) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (200) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (200) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (201) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (198) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (202) e3 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (108), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (116), (201), (202) are inconsistent by sub-proof % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | #318. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (203) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (204) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (205) all_58_22 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_6 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (206) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (207) e3 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (205) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (208) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (108), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (116), (207), (208) are inconsistent by sub-proof % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | #318. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (209) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_17 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (211) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (212) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (212) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (213) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (210) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (214) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (215) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (215) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (216) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (216) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (217) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (116), (122), (134), (215), (217) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (218) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (219) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (220) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_24 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (52), (54), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (57), (58), (59), (122), (132), (222) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #317. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (224) all_58_8 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (224) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (225) e3 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (25), (48), (57), (59), (116), (122), (134), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (225) are inconsistent by sub-proof #323. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (226) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (227) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (228) all_58_22 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (108), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (116), (150), (228) are inconsistent by sub-proof % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | #320. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (229) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (29), (32), (34), (36), (38), (46), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (54), (57), (58), (59), (122), (132), (229) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (230) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (231) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (35), (38), (46), (54), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (57), (58), (59), (122), (132), (232) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #315. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_6 = e3 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (235) all_58_4 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (235) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (236) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (236) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (237) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (234) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (238) e3 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (54), (57), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (122), (132), (237), (238) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #371. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (239) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (36), (38), (46), (54), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (57), (58), (59), (120), (122), (132), (239) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #313. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (240) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (241) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (242) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (36), (38), (46), (52), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (54), (57), (58), (59), (120), (122), (132), (242) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #311. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (243) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (244) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (246) all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (247) all_58_22 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (247) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (248) e2 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (249) e2 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (246) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (250) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (250) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (251) e1 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (251) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (252) all_58_28 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (32), (34), (38), (46), (54), (57), (58), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (59), (122), (132), (252) are inconsistent by % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (35), (38), (46), (54), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (57), (58), (59), (122), (132), (253) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #310. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (254) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_22 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (59), (108), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (116), (150), (256) are inconsistent by sub-proof % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | #320. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (258) all_58_13 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (259) all_58_11 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (259) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (260) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (260) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (261) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (258) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (262) e2 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (262) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (263) e2 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (54), (57), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (122), (132), (261), (263) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (264) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (265) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (266) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_26 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (35), (38), (46), (54), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (57), (58), (59), (122), (132), (268) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #309. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_17 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (271) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (272) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (272) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (273) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (270) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (274) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (274) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (275) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (116), (122), (134), (273), (275) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | (276) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_20 = e0 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (38), (46), (54), (57), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (120), (122), (132), (278) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #369. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (280) e2 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_17 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (281) imply: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (282) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (282) implies: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | (283) e3 = e1 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (116), (122), (134), (280), (283) are % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (284) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (29), (32), (34), (35), (38), (46), (52), % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | (54), (57), (58), (59), (120), (122), (132), (284) % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #308. % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | (285) ~ (all_56_12 = e2) % 154.17/23.21 | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | REDUCE: (24), (285) imply: % 154.17/23.21 | | | | | | | | | | | | | | (286) ~ (all_52_3 = e2) % 154.17/23.21 | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | | REF_CLOSE: (15), (62), (63), (137), (286) are inconsistent by % 154.17/23.21 | | | | | | | | | | | | | | sub-proof #557. % 154.17/23.21 | | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | (287) ~ (all_56_2 = e3) % 154.17/23.21 | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | REDUCE: (39), (287) imply: % 154.17/23.21 | | | | | | | | | | | | (288) ~ (all_52_1 = e3) % 154.17/23.21 | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | BETA: splitting (53) gives: % 154.17/23.21 | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | Case 1: % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | (289) all_56_12 = e2 % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | COMBINE_EQS: (24), (289) imply: % 154.17/23.21 | | | | | | | | | | | | | (290) all_52_3 = e2 % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | SIMP: (290) implies: % 154.17/23.21 | | | | | | | | | | | | | (291) all_52_3 = e2 % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | REDUCE: (43), (291) imply: % 154.17/23.21 | | | | | | | | | | | | | (292) ~ (all_52_1 = e2) % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | REF_CLOSE: (2), (14), (64), (288), (292) are inconsistent by % 154.17/23.21 | | | | | | | | | | | | | sub-proof #828. % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | (293) ~ (all_56_12 = e2) % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | REDUCE: (24), (293) imply: % 154.17/23.21 | | | | | | | | | | | | | (294) ~ (all_52_3 = e2) % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | | REF_CLOSE: (15), (62), (63), (137), (294) are inconsistent by % 154.17/23.21 | | | | | | | | | | | | | sub-proof #557. % 154.17/23.21 | | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | | % 154.17/23.21 | | | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | (295) ~ (all_56_5 = e1) % 154.17/23.21 | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | REDUCE: (23), (295) imply: % 154.17/23.21 | | | | | | | | | | (296) ~ (all_52_9 = e1) % 154.17/23.21 | | | | | | | | | | % 154.17/23.21 | | | | | | | | | | REF_CLOSE: (18), (26), (109), (114), (296) are inconsistent % 154.17/23.21 | | | | | | | | | | by sub-proof #771. % 154.17/23.21 | | | | | | | | | | % 154.17/23.21 | | | | | | | | | End of split % 154.17/23.21 | | | | | | | | | % 154.17/23.21 | | | | | | | | End of split % 154.17/23.21 | | | | | | | | % 154.17/23.21 | | | | | | | Case 2: % 154.17/23.21 | | | | | | | | % 154.17/23.21 | | | | | | | | (297) all_54_11 = e3 | all_54_11 = e2 % 154.17/23.21 | | | | | | | | % 154.17/23.21 | | | | | | | | REF_CLOSE: (12), (50), (110), (297) are inconsistent by % 154.17/23.21 | | | | | | | | sub-proof #775. % 154.17/23.21 | | | | | | | | % 154.17/23.21 | | | | | | | End of split % 154.17/23.21 | | | | | | | % 154.17/23.21 | | | | | | End of split % 154.17/23.21 | | | | | | % 154.17/23.21 | | | | | End of split % 154.17/23.21 | | | | | % 154.17/23.21 | | | | Case 2: % 154.17/23.21 | | | | | % 154.17/23.21 | | | | | (298) all_54_10 = e3 % 154.17/23.21 | | | | | % 154.17/23.21 | | | | | COMBINE_EQS: (17), (298) imply: % 154.17/23.21 | | | | | (299) all_6_2 = e3 % 154.17/23.21 | | | | | % 154.17/23.21 | | | | | REDUCE: (48), (299) imply: % 154.17/23.21 | | | | | (300) $false % 154.17/23.21 | | | | | % 154.17/23.21 | | | | | CLOSE: (300) is inconsistent. % 154.17/23.21 | | | | | % 154.17/23.21 | | | | End of split % 154.17/23.21 | | | | % 154.17/23.21 | | | End of split % 154.17/23.21 | | | % 154.17/23.21 | | End of split % 154.17/23.21 | | % 154.17/23.21 | End of split % 154.17/23.21 | % 154.17/23.21 End of proof % 154.17/23.21 % 154.17/23.21 Sub-proof #308 shows that the following formulas are inconsistent: % 154.17/23.21 ---------------------------------------------------------------- % 154.17/23.21 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.21 (2) ~ (e3 = e1) % 154.17/23.21 (3) all_58_28 = e1 % 154.17/23.21 (4) all_58_29 = e0 % 154.17/23.21 (5) ~ (e2 = e1) % 154.17/23.21 (6) all_58_26 = e0 % 154.17/23.21 (7) ~ (e3 = e0) % 154.17/23.21 (8) ~ (e2 = e0) % 154.17/23.21 (9) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.17/23.21 (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.17/23.21 (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 % 154.17/23.21 = e0 & e1 = e0) % 154.17/23.21 (10) all_58_24 = e1 % 154.17/23.21 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.21 (12) ~ (e1 = e0) % 154.17/23.21 (13) all_58_20 = e1 % 154.17/23.21 (14) all_58_30 = all_6_2 % 154.17/23.21 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.21 (16) ~ (e3 = e2) % 154.17/23.21 % 154.17/23.21 Begin of proof % 154.17/23.21 | % 154.17/23.21 | BETA: splitting (9) gives: % 154.17/23.21 | % 154.17/23.21 | Case 1: % 154.17/23.21 | | % 154.17/23.21 | | (17) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) % 154.17/23.21 | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = % 154.17/23.21 | | e1) % 154.17/23.21 | | % 154.17/23.21 | | BETA: splitting (17) gives: % 154.17/23.21 | | % 154.17/23.21 | | Case 1: % 154.17/23.21 | | | % 154.17/23.21 | | | (18) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0 % 154.17/23.21 | | | % 154.17/23.21 | | | ALPHA: (18) implies: % 154.17/23.21 | | | (19) all_58_20 = e0 % 154.17/23.21 | | | % 154.17/23.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (14), % 154.17/23.21 | | | (15), (16), (19) are inconsistent by sub-proof #369. % 154.17/23.21 | | | % 154.17/23.21 | | Case 2: % 154.17/23.21 | | | % 154.17/23.21 | | | (20) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1 % 154.17/23.21 | | | % 154.17/23.21 | | | ALPHA: (20) implies: % 154.17/23.21 | | | (21) all_58_26 = e1 % 154.17/23.21 | | | % 154.17/23.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (14), (15), % 154.17/23.21 | | | (16), (21) are inconsistent by sub-proof #309. % 154.17/23.21 | | | % 154.17/23.21 | | End of split % 154.17/23.21 | | % 154.17/23.21 | Case 2: % 154.17/23.21 | | % 154.17/23.21 | | (22) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.17/23.21 | | all_58_26 = e0 & e1 = e0) % 154.17/23.21 | | % 154.17/23.21 | | BETA: splitting (22) gives: % 154.17/23.21 | | % 154.17/23.21 | | Case 1: % 154.17/23.21 | | | % 154.17/23.21 | | | (23) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.17/23.21 | | | % 154.17/23.21 | | | ALPHA: (23) implies: % 154.17/23.21 | | | (24) all_58_24 = e0 % 154.17/23.21 | | | % 154.17/23.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (14), % 154.17/23.21 | | | (15), (16), (24) are inconsistent by sub-proof #317. % 154.17/23.21 | | | % 154.17/23.21 | | Case 2: % 154.17/23.21 | | | % 154.17/23.21 | | | (25) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.17/23.21 | | | % 154.17/23.21 | | | ALPHA: (25) implies: % 154.17/23.21 | | | (26) all_58_20 = e0 % 154.17/23.21 | | | % 154.17/23.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (14), % 154.17/23.21 | | | (15), (16), (26) are inconsistent by sub-proof #369. % 154.17/23.21 | | | % 154.17/23.21 | | End of split % 154.17/23.21 | | % 154.17/23.21 | End of split % 154.17/23.21 | % 154.17/23.21 End of proof % 154.17/23.21 % 154.17/23.21 Sub-proof #309 shows that the following formulas are inconsistent: % 154.17/23.21 ---------------------------------------------------------------- % 154.17/23.21 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.21 (2) ~ (e3 = e1) % 154.17/23.21 (3) all_58_26 = e1 % 154.17/23.21 (4) all_58_28 = e1 % 154.17/23.21 (5) all_58_29 = e0 % 154.17/23.21 (6) ~ (e2 = e1) % 154.17/23.21 (7) all_58_26 = e0 % 154.17/23.21 (8) ~ (e3 = e0) % 154.17/23.21 (9) ~ (e2 = e0) % 154.17/23.21 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.21 (11) ~ (e1 = e0) % 154.17/23.21 (12) all_58_30 = all_6_2 % 154.17/23.21 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.21 (14) ~ (e3 = e2) % 154.17/23.21 % 154.17/23.21 Begin of proof % 154.17/23.21 | % 154.17/23.21 | COMBINE_EQS: (3), (7) imply: % 154.17/23.21 | (15) e1 = e0 % 154.17/23.21 | % 154.17/23.21 | SIMP: (15) implies: % 154.17/23.21 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (4), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (13), (14), (17) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #310 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1 % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) all_58_26 = e0 % 154.17/23.22 (8) ~ (e3 = e0) % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | ALPHA: (3) implies: % 154.17/23.22 | (15) all_58_26 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (7), (15) imply: % 154.17/23.22 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (4), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (13), (14), (17) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #311 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = % 154.17/23.22 e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.17/23.22 & all_58_22 = e3 & all_58_26 = e0) % 154.17/23.22 (3) ~ (e3 = e1) % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) all_58_15 = e0 % 154.17/23.22 (8) ~ (e3 = e0) % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_24 = e1 % 154.17/23.22 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (12) ~ (e1 = e0) % 154.17/23.22 (13) all_58_20 = e1 % 154.17/23.22 (14) all_58_30 = all_6_2 % 154.17/23.22 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (16) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (2) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (17) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15), % 154.17/23.22 | | (16), (17) are inconsistent by sub-proof #312. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (18) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.17/23.22 | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) % 154.17/23.22 | | % 154.17/23.22 | | BETA: splitting (18) gives: % 154.17/23.22 | | % 154.17/23.22 | | Case 1: % 154.17/23.22 | | | % 154.17/23.22 | | | (19) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0 % 154.17/23.22 | | | % 154.17/23.22 | | | ALPHA: (19) implies: % 154.17/23.22 | | | (20) all_58_24 = e0 % 154.17/23.22 | | | % 154.17/23.22 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), % 154.17/23.22 | | | (15), (16), (20) are inconsistent by sub-proof #317. % 154.17/23.22 | | | % 154.17/23.22 | | Case 2: % 154.17/23.22 | | | % 154.17/23.22 | | | (21) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0 % 154.17/23.22 | | | % 154.17/23.22 | | | ALPHA: (21) implies: % 154.17/23.22 | | | (22) all_58_20 = e0 % 154.17/23.22 | | | % 154.17/23.22 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14), % 154.17/23.22 | | | (15), (16), (22) are inconsistent by sub-proof #369. % 154.17/23.22 | | | % 154.17/23.22 | | End of split % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #312 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) all_58_28 = e1 % 154.17/23.22 (4) all_58_29 = e0 % 154.17/23.22 (5) ~ (e2 = e1) % 154.17/23.22 (6) all_58_15 = e0 % 154.17/23.22 (7) ~ (e3 = e0) % 154.17/23.22 (8) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | ALPHA: (8) implies: % 154.17/23.22 | (15) all_58_15 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (6), (15) imply: % 154.17/23.22 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (3), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12), (13), (14), (17) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #313 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) all_58_28 = e1 % 154.17/23.22 (4) all_58_29 = e0 % 154.17/23.22 (5) ~ (e2 = e1) % 154.17/23.22 (6) all_58_15 = e0 % 154.17/23.22 (7) ~ (e3 = e0) % 154.17/23.22 (8) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.17/23.22 (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_20 = e1 % 154.17/23.22 (13) all_58_30 = all_6_2 % 154.17/23.22 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (15) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (8) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (16) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), % 154.17/23.22 | | (15), (16) are inconsistent by sub-proof #314. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (17) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0 % 154.17/23.22 | | % 154.17/23.22 | | ALPHA: (17) implies: % 154.17/23.22 | | (18) all_58_20 = e0 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14), % 154.17/23.22 | | (15), (18) are inconsistent by sub-proof #369. % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #314 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) all_58_28 = e1 % 154.17/23.22 (4) all_58_29 = e0 % 154.17/23.22 (5) ~ (e2 = e1) % 154.17/23.22 (6) all_58_15 = e0 % 154.17/23.22 (7) ~ (e3 = e0) % 154.17/23.22 (8) ~ (e2 = e0) % 154.17/23.22 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (10) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | ALPHA: (10) implies: % 154.17/23.22 | (15) all_58_15 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (6), (15) imply: % 154.17/23.22 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (3), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13), (14), (17) are % 154.17/23.22 | inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #315 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1 % 154.17/23.22 (3) ~ (e3 = e1) % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) all_58_26 = e0 % 154.17/23.22 (8) ~ (e3 = e0) % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | ALPHA: (2) implies: % 154.17/23.22 | (15) all_58_26 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (7), (15) imply: % 154.17/23.22 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (4), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14), (17) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #316 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_17 = e3 % 154.17/23.22 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (3) ~ (e3 = e1) % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) all_58_15 = e0 % 154.17/23.22 (8) ~ (e3 = e0) % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 (15) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1 % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | ALPHA: (15) implies: % 154.17/23.22 | (16) all_58_17 = e1 % 154.17/23.22 | (17) all_58_15 = e3 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (7), (17) imply: % 154.17/23.22 | (18) e3 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (1), (16) imply: % 154.17/23.22 | (19) e3 = e1 % 154.17/23.22 | % 154.17/23.22 | SIMP: (19) implies: % 154.17/23.22 | (20) e3 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (18), (20) imply: % 154.17/23.22 | (21) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (4), (21) imply: % 154.17/23.22 | (22) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14), (22) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #317 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) all_58_24 = e0 % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) ~ (e3 = e0) % 154.17/23.22 (8) ~ (e2 = e0) % 154.17/23.22 (9) all_58_24 = e1 % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (3), (9) imply: % 154.17/23.22 | (15) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | SIMP: (15) implies: % 154.17/23.22 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (4), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (17) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #318 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) all_58_30 = e2 % 154.17/23.22 (3) all_58_28 = e1 % 154.17/23.22 (4) all_58_29 = e0 % 154.17/23.22 (5) ~ (e2 = e1) % 154.17/23.22 (6) ~ (e3 = e0) % 154.17/23.22 (7) e3 = e0 % 154.17/23.22 (8) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) ~ (e3 = e2) % 154.17/23.22 (11) e3 = e2 % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (7), (11) imply: % 154.17/23.22 | (12) e2 = e0 % 154.17/23.22 | % 154.17/23.22 | SIMP: (12) implies: % 154.17/23.22 | (13) e2 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (2), (13) imply: % 154.17/23.22 | (14) all_58_30 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (14) are inconsistent by % 154.17/23.22 | sub-proof #322. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #319 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_30 = e2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) e3 = e1 % 154.17/23.22 (4) e2 = e1 % 154.17/23.22 (5) all_58_31 = e3 % 154.17/23.22 (6) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (3), (5) imply: % 154.17/23.22 | (7) all_58_31 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (1), (4) imply: % 154.17/23.22 | (8) all_58_30 = e1 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (2), (6), (7), (8) are inconsistent by sub-proof #498. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #320 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_22 = e0 % 154.17/23.22 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (3) all_58_30 = e2 % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) ~ (e3 = e0) % 154.17/23.22 (8) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_22 = e2 % 154.17/23.22 (11) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (1), (10) imply: % 154.17/23.22 | (12) e2 = e0 % 154.17/23.22 | % 154.17/23.22 | SIMP: (12) implies: % 154.17/23.22 | (13) e2 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (3), (13) imply: % 154.17/23.22 | (14) all_58_30 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (14) are inconsistent by % 154.17/23.22 | sub-proof #322. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #321 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1 % 154.17/23.22 (3) ~ (e3 = e1) % 154.17/23.22 (4) all_58_28 = e1 % 154.17/23.22 (5) all_58_29 = e0 % 154.17/23.22 (6) ~ (e2 = e1) % 154.17/23.22 (7) all_58_15 = e0 % 154.17/23.22 (8) ~ (e3 = e0) % 154.17/23.22 (9) ~ (e2 = e0) % 154.17/23.22 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (11) ~ (e1 = e0) % 154.17/23.22 (12) all_58_30 = all_6_2 % 154.17/23.22 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | ALPHA: (2) implies: % 154.17/23.22 | (15) all_58_15 = e1 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (7), (15) imply: % 154.17/23.22 | (16) e1 = e0 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (4), (16) imply: % 154.17/23.22 | (17) all_58_28 = e0 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14), (17) % 154.17/23.22 | are inconsistent by sub-proof #483. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #322 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (2) all_58_28 = e1 % 154.17/23.22 (3) all_58_29 = e0 % 154.17/23.22 (4) all_58_30 = e0 % 154.17/23.22 (5) ~ (e2 = e1) % 154.17/23.22 (6) ~ (e3 = e0) % 154.17/23.22 (7) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (8) ~ (e2 = e0) % 154.17/23.22 (9) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (1) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (10) all_58_28 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #856. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (11) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (11) are inconsistent by sub-proof % 154.17/23.22 | | #703. % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #323 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_54_10 = all_6_2 % 154.17/23.22 (2) ~ (e3 = e1) % 154.17/23.22 (3) e3 = e2 % 154.17/23.22 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.17/23.22 (5) all_58_31 = e3 % 154.17/23.22 (6) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (7) ~ (all_6_2 = e3) % 154.17/23.22 (8) all_58_30 = all_6_2 % 154.17/23.22 (9) ~ (e3 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | SIMP: (3) implies: % 154.17/23.22 | (10) e3 = e2 % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (5), (10) imply: % 154.17/23.22 | (11) all_58_31 = e2 % 154.17/23.22 | % 154.17/23.22 | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11) are inconsistent by % 154.17/23.22 | sub-proof #475. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #324 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_56_6 = e0 % 154.17/23.22 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 (3) all_56_12 = e2 % 154.17/23.22 (4) ~ (e3 = e1) % 154.17/23.22 (5) all_58_28 = e1 % 154.17/23.22 (6) all_58_29 = e0 % 154.17/23.22 (7) ~ (e2 = e1) % 154.17/23.22 (8) ~ (e3 = e0) % 154.17/23.22 (9) all_56_2 = all_52_1 % 154.17/23.22 (10) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.17/23.22 (11) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (12) all_58_30 = e1 % 154.17/23.22 (13) ~ (e2 = e0) % 154.17/23.22 (14) ~ (e3 = e2) % 154.17/23.22 (15) ~ (all_52_1 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (2) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (16) all_58_28 = e2 % 154.17/23.22 | | % 154.17/23.22 | | COMBINE_EQS: (5), (16) imply: % 154.17/23.22 | | (17) e2 = e1 % 154.17/23.22 | | % 154.17/23.22 | | COMBINE_EQS: (3), (17) imply: % 154.17/23.22 | | (18) all_56_12 = e1 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (1), (7), (9), (10), (13), (15), (18) are inconsistent by % 154.17/23.22 | | sub-proof #326. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (19) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (4), (6), (7), (8), (11), (12), (13), (14), (19) are inconsistent % 154.17/23.22 | | by sub-proof #661. % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #325 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_23 = all_8_0 % 154.17/23.22 (2) all_58_31 = all_4_2 % 154.17/23.22 (3) ~ (all_52_1 = e1) % 154.17/23.22 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.17/23.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.17/23.22 (5) all_56_6 = e0 % 154.17/23.22 (6) op(e0, e2) = all_8_1 % 154.17/23.22 (7) all_56_13 = all_8_1 % 154.17/23.22 (8) all_58_5 = e0 % 154.17/23.22 (9) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.17/23.22 (10) op(e2, e3) = all_52_1 % 154.17/23.22 (11) op(e0, all_8_1) = all_8_0 % 154.17/23.22 (12) all_56_12 = e1 % 154.17/23.22 (13) ~ (all_10_2 = e1) % 154.17/23.22 (14) all_58_29 = e0 % 154.17/23.22 (15) ~ (e2 = e1) % 154.17/23.22 (16) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.17/23.22 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.17/23.22 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.17/23.22 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.17/23.22 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.17/23.22 (all_58_27 = e0)) % 154.17/23.22 (17) all_54_13 = all_8_1 % 154.17/23.22 (18) all_56_2 = all_52_1 % 154.17/23.22 (19) all_58_18 = e1 % 154.17/23.22 (20) all_58_28 = all_10_2 % 154.17/23.22 (21) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.17/23.22 (22) all_58_30 = e1 % 154.17/23.22 (23) ~ (e2 = e0) % 154.17/23.22 (24) ~ (all_8_1 = all_4_2) % 154.17/23.22 (25) all_56_0 = all_10_2 % 154.17/23.22 (26) ~ (all_52_1 = e0) % 154.17/23.22 (27) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.17/23.22 (28) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.22 (29) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.17/23.22 (30) ~ (all_8_1 = e1) % 154.17/23.22 (31) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.17/23.22 (32) op(e2, all_52_1) = all_58_7 % 154.17/23.22 (33) ~ (all_52_1 = e2) % 154.17/23.22 (34) all_54_4 = all_52_1 % 154.17/23.22 (35) ~ (all_52_1 = all_10_2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (9) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (36) all_54_4 = e1 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (3), (34), (36) are inconsistent by sub-proof #832. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (37) ~ (all_54_4 = e1) % 154.17/23.22 | | (38) all_54_4 = e3 | all_54_4 = e2 % 154.17/23.22 | | % 154.17/23.22 | | BETA: splitting (21) gives: % 154.17/23.22 | | % 154.17/23.22 | | Case 1: % 154.17/23.22 | | | % 154.17/23.22 | | | (39) all_56_0 = e2 % 154.17/23.22 | | | % 154.17/23.22 | | | COMBINE_EQS: (25), (39) imply: % 154.17/23.22 | | | (40) all_10_2 = e2 % 154.17/23.22 | | | % 154.17/23.22 | | | SIMP: (40) implies: % 154.17/23.22 | | | (41) all_10_2 = e2 % 154.17/23.22 | | | % 154.17/23.22 | | | COMBINE_EQS: (20), (41) imply: % 154.17/23.22 | | | (42) all_58_28 = e2 % 154.17/23.22 | | | % 154.17/23.22 | | | BETA: splitting (29) gives: % 154.17/23.22 | | | % 154.17/23.22 | | | Case 1: % 154.17/23.22 | | | | % 154.17/23.22 | | | | (43) all_56_2 = e3 % 154.17/23.22 | | | | % 154.17/23.22 | | | | COMBINE_EQS: (18), (43) imply: % 154.17/23.22 | | | | (44) all_52_1 = e3 % 154.17/23.22 | | | | % 154.17/23.22 | | | | REDUCE: (33), (44) imply: % 154.17/23.22 | | | | (45) ~ (e3 = e2) % 154.17/23.22 | | | | % 154.17/23.22 | | | | REDUCE: (3), (44) imply: % 154.17/23.22 | | | | (46) ~ (e3 = e1) % 154.17/23.22 | | | | % 154.17/23.22 | | | | REDUCE: (26), (44) imply: % 154.17/23.22 | | | | (47) ~ (e3 = e0) % 154.17/23.22 | | | | % 154.17/23.22 | | | | REDUCE: (32), (44) imply: % 154.17/23.22 | | | | (48) op(e2, e3) = all_58_7 % 154.17/23.22 | | | | % 154.17/23.22 | | | | REDUCE: (10), (44) imply: % 154.17/23.22 | | | | (49) op(e2, e3) = e3 % 154.17/23.22 | | | | % 154.17/23.22 | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (12), (14), (15), (16), % 154.17/23.22 | | | | (17), (19), (22), (24), (27), (28), (30), (31), (42), (45), % 154.17/23.22 | | | | (46), (47), (48), (49) are inconsistent by sub-proof #330. % 154.17/23.22 | | | | % 154.17/23.22 | | | Case 2: % 154.17/23.22 | | | | % 154.17/23.22 | | | | (50) ~ (all_56_2 = e3) % 154.17/23.22 | | | | % 154.17/23.22 | | | | REDUCE: (18), (50) imply: % 154.17/23.22 | | | | (51) ~ (all_52_1 = e3) % 154.17/23.22 | | | | % 154.17/23.22 | | | | REF_CLOSE: (33), (34), (38), (51) are inconsistent by sub-proof #329. % 154.17/23.22 | | | | % 154.17/23.22 | | | End of split % 154.17/23.22 | | | % 154.17/23.22 | | Case 2: % 154.17/23.22 | | | % 154.17/23.22 | | | (52) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.17/23.22 | | | % 154.17/23.22 | | | REF_CLOSE: (5), (12), (15), (18), (23), (33), (52) are inconsistent by % 154.17/23.22 | | | sub-proof #326. % 154.17/23.22 | | | % 154.17/23.22 | | End of split % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #326 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_56_6 = e0 % 154.17/23.22 (2) all_56_12 = e1 % 154.17/23.22 (3) ~ (e2 = e1) % 154.17/23.22 (4) all_56_2 = all_52_1 % 154.17/23.22 (5) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.17/23.22 (6) ~ (e2 = e0) % 154.17/23.22 (7) ~ (all_52_1 = e2) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (5) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (8) all_56_2 = e2 % 154.17/23.22 | | % 154.17/23.22 | | COMBINE_EQS: (4), (8) imply: % 154.17/23.22 | | (9) all_52_1 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REDUCE: (7), (9) imply: % 154.17/23.22 | | (10) $false % 154.17/23.22 | | % 154.17/23.22 | | CLOSE: (10) is inconsistent. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (11) all_56_6 = e2 | all_56_12 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (1), (2), (3), (6), (11) are inconsistent by sub-proof #327. % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #327 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_56_6 = e0 % 154.17/23.22 (2) all_56_12 = e1 % 154.17/23.22 (3) ~ (e2 = e1) % 154.17/23.22 (4) ~ (e2 = e0) % 154.17/23.22 (5) all_56_6 = e2 | all_56_12 = e2 % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (5) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (6) all_56_6 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #328. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (7) all_56_12 = e2 % 154.17/23.22 | | % 154.17/23.22 | | COMBINE_EQS: (2), (7) imply: % 154.17/23.22 | | (8) e2 = e1 % 154.17/23.22 | | % 154.17/23.22 | | REDUCE: (3), (8) imply: % 154.17/23.22 | | (9) $false % 154.17/23.22 | | % 154.17/23.22 | | CLOSE: (9) is inconsistent. % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #328 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_56_6 = e2 % 154.17/23.22 (2) all_56_6 = e0 % 154.17/23.22 (3) ~ (e2 = e0) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | COMBINE_EQS: (1), (2) imply: % 154.17/23.22 | (4) e2 = e0 % 154.17/23.22 | % 154.17/23.22 | SIMP: (4) implies: % 154.17/23.22 | (5) e2 = e0 % 154.17/23.22 | % 154.17/23.22 | REDUCE: (3), (5) imply: % 154.17/23.22 | (6) $false % 154.17/23.22 | % 154.17/23.22 | CLOSE: (6) is inconsistent. % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #329 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_54_4 = e3 | all_54_4 = e2 % 154.17/23.22 (2) all_54_4 = all_52_1 % 154.17/23.22 (3) ~ (all_52_1 = e2) % 154.17/23.22 (4) ~ (all_52_1 = e3) % 154.17/23.22 % 154.17/23.22 Begin of proof % 154.17/23.22 | % 154.17/23.22 | BETA: splitting (1) gives: % 154.17/23.22 | % 154.17/23.22 | Case 1: % 154.17/23.22 | | % 154.17/23.22 | | (5) all_54_4 = e2 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #831. % 154.17/23.22 | | % 154.17/23.22 | Case 2: % 154.17/23.22 | | % 154.17/23.22 | | (6) all_54_4 = e3 % 154.17/23.22 | | % 154.17/23.22 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #830. % 154.17/23.22 | | % 154.17/23.22 | End of split % 154.17/23.22 | % 154.17/23.22 End of proof % 154.17/23.22 % 154.17/23.22 Sub-proof #330 shows that the following formulas are inconsistent: % 154.17/23.22 ---------------------------------------------------------------- % 154.17/23.22 (1) all_58_23 = all_8_0 % 154.17/23.22 (2) all_58_31 = all_4_2 % 154.17/23.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.17/23.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.17/23.22 (4) op(e2, e3) = all_58_7 % 154.17/23.22 (5) op(e0, e2) = all_8_1 % 154.17/23.22 (6) all_56_13 = all_8_1 % 154.17/23.22 (7) all_58_5 = e0 % 154.17/23.22 (8) ~ (e3 = e1) % 154.17/23.22 (9) op(e0, all_8_1) = all_8_0 % 154.17/23.22 (10) all_56_12 = e1 % 154.17/23.22 (11) all_58_29 = e0 % 154.17/23.22 (12) ~ (e2 = e1) % 154.17/23.22 (13) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.17/23.22 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.17/23.22 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.17/23.23 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.17/23.23 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.17/23.23 (all_58_27 = e0)) % 154.17/23.23 (14) all_54_13 = all_8_1 % 154.17/23.23 (15) ~ (e3 = e0) % 154.17/23.23 (16) all_58_18 = e1 % 154.17/23.23 (17) all_58_30 = e1 % 154.17/23.23 (18) ~ (all_8_1 = all_4_2) % 154.17/23.23 (19) op(e2, e3) = e3 % 154.17/23.23 (20) all_58_28 = e2 % 154.17/23.23 (21) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.17/23.23 (22) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.23 (23) ~ (all_8_1 = e1) % 154.17/23.23 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.17/23.23 (25) ~ (e3 = e2) % 154.17/23.23 % 154.17/23.23 Begin of proof % 154.17/23.23 | % 154.17/23.23 | BETA: splitting (22) gives: % 154.17/23.23 | % 154.17/23.23 | Case 1: % 154.17/23.23 | | % 154.17/23.23 | | (26) all_58_28 = e3 % 154.17/23.23 | | % 154.17/23.23 | | REF_CLOSE: (20), (25), (26) are inconsistent by sub-proof #849. % 154.17/23.23 | | % 154.17/23.23 | Case 2: % 154.17/23.23 | | % 154.17/23.23 | | (27) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.23 | | % 154.17/23.23 | | BETA: splitting (27) gives: % 154.17/23.23 | | % 154.17/23.23 | | Case 1: % 154.17/23.23 | | | % 154.17/23.23 | | | (28) all_58_29 = e3 % 154.17/23.23 | | | % 154.17/23.23 | | | REF_CLOSE: (11), (15), (28) are inconsistent by sub-proof #707. % 154.17/23.23 | | | % 154.17/23.23 | | Case 2: % 154.17/23.23 | | | % 154.17/23.23 | | | (29) all_58_30 = e3 | all_58_31 = e3 % 154.17/23.23 | | | % 154.17/23.23 | | | BETA: splitting (29) gives: % 154.17/23.23 | | | % 154.17/23.23 | | | Case 1: % 154.17/23.23 | | | | % 154.17/23.23 | | | | (30) all_58_30 = e3 % 154.17/23.23 | | | | % 154.17/23.23 | | | | COMBINE_EQS: (17), (30) imply: % 154.17/23.23 | | | | (31) e3 = e1 % 154.17/23.23 | | | | % 154.17/23.23 | | | | REDUCE: (8), (31) imply: % 154.17/23.23 | | | | (32) $false % 154.17/23.23 | | | | % 154.17/23.23 | | | | CLOSE: (32) is inconsistent. % 154.17/23.23 | | | | % 154.17/23.23 | | | Case 2: % 154.17/23.23 | | | | % 154.17/23.23 | | | | (33) all_58_31 = e3 % 154.17/23.23 | | | | % 154.17/23.23 | | | | COMBINE_EQS: (2), (33) imply: % 154.17/23.23 | | | | (34) all_4_2 = e3 % 154.17/23.23 | | | | % 154.17/23.23 | | | | SIMP: (34) implies: % 154.17/23.23 | | | | (35) all_4_2 = e3 % 154.17/23.23 | | | | % 154.17/23.23 | | | | REDUCE: (18), (35) imply: % 154.17/23.23 | | | | (36) ~ (all_8_1 = e3) % 154.17/23.23 | | | | % 154.17/23.23 | | | | BETA: splitting (21) gives: % 154.17/23.23 | | | | % 154.17/23.23 | | | | Case 1: % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | (37) all_56_12 = e2 % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | COMBINE_EQS: (10), (37) imply: % 154.17/23.23 | | | | | (38) e2 = e1 % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | REDUCE: (12), (38) imply: % 154.17/23.23 | | | | | (39) $false % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | CLOSE: (39) is inconsistent. % 154.17/23.23 | | | | | % 154.17/23.23 | | | | Case 2: % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | (40) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | BETA: splitting (24) gives: % 154.17/23.23 | | | | | % 154.17/23.23 | | | | | Case 1: % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | (41) all_54_13 = e1 % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | COMBINE_EQS: (14), (41) imply: % 154.17/23.23 | | | | | | (42) all_8_1 = e1 % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | REDUCE: (23), (42) imply: % 154.17/23.23 | | | | | | (43) $false % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | CLOSE: (43) is inconsistent. % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | Case 2: % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | (44) all_54_13 = e3 | all_54_13 = e2 % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | BETA: splitting (40) gives: % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | | Case 1: % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | (45) all_56_13 = e2 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | COMBINE_EQS: (6), (45) imply: % 154.17/23.23 | | | | | | | (46) all_8_1 = e2 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | SIMP: (46) implies: % 154.17/23.23 | | | | | | | (47) all_8_1 = e2 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | REDUCE: (9), (47) imply: % 154.17/23.23 | | | | | | | (48) op(e0, e2) = all_8_0 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | REDUCE: (5), (47) imply: % 154.17/23.23 | | | | | | | (49) op(e0, e2) = e2 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | GROUND_INST: instantiating (3) with e2, all_8_0, e2, e0, % 154.17/23.23 | | | | | | | simplifying with (48), (49) gives: % 154.17/23.23 | | | | | | | (50) all_8_0 = e2 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | GROUND_INST: instantiating (3) with e3, all_58_7, e3, e2, % 154.17/23.23 | | | | | | | simplifying with (4), (19) gives: % 154.17/23.23 | | | | | | | (51) all_58_7 = e3 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | COMBINE_EQS: (1), (50) imply: % 154.17/23.23 | | | | | | | (52) all_58_23 = e2 % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | BETA: splitting (13) gives: % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | Case 1: % 154.17/23.23 | | | | | | | | % 154.17/23.23 | | | | | | | | (53) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 % 154.17/23.23 | | | | | | | | = e1) & ~ (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & % 154.17/23.23 | | | | | | | | ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 154.17/23.23 | | | | | | | | (all_58_12 = e0)) % 154.17/23.23 | | | | | | | | % 154.17/23.23 | | | | | | | | REF_CLOSE: (7), (51), (53) are inconsistent by sub-proof #393. % 154.17/23.23 | | | | | | | | % 154.17/23.23 | | | | | | | Case 2: % 154.17/23.23 | | | | | | | | % 154.17/23.23 | | | | | | | | (54) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.17/23.23 | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.17/23.23 | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 % 154.17/23.23 | | | | | | | | = e1) & ~ (all_58_27 = e0)) % 154.17/23.23 | | | | | | | | % 154.17/23.23 | | | | | | | | REF_CLOSE: (16), (52), (54) are inconsistent by sub-proof #600. % 154.17/23.23 | | | | | | | | % 154.17/23.23 | | | | | | | End of split % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | Case 2: % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | (55) ~ (all_56_13 = e2) % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | REDUCE: (6), (55) imply: % 154.17/23.23 | | | | | | | (56) ~ (all_8_1 = e2) % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | | REF_CLOSE: (14), (36), (44), (56) are inconsistent by sub-proof % 154.17/23.23 | | | | | | | #339. % 154.17/23.23 | | | | | | | % 154.17/23.23 | | | | | | End of split % 154.17/23.23 | | | | | | % 154.17/23.23 | | | | | End of split % 154.17/23.23 | | | | | % 154.17/23.23 | | | | End of split % 154.17/23.23 | | | | % 154.17/23.23 | | | End of split % 154.17/23.23 | | | % 154.17/23.23 | | End of split % 154.17/23.23 | | % 154.17/23.23 | End of split % 154.17/23.23 | % 154.17/23.23 End of proof % 154.17/23.23 % 154.17/23.23 Sub-proof #331 shows that the following formulas are inconsistent: % 154.17/23.23 ---------------------------------------------------------------- % 154.17/23.23 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.23 (2) ~ (e3 = e1) % 154.17/23.23 (3) all_58_29 = e0 % 154.17/23.23 (4) ~ (e2 = e1) % 154.17/23.23 (5) all_54_0 = e0 % 154.17/23.23 (6) ~ (e3 = e0) % 154.17/23.23 (7) all_58_28 = all_10_2 % 154.17/23.23 (8) ~ (e2 = e0) % 154.17/23.23 (9) all_58_30 = e1 | all_58_31 = e1 % 154.17/23.23 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.17/23.23 (11) all_54_0 = all_10_2 % 154.17/23.23 (12) all_58_30 = all_6_2 % 154.17/23.23 (13) ~ (e3 = e2) % 154.17/23.23 % 154.17/23.23 Begin of proof % 154.17/23.23 | % 154.17/23.23 | COMBINE_EQS: (5), (11) imply: % 154.17/23.23 | (14) all_10_2 = e0 % 154.17/23.23 | % 154.17/23.23 | SIMP: (14) implies: % 154.17/23.23 | (15) all_10_2 = e0 % 154.17/23.23 | % 154.17/23.23 | COMBINE_EQS: (7), (15) imply: % 154.17/23.23 | (16) all_58_28 = e0 % 154.17/23.23 | % 154.17/23.23 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13), (16) are % 154.17/23.23 | inconsistent by sub-proof #652. % 154.17/23.23 | % 154.17/23.23 End of proof % 154.17/23.23 % 154.17/23.23 Sub-proof #332 shows that the following formulas are inconsistent: % 154.17/23.23 ---------------------------------------------------------------- % 154.17/23.23 (1) all_58_31 = all_4_2 % 154.17/23.23 (2) ~ (all_52_1 = e1) % 154.17/23.23 (3) ~ (all_6_2 = e0) % 154.17/23.23 (4) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.17/23.23 (5) ~ (all_52_2 = all_6_2) % 154.17/23.23 (6) all_56_12 = e1 % 154.17/23.23 (7) ~ (all_10_2 = e1) % 154.17/23.23 (8) all_58_29 = e0 % 154.17/23.23 (9) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.17/23.23 (10) all_56_6 = all_52_2 % 154.17/23.23 (11) all_58_29 = e1 % 154.17/23.23 (12) all_56_2 = all_52_1 % 154.17/23.23 (13) all_56_0 = all_10_2 % 154.17/23.23 (14) ~ (e1 = e0) % 154.17/23.23 (15) ~ (all_4_2 = e1) % 154.17/23.23 (16) all_58_30 = all_6_2 % 154.17/23.23 % 154.17/23.23 Begin of proof % 154.17/23.23 | % 154.17/23.23 | COMBINE_EQS: (8), (11) imply: % 154.17/23.23 | (17) e1 = e0 % 154.17/23.23 | % 154.17/23.23 | SIMP: (17) implies: % 154.17/23.23 | (18) e1 = e0 % 154.17/23.23 | % 154.17/23.23 | COMBINE_EQS: (6), (18) imply: % 154.17/23.23 | (19) all_56_12 = e0 % 154.17/23.23 | % 154.17/23.23 | BETA: splitting (4) gives: % 154.17/23.23 | % 154.17/23.23 | Case 1: % 154.17/23.23 | | % 154.17/23.23 | | (20) all_56_0 = e1 % 154.17/23.23 | | % 154.17/23.23 | | COMBINE_EQS: (13), (20) imply: % 154.17/23.23 | | (21) all_10_2 = e1 % 154.17/23.23 | | % 154.17/23.23 | | REDUCE: (7), (21) imply: % 154.17/23.23 | | (22) $false % 154.17/23.23 | | % 154.17/23.23 | | CLOSE: (22) is inconsistent. % 154.17/23.23 | | % 154.17/23.23 | Case 2: % 154.17/23.23 | | % 154.17/23.23 | | (23) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.17/23.23 | | % 154.17/23.23 | | BETA: splitting (9) gives: % 154.17/23.23 | | % 154.17/23.23 | | Case 1: % 154.17/23.23 | | | % 154.17/23.23 | | | % 154.17/23.23 | | | REDUCE: (14), (18) imply: % 154.17/23.23 | | | (24) $false % 154.17/23.23 | | | % 154.17/23.23 | | | CLOSE: (24) is inconsistent. % 154.17/23.23 | | | % 154.17/23.23 | | Case 2: % 154.17/23.23 | | | % 154.17/23.23 | | | (25) all_58_30 = e1 | all_58_31 = e1 % 154.17/23.23 | | | % 154.17/23.23 | | | BETA: splitting (25) gives: % 154.17/23.23 | | | % 154.17/23.23 | | | Case 1: % 154.17/23.23 | | | | % 154.17/23.23 | | | | (26) all_58_30 = e1 % 154.17/23.23 | | | | % 154.17/23.23 | | | | COMBINE_EQS: (16), (26) imply: % 154.17/23.23 | | | | (27) all_6_2 = e1 % 154.17/23.23 | | | | % 154.17/23.23 | | | | SIMP: (27) implies: % 154.17/23.23 | | | | (28) all_6_2 = e1 % 154.17/23.23 | | | | % 154.17/23.23 | | | | REDUCE: (5), (28) imply: % 154.17/23.23 | | | | (29) ~ (all_52_2 = e1) % 154.17/23.23 | | | | % 154.17/23.23 | | | | REF_CLOSE: (2), (10), (12), (14), (19), (23), (29) are inconsistent by % 154.17/23.23 | | | | sub-proof #637. % 154.17/23.23 | | | | % 154.17/23.23 | | | Case 2: % 154.17/23.23 | | | | % 154.17/23.23 | | | | (30) all_58_31 = e1 % 154.17/23.23 | | | | % 154.17/23.23 | | | | COMBINE_EQS: (1), (30) imply: % 154.17/23.23 | | | | (31) all_4_2 = e1 % 154.17/23.23 | | | | % 154.17/23.23 | | | | REDUCE: (15), (31) imply: % 154.17/23.23 | | | | (32) $false % 154.17/23.23 | | | | % 154.17/23.23 | | | | CLOSE: (32) is inconsistent. % 154.17/23.23 | | | | % 154.17/23.23 | | | End of split % 154.17/23.23 | | | % 154.17/23.23 | | End of split % 154.17/23.23 | | % 154.17/23.23 | End of split % 154.17/23.23 | % 154.17/23.23 End of proof % 154.17/23.23 % 154.17/23.23 Sub-proof #333 shows that the following formulas are inconsistent: % 154.17/23.23 ---------------------------------------------------------------- % 154.17/23.23 (1) all_58_23 = all_8_0 % 154.17/23.23 (2) all_58_31 = all_4_2 % 154.17/23.23 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.17/23.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.17/23.23 (4) all_58_11 = all_52_9 % 154.17/23.23 (5) all_56_15 = all_4_2 % 154.17/23.23 (6) all_56_7 = all_52_6 % 154.17/23.23 (7) ~ (all_52_6 = all_6_2) % 154.17/23.23 (8) all_58_22 = e0 % 154.17/23.23 (9) ~ (all_52_2 = e0) % 154.17/23.23 (10) all_54_8 = all_52_2 % 154.17/23.23 (11) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.17/23.23 (12) all_58_15 = all_52_2 % 154.17/23.23 (13) all_58_26 = all_52_11 % 154.17/23.23 (14) all_56_3 = e0 % 154.17/23.23 (15) all_58_24 = all_8_1 % 154.17/23.23 (16) ~ (all_52_11 = all_4_2) % 154.17/23.23 (17) all_58_6 = all_52_12 % 154.17/23.23 (18) all_58_4 = e0 % 154.17/23.23 (19) all_54_3 = all_52_12 % 154.17/23.23 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.17/23.23 (21) all_54_1 = all_52_4 % 154.17/23.23 (22) ~ (all_6_2 = e0) % 154.17/23.23 (23) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 154.17/23.23 (24) ~ (all_52_4 = all_52_6) % 154.17/23.23 (25) all_58_13 = all_52_13 % 154.17/23.23 (26) op(e0, e1) = all_52_11 % 154.17/23.23 (27) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.17/23.23 (28) all_56_13 = all_8_1 % 154.17/23.23 (29) all_58_20 = e0 % 154.17/23.23 (30) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.17/23.23 (31) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.17/23.23 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.17/23.23 (33) ~ (all_52_12 = all_52_13) % 154.17/23.23 (34) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.17/23.23 (35) all_54_10 = all_6_2 % 154.17/23.23 (36) all_54_6 = all_52_9 % 154.17/23.23 (37) all_54_15 = all_4_2 % 154.17/23.23 (38) ~ (all_10_2 = e0) % 154.17/23.23 (39) ~ (all_52_2 = all_6_2) % 154.17/23.23 (40) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.17/23.23 (41) all_54_9 = all_52_6 % 154.17/23.23 (42) ~ (all_52_13 = all_4_2) % 154.17/23.23 (43) all_58_19 = e0 % 154.17/23.23 (44) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.17/23.23 (45) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.17/23.23 (46) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.17/23.23 (47) ~ (e3 = e1) % 154.17/23.23 (48) ~ (all_52_6 = e0) % 154.17/23.23 (49) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.17/23.23 (50) ~ (all_52_1 = all_52_13) % 154.17/23.23 (51) all_56_5 = all_52_9 % 154.17/23.23 (52) all_54_14 = all_52_11 % 154.17/23.23 (53) op(e0, all_8_1) = all_8_0 % 154.17/23.23 (54) ~ (all_52_12 = e0) % 154.17/23.23 (55) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.17/23.23 (56) all_58_2 = all_52_4 % 154.17/23.23 (57) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 154.17/23.23 (58) all_56_1 = all_52_4 % 154.17/23.23 (59) ~ (all_52_13 = e0) % 154.17/23.23 (60) ~ (all_52_4 = all_8_1) % 154.23/23.23 (61) ~ (all_52_9 = e0) % 154.23/23.23 (62) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.23/23.23 (63) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.23/23.23 (64) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.23/23.23 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.23/23.23 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.23/23.23 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.23/23.23 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.23/23.23 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.23/23.23 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.23/23.23 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.23/23.23 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.23/23.23 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.23/23.23 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.23/23.23 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.23/23.23 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.23/23.23 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.23/23.23 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.23/23.23 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.23/23.23 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.23/23.23 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.23/23.23 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.23/23.23 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.23/23.23 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.23/23.23 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.23/23.23 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.23/23.23 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.23/23.23 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.23/23.23 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.23/23.23 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.23/23.23 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.23/23.23 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.23/23.23 e0) % 154.23/23.23 (65) all_58_29 = e0 % 154.23/23.23 (66) op(e2, e1) = all_52_9 % 154.23/23.23 (67) all_56_9 = all_52_12 % 154.23/23.23 (68) all_58_8 = all_52_1 % 154.23/23.23 (69) ~ (e2 = e1) % 154.23/23.23 (70) all_56_6 = all_52_2 % 154.23/23.23 (71) ~ (all_52_2 = all_52_6) % 154.23/23.23 (72) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.23/23.23 (73) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.23/23.23 (74) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.23/23.23 (75) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.23/23.23 (76) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.23/23.23 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.23/23.23 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.23/23.23 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.23/23.23 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.23/23.23 (all_58_27 = e0)) % 154.23/23.23 (77) ~ (all_52_9 = all_52_13) % 154.23/23.23 (78) ~ (all_52_11 = all_8_1) % 154.23/23.23 (79) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.23/23.23 (80) all_54_13 = all_8_1 % 154.23/23.23 (81) ~ (all_52_4 = e0) % 154.23/23.23 (82) ~ (all_52_11 = all_6_2) % 154.23/23.23 (83) ~ (e3 = e0) % 154.23/23.23 (84) all_56_2 = all_52_1 % 154.23/23.23 (85) all_56_4 = e0 % 154.23/23.23 (86) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 154.23/23.23 (87) ~ (all_52_11 = e0) % 154.23/23.23 (88) op(e3, all_52_12) = all_58_5 % 154.23/23.23 (89) all_56_10 = all_52_13 % 154.23/23.23 (90) ~ (all_52_12 = all_10_2) % 154.23/23.23 (91) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.23/23.23 (92) all_56_14 = all_52_11 % 154.23/23.23 (93) all_58_28 = all_10_2 % 154.23/23.23 (94) all_58_17 = all_52_6 % 154.23/23.23 (95) ~ (all_52_1 = all_52_9) % 154.23/23.23 (96) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.23/23.23 (97) all_14_0 = all_8_0 % 154.23/23.23 (98) ~ (e2 = e0) % 154.23/23.23 (99) ~ (all_4_2 = e0) % 154.23/23.23 (100) ~ (all_52_9 = all_6_2) % 154.23/23.23 (101) all_56_12 = e0 % 154.23/23.23 (102) ~ (all_52_2 = all_10_2) % 154.23/23.23 (103) all_56_0 = all_10_2 % 154.23/23.23 (104) ~ (all_52_1 = e0) % 154.23/23.23 (105) ~ (all_52_12 = all_4_2) % 154.23/23.23 (106) all_56_8 = all_6_2 % 154.23/23.23 (107) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.23/23.23 (108) ~ (all_52_1 = all_52_2) % 154.23/23.23 (109) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.23/23.23 (110) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.23/23.23 (111) ~ (all_8_1 = e0) % 154.23/23.23 (112) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.23/23.23 (113) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.23/23.23 (114) all_54_0 = all_10_2 % 154.23/23.23 (115) all_14_1 = all_8_1 % 154.23/23.23 (116) ~ (e1 = e0) % 154.23/23.23 (117) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 154.23/23.23 (118) ~ (all_4_2 = e1) % 154.23/23.23 (119) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.23/23.23 (120) ~ (all_52_4 = all_10_2) % 154.23/23.23 (121) all_58_30 = all_6_2 % 154.23/23.23 (122) op(e2, all_52_1) = all_58_7 % 154.23/23.23 (123) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.23/23.23 (124) all_56_11 = e0 % 154.23/23.23 (125) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.23/23.23 (126) ~ (all_52_4 = all_52_12) % 154.23/23.23 (127) all_54_4 = all_52_1 % 154.23/23.23 (128) ~ (all_52_1 = all_10_2) % 154.23/23.23 (129) op(e3, e1) = e0 % 154.23/23.23 % 154.23/23.23 Begin of proof % 154.23/23.23 | % 154.23/23.23 | BETA: splitting (79) gives: % 154.23/23.23 | % 154.23/23.23 | Case 1: % 154.23/23.23 | | % 154.23/23.23 | | (130) all_56_9 = e1 % 154.23/23.23 | | % 154.23/23.23 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (14), (22), (26), (27), (28), (39), % 154.23/23.23 | | (42), (43), (47), (49), (51), (52), (53), (54), (57), (58), (63), % 154.23/23.23 | | (65), (66), (67), (70), (74), (76), (78), (83), (84), (87), (88), % 154.23/23.23 | | (89), (90), (91), (92), (93), (97), (101), (103), (104), (105), % 154.23/23.23 | | (113), (115), (121), (122), (123), (126), (129), (130) are % 154.23/23.23 | | inconsistent by sub-proof #389. % 154.23/23.23 | | % 154.23/23.23 | Case 2: % 154.23/23.23 | | % 154.23/23.23 | | (131) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.23/23.23 | | % 154.23/23.23 | | BETA: splitting (131) gives: % 154.23/23.23 | | % 154.23/23.23 | | Case 1: % 154.23/23.23 | | | % 154.23/23.23 | | | (132) all_56_10 = e1 % 154.23/23.23 | | | % 154.23/23.23 | | | COMBINE_EQS: (89), (132) imply: % 154.23/23.23 | | | (133) all_52_13 = e1 % 154.23/23.23 | | | % 154.23/23.23 | | | SIMP: (133) implies: % 154.23/23.23 | | | (134) all_52_13 = e1 % 154.23/23.23 | | | % 154.23/23.23 | | | COMBINE_EQS: (25), (134) imply: % 154.23/23.23 | | | (135) all_58_13 = e1 % 154.23/23.23 | | | % 154.23/23.23 | | | REDUCE: (50), (134) imply: % 154.23/23.23 | | | (136) ~ (all_52_1 = e1) % 154.23/23.23 | | | % 154.23/23.23 | | | REDUCE: (77), (134) imply: % 154.23/23.23 | | | (137) ~ (all_52_9 = e1) % 154.23/23.23 | | | % 154.23/23.23 | | | REDUCE: (33), (134) imply: % 154.23/23.23 | | | (138) ~ (all_52_12 = e1) % 154.23/23.23 | | | % 154.23/23.23 | | | REDUCE: (42), (134) imply: % 154.23/23.23 | | | (139) ~ (all_4_2 = e1) % 154.23/23.23 | | | % 154.23/23.23 | | | BETA: splitting (73) gives: % 154.23/23.23 | | | % 154.23/23.23 | | | Case 1: % 154.23/23.23 | | | | % 154.23/23.23 | | | | (140) all_54_4 = e0 % 154.23/23.23 | | | | % 154.23/23.23 | | | | REF_CLOSE: (104), (127), (140) are inconsistent by sub-proof #859. % 154.23/23.23 | | | | % 154.23/23.23 | | | Case 2: % 154.23/23.23 | | | | % 154.23/23.23 | | | | (141) ~ (all_54_4 = e0) % 154.23/23.23 | | | | (142) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.23/23.23 | | | | % 154.23/23.23 | | | | BETA: splitting (109) gives: % 154.23/23.23 | | | | % 154.23/23.23 | | | | Case 1: % 154.23/23.23 | | | | | % 154.23/23.23 | | | | | (143) all_54_1 = e0 % 154.23/23.23 | | | | | % 154.23/23.23 | | | | | REF_CLOSE: (21), (81), (143) are inconsistent by sub-proof #798. % 154.23/23.23 | | | | | % 154.23/23.23 | | | | Case 2: % 154.23/23.23 | | | | | % 154.23/23.23 | | | | | (144) ~ (all_54_1 = e0) % 154.23/23.23 | | | | | (145) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.23/23.23 | | | | | % 154.23/23.23 | | | | | BETA: splitting (44) gives: % 154.23/23.23 | | | | | % 154.23/23.23 | | | | | Case 1: % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | (146) all_56_2 = e2 % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | COMBINE_EQS: (84), (146) imply: % 154.23/23.23 | | | | | | (147) all_52_1 = e2 % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | COMBINE_EQS: (68), (147) imply: % 154.23/23.23 | | | | | | (148) all_58_8 = e2 % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | REDUCE: (95), (147) imply: % 154.23/23.23 | | | | | | (149) ~ (all_52_9 = e2) % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | SIMP: (149) implies: % 154.23/23.23 | | | | | | (150) ~ (all_52_9 = e2) % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | REDUCE: (128), (147) imply: % 154.23/23.23 | | | | | | (151) ~ (all_10_2 = e2) % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | SIMP: (151) implies: % 154.23/23.23 | | | | | | (152) ~ (all_10_2 = e2) % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | BETA: splitting (40) gives: % 154.23/23.23 | | | | | | % 154.23/23.23 | | | | | | Case 1: % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | (153) all_54_6 = e1 % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | COMBINE_EQS: (36), (153) imply: % 154.23/23.23 | | | | | | | (154) all_52_9 = e1 % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | REDUCE: (137), (154) imply: % 154.23/23.23 | | | | | | | (155) $false % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | CLOSE: (155) is inconsistent. % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | Case 2: % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | (156) all_54_6 = e3 | all_54_6 = e2 % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | BETA: splitting (156) gives: % 154.23/23.23 | | | | | | | % 154.23/23.23 | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | (157) all_54_6 = e2 % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | COMBINE_EQS: (36), (157) imply: % 154.23/23.23 | | | | | | | | (158) all_52_9 = e2 % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | REDUCE: (150), (158) imply: % 154.23/23.23 | | | | | | | | (159) $false % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | CLOSE: (159) is inconsistent. % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | Case 2: % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | (160) all_54_6 = e3 % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | COMBINE_EQS: (36), (160) imply: % 154.23/23.23 | | | | | | | | (161) all_52_9 = e3 % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | COMBINE_EQS: (4), (161) imply: % 154.23/23.23 | | | | | | | | (162) all_58_11 = e3 % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | REDUCE: (100), (161) imply: % 154.23/23.23 | | | | | | | | (163) ~ (all_6_2 = e3) % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | SIMP: (163) implies: % 154.23/23.23 | | | | | | | | (164) ~ (all_6_2 = e3) % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | BETA: splitting (11) gives: % 154.23/23.23 | | | | | | | | % 154.23/23.23 | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | (165) all_56_9 = e2 % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | COMBINE_EQS: (67), (165) imply: % 154.23/23.23 | | | | | | | | | (166) all_52_12 = e2 % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | SIMP: (166) implies: % 154.23/23.23 | | | | | | | | | (167) all_52_12 = e2 % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | COMBINE_EQS: (17), (167) imply: % 154.23/23.23 | | | | | | | | | (168) all_58_6 = e2 % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | REDUCE: (126), (167) imply: % 154.23/23.23 | | | | | | | | | (169) ~ (all_52_4 = e2) % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | REDUCE: (105), (167) imply: % 154.23/23.23 | | | | | | | | | (170) ~ (all_4_2 = e2) % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | SIMP: (170) implies: % 154.23/23.23 | | | | | | | | | (171) ~ (all_4_2 = e2) % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | BETA: splitting (20) gives: % 154.23/23.23 | | | | | | | | | % 154.23/23.23 | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | (172) all_58_28 = e2 % 154.23/23.23 | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | REF_CLOSE: (93), (152), (172) are inconsistent by sub-proof % 154.23/23.23 | | | | | | | | | | #388. % 154.23/23.23 | | | | | | | | | | % 154.23/23.23 | | | | | | | | | Case 2: % 154.23/23.23 | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | (173) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.23/23.23 | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | BETA: splitting (173) gives: % 154.23/23.23 | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | (174) all_58_29 = e2 % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | COMBINE_EQS: (65), (174) imply: % 154.23/23.23 | | | | | | | | | | | (175) e2 = e0 % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | REDUCE: (98), (175) imply: % 154.23/23.23 | | | | | | | | | | | (176) $false % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | CLOSE: (176) is inconsistent. % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | Case 2: % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | (177) all_58_30 = e2 | all_58_31 = e2 % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | BETA: splitting (31) gives: % 154.23/23.23 | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | (178) all_54_15 = e1 % 154.23/23.23 | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | REF_CLOSE: (37), (118), (178) are inconsistent by sub-proof % 154.23/23.23 | | | | | | | | | | | | #587. % 154.23/23.23 | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | Case 2: % 154.23/23.23 | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | (179) ~ (all_54_15 = e1) % 154.23/23.23 | | | | | | | | | | | | (180) all_54_15 = e3 | all_54_15 = e2 % 154.23/23.23 | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | BETA: splitting (180) gives: % 154.23/23.23 | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | (181) all_54_15 = e2 % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | REF_CLOSE: (37), (171), (181) are inconsistent by sub-proof % 154.23/23.23 | | | | | | | | | | | | | #490. % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | Case 2: % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | (182) all_54_15 = e3 % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | COMBINE_EQS: (37), (182) imply: % 154.23/23.23 | | | | | | | | | | | | | (183) all_4_2 = e3 % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | SIMP: (183) implies: % 154.23/23.23 | | | | | | | | | | | | | (184) all_4_2 = e3 % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | COMBINE_EQS: (2), (184) imply: % 154.23/23.23 | | | | | | | | | | | | | (185) all_58_31 = e3 % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | REDUCE: (16), (184) imply: % 154.23/23.23 | | | | | | | | | | | | | (186) ~ (all_52_11 = e3) % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | REDUCE: (171), (184) imply: % 154.23/23.23 | | | | | | | | | | | | | (187) ~ (e3 = e2) % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | BETA: splitting (177) gives: % 154.23/23.23 | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | (188) all_58_30 = e2 % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | COMBINE_EQS: (121), (188) imply: % 154.23/23.23 | | | | | | | | | | | | | | (189) all_6_2 = e2 % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | SIMP: (189) implies: % 154.23/23.23 | | | | | | | | | | | | | | (190) all_6_2 = e2 % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | REDUCE: (39), (190) imply: % 154.23/23.23 | | | | | | | | | | | | | | (191) ~ (all_52_2 = e2) % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | REDUCE: (7), (190) imply: % 154.23/23.23 | | | | | | | | | | | | | | (192) ~ (all_52_6 = e2) % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | BETA: splitting (123) gives: % 154.23/23.23 | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | (193) all_58_28 = e1 % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | COMBINE_EQS: (93), (193) imply: % 154.23/23.23 | | | | | | | | | | | | | | | (194) all_10_2 = e1 % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | SIMP: (194) implies: % 154.23/23.23 | | | | | | | | | | | | | | | (195) all_10_2 = e1 % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | REDUCE: (102), (195) imply: % 154.23/23.23 | | | | | | | | | | | | | | | (196) ~ (all_52_2 = e1) % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | REDUCE: (120), (195) imply: % 154.23/23.23 | | | | | | | | | | | | | | | (197) ~ (all_52_4 = e1) % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 154.23/23.23 | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | Case 1: % 154.23/23.23 | | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | | (198) all_56_1 = e2 % 154.23/23.23 | | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (198) imply: % 154.23/23.23 | | | | | | | | | | | | | | | | (199) all_52_4 = e2 % 154.23/23.23 | | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | | REDUCE: (169), (199) imply: % 154.23/23.23 | | | | | | | | | | | | | | | | (200) $false % 154.23/23.23 | | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent. % 154.23/23.23 | | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | Case 2: % 154.23/23.23 | | | | | | | | | | | | | | | | % 154.23/23.23 | | | | | | | | | | | | | | | | (201) ~ (all_56_1 = e2) % 154.23/23.23 | | | | | | | | | | | | | | | | (202) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | (203) all_56_6 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (203) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | (204) all_52_2 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | REDUCE: (196), (204) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | (205) $false % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | (206) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | (207) all_56_7 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (207) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | (208) all_52_6 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (208) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | (209) all_58_17 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | REDUCE: (192), (208) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | (210) ~ (e2 = e1) % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | (211) all_56_6 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (211) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | (212) all_52_2 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (212) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | (213) all_58_15 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (214) all_56_1 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (214) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (215) all_52_4 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (215) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (216) all_58_2 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (215) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (217) ~ (all_8_1 = e3) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | SIMP: (217) implies: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (218) ~ (all_8_1 = e3) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (219) all_56_3 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (219) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (220) e2 = e0 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | SIMP: (220) implies: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (221) e2 = e0 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (221) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (222) all_58_30 = e0 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (47), (65), (69), (83), (98), (112), (187), % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (193), (222) are inconsistent by sub-proof #701. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (223) ~ (all_56_3 = e2) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (224) all_56_7 = e2 | all_56_13 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (223) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | (225) ~ (e2 = e0) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | (226) all_58_31 = e0 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (47), (65), (69), (83), (98), (112), (187), % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | (193), (226) are inconsistent by sub-proof #850. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_58_31 = e0) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | (228) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | e0) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (229) all_56_7 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (207), (229) are inconsistent by sub-proof % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | #387. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (230) all_56_13 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (230) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (231) all_8_1 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (231) implies: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (232) all_8_1 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (232) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_24 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (232) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_52_11 = e2) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (218), (232) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (e3 = e2) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (236) all_54_14 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (236) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (237) all_52_11 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (237) implies: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (238) all_52_11 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (238) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_26 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (238) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (240) ~ (e3 = e1) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18), (20), (29), (47), (65), (69), (83), % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (98), (112), (116), (121), (123), (135), (148), % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (162), (168), (173), (185), (187), (188), (193), % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (209), (213), (216), (228), (233), (239) are % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #361. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | (241) all_54_14 = e3 | all_54_14 = e2 % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (186), (234), (241) are inconsistent by % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #358. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (242) ~ (all_56_1 = e3) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (242) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | (243) ~ (all_52_4 = e3) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (145), (169), (197), (243) are inconsistent % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | (244) ~ (all_56_6 = e3) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | REDUCE: (70), (244) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | | (245) ~ (all_52_2 = e3) % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (110), (191), (196), (245) are inconsistent % 154.23/23.24 | | | | | | | | | | | | | | | | | | | by sub-proof #416. % 154.23/23.24 | | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | (246) ~ (all_56_7 = e1) % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | REDUCE: (6), (246) imply: % 154.23/23.24 | | | | | | | | | | | | | | | | | | (247) ~ (all_52_6 = e1) % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (41), (45), (145), (169), (192), % 154.23/23.24 | | | | | | | | | | | | | | | | | | (197), (247) are inconsistent by sub-proof #421. % 154.23/23.24 | | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | (248) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | REF_CLOSE: (47), (65), (69), (116), (185), (188), (248) are % 154.23/23.24 | | | | | | | | | | | | | | | inconsistent by sub-proof #357. % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | (249) all_58_31 = e2 % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | COMBINE_EQS: (185), (249) imply: % 154.23/23.24 | | | | | | | | | | | | | | (250) e3 = e2 % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | REDUCE: (187), (250) imply: % 154.23/23.24 | | | | | | | | | | | | | | (251) $false % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | % 154.23/23.24 | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | % 154.23/23.24 | | | | | | | | | (252) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.23/23.24 | | | | | | | | | % 154.23/23.24 | | | | | | | | | BETA: splitting (62) gives: % 154.23/23.24 | | | | | | | | | % 154.23/23.24 | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | (253) all_54_3 = e1 % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | REF_CLOSE: (19), (138), (253) are inconsistent by sub-proof % 154.23/23.24 | | | | | | | | | | #723. % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | (254) all_54_3 = e3 | all_54_3 = e2 % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | BETA: splitting (252) gives: % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | (255) all_56_10 = e2 % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | COMBINE_EQS: (132), (255) imply: % 154.23/23.24 | | | | | | | | | | | (256) e2 = e1 % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | SIMP: (256) implies: % 154.23/23.24 | | | | | | | | | | | (257) e2 = e1 % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | REDUCE: (69), (257) imply: % 154.23/23.24 | | | | | | | | | | | (258) $false % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | CLOSE: (258) is inconsistent. % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | (259) all_56_11 = e2 | all_56_15 = e2 % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | BETA: splitting (259) gives: % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | (260) all_56_11 = e2 % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | COMBINE_EQS: (124), (260) imply: % 154.23/23.24 | | | | | | | | | | | | (261) e2 = e0 % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | REDUCE: (98), (261) imply: % 154.23/23.24 | | | | | | | | | | | | (262) $false % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | (263) all_56_15 = e2 % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | COMBINE_EQS: (5), (263) imply: % 154.23/23.24 | | | | | | | | | | | | (264) all_4_2 = e2 % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | SIMP: (264) implies: % 154.23/23.24 | | | | | | | | | | | | (265) all_4_2 = e2 % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | COMBINE_EQS: (2), (265) imply: % 154.23/23.24 | | | | | | | | | | | | (266) all_58_31 = e2 % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | REDUCE: (105), (265) imply: % 154.23/23.24 | | | | | | | | | | | | (267) ~ (all_52_12 = e2) % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | BETA: splitting (75) gives: % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | (268) all_56_9 = e3 % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | COMBINE_EQS: (67), (268) imply: % 154.23/23.24 | | | | | | | | | | | | | (269) all_52_12 = e3 % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | SIMP: (269) implies: % 154.23/23.24 | | | | | | | | | | | | | (270) all_52_12 = e3 % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | REDUCE: (90), (270) imply: % 154.23/23.24 | | | | | | | | | | | | | (271) ~ (all_10_2 = e3) % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | SIMP: (271) implies: % 154.23/23.24 | | | | | | | | | | | | | (272) ~ (all_10_2 = e3) % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | REDUCE: (267), (270) imply: % 154.23/23.24 | | | | | | | | | | | | | (273) ~ (e3 = e2) % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | BETA: splitting (27) gives: % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | (274) all_56_0 = e1 % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | COMBINE_EQS: (103), (274) imply: % 154.23/23.24 | | | | | | | | | | | | | | (275) all_10_2 = e1 % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | COMBINE_EQS: (93), (275) imply: % 154.23/23.24 | | | | | | | | | | | | | | (276) all_58_28 = e1 % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | REDUCE: (272), (275) imply: % 154.23/23.24 | | | | | | | | | | | | | | (277) ~ (e3 = e1) % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | BETA: splitting (112) gives: % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | Case 1: % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | (278) all_58_28 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | REF_CLOSE: (47), (276), (278) are inconsistent by sub-proof % 154.23/23.24 | | | | | | | | | | | | | | | #857. % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | (279) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | | REF_CLOSE: (35), (47), (55), (65), (83), (121), (164), (266), % 154.23/23.24 | | | | | | | | | | | | | | | (273), (279) are inconsistent by sub-proof #356. % 154.23/23.24 | | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | (280) ~ (all_56_0 = e1) % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | REDUCE: (103), (280) imply: % 154.23/23.24 | | | | | | | | | | | | | | (281) ~ (all_10_2 = e1) % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | | REF_CLOSE: (32), (114), (152), (272), (281) are inconsistent % 154.23/23.24 | | | | | | | | | | | | | | by sub-proof #813. % 154.23/23.24 | | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | Case 2: % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | (282) ~ (all_56_9 = e3) % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | | REF_CLOSE: (19), (67), (254), (267), (282) are inconsistent % 154.23/23.24 | | | | | | | | | | | | | by sub-proof #523. % 154.23/23.24 | | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | | % 154.23/23.24 | | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | | % 154.23/23.24 | | | | | | | | | End of split % 154.23/23.24 | | | | | | | | | % 154.23/23.24 | | | | | | | | End of split % 154.23/23.24 | | | | | | | | % 154.23/23.24 | | | | | | | End of split % 154.23/23.24 | | | | | | | % 154.23/23.24 | | | | | | End of split % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | Case 2: % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | | (283) ~ (all_56_2 = e2) % 154.23/23.24 | | | | | | (284) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (12), (13), (14), % 154.23/23.24 | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), % 154.23/23.24 | | | | | | (24), (27), (28), (29), (30), (32), (34), (35), (38), % 154.23/23.24 | | | | | | (39), (48), (51), (54), (56), (58), (60), (61), (62), % 154.23/23.24 | | | | | | (63), (64), (65), (67), (68), (69), (70), (71), (74), % 154.23/23.24 | | | | | | (75), (78), (80), (81), (82), (84), (85), (86), (87), % 154.23/23.24 | | | | | | (90), (92), (93), (94), (98), (99), (100), (101), (102), % 154.23/23.24 | | | | | | (103), (105), (106), (108), (109), (111), (112), (114), % 154.23/23.24 | | | | | | (118), (119), (120), (121), (123), (124), (125), (126), % 154.23/23.24 | | | | | | (127), (128), (132), (135), (136), (137), (142), (283), % 154.23/23.24 | | | | | | (284) are inconsistent by sub-proof #335. % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | End of split % 154.23/23.24 | | | | | % 154.23/23.24 | | | | End of split % 154.23/23.24 | | | | % 154.23/23.24 | | | End of split % 154.23/23.24 | | | % 154.23/23.24 | | Case 2: % 154.23/23.24 | | | % 154.23/23.24 | | | (285) all_56_11 = e1 | all_56_15 = e1 % 154.23/23.24 | | | % 154.23/23.24 | | | REF_CLOSE: (5), (116), (118), (124), (285) are inconsistent by sub-proof % 154.23/23.24 | | | #334. % 154.23/23.24 | | | % 154.23/23.24 | | End of split % 154.23/23.24 | | % 154.23/23.24 | End of split % 154.23/23.24 | % 154.23/23.24 End of proof % 154.23/23.24 % 154.23/23.24 Sub-proof #334 shows that the following formulas are inconsistent: % 154.23/23.24 ---------------------------------------------------------------- % 154.23/23.24 (1) all_56_15 = all_4_2 % 154.23/23.24 (2) all_56_11 = e1 | all_56_15 = e1 % 154.23/23.24 (3) ~ (e1 = e0) % 154.23/23.24 (4) ~ (all_4_2 = e1) % 154.23/23.24 (5) all_56_11 = e0 % 154.23/23.24 % 154.23/23.24 Begin of proof % 154.23/23.24 | % 154.23/23.24 | BETA: splitting (2) gives: % 154.23/23.24 | % 154.23/23.24 | Case 1: % 154.23/23.24 | | % 154.23/23.24 | | (6) all_56_11 = e1 % 154.23/23.24 | | % 154.23/23.24 | | COMBINE_EQS: (5), (6) imply: % 154.23/23.24 | | (7) e1 = e0 % 154.23/23.24 | | % 154.23/23.24 | | REDUCE: (3), (7) imply: % 154.23/23.24 | | (8) $false % 154.23/23.24 | | % 154.23/23.24 | | CLOSE: (8) is inconsistent. % 154.23/23.24 | | % 154.23/23.24 | Case 2: % 154.23/23.24 | | % 154.23/23.24 | | (9) all_56_15 = e1 % 154.23/23.24 | | % 154.23/23.24 | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #671. % 154.23/23.24 | | % 154.23/23.24 | End of split % 154.23/23.24 | % 154.23/23.24 End of proof % 154.23/23.24 % 154.23/23.24 Sub-proof #335 shows that the following formulas are inconsistent: % 154.23/23.24 ---------------------------------------------------------------- % 154.23/23.24 (1) all_58_31 = all_4_2 % 154.23/23.24 (2) ~ (all_52_1 = e1) % 154.23/23.24 (3) all_58_11 = all_52_9 % 154.23/23.24 (4) all_56_7 = all_52_6 % 154.23/23.24 (5) ~ (all_52_6 = all_6_2) % 154.23/23.24 (6) all_58_22 = e0 % 154.23/23.24 (7) ~ (all_52_2 = e0) % 154.23/23.24 (8) all_54_8 = all_52_2 % 154.23/23.24 (9) all_58_15 = all_52_2 % 154.23/23.24 (10) all_58_26 = all_52_11 % 154.23/23.24 (11) all_56_3 = e0 % 154.23/23.24 (12) all_58_24 = all_8_1 % 154.23/23.24 (13) ~ (all_52_11 = all_4_2) % 154.23/23.24 (14) all_58_6 = all_52_12 % 154.23/23.24 (15) all_58_4 = e0 % 154.23/23.24 (16) all_54_3 = all_52_12 % 154.23/23.24 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.23/23.24 (18) all_54_1 = all_52_4 % 154.23/23.24 (19) ~ (all_6_2 = e0) % 154.23/23.24 (20) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.23/23.24 (21) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 154.23/23.24 (22) ~ (all_52_4 = all_52_6) % 154.23/23.24 (23) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.23/23.24 (24) all_56_13 = all_8_1 % 154.23/23.24 (25) all_58_20 = e0 % 154.23/23.24 (26) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.23/23.24 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.23/23.24 (28) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.23/23.24 (29) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.23/23.24 (30) all_54_10 = all_6_2 % 154.23/23.24 (31) ~ (all_10_2 = e0) % 154.23/23.24 (32) all_56_10 = e1 % 154.23/23.24 (33) ~ (all_52_2 = all_6_2) % 154.23/23.24 (34) ~ (all_52_6 = e0) % 154.23/23.24 (35) all_56_5 = all_52_9 % 154.23/23.24 (36) ~ (all_52_12 = e0) % 154.23/23.24 (37) all_58_2 = all_52_4 % 154.23/23.24 (38) all_56_1 = all_52_4 % 154.23/23.24 (39) ~ (all_52_4 = all_8_1) % 154.23/23.24 (40) ~ (all_52_9 = e0) % 154.23/23.24 (41) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.23/23.24 (42) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.23/23.24 (43) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.23/23.24 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.23/23.24 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.23/23.24 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.23/23.24 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.23/23.24 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.23/23.24 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.23/23.24 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.23/23.24 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.23/23.24 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.23/23.24 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.23/23.24 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.23/23.24 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.23/23.24 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.23/23.24 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.23/23.24 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.23/23.24 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.23/23.24 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.23/23.24 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.23/23.24 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.23/23.24 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.23/23.24 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.23/23.24 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.23/23.24 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.23/23.24 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.23/23.24 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.23/23.24 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.23/23.24 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.23/23.24 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.23/23.24 e0) % 154.23/23.24 (44) all_58_29 = e0 % 154.23/23.24 (45) all_56_9 = all_52_12 % 154.23/23.24 (46) ~ (all_56_2 = e2) % 154.23/23.24 (47) all_58_8 = all_52_1 % 154.23/23.24 (48) ~ (e2 = e1) % 154.23/23.24 (49) all_56_6 = all_52_2 % 154.23/23.24 (50) ~ (all_52_2 = all_52_6) % 154.23/23.24 (51) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.23/23.24 (52) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.23/23.24 (53) ~ (all_52_11 = all_8_1) % 154.23/23.24 (54) all_54_13 = all_8_1 % 154.23/23.24 (55) ~ (all_52_4 = e0) % 154.23/23.24 (56) ~ (all_52_11 = all_6_2) % 154.23/23.24 (57) all_56_2 = all_52_1 % 154.23/23.24 (58) all_56_4 = e0 % 154.23/23.24 (59) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 154.23/23.24 (60) ~ (all_52_11 = e0) % 154.23/23.24 (61) all_58_13 = e1 % 154.23/23.24 (62) ~ (all_52_12 = all_10_2) % 154.23/23.24 (63) all_56_14 = all_52_11 % 154.23/23.24 (64) all_58_28 = all_10_2 % 154.23/23.24 (65) all_58_17 = all_52_6 % 154.23/23.24 (66) ~ (e2 = e0) % 154.23/23.24 (67) ~ (all_4_2 = e0) % 154.23/23.24 (68) ~ (all_52_9 = all_6_2) % 154.23/23.24 (69) all_56_12 = e0 % 154.23/23.24 (70) ~ (all_52_2 = all_10_2) % 154.23/23.24 (71) all_56_0 = all_10_2 % 154.23/23.24 (72) ~ (all_52_12 = all_4_2) % 154.23/23.24 (73) all_56_8 = all_6_2 % 154.23/23.24 (74) ~ (all_52_1 = all_52_2) % 154.23/23.24 (75) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.23/23.24 (76) ~ (all_52_9 = e1) % 154.23/23.24 (77) ~ (all_8_1 = e0) % 154.23/23.24 (78) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.23/23.24 (79) all_54_0 = all_10_2 % 154.23/23.24 (80) ~ (all_4_2 = e1) % 154.23/23.24 (81) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.23/23.24 (82) ~ (all_52_4 = all_10_2) % 154.23/23.24 (83) all_58_30 = all_6_2 % 154.23/23.24 (84) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.23/23.24 (85) all_56_11 = e0 % 154.23/23.24 (86) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.23/23.24 (87) ~ (all_52_4 = all_52_12) % 154.23/23.24 (88) all_54_4 = all_52_1 % 154.23/23.24 (89) ~ (all_52_1 = all_10_2) % 154.23/23.24 % 154.23/23.24 Begin of proof % 154.23/23.24 | % 154.23/23.24 | REDUCE: (46), (57) imply: % 154.23/23.24 | (90) ~ (all_52_1 = e2) % 154.23/23.24 | % 154.23/23.24 | BETA: splitting (28) gives: % 154.23/23.24 | % 154.23/23.24 | Case 1: % 154.23/23.24 | | % 154.23/23.24 | | (91) all_54_4 = e1 % 154.23/23.24 | | % 154.23/23.24 | | REF_CLOSE: (2), (88), (91) are inconsistent by sub-proof #832. % 154.23/23.24 | | % 154.23/23.24 | Case 2: % 154.23/23.24 | | % 154.23/23.24 | | (92) all_54_4 = e3 | all_54_4 = e2 % 154.23/23.24 | | % 154.23/23.24 | | BETA: splitting (20) gives: % 154.23/23.24 | | % 154.23/23.24 | | Case 1: % 154.23/23.24 | | | % 154.23/23.24 | | | (93) all_56_3 = e2 % 154.23/23.24 | | | % 154.23/23.24 | | | COMBINE_EQS: (11), (93) imply: % 154.23/23.24 | | | (94) e2 = e0 % 154.23/23.24 | | | % 154.23/23.24 | | | REDUCE: (66), (94) imply: % 154.23/23.24 | | | (95) $false % 154.23/23.24 | | | % 154.23/23.24 | | | CLOSE: (95) is inconsistent. % 154.23/23.24 | | | % 154.23/23.24 | | Case 2: % 154.23/23.24 | | | % 154.23/23.24 | | | (96) all_56_5 = e2 | all_56_10 = e2 % 154.23/23.24 | | | % 154.23/23.24 | | | BETA: splitting (92) gives: % 154.23/23.24 | | | % 154.23/23.24 | | | Case 1: % 154.23/23.24 | | | | % 154.23/23.24 | | | | (97) all_54_4 = e2 % 154.23/23.24 | | | | % 154.23/23.24 | | | | REF_CLOSE: (88), (90), (97) are inconsistent by sub-proof #831. % 154.23/23.24 | | | | % 154.23/23.24 | | | Case 2: % 154.23/23.24 | | | | % 154.23/23.24 | | | | (98) all_54_4 = e3 % 154.23/23.24 | | | | % 154.23/23.24 | | | | COMBINE_EQS: (88), (98) imply: % 154.23/23.24 | | | | (99) all_52_1 = e3 % 154.23/23.24 | | | | % 154.23/23.24 | | | | SIMP: (99) implies: % 154.23/23.24 | | | | (100) all_52_1 = e3 % 154.23/23.24 | | | | % 154.23/23.24 | | | | COMBINE_EQS: (47), (100) imply: % 154.23/23.24 | | | | (101) all_58_8 = e3 % 154.23/23.24 | | | | % 154.23/23.24 | | | | REDUCE: (74), (100) imply: % 154.23/23.24 | | | | (102) ~ (all_52_2 = e3) % 154.23/23.24 | | | | % 154.23/23.24 | | | | SIMP: (102) implies: % 154.23/23.24 | | | | (103) ~ (all_52_2 = e3) % 154.23/23.24 | | | | % 154.23/23.24 | | | | REDUCE: (89), (100) imply: % 154.23/23.24 | | | | (104) ~ (all_10_2 = e3) % 154.23/23.24 | | | | % 154.23/23.24 | | | | SIMP: (104) implies: % 154.23/23.24 | | | | (105) ~ (all_10_2 = e3) % 154.23/23.24 | | | | % 154.23/23.24 | | | | BETA: splitting (96) gives: % 154.23/23.24 | | | | % 154.23/23.24 | | | | Case 1: % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | (106) all_56_5 = e2 % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | COMBINE_EQS: (35), (106) imply: % 154.23/23.24 | | | | | (107) all_52_9 = e2 % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | SIMP: (107) implies: % 154.23/23.24 | | | | | (108) all_52_9 = e2 % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | COMBINE_EQS: (3), (108) imply: % 154.23/23.24 | | | | | (109) all_58_11 = e2 % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | REDUCE: (68), (108) imply: % 154.23/23.24 | | | | | (110) ~ (all_6_2 = e2) % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | SIMP: (110) implies: % 154.23/23.24 | | | | | (111) ~ (all_6_2 = e2) % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | BETA: splitting (21) gives: % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | Case 1: % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | | (112) all_54_8 = e0 % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | | REF_CLOSE: (7), (8), (112) are inconsistent by sub-proof #731. % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | Case 2: % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | | (113) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 154.23/23.24 | | | | | | (13), (14), (15), (16), (17), (18), (19), (22), (23), % 154.23/23.24 | | | | | | (24), (25), (26), (27), (29), (30), (31), (33), (34), % 154.23/23.24 | | | | | | (36), (37), (38), (39), (41), (42), (43), (44), (45), % 154.23/23.24 | | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), % 154.23/23.24 | | | | | | (58), (59), (60), (61), (62), (63), (64), (65), (66), % 154.23/23.24 | | | | | | (67), (69), (70), (71), (72), (73), (75), (77), (78), % 154.23/23.24 | | | | | | (79), (80), (81), (82), (83), (84), (85), (86), (87), % 154.23/23.24 | | | | | | (101), (103), (105), (106), (109), (111), (113) are % 154.23/23.24 | | | | | | inconsistent by sub-proof #336. % 154.23/23.24 | | | | | | % 154.23/23.24 | | | | | End of split % 154.23/23.24 | | | | | % 154.23/23.24 | | | | Case 2: % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | (114) all_56_10 = e2 % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | COMBINE_EQS: (32), (114) imply: % 154.23/23.24 | | | | | (115) e2 = e1 % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | REDUCE: (48), (115) imply: % 154.23/23.24 | | | | | (116) $false % 154.23/23.24 | | | | | % 154.23/23.24 | | | | | CLOSE: (116) is inconsistent. % 154.23/23.24 | | | | | % 154.23/23.24 | | | | End of split % 154.23/23.24 | | | | % 154.23/23.24 | | | End of split % 154.23/23.24 | | | % 154.23/23.24 | | End of split % 154.23/23.24 | | % 154.23/23.24 | End of split % 154.23/23.24 | % 154.23/23.24 End of proof % 154.23/23.24 % 154.23/23.24 Sub-proof #336 shows that the following formulas are inconsistent: % 154.23/23.24 ---------------------------------------------------------------- % 154.23/23.24 (1) all_58_31 = all_4_2 % 154.23/23.24 (2) all_56_7 = all_52_6 % 154.23/23.24 (3) ~ (all_52_6 = all_6_2) % 154.23/23.24 (4) all_58_22 = e0 % 154.23/23.24 (5) ~ (all_52_2 = e0) % 154.23/23.24 (6) all_56_5 = e2 % 154.23/23.24 (7) all_54_8 = all_52_2 % 154.23/23.24 (8) all_58_15 = all_52_2 % 154.23/23.24 (9) all_58_26 = all_52_11 % 154.23/23.24 (10) all_56_3 = e0 % 154.23/23.24 (11) all_58_24 = all_8_1 % 154.23/23.24 (12) ~ (all_52_11 = all_4_2) % 154.23/23.24 (13) all_58_6 = all_52_12 % 154.23/23.24 (14) all_58_4 = e0 % 154.23/23.24 (15) all_54_3 = all_52_12 % 154.23/23.24 (16) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.23/23.24 (17) all_54_1 = all_52_4 % 154.23/23.24 (18) ~ (all_6_2 = e0) % 154.23/23.24 (19) all_58_8 = e3 % 154.23/23.24 (20) ~ (all_52_4 = all_52_6) % 154.23/23.24 (21) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.23/23.24 (22) all_56_13 = all_8_1 % 154.23/23.24 (23) all_58_20 = e0 % 154.23/23.24 (24) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.23/23.24 (25) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.23/23.24 (26) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.23/23.24 (27) all_54_10 = all_6_2 % 154.23/23.24 (28) ~ (all_10_2 = e0) % 154.23/23.24 (29) ~ (all_52_2 = all_6_2) % 154.23/23.24 (30) ~ (all_10_2 = e3) % 154.23/23.24 (31) ~ (all_52_6 = e0) % 154.23/23.24 (32) ~ (all_52_12 = e0) % 154.23/23.24 (33) all_58_2 = all_52_4 % 154.23/23.24 (34) all_56_1 = all_52_4 % 154.23/23.25 (35) all_58_11 = e2 % 154.23/23.25 (36) ~ (all_52_4 = all_8_1) % 154.23/23.25 (37) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.23/23.25 (38) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.23/23.25 (39) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.23/23.25 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.23/23.25 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.23/23.25 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.23/23.25 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.23/23.25 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.23/23.25 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.23/23.25 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.23/23.25 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.23/23.25 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.23/23.25 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.23/23.25 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.23/23.25 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.23/23.25 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.23/23.25 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.23/23.25 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.23/23.25 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.23/23.25 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.23/23.25 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.23/23.25 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.23/23.25 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.23/23.25 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.23/23.25 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.23/23.25 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.23/23.25 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.23/23.25 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.23/23.25 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.23/23.25 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.23/23.25 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.23/23.25 e0) % 154.23/23.25 (40) all_58_29 = e0 % 154.23/23.25 (41) all_56_9 = all_52_12 % 154.23/23.25 (42) ~ (e2 = e1) % 154.23/23.25 (43) all_56_6 = all_52_2 % 154.23/23.25 (44) ~ (all_52_2 = all_52_6) % 154.23/23.25 (45) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.23/23.25 (46) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.23/23.25 (47) ~ (all_52_11 = all_8_1) % 154.23/23.25 (48) all_54_13 = all_8_1 % 154.23/23.25 (49) ~ (all_52_4 = e0) % 154.23/23.25 (50) ~ (all_52_11 = all_6_2) % 154.23/23.25 (51) all_56_4 = e0 % 154.23/23.25 (52) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 154.23/23.25 (53) ~ (all_52_11 = e0) % 154.23/23.25 (54) all_58_13 = e1 % 154.23/23.25 (55) ~ (all_52_12 = all_10_2) % 154.23/23.25 (56) all_56_14 = all_52_11 % 154.23/23.25 (57) all_58_28 = all_10_2 % 154.23/23.25 (58) all_58_17 = all_52_6 % 154.23/23.25 (59) ~ (e2 = e0) % 154.23/23.25 (60) ~ (all_4_2 = e0) % 154.23/23.25 (61) all_56_12 = e0 % 154.23/23.25 (62) ~ (all_52_2 = all_10_2) % 154.23/23.25 (63) all_56_0 = all_10_2 % 154.23/23.25 (64) ~ (all_52_2 = e3) % 154.23/23.25 (65) ~ (all_52_12 = all_4_2) % 154.23/23.25 (66) all_56_8 = all_6_2 % 154.23/23.25 (67) ~ (all_6_2 = e2) % 154.23/23.25 (68) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.23/23.25 (69) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.23/23.25 (70) ~ (all_8_1 = e0) % 154.23/23.25 (71) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.23/23.25 (72) all_54_0 = all_10_2 % 154.23/23.25 (73) ~ (all_4_2 = e1) % 154.23/23.25 (74) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.23/23.25 (75) ~ (all_52_4 = all_10_2) % 154.23/23.25 (76) all_58_30 = all_6_2 % 154.23/23.25 (77) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.23/23.25 (78) all_56_11 = e0 % 154.23/23.25 (79) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.23/23.25 (80) ~ (all_52_4 = all_52_12) % 154.23/23.25 % 154.23/23.25 Begin of proof % 154.23/23.25 | % 154.23/23.25 | BETA: splitting (52) gives: % 154.23/23.25 | % 154.23/23.25 | Case 1: % 154.23/23.25 | | % 154.23/23.25 | | (81) all_54_10 = e0 % 154.23/23.25 | | % 154.23/23.25 | | COMBINE_EQS: (27), (81) imply: % 154.23/23.25 | | (82) all_6_2 = e0 % 154.23/23.25 | | % 154.23/23.25 | | REDUCE: (18), (82) imply: % 154.23/23.25 | | (83) $false % 154.23/23.25 | | % 154.23/23.25 | | CLOSE: (83) is inconsistent. % 154.23/23.25 | | % 154.23/23.25 | Case 2: % 154.23/23.25 | | % 154.23/23.25 | | (84) ~ (all_54_10 = e0) % 154.23/23.25 | | (85) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.23/23.25 | | % 154.23/23.25 | | BETA: splitting (21) gives: % 154.23/23.25 | | % 154.23/23.25 | | Case 1: % 154.23/23.25 | | | % 154.23/23.25 | | | (86) all_56_0 = e1 % 154.23/23.25 | | | % 154.23/23.25 | | | COMBINE_EQS: (63), (86) imply: % 154.23/23.25 | | | (87) all_10_2 = e1 % 154.23/23.25 | | | % 154.23/23.25 | | | COMBINE_EQS: (57), (87) imply: % 154.23/23.25 | | | (88) all_58_28 = e1 % 154.23/23.25 | | | % 154.23/23.25 | | | REDUCE: (62), (87) imply: % 154.23/23.25 | | | (89) ~ (all_52_2 = e1) % 154.23/23.25 | | | % 154.23/23.25 | | | REDUCE: (75), (87) imply: % 154.23/23.25 | | | (90) ~ (all_52_4 = e1) % 154.23/23.25 | | | % 154.23/23.25 | | | REDUCE: (55), (87) imply: % 154.23/23.25 | | | (91) ~ (all_52_12 = e1) % 154.23/23.25 | | | % 154.23/23.25 | | | REDUCE: (28), (87) imply: % 154.23/23.25 | | | (92) ~ (e1 = e0) % 154.23/23.25 | | | % 154.23/23.25 | | | BETA: splitting (16) gives: % 154.23/23.25 | | | % 154.23/23.25 | | | Case 1: % 154.23/23.25 | | | | % 154.23/23.25 | | | | (93) all_58_28 = e2 % 154.23/23.25 | | | | % 154.23/23.25 | | | | REF_CLOSE: (42), (88), (93) are inconsistent by sub-proof #856. % 154.23/23.25 | | | | % 154.23/23.25 | | | Case 2: % 154.23/23.25 | | | | % 154.23/23.25 | | | | (94) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.23/23.25 | | | | % 154.23/23.25 | | | | BETA: splitting (94) gives: % 154.23/23.25 | | | | % 154.23/23.25 | | | | Case 1: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | (95) all_58_29 = e2 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REF_CLOSE: (40), (59), (95) are inconsistent by sub-proof #706. % 154.23/23.25 | | | | | % 154.23/23.25 | | | | Case 2: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | (96) all_58_30 = e2 | all_58_31 = e2 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | BETA: splitting (96) gives: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | Case 1: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | (97) all_58_30 = e2 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | COMBINE_EQS: (76), (97) imply: % 154.23/23.25 | | | | | | (98) all_6_2 = e2 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | REDUCE: (67), (98) imply: % 154.23/23.25 | | | | | | (99) $false % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | CLOSE: (99) is inconsistent. % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | Case 2: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | (100) all_58_31 = e2 % 154.23/23.25 | | | | | | (101) ~ (all_58_30 = e2) % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | COMBINE_EQS: (1), (100) imply: % 154.23/23.25 | | | | | | (102) all_4_2 = e2 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | REDUCE: (12), (102) imply: % 154.23/23.25 | | | | | | (103) ~ (all_52_11 = e2) % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | REDUCE: (65), (102) imply: % 154.23/23.25 | | | | | | (104) ~ (all_52_12 = e2) % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | BETA: splitting (46) gives: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | Case 1: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | (105) all_56_9 = e3 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | COMBINE_EQS: (41), (105) imply: % 154.23/23.25 | | | | | | | (106) all_52_12 = e3 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | SIMP: (106) implies: % 154.23/23.25 | | | | | | | (107) all_52_12 = e3 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | COMBINE_EQS: (13), (107) imply: % 154.23/23.25 | | | | | | | (108) all_58_6 = e3 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (80), (107) imply: % 154.23/23.25 | | | | | | | (109) ~ (all_52_4 = e3) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (104), (107) imply: % 154.23/23.25 | | | | | | | (110) ~ (e3 = e2) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (91), (107) imply: % 154.23/23.25 | | | | | | | (111) ~ (e3 = e1) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (32), (107) imply: % 154.23/23.25 | | | | | | | (112) ~ (e3 = e0) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | BETA: splitting (68) gives: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | | (113) all_54_1 = e0 % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | | REF_CLOSE: (17), (49), (113) are inconsistent by sub-proof #798. % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | | (114) ~ (all_54_1 = e0) % 154.23/23.25 | | | | | | | | (115) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | | BETA: splitting (115) gives: % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | | (116) all_54_1 = e1 % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | | REF_CLOSE: (17), (90), (116) are inconsistent by sub-proof % 154.23/23.25 | | | | | | | | | #741. % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | | (117) all_54_1 = e3 | all_54_1 = e2 % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | | BETA: splitting (39) gives: % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | (118) all_58_31 = e0 % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | REF_CLOSE: (59), (67), (76), (96), (118) are inconsistent by % 154.23/23.25 | | | | | | | | | | sub-proof #817. % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | (119) ~ (all_58_31 = e0) % 154.23/23.25 | | | | | | | | | | (120) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.23/23.25 | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.23/23.25 | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.23/23.25 | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.23/23.25 | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = % 154.23/23.25 | | | | | | | | | | e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 % 154.23/23.25 | | | | | | | | | | = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 154.23/23.25 | | | | | | | | | | all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.23/23.25 | | | | | | | | | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.23/23.25 | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.23/23.25 | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.23/23.25 | | | | | | | | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.23/23.25 | | | | | | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.23/23.25 | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.23/23.25 | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.23/23.25 | | | | | | | | | | & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 154.23/23.25 | | | | | | | | | | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 % 154.23/23.25 | | | | | | | | | | = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.23/23.25 | | | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 % 154.23/23.25 | | | | | | | | | | & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = % 154.23/23.25 | | | | | | | | | | e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 % 154.23/23.25 | | | | | | | | | | = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 154.23/23.25 | | | | | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.23/23.25 | | | | | | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) % 154.23/23.25 | | | | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 % 154.23/23.25 | | | | | | | | | | & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.23/23.25 | | | | | | | | | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 % 154.23/23.25 | | | | | | | | | | = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.23/23.25 | | | | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 % 154.23/23.25 | | | | | | | | | | & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.23/23.25 | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.23/23.25 | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.23/23.25 | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.23/23.25 | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.23/23.25 | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.23/23.25 | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.23/23.25 | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.23/23.25 | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.23/23.25 | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.23/23.25 | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.23/23.25 | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | BETA: splitting (24) gives: % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | (121) all_56_0 = e2 % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | COMBINE_EQS: (86), (121) imply: % 154.23/23.25 | | | | | | | | | | | (122) e2 = e1 % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | COMBINE_EQS: (100), (122) imply: % 154.23/23.25 | | | | | | | | | | | (123) all_58_31 = e1 % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | REF_CLOSE: (16), (40), (42), (59), (71), (76), (88), (110), % 154.23/23.25 | | | | | | | | | | | (111), (112), (123) are inconsistent by sub-proof % 154.23/23.25 | | | | | | | | | | | #383. % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | (124) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | BETA: splitting (124) gives: % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | (125) all_56_1 = e2 % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | COMBINE_EQS: (34), (125) imply: % 154.23/23.25 | | | | | | | | | | | | (126) all_52_4 = e2 % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | SIMP: (126) implies: % 154.23/23.25 | | | | | | | | | | | | (127) all_52_4 = e2 % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | COMBINE_EQS: (33), (127) imply: % 154.23/23.25 | | | | | | | | | | | | (128) all_58_2 = e2 % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | REDUCE: (20), (127) imply: % 154.23/23.25 | | | | | | | | | | | | (129) ~ (all_52_6 = e2) % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | SIMP: (129) implies: % 154.23/23.25 | | | | | | | | | | | | (130) ~ (all_52_6 = e2) % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | REDUCE: (36), (127) imply: % 154.23/23.25 | | | | | | | | | | | | (131) ~ (all_8_1 = e2) % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | SIMP: (131) implies: % 154.23/23.25 | | | | | | | | | | | | (132) ~ (all_8_1 = e2) % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | BETA: splitting (79) gives: % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | (133) all_56_6 = e2 % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | COMBINE_EQS: (43), (133) imply: % 154.23/23.25 | | | | | | | | | | | | | (134) all_52_2 = e2 % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | SIMP: (134) implies: % 154.23/23.25 | | | | | | | | | | | | | (135) all_52_2 = e2 % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | COMBINE_EQS: (8), (135) imply: % 154.23/23.25 | | | | | | | | | | | | | (136) all_58_15 = e2 % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | REDUCE: (29), (135) imply: % 154.23/23.25 | | | | | | | | | | | | | (137) ~ (all_6_2 = e2) % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | REDUCE: (64), (135) imply: % 154.23/23.25 | | | | | | | | | | | | | (138) ~ (e3 = e2) % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (9), (10), (11), (14), (16), % 154.23/23.25 | | | | | | | | | | | | | (18), (19), (22), (23), (26), (27), (31), (35), % 154.23/23.25 | | | | | | | | | | | | | (38), (40), (42), (45), (47), (48), (50), (51), % 154.23/23.25 | | | | | | | | | | | | | (53), (54), (56), (58), (59), (61), (66), (67), % 154.23/23.25 | | | | | | | | | | | | | (70), (71), (74), (76), (85), (88), (92), (94), % 154.23/23.25 | | | | | | | | | | | | | (96), (100), (103), (108), (110), (111), (112), % 154.23/23.25 | | | | | | | | | | | | | (120), (125), (128), (130), (132), (136) are % 154.23/23.25 | | | | | | | | | | | | | inconsistent by sub-proof #338. % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | (139) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | BETA: splitting (139) gives: % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | (140) all_56_7 = e2 % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | COMBINE_EQS: (2), (140) imply: % 154.23/23.25 | | | | | | | | | | | | | | (141) all_52_6 = e2 % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | REDUCE: (130), (141) imply: % 154.23/23.25 | | | | | | | | | | | | | | (142) $false % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | CLOSE: (142) is inconsistent. % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | (143) all_56_8 = e2 | all_56_11 = e2 % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | BETA: splitting (143) gives: % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | | (144) all_56_8 = e2 % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | | REF_CLOSE: (66), (67), (144) are inconsistent by sub-proof % 154.23/23.25 | | | | | | | | | | | | | | | #337. % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | | (145) all_56_11 = e2 % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | | COMBINE_EQS: (78), (145) imply: % 154.23/23.25 | | | | | | | | | | | | | | | (146) e2 = e0 % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | | COMBINE_EQS: (100), (146) imply: % 154.23/23.25 | | | | | | | | | | | | | | | (147) all_58_31 = e0 % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | | REF_CLOSE: (59), (67), (76), (96), (147) are inconsistent by % 154.23/23.25 | | | | | | | | | | | | | | | sub-proof #817. % 154.23/23.25 | | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | | End of split % 154.23/23.25 | | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | | End of split % 154.23/23.25 | | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | End of split % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | Case 2: % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | (148) ~ (all_56_1 = e2) % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | REDUCE: (34), (148) imply: % 154.23/23.25 | | | | | | | | | | | | (149) ~ (all_52_4 = e2) % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | | REF_CLOSE: (17), (109), (117), (149) are inconsistent by % 154.23/23.25 | | | | | | | | | | | | sub-proof #722. % 154.23/23.25 | | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | | End of split % 154.23/23.25 | | | | | | | | | | | % 154.23/23.25 | | | | | | | | | | End of split % 154.23/23.25 | | | | | | | | | | % 154.23/23.25 | | | | | | | | | End of split % 154.23/23.25 | | | | | | | | | % 154.23/23.25 | | | | | | | | End of split % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | End of split % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | Case 2: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | (150) ~ (all_56_9 = e3) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (41), (150) imply: % 154.23/23.25 | | | | | | | (151) ~ (all_52_12 = e3) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REF_CLOSE: (15), (37), (91), (104), (151) are inconsistent by % 154.23/23.25 | | | | | | | sub-proof #612. % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | End of split % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | End of split % 154.23/23.25 | | | | | % 154.23/23.25 | | | | End of split % 154.23/23.25 | | | | % 154.23/23.25 | | | End of split % 154.23/23.25 | | | % 154.23/23.25 | | Case 2: % 154.23/23.25 | | | % 154.23/23.25 | | | (152) ~ (all_56_0 = e1) % 154.23/23.25 | | | % 154.23/23.25 | | | REDUCE: (63), (152) imply: % 154.23/23.25 | | | (153) ~ (all_10_2 = e1) % 154.23/23.25 | | | % 154.23/23.25 | | | BETA: splitting (25) gives: % 154.23/23.25 | | | % 154.23/23.25 | | | Case 1: % 154.23/23.25 | | | | % 154.23/23.25 | | | | (154) all_54_0 = e1 % 154.23/23.25 | | | | % 154.23/23.25 | | | | REF_CLOSE: (72), (153), (154) are inconsistent by sub-proof #841. % 154.23/23.25 | | | | % 154.23/23.25 | | | Case 2: % 154.23/23.25 | | | | % 154.23/23.25 | | | | (155) ~ (all_54_0 = e1) % 154.23/23.25 | | | | (156) all_54_0 = e3 | all_54_0 = e2 % 154.23/23.25 | | | | % 154.23/23.25 | | | | BETA: splitting (156) gives: % 154.23/23.25 | | | | % 154.23/23.25 | | | | Case 1: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | (157) all_54_0 = e2 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | COMBINE_EQS: (72), (157) imply: % 154.23/23.25 | | | | | (158) all_10_2 = e2 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | SIMP: (158) implies: % 154.23/23.25 | | | | | (159) all_10_2 = e2 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | COMBINE_EQS: (57), (159) imply: % 154.23/23.25 | | | | | (160) all_58_28 = e2 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REDUCE: (62), (159) imply: % 154.23/23.25 | | | | | (161) ~ (all_52_2 = e2) % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | BETA: splitting (77) gives: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | Case 1: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | (162) all_58_28 = e1 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | COMBINE_EQS: (160), (162) imply: % 154.23/23.25 | | | | | | (163) e2 = e1 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | REDUCE: (42), (163) imply: % 154.23/23.25 | | | | | | (164) $false % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | CLOSE: (164) is inconsistent. % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | Case 2: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | (165) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | BETA: splitting (69) gives: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | Case 1: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | (166) all_54_8 = e1 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | COMBINE_EQS: (7), (166) imply: % 154.23/23.25 | | | | | | | (167) all_52_2 = e1 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | SIMP: (167) implies: % 154.23/23.25 | | | | | | | (168) all_52_2 = e1 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (29), (168) imply: % 154.23/23.25 | | | | | | | (169) ~ (all_6_2 = e1) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | SIMP: (169) implies: % 154.23/23.25 | | | | | | | (170) ~ (all_6_2 = e1) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (5), (168) imply: % 154.23/23.25 | | | | | | | (171) ~ (e1 = e0) % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REF_CLOSE: (1), (40), (73), (76), (165), (170), (171) are % 154.23/23.25 | | | | | | | inconsistent by sub-proof #672. % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | Case 2: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | (172) all_54_8 = e3 | all_54_8 = e2 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REF_CLOSE: (7), (64), (161), (172) are inconsistent by sub-proof % 154.23/23.25 | | | | | | | #785. % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | End of split % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | End of split % 154.23/23.25 | | | | | % 154.23/23.25 | | | | Case 2: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | (173) all_54_0 = e3 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REF_CLOSE: (30), (72), (173) are inconsistent by sub-proof #827. % 154.23/23.25 | | | | | % 154.23/23.25 | | | | End of split % 154.23/23.25 | | | | % 154.23/23.25 | | | End of split % 154.23/23.25 | | | % 154.23/23.25 | | End of split % 154.23/23.25 | | % 154.23/23.25 | End of split % 154.23/23.25 | % 154.23/23.25 End of proof % 154.23/23.25 % 154.23/23.25 Sub-proof #337 shows that the following formulas are inconsistent: % 154.23/23.25 ---------------------------------------------------------------- % 154.23/23.25 (1) all_56_8 = all_6_2 % 154.23/23.25 (2) all_56_8 = e2 % 154.23/23.25 (3) ~ (all_6_2 = e2) % 154.23/23.25 % 154.23/23.25 Begin of proof % 154.23/23.25 | % 154.23/23.25 | COMBINE_EQS: (1), (2) imply: % 154.23/23.25 | (4) all_6_2 = e2 % 154.23/23.25 | % 154.23/23.25 | SIMP: (4) implies: % 154.23/23.25 | (5) all_6_2 = e2 % 154.23/23.25 | % 154.23/23.25 | REDUCE: (3), (5) imply: % 154.23/23.25 | (6) $false % 154.23/23.25 | % 154.23/23.25 | CLOSE: (6) is inconsistent. % 154.23/23.25 | % 154.23/23.25 End of proof % 154.23/23.25 % 154.23/23.25 Sub-proof #338 shows that the following formulas are inconsistent: % 154.23/23.25 ---------------------------------------------------------------- % 154.23/23.25 (1) all_58_31 = e2 % 154.23/23.25 (2) all_58_2 = e2 % 154.23/23.25 (3) all_56_7 = all_52_6 % 154.23/23.25 (4) ~ (all_52_6 = all_6_2) % 154.23/23.25 (5) all_58_22 = e0 % 154.23/23.25 (6) all_56_5 = e2 % 154.23/23.25 (7) ~ (all_52_6 = e2) % 154.23/23.25 (8) all_58_26 = all_52_11 % 154.23/23.25 (9) all_56_3 = e0 % 154.23/23.25 (10) all_58_24 = all_8_1 % 154.23/23.25 (11) all_58_4 = e0 % 154.23/23.25 (12) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.23/23.25 (13) ~ (all_6_2 = e0) % 154.23/23.25 (14) all_58_8 = e3 % 154.23/23.25 (15) all_56_13 = all_8_1 % 154.23/23.25 (16) all_58_20 = e0 % 154.23/23.25 (17) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.23/23.25 (18) all_54_10 = all_6_2 % 154.23/23.25 (19) all_58_15 = e2 % 154.23/23.25 (20) ~ (e3 = e1) % 154.23/23.25 (21) ~ (all_52_6 = e0) % 154.23/23.25 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.23/23.25 (23) all_58_28 = e1 % 154.23/23.25 (24) all_58_11 = e2 % 154.23/23.25 (25) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.23/23.25 (26) all_58_29 = e0 % 154.23/23.25 (27) ~ (e2 = e1) % 154.23/23.25 (28) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.23/23.25 (29) ~ (all_52_11 = all_8_1) % 154.23/23.25 (30) all_54_13 = all_8_1 % 154.23/23.25 (31) ~ (all_52_11 = all_6_2) % 154.23/23.25 (32) ~ (e3 = e0) % 154.23/23.25 (33) all_58_30 = e2 | all_58_31 = e2 % 154.23/23.25 (34) all_56_4 = e0 % 154.23/23.25 (35) ~ (all_52_11 = e0) % 154.23/23.25 (36) ~ (all_52_11 = e2) % 154.23/23.25 (37) all_58_13 = e1 % 154.23/23.25 (38) all_58_6 = e3 % 154.23/23.25 (39) all_56_14 = all_52_11 % 154.23/23.25 (40) all_56_1 = e2 % 154.23/23.25 (41) all_58_17 = all_52_6 % 154.23/23.25 (42) ~ (e2 = e0) % 154.23/23.25 (43) all_56_12 = e0 % 154.23/23.25 (44) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.23/23.25 (45) all_56_8 = all_6_2 % 154.23/23.25 (46) ~ (all_6_2 = e2) % 154.23/23.25 (47) ~ (all_8_1 = e0) % 154.23/23.25 (48) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.23/23.25 (49) ~ (e1 = e0) % 154.23/23.25 (50) ~ (all_8_1 = e2) % 154.23/23.25 (51) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = e3 & % 154.23/23.25 all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 154.23/23.25 all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.23/23.25 all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.23/23.25 all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 154.23/23.25 all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.23/23.25 all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.23/23.25 all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.23/23.25 all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.23/23.25 all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 % 154.23/23.25 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = % 154.23/23.25 e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = % 154.23/23.25 e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 % 154.23/23.25 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.23/23.25 all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.23/23.25 all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.23/23.25 (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.23/23.25 (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.23/23.25 (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.23/23.25 (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.23/23.25 (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.23/23.25 = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.23/23.25 = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.23/23.25 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.23/23.25 = e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.23/23.25 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.23/23.25 all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.23/23.25 all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.23/23.25 (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.23/23.25 (52) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.23/23.25 (53) all_58_30 = all_6_2 % 154.23/23.25 (54) ~ (e3 = e2) % 154.23/23.25 % 154.23/23.25 Begin of proof % 154.23/23.25 | % 154.23/23.25 | BETA: splitting (51) gives: % 154.23/23.25 | % 154.23/23.25 | Case 1: % 154.23/23.25 | | % 154.23/23.25 | | (55) all_58_30 = e1 % 154.23/23.25 | | % 154.23/23.25 | | REF_CLOSE: (1), (20), (23), (26), (32), (48), (54), (55) are inconsistent by % 154.23/23.25 | | sub-proof #355. % 154.23/23.25 | | % 154.23/23.25 | Case 2: % 154.23/23.25 | | % 154.23/23.25 | | (56) ~ (all_58_30 = e1) % 154.23/23.25 | | (57) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 = e1 & % 154.23/23.25 | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.23/23.25 | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.23/23.25 | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 % 154.23/23.25 | | & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = % 154.23/23.25 | | e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 154.23/23.25 | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = % 154.23/23.25 | | e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 % 154.23/23.25 | | = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.23/23.25 | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.23/23.25 | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.23/23.25 | | & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.23/23.25 | | e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 % 154.23/23.25 | | = e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.23/23.25 | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 % 154.23/23.25 | | & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.23/23.25 | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.23/23.25 | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.23/23.25 | | & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.23/23.25 | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 % 154.23/23.25 | | = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.23/23.25 | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.23/23.25 | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = % 154.23/23.25 | | e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.23/23.25 | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.23/23.25 | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.23/23.25 | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.23/23.25 | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.23/23.25 | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.23/23.25 | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.23/23.25 | | all_58_26 = e0 & e1 = e0) % 154.23/23.25 | | % 154.23/23.25 | | REDUCE: (53), (56) imply: % 154.23/23.25 | | (58) ~ (all_6_2 = e1) % 154.23/23.25 | | % 154.23/23.25 | | BETA: splitting (17) gives: % 154.23/23.25 | | % 154.23/23.25 | | Case 1: % 154.23/23.25 | | | % 154.23/23.25 | | | (59) all_56_4 = e1 % 154.23/23.25 | | | % 154.23/23.25 | | | COMBINE_EQS: (34), (59) imply: % 154.23/23.25 | | | (60) e1 = e0 % 154.23/23.25 | | | % 154.23/23.25 | | | REDUCE: (49), (60) imply: % 154.23/23.25 | | | (61) $false % 154.23/23.25 | | | % 154.23/23.25 | | | CLOSE: (61) is inconsistent. % 154.23/23.25 | | | % 154.23/23.25 | | Case 2: % 154.23/23.25 | | | % 154.23/23.25 | | | (62) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.23/23.25 | | | % 154.23/23.25 | | | BETA: splitting (62) gives: % 154.23/23.25 | | | % 154.23/23.25 | | | Case 1: % 154.23/23.25 | | | | % 154.23/23.25 | | | | (63) all_56_5 = e1 % 154.23/23.25 | | | | % 154.23/23.25 | | | | COMBINE_EQS: (6), (63) imply: % 154.23/23.25 | | | | (64) e2 = e1 % 154.23/23.25 | | | | % 154.23/23.25 | | | | REF_CLOSE: (1), (12), (20), (23), (26), (27), (32), (42), (48), (53), % 154.23/23.25 | | | | (54), (64) are inconsistent by sub-proof #354. % 154.23/23.25 | | | | % 154.23/23.25 | | | Case 2: % 154.23/23.25 | | | | % 154.23/23.25 | | | | (65) all_56_8 = e1 | all_56_14 = e1 % 154.23/23.25 | | | | % 154.23/23.25 | | | | BETA: splitting (65) gives: % 154.23/23.25 | | | | % 154.23/23.25 | | | | Case 1: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | (66) all_56_8 = e1 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REF_CLOSE: (45), (58), (66) are inconsistent by sub-proof #353. % 154.23/23.25 | | | | | % 154.23/23.25 | | | | Case 2: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | (67) all_56_14 = e1 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | COMBINE_EQS: (39), (67) imply: % 154.23/23.25 | | | | | (68) all_52_11 = e1 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | SIMP: (68) implies: % 154.23/23.25 | | | | | (69) all_52_11 = e1 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | COMBINE_EQS: (8), (69) imply: % 154.23/23.25 | | | | | (70) all_58_26 = e1 % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REDUCE: (29), (69) imply: % 154.23/23.25 | | | | | (71) ~ (all_8_1 = e1) % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | SIMP: (71) implies: % 154.23/23.25 | | | | | (72) ~ (all_8_1 = e1) % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REDUCE: (31), (69) imply: % 154.23/23.25 | | | | | (73) ~ (all_6_2 = e1) % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | REDUCE: (36), (69) imply: % 154.23/23.25 | | | | | (74) ~ (e2 = e1) % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | BETA: splitting (25) gives: % 154.23/23.25 | | | | | % 154.23/23.25 | | | | | Case 1: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | (75) all_56_12 = e3 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | COMBINE_EQS: (43), (75) imply: % 154.23/23.25 | | | | | | (76) e3 = e0 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | REDUCE: (32), (76) imply: % 154.23/23.25 | | | | | | (77) $false % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | CLOSE: (77) is inconsistent. % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | Case 2: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | (78) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | BETA: splitting (22) gives: % 154.23/23.25 | | | | | | % 154.23/23.25 | | | | | | Case 1: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | (79) all_54_10 = e1 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | COMBINE_EQS: (18), (79) imply: % 154.23/23.25 | | | | | | | (80) all_6_2 = e1 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | SIMP: (80) implies: % 154.23/23.25 | | | | | | | (81) all_6_2 = e1 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | REDUCE: (58), (81) imply: % 154.23/23.25 | | | | | | | (82) $false % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | CLOSE: (82) is inconsistent. % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | Case 2: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | (83) all_54_10 = e3 | all_54_10 = e2 % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | BETA: splitting (48) gives: % 154.23/23.25 | | | | | | | % 154.23/23.25 | | | | | | | Case 1: % 154.23/23.25 | | | | | | | | % 154.23/23.25 | | | | | | | | (84) all_58_28 = e3 % 154.23/23.26 | | | | | | | | % 154.23/23.26 | | | | | | | | COMBINE_EQS: (23), (84) imply: % 154.23/23.26 | | | | | | | | (85) e3 = e1 % 154.23/23.26 | | | | | | | | % 154.23/23.26 | | | | | | | | REDUCE: (20), (85) imply: % 154.23/23.26 | | | | | | | | (86) $false % 154.23/23.26 | | | | | | | | % 154.23/23.26 | | | | | | | | CLOSE: (86) is inconsistent. % 154.23/23.26 | | | | | | | | % 154.23/23.26 | | | | | | | Case 2: % 154.23/23.26 | | | | | | | | % 154.23/23.26 | | | | | | | | (87) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.23/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | BETA: splitting (52) gives: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | | (88) all_54_13 = e1 % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | | REF_CLOSE: (30), (72), (88) are inconsistent by sub-proof % 154.26/23.26 | | | | | | | | | #352. % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | | (89) ~ (all_54_13 = e1) % 154.26/23.26 | | | | | | | | | (90) all_54_13 = e3 | all_54_13 = e2 % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | | BETA: splitting (78) gives: % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | (91) all_56_13 = e3 % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | COMBINE_EQS: (15), (91) imply: % 154.26/23.26 | | | | | | | | | | (92) all_8_1 = e3 % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | SIMP: (92) implies: % 154.26/23.26 | | | | | | | | | | (93) all_8_1 = e3 % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | COMBINE_EQS: (10), (93) imply: % 154.26/23.26 | | | | | | | | | | (94) all_58_24 = e3 % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | BETA: splitting (28) gives: % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | (95) all_56_1 = e1 % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | COMBINE_EQS: (40), (95) imply: % 154.26/23.26 | | | | | | | | | | | (96) e2 = e1 % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | SIMP: (96) implies: % 154.26/23.26 | | | | | | | | | | | (97) e2 = e1 % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | COMBINE_EQS: (1), (97) imply: % 154.26/23.26 | | | | | | | | | | | (98) all_58_31 = e1 % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | REF_CLOSE: (20), (26), (27), (32), (42), (44), (53), (54), % 154.26/23.26 | | | | | | | | | | | (87), (98) are inconsistent by sub-proof #385. % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | (99) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | BETA: splitting (99) gives: % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | (100) all_56_3 = e1 % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | COMBINE_EQS: (9), (100) imply: % 154.26/23.26 | | | | | | | | | | | | (101) e1 = e0 % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | REDUCE: (49), (101) imply: % 154.26/23.26 | | | | | | | | | | | | (102) $false % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | CLOSE: (102) is inconsistent. % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | (103) all_56_7 = e1 | all_56_13 = e1 % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | BETA: splitting (103) gives: % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | (104) all_56_7 = e1 % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | COMBINE_EQS: (3), (104) imply: % 154.26/23.26 | | | | | | | | | | | | | (105) all_52_6 = e1 % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | COMBINE_EQS: (41), (105) imply: % 154.26/23.26 | | | | | | | | | | | | | (106) all_58_17 = e1 % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | BETA: splitting (83) gives: % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | (107) all_54_10 = e2 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | COMBINE_EQS: (18), (107) imply: % 154.26/23.26 | | | | | | | | | | | | | | (108) all_6_2 = e2 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | SIMP: (108) implies: % 154.26/23.26 | | | | | | | | | | | | | | (109) all_6_2 = e2 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | REDUCE: (46), (109) imply: % 154.26/23.26 | | | | | | | | | | | | | | (110) $false % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | CLOSE: (110) is inconsistent. % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | (111) all_54_10 = e3 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | COMBINE_EQS: (18), (111) imply: % 154.26/23.26 | | | | | | | | | | | | | | (112) all_6_2 = e3 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | SIMP: (112) implies: % 154.26/23.26 | | | | | | | | | | | | | | (113) all_6_2 = e3 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | COMBINE_EQS: (53), (113) imply: % 154.26/23.26 | | | | | | | | | | | | | | (114) all_58_30 = e3 % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (11), (14), (16), (19), (20), (23), % 154.26/23.26 | | | | | | | | | | | | | | (24), (26), (27), (32), (33), (37), (38), (42), % 154.26/23.26 | | | | | | | | | | | | | | (44), (49), (54), (57), (70), (94), (106), (114) % 154.26/23.26 | | | | | | | | | | | | | | are inconsistent by sub-proof #342. % 154.26/23.26 | | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | End of split % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | (115) all_56_13 = e1 % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | | REF_CLOSE: (20), (91), (115) are inconsistent by sub-proof % 154.26/23.26 | | | | | | | | | | | | | #341. % 154.26/23.26 | | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | | End of split % 154.26/23.26 | | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | | End of split % 154.26/23.26 | | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | End of split % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | (116) ~ (all_56_13 = e3) % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | REDUCE: (15), (116) imply: % 154.26/23.26 | | | | | | | | | | (117) ~ (all_8_1 = e3) % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | | REF_CLOSE: (30), (50), (90), (117) are inconsistent by % 154.26/23.26 | | | | | | | | | | sub-proof #339. % 154.26/23.26 | | | | | | | | | | % 154.26/23.26 | | | | | | | | | End of split % 154.26/23.26 | | | | | | | | | % 154.26/23.26 | | | | | | | | End of split % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | End of split % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | End of split % 154.26/23.26 | | | | | % 154.26/23.26 | | | | End of split % 154.26/23.26 | | | | % 154.26/23.26 | | | End of split % 154.26/23.26 | | | % 154.26/23.26 | | End of split % 154.26/23.26 | | % 154.26/23.26 | End of split % 154.26/23.26 | % 154.26/23.26 End of proof % 154.26/23.26 % 154.26/23.26 Sub-proof #339 shows that the following formulas are inconsistent: % 154.26/23.26 ---------------------------------------------------------------- % 154.26/23.26 (1) all_54_13 = e3 | all_54_13 = e2 % 154.26/23.26 (2) all_54_13 = all_8_1 % 154.26/23.26 (3) ~ (all_8_1 = e2) % 154.26/23.26 (4) ~ (all_8_1 = e3) % 154.26/23.26 % 154.26/23.26 Begin of proof % 154.26/23.26 | % 154.26/23.26 | BETA: splitting (1) gives: % 154.26/23.26 | % 154.26/23.26 | Case 1: % 154.26/23.26 | | % 154.26/23.26 | | (5) all_54_13 = e2 % 154.26/23.26 | | % 154.26/23.26 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #340. % 154.26/23.26 | | % 154.26/23.26 | Case 2: % 154.26/23.26 | | % 154.26/23.26 | | (6) all_54_13 = e3 % 154.26/23.26 | | % 154.26/23.26 | | COMBINE_EQS: (2), (6) imply: % 154.26/23.26 | | (7) all_8_1 = e3 % 154.26/23.26 | | % 154.26/23.26 | | SIMP: (7) implies: % 154.26/23.26 | | (8) all_8_1 = e3 % 154.26/23.26 | | % 154.26/23.26 | | REDUCE: (4), (8) imply: % 154.26/23.26 | | (9) $false % 154.26/23.26 | | % 154.26/23.26 | | CLOSE: (9) is inconsistent. % 154.26/23.26 | | % 154.26/23.26 | End of split % 154.26/23.26 | % 154.26/23.26 End of proof % 154.26/23.26 % 154.26/23.26 Sub-proof #340 shows that the following formulas are inconsistent: % 154.26/23.26 ---------------------------------------------------------------- % 154.26/23.26 (1) all_54_13 = all_8_1 % 154.26/23.26 (2) all_54_13 = e2 % 154.26/23.26 (3) ~ (all_8_1 = e2) % 154.26/23.26 % 154.26/23.26 Begin of proof % 154.26/23.26 | % 154.26/23.26 | COMBINE_EQS: (1), (2) imply: % 154.26/23.26 | (4) all_8_1 = e2 % 154.26/23.26 | % 154.26/23.26 | SIMP: (4) implies: % 154.26/23.26 | (5) all_8_1 = e2 % 154.26/23.26 | % 154.26/23.26 | REDUCE: (3), (5) imply: % 154.26/23.26 | (6) $false % 154.26/23.26 | % 154.26/23.26 | CLOSE: (6) is inconsistent. % 154.26/23.26 | % 154.26/23.26 End of proof % 154.26/23.26 % 154.26/23.26 Sub-proof #341 shows that the following formulas are inconsistent: % 154.26/23.26 ---------------------------------------------------------------- % 154.26/23.26 (1) all_56_13 = e3 % 154.26/23.26 (2) all_56_13 = e1 % 154.26/23.26 (3) ~ (e3 = e1) % 154.26/23.26 % 154.26/23.26 Begin of proof % 154.26/23.26 | % 154.26/23.26 | COMBINE_EQS: (1), (2) imply: % 154.26/23.26 | (4) e3 = e1 % 154.26/23.26 | % 154.26/23.26 | SIMP: (4) implies: % 154.26/23.26 | (5) e3 = e1 % 154.26/23.26 | % 154.26/23.26 | REDUCE: (3), (5) imply: % 154.26/23.26 | (6) $false % 154.26/23.26 | % 154.26/23.26 | CLOSE: (6) is inconsistent. % 154.26/23.26 | % 154.26/23.26 End of proof % 154.26/23.26 % 154.26/23.26 Sub-proof #342 shows that the following formulas are inconsistent: % 154.26/23.26 ---------------------------------------------------------------- % 154.26/23.26 (1) all_58_31 = e2 % 154.26/23.26 (2) all_58_2 = e2 % 154.26/23.26 (3) all_58_22 = e0 % 154.26/23.26 (4) all_58_4 = e0 % 154.26/23.26 (5) all_58_30 = e3 % 154.26/23.26 (6) all_58_8 = e3 % 154.26/23.26 (7) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 = e1 & % 154.26/23.26 all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.26/23.26 all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.26 all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.26 all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.26 all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 154.26/23.26 all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.26 all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.26 all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 % 154.26/23.26 = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = % 154.26/23.26 e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = % 154.26/23.26 e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.26/23.26 e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) % 154.26/23.26 | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.26 (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.26 (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = % 154.26/23.26 e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.26/23.26 & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.26 all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.26 all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 % 154.26/23.26 = e0) | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.26/23.26 e0) | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = % 154.26/23.26 e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = % 154.26/23.26 e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 154.26/23.26 e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.26 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.26 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.26 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.26 (8) all_58_20 = e0 % 154.26/23.26 (9) all_58_24 = e3 % 154.26/23.26 (10) all_58_15 = e2 % 154.26/23.26 (11) ~ (e3 = e1) % 154.26/23.26 (12) all_58_26 = e1 % 154.26/23.26 (13) all_58_28 = e1 % 154.26/23.26 (14) all_58_11 = e2 % 154.26/23.26 (15) all_58_29 = e0 % 154.26/23.26 (16) ~ (e2 = e1) % 154.26/23.26 (17) all_58_17 = e1 % 154.26/23.26 (18) ~ (e3 = e0) % 154.26/23.26 (19) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.26 (20) all_58_13 = e1 % 154.26/23.26 (21) all_58_6 = e3 % 154.26/23.26 (22) ~ (e2 = e0) % 154.26/23.26 (23) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.26 (24) ~ (e1 = e0) % 154.26/23.26 (25) ~ (e3 = e2) % 154.26/23.26 % 154.26/23.26 Begin of proof % 154.26/23.26 | % 154.26/23.26 | BETA: splitting (7) gives: % 154.26/23.26 | % 154.26/23.26 | Case 1: % 154.26/23.26 | | % 154.26/23.26 | | (26) all_58_29 = e2 % 154.26/23.26 | | % 154.26/23.26 | | COMBINE_EQS: (15), (26) imply: % 154.26/23.26 | | (27) e2 = e0 % 154.26/23.26 | | % 154.26/23.26 | | COMBINE_EQS: (1), (27) imply: % 154.26/23.26 | | (28) all_58_31 = e0 % 154.26/23.26 | | % 154.26/23.26 | | REF_CLOSE: (5), (19), (22), (25), (28) are inconsistent by sub-proof #854. % 154.26/23.26 | | % 154.26/23.26 | Case 2: % 154.26/23.26 | | % 154.26/23.26 | | (29) ~ (all_58_29 = e2) % 154.26/23.26 | | (30) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.26 | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.26 | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 % 154.26/23.26 | | & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = % 154.26/23.26 | | e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = % 154.26/23.26 | | e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = % 154.26/23.26 | | e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.26 | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.26 | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.26 | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.26 | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.26/23.26 | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = % 154.26/23.26 | | e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 % 154.26/23.26 | | = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.26 | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 % 154.26/23.26 | | & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.26/23.26 | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.26 | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 % 154.26/23.26 | | & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = % 154.26/23.26 | | e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 % 154.26/23.26 | | = e0 & all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.26 | | e0) | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.26/23.26 | | all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = % 154.26/23.26 | | e1 & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.26 | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = % 154.26/23.26 | | e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 154.26/23.26 | | all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.26 | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = % 154.26/23.26 | | e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.26 | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 % 154.26/23.26 | | = e0) % 154.26/23.26 | | % 154.26/23.26 | | REDUCE: (15), (29) imply: % 154.26/23.26 | | (31) ~ (e2 = e0) % 154.26/23.26 | | % 154.26/23.26 | | BETA: splitting (30) gives: % 154.26/23.26 | | % 154.26/23.26 | | Case 1: % 154.26/23.26 | | | % 154.26/23.26 | | | (32) all_58_28 = e3 % 154.26/23.26 | | | % 154.26/23.26 | | | COMBINE_EQS: (13), (32) imply: % 154.26/23.26 | | | (33) e3 = e1 % 154.26/23.26 | | | % 154.26/23.26 | | | REDUCE: (11), (33) imply: % 154.26/23.26 | | | (34) $false % 154.26/23.26 | | | % 154.26/23.26 | | | CLOSE: (34) is inconsistent. % 154.26/23.26 | | | % 154.26/23.26 | | Case 2: % 154.26/23.26 | | | % 154.26/23.26 | | | (35) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.26/23.26 | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.26/23.26 | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) % 154.26/23.26 | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = % 154.26/23.26 | | | e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 % 154.26/23.26 | | | = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.26 | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = % 154.26/23.26 | | | e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.26 | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.26 | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 % 154.26/23.26 | | | & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 % 154.26/23.26 | | | = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.26 | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = % 154.26/23.26 | | | e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.26/23.26 | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.26 | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.26 | | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.26/23.26 | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.26 | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.26 | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) % 154.26/23.26 | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = % 154.26/23.26 | | | e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 154.26/23.26 | | | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.26/23.26 | | | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = % 154.26/23.26 | | | e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.26 | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = % 154.26/23.26 | | | e0 & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.26 | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.26 | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = % 154.26/23.26 | | | e0 & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.26 | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.26 | | | % 154.26/23.26 | | | BETA: splitting (35) gives: % 154.26/23.26 | | | % 154.26/23.26 | | | Case 1: % 154.26/23.26 | | | | % 154.26/23.26 | | | | (36) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.26/23.26 | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.26/23.26 | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.26 | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = % 154.26/23.26 | | | | e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.26 | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 154.26/23.26 | | | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.26 | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.26/23.26 | | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.26 | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.26 | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.26 | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.26 | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.26/23.26 | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.26 | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 % 154.26/23.26 | | | | = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.26 | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.26 | | | | % 154.26/23.26 | | | | BETA: splitting (36) gives: % 154.26/23.26 | | | | % 154.26/23.26 | | | | Case 1: % 154.26/23.26 | | | | | % 154.26/23.26 | | | | | (37) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.26/23.26 | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.26 | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.26/23.26 | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.26 | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 % 154.26/23.26 | | | | | = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.26 | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 % 154.26/23.26 | | | | | = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.26 | | | | | % 154.26/23.26 | | | | | BETA: splitting (37) gives: % 154.26/23.26 | | | | | % 154.26/23.26 | | | | | Case 1: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | (38) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.26/23.26 | | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.26 | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.26 | | | | | | all_58_11 = e2 & all_58_17 = e2) % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | BETA: splitting (38) gives: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | Case 1: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (39) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 % 154.26/23.26 | | | | | | | = e1 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | ALPHA: (39) implies: % 154.26/23.26 | | | | | | | (40) all_58_15 = e1 % 154.26/23.26 | | | | | | | (41) all_58_4 = e1 % 154.26/23.26 | | | | | | | (42) all_58_2 = e3 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | COMBINE_EQS: (2), (42) imply: % 154.26/23.26 | | | | | | | (43) e3 = e2 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | SIMP: (43) implies: % 154.26/23.26 | | | | | | | (44) e3 = e2 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | COMBINE_EQS: (4), (41) imply: % 154.26/23.26 | | | | | | | (45) e1 = e0 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | COMBINE_EQS: (10), (40) imply: % 154.26/23.26 | | | | | | | (46) e2 = e1 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | SIMP: (46) implies: % 154.26/23.26 | | | | | | | (47) e2 = e1 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | COMBINE_EQS: (45), (47) imply: % 154.26/23.26 | | | | | | | (48) e2 = e0 % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | REF_CLOSE: (1), (5), (19), (22), (44), (48) are inconsistent by % 154.26/23.26 | | | | | | | sub-proof #351. % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | Case 2: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (49) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 % 154.26/23.26 | | | | | | | = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 % 154.26/23.26 | | | | | | | & all_58_17 = e2) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (49) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (50) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.26 | | | | | | | | all_58_22 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (50) implies: % 154.26/23.26 | | | | | | | | (51) all_58_6 = e0 % 154.26/23.26 | | | | | | | | (52) all_58_2 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (2), (52) imply: % 154.26/23.26 | | | | | | | | (53) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (53) implies: % 154.26/23.26 | | | | | | | | (54) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (21), (51) imply: % 154.26/23.26 | | | | | | | | (55) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (54), (55) imply: % 154.26/23.26 | | | | | | | | (56) e2 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (54), (56) are inconsistent by % 154.26/23.26 | | | | | | | | sub-proof #351. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (57) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.26 | | | | | | | | all_58_17 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (57) implies: % 154.26/23.26 | | | | | | | | (58) all_58_17 = e2 % 154.26/23.26 | | | | | | | | (59) all_58_2 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (2), (59) imply: % 154.26/23.26 | | | | | | | | (60) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (60) implies: % 154.26/23.26 | | | | | | | | (61) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (17), (58) imply: % 154.26/23.26 | | | | | | | | (62) e2 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (15), (16), (22), (23), (61), (62) are % 154.26/23.26 | | | | | | | | inconsistent by sub-proof #350. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | End of split % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | Case 2: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | (63) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.26/23.26 | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.26 | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 154.26/23.26 | | | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.26 | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | BETA: splitting (63) gives: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | Case 1: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (64) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.26 | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.26 | | | | | | | all_58_8 = e2 & all_58_15 = e3) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (64) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (65) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.26 | | | | | | | | all_58_24 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (65) implies: % 154.26/23.26 | | | | | | | | (66) all_58_24 = e2 % 154.26/23.26 | | | | | | | | (67) all_58_13 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (9), (15), (16), (20), (22), (23), (66), % 154.26/23.26 | | | | | | | | (67) are inconsistent by sub-proof #349. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (68) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.26 | | | | | | | | all_58_15 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (68) implies: % 154.26/23.26 | | | | | | | | (69) all_58_15 = e3 % 154.26/23.26 | | | | | | | | (70) all_58_4 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (4), (70) imply: % 154.26/23.26 | | | | | | | | (71) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (10), (69) imply: % 154.26/23.26 | | | | | | | | (72) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (71), (72) are inconsistent by % 154.26/23.26 | | | | | | | | sub-proof #348. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | Case 2: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (73) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 % 154.26/23.26 | | | | | | | = e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 % 154.26/23.26 | | | | | | | & all_58_17 = e1) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (73) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (74) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.26 | | | | | | | | all_58_22 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (74) implies: % 154.26/23.26 | | | | | | | | (75) all_58_22 = e3 % 154.26/23.26 | | | | | | | | (76) all_58_8 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (6), (76) imply: % 154.26/23.26 | | | | | | | | (77) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (77) implies: % 154.26/23.26 | | | | | | | | (78) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (3), (75) imply: % 154.26/23.26 | | | | | | | | (79) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (79) implies: % 154.26/23.26 | | | | | | | | (80) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (78), (80) imply: % 154.26/23.26 | | | | | | | | (81) e2 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (78), (81) are inconsistent by % 154.26/23.26 | | | | | | | | sub-proof #351. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (82) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.26 | | | | | | | | all_58_17 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (82) implies: % 154.26/23.26 | | | | | | | | (83) all_58_11 = e1 % 154.26/23.26 | | | | | | | | (84) all_58_8 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (6), (84) imply: % 154.26/23.26 | | | | | | | | (85) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (85) implies: % 154.26/23.26 | | | | | | | | (86) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (14), (83) imply: % 154.26/23.26 | | | | | | | | (87) e2 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (15), (16), (22), (23), (86), (87) are % 154.26/23.26 | | | | | | | | inconsistent by sub-proof #350. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | End of split % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | End of split % 154.26/23.26 | | | | | % 154.26/23.26 | | | | Case 2: % 154.26/23.26 | | | | | % 154.26/23.26 | | | | | (88) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.26/23.26 | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 % 154.26/23.26 | | | | | = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.26/23.26 | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = % 154.26/23.26 | | | | | e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.26 | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 % 154.26/23.26 | | | | | = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.26 | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 154.26/23.26 | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.26 | | | | | % 154.26/23.26 | | | | | BETA: splitting (88) gives: % 154.26/23.26 | | | | | % 154.26/23.26 | | | | | Case 1: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | (89) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 % 154.26/23.26 | | | | | | = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.26 | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 % 154.26/23.26 | | | | | | = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.26 | | | | | | all_58_17 = e1) % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | BETA: splitting (89) gives: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | Case 1: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (90) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.26 | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 154.26/23.26 | | | | | | | e2) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (90) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (91) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.26 | | | | | | | | all_58_24 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (91) implies: % 154.26/23.26 | | | | | | | | (92) all_58_24 = e0 % 154.26/23.26 | | | | | | | | (93) all_58_8 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (6), (93) imply: % 154.26/23.26 | | | | | | | | (94) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (94) implies: % 154.26/23.26 | | | | | | | | (95) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (9), (92) imply: % 154.26/23.26 | | | | | | | | (96) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (96) implies: % 154.26/23.26 | | | | | | | | (97) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (95), (97) are inconsistent by % 154.26/23.26 | | | | | | | | sub-proof #348. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (98) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (98) implies: % 154.26/23.26 | | | | | | | | (99) all_58_8 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (6), (25), (99) are inconsistent by sub-proof #347. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | Case 2: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (100) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.26 | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.26/23.26 | | | | | | | all_58_15 = e3 & all_58_17 = e1) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (100) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (101) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.26 | | | | | | | | all_58_22 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (101) implies: % 154.26/23.26 | | | | | | | | (102) all_58_15 = e3 % 154.26/23.26 | | | | | | | | (103) all_58_6 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (21), (103) imply: % 154.26/23.26 | | | | | | | | (104) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (10), (102) imply: % 154.26/23.26 | | | | | | | | (105) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (104), (105) are inconsistent % 154.26/23.26 | | | | | | | | by sub-proof #348. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (106) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.26 | | | | | | | | all_58_17 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (106) implies: % 154.26/23.26 | | | | | | | | (107) all_58_15 = e3 % 154.26/23.26 | | | | | | | | (108) all_58_11 = e1 % 154.26/23.26 | | | | | | | | (109) all_58_4 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (4), (109) imply: % 154.26/23.26 | | | | | | | | (110) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (14), (108) imply: % 154.26/23.26 | | | | | | | | (111) e2 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (10), (107) imply: % 154.26/23.26 | | | | | | | | (112) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (110), (112) imply: % 154.26/23.26 | | | | | | | | (113) e2 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (111), (113) imply: % 154.26/23.26 | | | | | | | | (114) e1 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (112), (113) are inconsistent % 154.26/23.26 | | | | | | | | by sub-proof #351. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | End of split % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | Case 2: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | (115) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.26 | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.26 | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.26/23.26 | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.26 | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.26 | | | | | | all_58_26 = e0) % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | BETA: splitting (115) gives: % 154.26/23.26 | | | | | | % 154.26/23.26 | | | | | | Case 1: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (116) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.26 | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.26 | | | | | | | all_58_15 = e1 & all_58_22 = e3) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (116) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (117) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.26 | | | | | | | | all_58_26 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (117) implies: % 154.26/23.26 | | | | | | | | (118) all_58_15 = e3 % 154.26/23.26 | | | | | | | | (119) all_58_4 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (4), (119) imply: % 154.26/23.26 | | | | | | | | (120) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (10), (118) imply: % 154.26/23.26 | | | | | | | | (121) e3 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (120), (121) imply: % 154.26/23.26 | | | | | | | | (122) e2 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (121), (122) are inconsistent % 154.26/23.26 | | | | | | | | by sub-proof #351. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (123) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.26 | | | | | | | | all_58_22 = e3 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (123) implies: % 154.26/23.26 | | | | | | | | (124) all_58_22 = e3 % 154.26/23.26 | | | | | | | | (125) all_58_15 = e1 % 154.26/23.26 | | | | | | | | (126) all_58_4 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (4), (126) imply: % 154.26/23.26 | | | | | | | | (127) e1 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (10), (125) imply: % 154.26/23.26 | | | | | | | | (128) e2 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (128) implies: % 154.26/23.26 | | | | | | | | (129) e2 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (3), (124) imply: % 154.26/23.26 | | | | | | | | (130) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | SIMP: (130) implies: % 154.26/23.26 | | | | | | | | (131) e3 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (127), (129), (131) are % 154.26/23.26 | | | | | | | | inconsistent by sub-proof #346. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | End of split % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | Case 2: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | (132) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.26 | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.26 | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | BETA: splitting (132) gives: % 154.26/23.26 | | | | | | | % 154.26/23.26 | | | | | | | Case 1: % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | (133) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.26 | | | | | | | | all_58_17 = e2 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | ALPHA: (133) implies: % 154.26/23.26 | | | | | | | | (134) all_58_17 = e2 % 154.26/23.26 | | | | | | | | (135) all_58_4 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (4), (135) imply: % 154.26/23.26 | | | | | | | | (136) e1 = e0 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | COMBINE_EQS: (17), (134) imply: % 154.26/23.26 | | | | | | | | (137) e2 = e1 % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (25), (136), (137) are % 154.26/23.26 | | | | | | | | inconsistent by sub-proof #345. % 154.26/23.26 | | | | | | | | % 154.26/23.26 | | | | | | | Case 2: % 154.26/23.26 | | | | | | | | % 154.26/23.27 | | | | | | | | (138) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.27 | | | | | | | | all_58_26 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (138) implies: % 154.26/23.27 | | | | | | | | (139) all_58_26 = e0 % 154.26/23.27 | | | | | | | | (140) all_58_15 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (10), (140) imply: % 154.26/23.27 | | | | | | | | (141) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (12), (19), (22), (25), (139), (141) are % 154.26/23.27 | | | | | | | | inconsistent by sub-proof #344. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | End of split % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | End of split % 154.26/23.27 | | | | | % 154.26/23.27 | | | | End of split % 154.26/23.27 | | | | % 154.26/23.27 | | | Case 2: % 154.26/23.27 | | | | % 154.26/23.27 | | | | (142) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.26/23.27 | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 % 154.26/23.27 | | | | = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.27 | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = % 154.26/23.27 | | | | e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.27 | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) % 154.26/23.27 | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 % 154.26/23.27 | | | | = e0) | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.27 | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.27 | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.26/23.27 | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.27 | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.27 | | | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.27 | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = % 154.26/23.27 | | | | e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.27 | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.27 | | | | % 154.26/23.27 | | | | BETA: splitting (142) gives: % 154.26/23.27 | | | | % 154.26/23.27 | | | | Case 1: % 154.26/23.27 | | | | | % 154.26/23.27 | | | | | (143) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.26/23.27 | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.27 | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.27 | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.27 | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.27 | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.27 | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = % 154.26/23.27 | | | | | e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.27 | | | | | % 154.26/23.27 | | | | | BETA: splitting (143) gives: % 154.26/23.27 | | | | | % 154.26/23.27 | | | | | Case 1: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | (144) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.26/23.27 | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.27 | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.27 | | | | | | all_58_26 = e0) % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | BETA: splitting (144) gives: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | Case 1: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (145) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | ALPHA: (145) implies: % 154.26/23.27 | | | | | | | (146) e3 = e1 % 154.26/23.27 | | | | | | | (147) all_58_15 = e1 % 154.26/23.27 | | | | | | | (148) all_58_4 = e1 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | COMBINE_EQS: (4), (148) imply: % 154.26/23.27 | | | | | | | (149) e1 = e0 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | COMBINE_EQS: (10), (147) imply: % 154.26/23.27 | | | | | | | (150) e2 = e1 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | SIMP: (150) implies: % 154.26/23.27 | | | | | | | (151) e2 = e1 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | COMBINE_EQS: (149), (151) imply: % 154.26/23.27 | | | | | | | (152) e2 = e0 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | COMBINE_EQS: (146), (149) imply: % 154.26/23.27 | | | | | | | (153) e3 = e0 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | COMBINE_EQS: (1), (152) imply: % 154.26/23.27 | | | | | | | (154) all_58_31 = e0 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | COMBINE_EQS: (5), (153) imply: % 154.26/23.27 | | | | | | | (155) all_58_30 = e0 % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | REF_CLOSE: (19), (22), (154), (155) are inconsistent by sub-proof % 154.26/23.27 | | | | | | | #674. % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | Case 2: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (156) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.27 | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.27 | | | | | | | all_58_22 = e3 & all_58_26 = e0) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (156) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (157) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.27 | | | | | | | | all_58_24 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (157) implies: % 154.26/23.27 | | | | | | | | (158) all_58_13 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (20), (158) imply: % 154.26/23.27 | | | | | | | | (159) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (159) implies: % 154.26/23.27 | | | | | | | | (160) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REDUCE: (24), (160) imply: % 154.26/23.27 | | | | | | | | (161) $false % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | CLOSE: (161) is inconsistent. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (162) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.27 | | | | | | | | all_58_26 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (162) implies: % 154.26/23.27 | | | | | | | | (163) all_58_26 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (12), (24), (163) are inconsistent by sub-proof #343. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | End of split % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | Case 2: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | (164) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.27 | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.27 | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.27 | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = % 154.26/23.27 | | | | | | e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | BETA: splitting (164) gives: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | Case 1: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (165) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.27 | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.27 | | | | | | | all_58_22 = e0 & all_58_26 = e1) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (165) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (166) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.27 | | | | | | | | all_58_24 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (166) implies: % 154.26/23.27 | | | | | | | | (167) all_58_24 = e2 % 154.26/23.27 | | | | | | | | (168) all_58_13 = e2 % 154.26/23.27 | | | | | | | | (169) all_58_6 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (21), (169) imply: % 154.26/23.27 | | | | | | | | (170) e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (20), (168) imply: % 154.26/23.27 | | | | | | | | (171) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (9), (167) imply: % 154.26/23.27 | | | | | | | | (172) e3 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (172) implies: % 154.26/23.27 | | | | | | | | (173) e3 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (170), (173) imply: % 154.26/23.27 | | | | | | | | (174) e2 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (174) implies: % 154.26/23.27 | | | | | | | | (175) e2 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (171), (175) imply: % 154.26/23.27 | | | | | | | | (176) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (170), (171), (176) are % 154.26/23.27 | | | | | | | | inconsistent by sub-proof #346. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (177) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.27 | | | | | | | | all_58_26 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (177) implies: % 154.26/23.27 | | | | | | | | (178) all_58_20 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (8), (178) imply: % 154.26/23.27 | | | | | | | | (179) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REDUCE: (24), (179) imply: % 154.26/23.27 | | | | | | | | (180) $false % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | CLOSE: (180) is inconsistent. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | Case 2: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (181) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 154.26/23.27 | | | | | | | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (181) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (182) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (182) implies: % 154.26/23.27 | | | | | | | | (183) all_58_6 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (21), (183) imply: % 154.26/23.27 | | | | | | | | (184) e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REDUCE: (18), (184) imply: % 154.26/23.27 | | | | | | | | (185) $false % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | CLOSE: (185) is inconsistent. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (186) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.26/23.27 | | | | | | | | all_58_24 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (186) implies: % 154.26/23.27 | | | | | | | | (187) all_58_24 = e0 % 154.26/23.27 | | | | | | | | (188) all_58_17 = e2 % 154.26/23.27 | | | | | | | | (189) all_58_13 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (20), (189) imply: % 154.26/23.27 | | | | | | | | (190) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (190) implies: % 154.26/23.27 | | | | | | | | (191) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (17), (188) imply: % 154.26/23.27 | | | | | | | | (192) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (9), (187) imply: % 154.26/23.27 | | | | | | | | (193) e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (193) implies: % 154.26/23.27 | | | | | | | | (194) e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (191), (192), (194) are % 154.26/23.27 | | | | | | | | inconsistent by sub-proof #346. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | End of split % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | End of split % 154.26/23.27 | | | | | % 154.26/23.27 | | | | Case 2: % 154.26/23.27 | | | | | % 154.26/23.27 | | | | | (195) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.27 | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.27 | | | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.26/23.27 | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 154.26/23.27 | | | | | all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.26/23.27 | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.27 | | | | | all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.27 | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.26/23.27 | | | | | & all_58_26 = e0 & e1 = e0) % 154.26/23.27 | | | | | % 154.26/23.27 | | | | | BETA: splitting (195) gives: % 154.26/23.27 | | | | | % 154.26/23.27 | | | | | Case 1: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | (196) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.27 | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.27 | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.26/23.27 | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.27 | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | BETA: splitting (196) gives: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | Case 1: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (197) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.27 | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.27 | | | | | | | all_58_17 = e1 & all_58_24 = e2) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (197) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (198) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.27 | | | | | | | | all_58_26 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (198) implies: % 154.26/23.27 | | | | | | | | (199) all_58_20 = e1 % 154.26/23.27 | | | | | | | | (200) all_58_17 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (17), (200) imply: % 154.26/23.27 | | | | | | | | (201) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (8), (199) imply: % 154.26/23.27 | | | | | | | | (202) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (25), (201), (202) are % 154.26/23.27 | | | | | | | | inconsistent by sub-proof #345. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (203) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.27 | | | | | | | | all_58_24 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (203) implies: % 154.26/23.27 | | | | | | | | (204) all_58_24 = e2 % 154.26/23.27 | | | | | | | | (205) all_58_13 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (9), (15), (16), (20), (22), (23), (204), % 154.26/23.27 | | | | | | | | (205) are inconsistent by sub-proof #349. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | Case 2: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (206) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.27 | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 % 154.26/23.27 | | | | | | | = e1) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (206) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (207) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.27 | | | | | | | | all_58_26 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (207) implies: % 154.26/23.27 | | | | | | | | (208) all_58_26 = e0 % 154.26/23.27 | | | | | | | | (209) all_58_11 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (14), (209) imply: % 154.26/23.27 | | | | | | | | (210) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (12), (19), (22), (25), (208), (210) are % 154.26/23.27 | | | | | | | | inconsistent by sub-proof #344. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (211) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (211) implies: % 154.26/23.27 | | | | | | | | (212) all_58_11 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (14), (212) imply: % 154.26/23.27 | | | | | | | | (213) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (213) implies: % 154.26/23.27 | | | | | | | | (214) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (1), (214) imply: % 154.26/23.27 | | | | | | | | (215) all_58_31 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (5), (15), (16), (22), (23), (25), (215) are % 154.26/23.27 | | | | | | | | inconsistent by sub-proof #657. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | End of split % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | Case 2: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | (216) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.27 | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.27 | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.27 | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.26/23.27 | | | | | | e0 & e1 = e0) % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | BETA: splitting (216) gives: % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | | Case 1: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (217) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.27 | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.27 | | | | | | | all_58_24 = e0 & all_58_26 = e1) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (217) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (218) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.27 | | | | | | | | all_58_26 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (218) implies: % 154.26/23.27 | | | | | | | | (219) all_58_26 = e0 % 154.26/23.27 | | | | | | | | (220) all_58_24 = e2 % 154.26/23.27 | | | | | | | | (221) all_58_13 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (20), (221) imply: % 154.26/23.27 | | | | | | | | (222) e2 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (9), (220) imply: % 154.26/23.27 | | | | | | | | (223) e3 = e2 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (12), (219) imply: % 154.26/23.27 | | | | | | | | (224) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (224) implies: % 154.26/23.27 | | | | | | | | (225) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (222), (225) imply: % 154.26/23.27 | | | | | | | | (226) e2 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (1), (5), (19), (22), (223), (226) are inconsistent % 154.26/23.27 | | | | | | | | by sub-proof #351. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (227) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.27 | | | | | | | | all_58_26 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (227) implies: % 154.26/23.27 | | | | | | | | (228) all_58_20 = e1 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (8), (228) imply: % 154.26/23.27 | | | | | | | | (229) e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REDUCE: (24), (229) imply: % 154.26/23.27 | | | | | | | | (230) $false % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | CLOSE: (230) is inconsistent. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | Case 2: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | (231) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 % 154.26/23.27 | | | | | | | = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | BETA: splitting (231) gives: % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | | Case 1: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (232) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (232) implies: % 154.26/23.27 | | | | | | | | (233) e2 = e0 % 154.26/23.27 | | | | | | | | (234) all_58_24 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (9), (234) imply: % 154.26/23.27 | | | | | | | | (235) e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | SIMP: (235) implies: % 154.26/23.27 | | | | | | | | (236) e3 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (1), (233) imply: % 154.26/23.27 | | | | | | | | (237) all_58_31 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | COMBINE_EQS: (5), (236) imply: % 154.26/23.27 | | | | | | | | (238) all_58_30 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (19), (22), (237), (238) are inconsistent by % 154.26/23.27 | | | | | | | | sub-proof #674. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | Case 2: % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | (239) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | ALPHA: (239) implies: % 154.26/23.27 | | | | | | | | (240) all_58_26 = e0 % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | | REF_CLOSE: (12), (24), (240) are inconsistent by sub-proof #343. % 154.26/23.27 | | | | | | | | % 154.26/23.27 | | | | | | | End of split % 154.26/23.27 | | | | | | | % 154.26/23.27 | | | | | | End of split % 154.26/23.27 | | | | | | % 154.26/23.27 | | | | | End of split % 154.26/23.27 | | | | | % 154.26/23.27 | | | | End of split % 154.26/23.27 | | | | % 154.26/23.27 | | | End of split % 154.26/23.27 | | | % 154.26/23.27 | | End of split % 154.26/23.27 | | % 154.26/23.27 | End of split % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #343 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_26 = e1 % 154.26/23.27 (2) all_58_26 = e0 % 154.26/23.27 (3) ~ (e1 = e0) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (2) imply: % 154.26/23.27 | (4) e1 = e0 % 154.26/23.27 | % 154.26/23.27 | SIMP: (4) implies: % 154.26/23.27 | (5) e1 = e0 % 154.26/23.27 | % 154.26/23.27 | REDUCE: (3), (5) imply: % 154.26/23.27 | (6) $false % 154.26/23.27 | % 154.26/23.27 | CLOSE: (6) is inconsistent. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #344 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) e2 = e1 % 154.26/23.27 (4) all_58_26 = e1 % 154.26/23.27 (5) all_58_26 = e0 % 154.26/23.27 (6) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (7) ~ (e2 = e0) % 154.26/23.27 (8) ~ (e3 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | SIMP: (3) implies: % 154.26/23.27 | (9) e2 = e1 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (4), (5) imply: % 154.26/23.27 | (10) e1 = e0 % 154.26/23.27 | % 154.26/23.27 | SIMP: (10) implies: % 154.26/23.27 | (11) e1 = e0 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (1), (2), (6), (7), (8), (9), (11) are inconsistent by sub-proof % 154.26/23.27 | #345. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #345 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) e2 = e1 % 154.26/23.27 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (5) ~ (e2 = e0) % 154.26/23.27 (6) e1 = e0 % 154.26/23.27 (7) ~ (e3 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (3), (6) imply: % 154.26/23.27 | (8) e2 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (8) imply: % 154.26/23.27 | (9) all_58_31 = e0 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (2), (4), (5), (7), (9) are inconsistent by sub-proof #854. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #346 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) e2 = e1 % 154.26/23.27 (4) e3 = e0 % 154.26/23.27 (5) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (6) ~ (e2 = e0) % 154.26/23.27 (7) e1 = e0 % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (3), (7) imply: % 154.26/23.27 | (8) e2 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (8) imply: % 154.26/23.27 | (9) all_58_31 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (2), (4) imply: % 154.26/23.27 | (10) all_58_30 = e0 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (5), (6), (9), (10) are inconsistent by sub-proof #674. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #347 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_8 = e3 % 154.26/23.27 (2) all_58_8 = e2 % 154.26/23.27 (3) ~ (e3 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (2) imply: % 154.26/23.27 | (4) e3 = e2 % 154.26/23.27 | % 154.26/23.27 | SIMP: (4) implies: % 154.26/23.27 | (5) e3 = e2 % 154.26/23.27 | % 154.26/23.27 | REDUCE: (3), (5) imply: % 154.26/23.27 | (6) $false % 154.26/23.27 | % 154.26/23.27 | CLOSE: (6) is inconsistent. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #348 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) e3 = e0 % 154.26/23.27 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (5) ~ (e2 = e0) % 154.26/23.27 (6) e3 = e2 % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (3), (6) imply: % 154.26/23.27 | (7) e2 = e0 % 154.26/23.27 | % 154.26/23.27 | SIMP: (7) implies: % 154.26/23.27 | (8) e2 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (8) imply: % 154.26/23.27 | (9) all_58_31 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (2), (3) imply: % 154.26/23.27 | (10) all_58_30 = e0 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (4), (5), (9), (10) are inconsistent by sub-proof #674. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #349 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) all_58_24 = e3 % 154.26/23.27 (4) all_58_29 = e0 % 154.26/23.27 (5) ~ (e2 = e1) % 154.26/23.27 (6) all_58_13 = e1 % 154.26/23.27 (7) all_58_13 = e2 % 154.26/23.27 (8) ~ (e2 = e0) % 154.26/23.27 (9) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (10) all_58_24 = e2 % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (6), (7) imply: % 154.26/23.27 | (11) e2 = e1 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (3), (10) imply: % 154.26/23.27 | (12) e3 = e2 % 154.26/23.27 | % 154.26/23.27 | SIMP: (12) implies: % 154.26/23.27 | (13) e3 = e2 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (1), (2), (4), (5), (8), (9), (11), (13) are inconsistent by % 154.26/23.27 | sub-proof #350. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #350 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) all_58_29 = e0 % 154.26/23.27 (4) ~ (e2 = e1) % 154.26/23.27 (5) e2 = e1 % 154.26/23.27 (6) ~ (e2 = e0) % 154.26/23.27 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (8) e3 = e2 % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (5), (8) imply: % 154.26/23.27 | (9) e3 = e1 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (5) imply: % 154.26/23.27 | (10) all_58_31 = e1 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (2), (9) imply: % 154.26/23.27 | (11) all_58_30 = e1 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (3), (4), (6), (7), (10), (11) are inconsistent by sub-proof #379. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #351 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_30 = e3 % 154.26/23.27 (3) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (4) ~ (e2 = e0) % 154.26/23.27 (5) e2 = e0 % 154.26/23.27 (6) e3 = e2 % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (5), (6) imply: % 154.26/23.27 | (7) e3 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (5) imply: % 154.26/23.27 | (8) all_58_31 = e0 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (2), (7) imply: % 154.26/23.27 | (9) all_58_30 = e0 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (3), (4), (8), (9) are inconsistent by sub-proof #674. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #352 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_54_13 = all_8_1 % 154.26/23.27 (2) all_54_13 = e1 % 154.26/23.27 (3) ~ (all_8_1 = e1) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (2) imply: % 154.26/23.27 | (4) all_8_1 = e1 % 154.26/23.27 | % 154.26/23.27 | SIMP: (4) implies: % 154.26/23.27 | (5) all_8_1 = e1 % 154.26/23.27 | % 154.26/23.27 | REDUCE: (3), (5) imply: % 154.26/23.27 | (6) $false % 154.26/23.27 | % 154.26/23.27 | CLOSE: (6) is inconsistent. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #353 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_56_8 = all_6_2 % 154.26/23.27 (2) all_56_8 = e1 % 154.26/23.27 (3) ~ (all_6_2 = e1) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (2) imply: % 154.26/23.27 | (4) all_6_2 = e1 % 154.26/23.27 | % 154.26/23.27 | SIMP: (4) implies: % 154.26/23.27 | (5) all_6_2 = e1 % 154.26/23.27 | % 154.26/23.27 | REDUCE: (3), (5) imply: % 154.26/23.27 | (6) $false % 154.26/23.27 | % 154.26/23.27 | CLOSE: (6) is inconsistent. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #354 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (3) e2 = e1 % 154.26/23.27 (4) ~ (e3 = e1) % 154.26/23.27 (5) all_58_28 = e1 % 154.26/23.27 (6) all_58_29 = e0 % 154.26/23.27 (7) ~ (e2 = e1) % 154.26/23.27 (8) ~ (e3 = e0) % 154.26/23.27 (9) ~ (e2 = e0) % 154.26/23.27 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.27 (11) all_58_30 = all_6_2 % 154.26/23.27 (12) ~ (e3 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | SIMP: (3) implies: % 154.26/23.27 | (13) e2 = e1 % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (13) imply: % 154.26/23.27 | (14) all_58_31 = e1 % 154.26/23.27 | % 154.26/23.27 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14) are % 154.26/23.27 | inconsistent by sub-proof #383. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #355 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) ~ (e3 = e1) % 154.26/23.27 (3) all_58_28 = e1 % 154.26/23.27 (4) all_58_29 = e0 % 154.26/23.27 (5) ~ (e3 = e0) % 154.26/23.27 (6) all_58_30 = e1 % 154.26/23.27 (7) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.27 (8) ~ (e3 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | BETA: splitting (7) gives: % 154.26/23.27 | % 154.26/23.27 | Case 1: % 154.26/23.27 | | % 154.26/23.27 | | (9) all_58_28 = e3 % 154.26/23.27 | | % 154.26/23.27 | | COMBINE_EQS: (3), (9) imply: % 154.26/23.27 | | (10) e3 = e1 % 154.26/23.27 | | % 154.26/23.27 | | REDUCE: (2), (10) imply: % 154.26/23.27 | | (11) $false % 154.26/23.27 | | % 154.26/23.27 | | CLOSE: (11) is inconsistent. % 154.26/23.27 | | % 154.26/23.27 | Case 2: % 154.26/23.27 | | % 154.26/23.27 | | (12) ~ (all_58_28 = e3) % 154.26/23.27 | | (13) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.27 | | % 154.26/23.27 | | REDUCE: (3), (12) imply: % 154.26/23.27 | | (14) ~ (e3 = e1) % 154.26/23.27 | | % 154.26/23.27 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (13) are inconsistent by sub-proof % 154.26/23.27 | | #663. % 154.26/23.27 | | % 154.26/23.27 | End of split % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #356 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_31 = e2 % 154.26/23.27 (2) all_54_10 = all_6_2 % 154.26/23.27 (3) ~ (e3 = e1) % 154.26/23.27 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.27 (5) all_58_29 = e0 % 154.26/23.27 (6) ~ (e3 = e0) % 154.26/23.27 (7) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.27 (8) ~ (all_6_2 = e3) % 154.26/23.27 (9) all_58_30 = all_6_2 % 154.26/23.27 (10) ~ (e3 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | BETA: splitting (7) gives: % 154.26/23.27 | % 154.26/23.27 | Case 1: % 154.26/23.27 | | % 154.26/23.27 | | (11) all_58_29 = e3 % 154.26/23.27 | | % 154.26/23.27 | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #707. % 154.26/23.27 | | % 154.26/23.27 | Case 2: % 154.26/23.27 | | % 154.26/23.27 | | (12) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.27 | | % 154.26/23.27 | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (12) are inconsistent by % 154.26/23.27 | | sub-proof #475. % 154.26/23.27 | | % 154.26/23.27 | End of split % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #357 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_30 = e2 % 154.26/23.27 (2) ~ (e3 = e1) % 154.26/23.27 (3) all_58_29 = e0 % 154.26/23.27 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.27 (5) ~ (e2 = e1) % 154.26/23.27 (6) all_58_31 = e3 % 154.26/23.27 (7) ~ (e1 = e0) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | BETA: splitting (4) gives: % 154.26/23.27 | % 154.26/23.27 | Case 1: % 154.26/23.27 | | % 154.26/23.27 | | (8) all_58_29 = e1 % 154.26/23.27 | | % 154.26/23.27 | | COMBINE_EQS: (3), (8) imply: % 154.26/23.27 | | (9) e1 = e0 % 154.26/23.27 | | % 154.26/23.27 | | REDUCE: (7), (9) imply: % 154.26/23.27 | | (10) $false % 154.26/23.27 | | % 154.26/23.27 | | CLOSE: (10) is inconsistent. % 154.26/23.27 | | % 154.26/23.27 | Case 2: % 154.26/23.27 | | % 154.26/23.27 | | (11) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.27 | | % 154.26/23.27 | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #458. % 154.26/23.27 | | % 154.26/23.27 | End of split % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #358 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_54_14 = e3 | all_54_14 = e2 % 154.26/23.27 (2) all_54_14 = all_52_11 % 154.26/23.27 (3) ~ (all_52_11 = e2) % 154.26/23.27 (4) ~ (all_52_11 = e3) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | BETA: splitting (1) gives: % 154.26/23.27 | % 154.26/23.27 | Case 1: % 154.26/23.27 | | % 154.26/23.27 | | (5) all_54_14 = e2 % 154.26/23.27 | | % 154.26/23.27 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #360. % 154.26/23.27 | | % 154.26/23.27 | Case 2: % 154.26/23.27 | | % 154.26/23.27 | | (6) all_54_14 = e3 % 154.26/23.27 | | % 154.26/23.27 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #359. % 154.26/23.27 | | % 154.26/23.27 | End of split % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #359 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_54_14 = all_52_11 % 154.26/23.27 (2) all_54_14 = e3 % 154.26/23.27 (3) ~ (all_52_11 = e3) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (2) imply: % 154.26/23.27 | (4) all_52_11 = e3 % 154.26/23.27 | % 154.26/23.27 | SIMP: (4) implies: % 154.26/23.27 | (5) all_52_11 = e3 % 154.26/23.27 | % 154.26/23.27 | REDUCE: (3), (5) imply: % 154.26/23.27 | (6) $false % 154.26/23.27 | % 154.26/23.27 | CLOSE: (6) is inconsistent. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #360 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_54_14 = all_52_11 % 154.26/23.27 (2) all_54_14 = e2 % 154.26/23.27 (3) ~ (all_52_11 = e2) % 154.26/23.27 % 154.26/23.27 Begin of proof % 154.26/23.27 | % 154.26/23.27 | COMBINE_EQS: (1), (2) imply: % 154.26/23.27 | (4) all_52_11 = e2 % 154.26/23.27 | % 154.26/23.27 | SIMP: (4) implies: % 154.26/23.27 | (5) all_52_11 = e2 % 154.26/23.27 | % 154.26/23.27 | REDUCE: (3), (5) imply: % 154.26/23.27 | (6) $false % 154.26/23.27 | % 154.26/23.27 | CLOSE: (6) is inconsistent. % 154.26/23.27 | % 154.26/23.27 End of proof % 154.26/23.27 % 154.26/23.27 Sub-proof #361 shows that the following formulas are inconsistent: % 154.26/23.27 ---------------------------------------------------------------- % 154.26/23.27 (1) all_58_22 = e0 % 154.26/23.27 (2) all_58_6 = e2 % 154.26/23.27 (3) all_58_4 = e0 % 154.26/23.27 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.27 (5) all_58_20 = e0 % 154.26/23.27 (6) all_58_30 = e2 % 154.26/23.27 (7) ~ (e3 = e1) % 154.26/23.28 (8) all_58_26 = e1 % 154.26/23.28 (9) all_58_28 = e1 % 154.26/23.28 (10) all_58_29 = e0 % 154.26/23.28 (11) all_58_8 = e2 % 154.26/23.28 (12) ~ (e2 = e1) % 154.26/23.28 (13) all_58_17 = e1 % 154.26/23.28 (14) ~ (e3 = e0) % 154.26/23.28 (15) all_58_13 = e1 % 154.26/23.28 (16) all_58_31 = e3 % 154.26/23.28 (17) ~ (e2 = e0) % 154.26/23.28 (18) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.28 (19) all_58_2 = e3 % 154.26/23.28 (20) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.28 (21) all_58_15 = e3 % 154.26/23.28 (22) ~ (e1 = e0) % 154.26/23.28 (23) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = e3 & % 154.26/23.28 all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 154.26/23.28 all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.26/23.28 all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.28 all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 154.26/23.28 all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.28 all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.28 all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.26/23.28 all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.26/23.28 all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 % 154.26/23.28 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = % 154.26/23.28 e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = % 154.26/23.28 e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 % 154.26/23.28 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.28 all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.28 all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.28 (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.28 (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.28 (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.26/23.28 (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.28 (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.28 = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.26/23.28 = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.28 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.26/23.28 = e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.28 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.28 all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.28 all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.28 (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.28 (24) all_58_11 = e3 % 154.26/23.28 (25) all_58_24 = e2 % 154.26/23.28 (26) all_58_30 = all_6_2 % 154.26/23.28 (27) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.28 (28) ~ (e3 = e2) % 154.26/23.28 % 154.26/23.28 Begin of proof % 154.26/23.28 | % 154.26/23.28 | BETA: splitting (23) gives: % 154.26/23.28 | % 154.26/23.28 | Case 1: % 154.26/23.28 | | % 154.26/23.28 | | (29) all_58_30 = e1 % 154.26/23.28 | | % 154.26/23.28 | | REF_CLOSE: (6), (12), (29) are inconsistent by sub-proof #500. % 154.26/23.28 | | % 154.26/23.28 | Case 2: % 154.26/23.28 | | % 154.26/23.28 | | (30) ~ (all_58_30 = e1) % 154.26/23.28 | | (31) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 = e1 & % 154.26/23.28 | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.26/23.28 | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.28 | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.28 | | & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = % 154.26/23.28 | | e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 154.26/23.28 | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = % 154.26/23.28 | | e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 % 154.26/23.28 | | = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.26/23.28 | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.28 | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.26/23.28 | | & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.28 | | e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 % 154.26/23.28 | | = e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.26/23.28 | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 % 154.26/23.28 | | & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.26/23.28 | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.28 | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.26/23.28 | | & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.26/23.28 | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 % 154.26/23.28 | | = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.28 | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.28 | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = % 154.26/23.28 | | e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.26/23.28 | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.28 | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.28 | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.28 | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.28 | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.28 | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.26/23.28 | | all_58_26 = e0 & e1 = e0) % 154.26/23.28 | | % 154.26/23.28 | | BETA: splitting (31) gives: % 154.26/23.28 | | % 154.26/23.28 | | Case 1: % 154.26/23.28 | | | % 154.26/23.28 | | | (32) all_58_29 = e2 % 154.26/23.28 | | | % 154.26/23.28 | | | REF_CLOSE: (4), (6), (7), (9), (10), (12), (14), (17), (20), (28), (32) % 154.26/23.28 | | | are inconsistent by sub-proof #386. % 154.26/23.28 | | | % 154.26/23.28 | | Case 2: % 154.26/23.28 | | | % 154.26/23.28 | | | (33) ~ (all_58_29 = e2) % 154.26/23.28 | | | (34) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.28 | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 % 154.26/23.28 | | | & all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = % 154.26/23.28 | | | e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.28 | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = % 154.26/23.28 | | | e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 % 154.26/23.28 | | | = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.28 | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.26/23.28 | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.28 | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.28 | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.28 | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.28 | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) % 154.26/23.28 | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 154.26/23.28 | | | e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.28 | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = % 154.26/23.28 | | | e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.28 | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.28 | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = % 154.26/23.28 | | | e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.28 | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.28 | | | e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.28 | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.28 | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = % 154.26/23.28 | | | e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.26/23.28 | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.28 | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.28 | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.28 | | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.28 | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.28 | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.26/23.28 | | | all_58_26 = e0 & e1 = e0) % 154.26/23.28 | | | % 154.26/23.28 | | | REDUCE: (10), (33) imply: % 154.26/23.28 | | | (35) ~ (e2 = e0) % 154.26/23.28 | | | % 154.26/23.28 | | | BETA: splitting (34) gives: % 154.26/23.28 | | | % 154.26/23.28 | | | Case 1: % 154.26/23.28 | | | | % 154.26/23.28 | | | | (36) all_58_28 = e3 % 154.26/23.28 | | | | % 154.26/23.28 | | | | COMBINE_EQS: (9), (36) imply: % 154.26/23.28 | | | | (37) e3 = e1 % 154.26/23.28 | | | | % 154.26/23.28 | | | | REF_CLOSE: (4), (7), (9), (10), (12), (14), (16), (17), (20), (26), % 154.26/23.28 | | | | (28), (37) are inconsistent by sub-proof #382. % 154.26/23.28 | | | | % 154.26/23.28 | | | Case 2: % 154.26/23.28 | | | | % 154.26/23.28 | | | | (38) ~ (all_58_28 = e3) % 154.26/23.28 | | | | (39) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.26/23.28 | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.26/23.28 | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.28 | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = % 154.26/23.28 | | | | e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.28 | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 154.26/23.28 | | | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.28 | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.26/23.28 | | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.28 | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.28 | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.28 | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.28 | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.26/23.28 | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.28 | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 % 154.26/23.28 | | | | = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.28 | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 % 154.26/23.28 | | | | = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 % 154.26/23.28 | | | | = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.28 | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 % 154.26/23.28 | | | | = e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 154.26/23.28 | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 % 154.26/23.28 | | | | = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.28 | | | | = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 154.26/23.28 | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 % 154.26/23.28 | | | | = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.28 | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 154.26/23.28 | | | | e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 % 154.26/23.28 | | | | = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.28 | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = % 154.26/23.28 | | | | e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 % 154.26/23.28 | | | | = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.28 | | | | % 154.26/23.28 | | | | REDUCE: (9), (38) imply: % 154.26/23.28 | | | | (40) ~ (e3 = e1) % 154.26/23.28 | | | | % 154.26/23.28 | | | | BETA: splitting (39) gives: % 154.26/23.28 | | | | % 154.26/23.28 | | | | Case 1: % 154.26/23.28 | | | | | % 154.26/23.28 | | | | | (41) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.26/23.28 | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.28 | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.26/23.28 | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.28 | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 % 154.26/23.28 | | | | | = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.28 | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 % 154.26/23.28 | | | | | = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.28 | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.26/23.28 | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 % 154.26/23.28 | | | | | = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.26/23.28 | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = % 154.26/23.28 | | | | | e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.28 | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 % 154.26/23.28 | | | | | = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.28 | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 154.26/23.28 | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.28 | | | | | % 154.26/23.28 | | | | | BETA: splitting (41) gives: % 154.26/23.28 | | | | | % 154.26/23.28 | | | | | Case 1: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | (42) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.26/23.28 | | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.28 | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.28 | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.28 | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.28 | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.28 | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.28 | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.28 | | | | | | all_58_11 = e1 & all_58_17 = e1) % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | BETA: splitting (42) gives: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | Case 1: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (43) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 % 154.26/23.28 | | | | | | | = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.28 | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.28 | | | | | | | all_58_11 = e2 & all_58_17 = e2) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | BETA: splitting (43) gives: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (44) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.28 | | | | | | | | all_58_15 = e1 % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | ALPHA: (44) implies: % 154.26/23.28 | | | | | | | | (45) all_58_4 = e1 % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | REF_CLOSE: (3), (4), (7), (9), (10), (12), (14), (17), (20), % 154.26/23.28 | | | | | | | | (22), (26), (27), (28), (45) are inconsistent by % 154.26/23.28 | | | | | | | | sub-proof #381. % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (46) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.28 | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.28 | | | | | | | | all_58_11 = e2 & all_58_17 = e2) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (46) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (47) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.28 | | | | | | | | | all_58_22 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (12), (14), (17), % 154.26/23.28 | | | | | | | | | (20), (28), (47) are inconsistent by sub-proof % 154.26/23.28 | | | | | | | | | #380. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (48) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.28 | | | | | | | | | all_58_17 = e2 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (6), (10), (12), (13), (16), (17), (18), (24), (48) % 154.26/23.28 | | | | | | | | | are inconsistent by sub-proof #377. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | End of split % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | Case 2: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (49) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.28 | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.28 | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.28 | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.28 | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.28 | | | | | | | all_58_17 = e1) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | BETA: splitting (49) gives: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (50) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.28 | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.28 | | | | | | | | all_58_8 = e2 & all_58_15 = e3) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (50) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (51) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.28 | | | | | | | | | all_58_24 = e2 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (6), (10), (11), (12), (15), (16), (17), (18), (51) % 154.26/23.28 | | | | | | | | | are inconsistent by sub-proof #376. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (52) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.28 | | | | | | | | | all_58_15 = e3 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (14), (17), % 154.26/23.28 | | | | | | | | | (19), (20), (28), (52) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #374. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (53) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.28 | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.28 | | | | | | | | all_58_11 = e1 & all_58_17 = e1) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (53) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (54) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.28 | | | | | | | | | all_58_22 = e3 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (54) implies: % 154.26/23.28 | | | | | | | | | (55) all_58_22 = e3 % 154.26/23.28 | | | | | | | | | (56) all_58_6 = e3 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (2), (56) imply: % 154.26/23.28 | | | | | | | | | (57) e3 = e2 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | SIMP: (57) implies: % 154.26/23.28 | | | | | | | | | (58) e3 = e2 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (1), (55) imply: % 154.26/23.28 | | | | | | | | | (59) e3 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (10), (12), (14), (17), (20), % 154.26/23.28 | | | | | | | | | (28), (58), (59) are inconsistent by sub-proof % 154.26/23.28 | | | | | | | | | #375. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (60) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.28 | | | | | | | | | all_58_17 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (6), (10), (12), (16), (17), (18), (19), (24), (60) % 154.26/23.28 | | | | | | | | | are inconsistent by sub-proof #373. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | End of split % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | End of split % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | Case 2: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | (61) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 % 154.26/23.28 | | | | | | = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.28 | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 % 154.26/23.28 | | | | | | = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.28 | | | | | | all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.28 | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & % 154.26/23.28 | | | | | | all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 154.26/23.28 | | | | | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.28 | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.28 | | | | | | all_58_26 = e0) % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | BETA: splitting (61) gives: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | Case 1: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (62) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.28 | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 154.26/23.28 | | | | | | | e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.28 | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.26/23.28 | | | | | | | all_58_15 = e3 & all_58_17 = e1) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (12), (14), (15), % 154.26/23.28 | | | | | | | (17), (19), (20), (22), (24), (26), (27), (28), (62) % 154.26/23.28 | | | | | | | are inconsistent by sub-proof #370. % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | Case 2: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (63) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.28 | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.26/23.28 | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.28 | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.28 | | | | | | | all_58_26 = e0) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | BETA: splitting (63) gives: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (64) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.28 | | | | | | | | all_58_15 = e1 & all_58_22 = e3) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (64) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (65) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | | | all_58_26 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (65) implies: % 154.26/23.28 | | | | | | | | | (66) all_58_20 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (10), (12), (14), (17), (20), % 154.26/23.28 | | | | | | | | | (22), (26), (27), (28), (66) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #369. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (67) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.28 | | | | | | | | | all_58_22 = e3 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (67) implies: % 154.26/23.28 | | | | | | | | | (68) all_58_22 = e3 % 154.26/23.28 | | | | | | | | | (69) all_58_15 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (21), (69) imply: % 154.26/23.28 | | | | | | | | | (70) e3 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | SIMP: (70) implies: % 154.26/23.28 | | | | | | | | | (71) e3 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (1), (68) imply: % 154.26/23.28 | | | | | | | | | (72) e3 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | SIMP: (72) implies: % 154.26/23.28 | | | | | | | | | (73) e3 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (12), (14), (17), (20), (22), % 154.26/23.28 | | | | | | | | | (26), (27), (28), (71), (73) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #371. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (74) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.28 | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.28 | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (14), (17), % 154.26/23.28 | | | | | | | | (20), (22), (26), (27), (28), (74) are inconsistent % 154.26/23.28 | | | | | | | | by sub-proof #368. % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | End of split % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | End of split % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | End of split % 154.26/23.28 | | | | | % 154.26/23.28 | | | | Case 2: % 154.26/23.28 | | | | | % 154.26/23.28 | | | | | (75) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.26/23.28 | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.28 | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = % 154.26/23.28 | | | | | e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.28 | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.28 | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.28 | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 % 154.26/23.28 | | | | | & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 154.26/23.28 | | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.28 | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.26/23.28 | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.28 | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.28 | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.28 | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.28 | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.28 | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 % 154.26/23.28 | | | | | & e1 = e0) % 154.26/23.28 | | | | | % 154.26/23.28 | | | | | BETA: splitting (75) gives: % 154.26/23.28 | | | | | % 154.26/23.28 | | | | | Case 1: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | (76) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.26/23.28 | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.28 | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.28 | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.28 | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.28 | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.28 | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = % 154.26/23.28 | | | | | | e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | BETA: splitting (76) gives: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | Case 1: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (77) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = % 154.26/23.28 | | | | | | | e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.28 | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.28 | | | | | | | all_58_26 = e0) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (14), (15), (17), % 154.26/23.28 | | | | | | | (20), (22), (26), (27), (28), (77) are inconsistent by % 154.26/23.28 | | | | | | | sub-proof #367. % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | Case 2: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (78) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.28 | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.28 | | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.28 | | | | | | | = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | BETA: splitting (78) gives: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (79) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.28 | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | | all_58_22 = e0 & all_58_26 = e1) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (79) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (80) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.28 | | | | | | | | | all_58_24 = e2 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (80) implies: % 154.26/23.28 | | | | | | | | | (81) all_58_13 = e2 % 154.26/23.28 | | | | | | | | | (82) all_58_6 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (2), (82) imply: % 154.26/23.28 | | | | | | | | | (83) e2 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (15), (81) imply: % 154.26/23.28 | | | | | | | | | (84) e2 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | SIMP: (84) implies: % 154.26/23.28 | | | | | | | | | (85) e2 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (12), (14), (17), (20), (22), % 154.26/23.28 | | | | | | | | | (26), (27), (28), (83), (85) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #366. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (86) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.28 | | | | | | | | | all_58_26 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (86) implies: % 154.26/23.28 | | | | | | | | | (87) all_58_20 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (10), (12), (14), (17), (20), % 154.26/23.28 | | | | | | | | | (22), (26), (27), (28), (87) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #369. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (88) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 % 154.26/23.28 | | | | | | | | = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.26/23.28 | | | | | | | | e0) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (12), (13), (14), % 154.26/23.28 | | | | | | | | (17), (20), (22), (25), (26), (27), (28), (88) are % 154.26/23.28 | | | | | | | | inconsistent by sub-proof #365. % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | End of split % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | End of split % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | Case 2: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | (89) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.28 | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.28 | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.26/23.28 | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.28 | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = % 154.26/23.28 | | | | | | e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.28 | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.28 | | | | | | all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.28 | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | BETA: splitting (89) gives: % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | | Case 1: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (90) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.28 | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.26/23.28 | | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.28 | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | BETA: splitting (90) gives: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (91) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.28 | | | | | | | | all_58_17 = e1 & all_58_24 = e2) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (91) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (92) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | | | all_58_26 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (92) implies: % 154.26/23.28 | | | | | | | | | (93) all_58_20 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (10), (12), (14), (17), (20), % 154.26/23.28 | | | | | | | | | (22), (26), (27), (28), (93) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #369. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (94) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.28 | | | | | | | | | all_58_24 = e2 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (6), (10), (12), (15), (16), (17), (18), (24), (94) % 154.26/23.28 | | | | | | | | | are inconsistent by sub-proof #364. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | (95) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.28 | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & % 154.26/23.28 | | | | | | | | e2 = e1) % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | BETA: splitting (95) gives: % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | | Case 1: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (96) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.28 | | | | | | | | | all_58_26 = e0 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (10), (12), (14), (17), (20), % 154.26/23.28 | | | | | | | | | (22), (26), (27), (28), (96) are inconsistent by % 154.26/23.28 | | | | | | | | | sub-proof #363. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | Case 2: % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | (97) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | ALPHA: (97) implies: % 154.26/23.28 | | | | | | | | | (98) e2 = e1 % 154.26/23.28 | | | | | | | | | (99) all_58_11 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | COMBINE_EQS: (24), (99) imply: % 154.26/23.28 | | | | | | | | | (100) e3 = e1 % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | | REF_CLOSE: (6), (10), (12), (16), (17), (18), (98), (100) are % 154.26/23.28 | | | | | | | | | inconsistent by sub-proof #378. % 154.26/23.28 | | | | | | | | | % 154.26/23.28 | | | | | | | | End of split % 154.26/23.28 | | | | | | | | % 154.26/23.28 | | | | | | | End of split % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | Case 2: % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | (101) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.28 | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.28 | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.28 | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 % 154.26/23.28 | | | | | | | = e0 & e1 = e0) % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (12), (14), (15), (17), % 154.26/23.28 | | | | | | | (20), (22), (26), (27), (28), (101) are inconsistent by % 154.26/23.28 | | | | | | | sub-proof #362. % 154.26/23.28 | | | | | | | % 154.26/23.28 | | | | | | End of split % 154.26/23.28 | | | | | | % 154.26/23.28 | | | | | End of split % 154.26/23.28 | | | | | % 154.26/23.28 | | | | End of split % 154.26/23.28 | | | | % 154.26/23.28 | | | End of split % 154.26/23.28 | | | % 154.26/23.28 | | End of split % 154.26/23.28 | | % 154.26/23.28 | End of split % 154.26/23.28 | % 154.26/23.28 End of proof % 154.26/23.28 % 154.26/23.28 Sub-proof #362 shows that the following formulas are inconsistent: % 154.26/23.28 ---------------------------------------------------------------- % 154.26/23.28 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.28 (2) all_58_20 = e0 % 154.26/23.28 (3) ~ (e3 = e1) % 154.26/23.28 (4) all_58_26 = e1 % 154.26/23.28 (5) all_58_28 = e1 % 154.26/23.28 (6) all_58_29 = e0 % 154.26/23.28 (7) ~ (e2 = e1) % 154.26/23.28 (8) ~ (e3 = e0) % 154.26/23.28 (9) all_58_13 = e1 % 154.26/23.28 (10) ~ (e2 = e0) % 154.26/23.28 (11) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.28 (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.28 (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.26/23.28 all_58_26 = e0 & e1 = e0) % 154.26/23.28 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.28 (13) ~ (e1 = e0) % 154.26/23.28 (14) all_58_30 = all_6_2 % 154.26/23.28 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.28 (16) ~ (e3 = e2) % 154.26/23.28 % 154.26/23.28 Begin of proof % 154.26/23.28 | % 154.26/23.28 | BETA: splitting (11) gives: % 154.26/23.28 | % 154.26/23.28 | Case 1: % 154.26/23.28 | | % 154.26/23.28 | | (17) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) % 154.26/23.28 | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = % 154.26/23.28 | | e1) % 154.26/23.28 | | % 154.26/23.28 | | BETA: splitting (17) gives: % 154.26/23.28 | | % 154.26/23.28 | | Case 1: % 154.26/23.28 | | | % 154.26/23.28 | | | (18) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | ALPHA: (18) implies: % 154.26/23.28 | | | (19) all_58_26 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | COMBINE_EQS: (4), (19) imply: % 154.26/23.28 | | | (20) e1 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | COMBINE_EQS: (5), (20) imply: % 154.26/23.28 | | | (21) all_58_28 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (12), (13), (14), (15), (16), % 154.26/23.28 | | | (21) are inconsistent by sub-proof #483. % 154.26/23.28 | | | % 154.26/23.28 | | Case 2: % 154.26/23.28 | | | % 154.26/23.28 | | | (22) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1 % 154.26/23.28 | | | % 154.26/23.28 | | | ALPHA: (22) implies: % 154.26/23.28 | | | (23) all_58_20 = e1 % 154.26/23.28 | | | % 154.26/23.28 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (13), (14), % 154.26/23.28 | | | (15), (16), (23) are inconsistent by sub-proof #369. % 154.26/23.28 | | | % 154.26/23.28 | | End of split % 154.26/23.28 | | % 154.26/23.28 | Case 2: % 154.26/23.28 | | % 154.26/23.28 | | (24) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.26/23.28 | | all_58_26 = e0 & e1 = e0) % 154.26/23.28 | | % 154.26/23.28 | | BETA: splitting (24) gives: % 154.26/23.28 | | % 154.26/23.28 | | Case 1: % 154.26/23.28 | | | % 154.26/23.28 | | | (25) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | ALPHA: (25) implies: % 154.26/23.28 | | | (26) all_58_13 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | COMBINE_EQS: (9), (26) imply: % 154.26/23.28 | | | (27) e1 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | COMBINE_EQS: (5), (27) imply: % 154.26/23.28 | | | (28) all_58_28 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (12), (13), (14), (15), (16), % 154.26/23.28 | | | (28) are inconsistent by sub-proof #483. % 154.26/23.28 | | | % 154.26/23.28 | | Case 2: % 154.26/23.28 | | | % 154.26/23.28 | | | (29) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | ALPHA: (29) implies: % 154.26/23.28 | | | (30) all_58_26 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | COMBINE_EQS: (4), (30) imply: % 154.26/23.28 | | | (31) e1 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | COMBINE_EQS: (5), (31) imply: % 154.26/23.28 | | | (32) all_58_28 = e0 % 154.26/23.28 | | | % 154.26/23.28 | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (12), (13), (14), (15), (16), % 154.26/23.28 | | | (32) are inconsistent by sub-proof #483. % 154.26/23.28 | | | % 154.26/23.28 | | End of split % 154.26/23.28 | | % 154.26/23.28 | End of split % 154.26/23.28 | % 154.26/23.28 End of proof % 154.26/23.28 % 154.26/23.28 Sub-proof #363 shows that the following formulas are inconsistent: % 154.26/23.28 ---------------------------------------------------------------- % 154.26/23.28 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (2) ~ (e3 = e1) % 154.26/23.29 (3) all_58_26 = e1 % 154.26/23.29 (4) all_58_28 = e1 % 154.26/23.29 (5) all_58_29 = e0 % 154.26/23.29 (6) ~ (e2 = e1) % 154.26/23.29 (7) ~ (e3 = e0) % 154.26/23.29 (8) ~ (e2 = e0) % 154.26/23.29 (9) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0 % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) ~ (e1 = e0) % 154.26/23.29 (12) all_58_30 = all_6_2 % 154.26/23.29 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (14) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (9) implies: % 154.26/23.29 | (15) all_58_26 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (3), (15) imply: % 154.26/23.29 | (16) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (4), (16) imply: % 154.26/23.29 | (17) all_58_28 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (17) % 154.26/23.29 | are inconsistent by sub-proof #483. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #364 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_30 = e2 % 154.26/23.29 (2) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2 % 154.26/23.29 (3) all_58_29 = e0 % 154.26/23.29 (4) ~ (e2 = e1) % 154.26/23.29 (5) all_58_13 = e1 % 154.26/23.29 (6) all_58_31 = e3 % 154.26/23.29 (7) ~ (e2 = e0) % 154.26/23.29 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (9) all_58_11 = e3 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (2) implies: % 154.26/23.29 | (10) all_58_13 = e2 % 154.26/23.29 | (11) all_58_11 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (9), (11) imply: % 154.26/23.29 | (12) e3 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (5), (10) imply: % 154.26/23.29 | (13) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | SIMP: (13) implies: % 154.26/23.29 | (14) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (3), (4), (6), (7), (8), (12), (14) are inconsistent by % 154.26/23.29 | sub-proof #378. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #365 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_6 = e2 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (3) all_58_30 = e2 % 154.26/23.29 (4) ~ (e3 = e1) % 154.26/23.29 (5) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.29 = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.29 (6) all_58_28 = e1 % 154.26/23.29 (7) all_58_29 = e0 % 154.26/23.29 (8) ~ (e2 = e1) % 154.26/23.29 (9) all_58_17 = e1 % 154.26/23.29 (10) ~ (e3 = e0) % 154.26/23.29 (11) ~ (e2 = e0) % 154.26/23.29 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (13) ~ (e1 = e0) % 154.26/23.29 (14) all_58_24 = e2 % 154.26/23.29 (15) all_58_30 = all_6_2 % 154.26/23.29 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (17) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | BETA: splitting (5) gives: % 154.26/23.29 | % 154.26/23.29 | Case 1: % 154.26/23.29 | | % 154.26/23.29 | | (18) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.26/23.29 | | % 154.26/23.29 | | ALPHA: (18) implies: % 154.26/23.29 | | (19) all_58_6 = e0 % 154.26/23.29 | | % 154.26/23.29 | | COMBINE_EQS: (1), (19) imply: % 154.26/23.29 | | (20) e2 = e0 % 154.26/23.29 | | % 154.26/23.29 | | COMBINE_EQS: (3), (20) imply: % 154.26/23.29 | | (21) all_58_30 = e0 % 154.26/23.29 | | % 154.26/23.29 | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (11), (12), (17), (21) are % 154.26/23.29 | | inconsistent by sub-proof #701. % 154.26/23.29 | | % 154.26/23.29 | Case 2: % 154.26/23.29 | | % 154.26/23.29 | | (22) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0 % 154.26/23.29 | | % 154.26/23.29 | | ALPHA: (22) implies: % 154.26/23.29 | | (23) all_58_24 = e0 % 154.26/23.29 | | (24) all_58_17 = e2 % 154.26/23.29 | | % 154.26/23.29 | | COMBINE_EQS: (9), (24) imply: % 154.26/23.29 | | (25) e2 = e1 % 154.26/23.29 | | % 154.26/23.29 | | SIMP: (25) implies: % 154.26/23.29 | | (26) e2 = e1 % 154.26/23.29 | | % 154.26/23.29 | | COMBINE_EQS: (14), (23) imply: % 154.26/23.29 | | (27) e2 = e0 % 154.26/23.29 | | % 154.26/23.29 | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (11), (12), (13), (15), (16), % 154.26/23.29 | | (17), (26), (27) are inconsistent by sub-proof #366. % 154.26/23.29 | | % 154.26/23.29 | End of split % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #366 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (2) ~ (e3 = e1) % 154.26/23.29 (3) all_58_28 = e1 % 154.26/23.29 (4) all_58_29 = e0 % 154.26/23.29 (5) ~ (e2 = e1) % 154.26/23.29 (6) e2 = e1 % 154.26/23.29 (7) ~ (e3 = e0) % 154.26/23.29 (8) ~ (e2 = e0) % 154.26/23.29 (9) e2 = e0 % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) ~ (e1 = e0) % 154.26/23.29 (12) all_58_30 = all_6_2 % 154.26/23.29 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (14) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (6), (9) imply: % 154.26/23.29 | (15) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | SIMP: (15) implies: % 154.26/23.29 | (16) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (3), (16) imply: % 154.26/23.29 | (17) all_58_28 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (12), (13), (14), (17) % 154.26/23.29 | are inconsistent by sub-proof #483. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #367 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_4 = e0 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (3) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = % 154.26/23.29 e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.26/23.29 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.29 (4) ~ (e3 = e1) % 154.26/23.29 (5) all_58_26 = e1 % 154.26/23.29 (6) all_58_28 = e1 % 154.26/23.29 (7) all_58_29 = e0 % 154.26/23.29 (8) ~ (e2 = e1) % 154.26/23.29 (9) ~ (e3 = e0) % 154.26/23.29 (10) all_58_13 = e1 % 154.26/23.29 (11) ~ (e2 = e0) % 154.26/23.29 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (13) ~ (e1 = e0) % 154.26/23.29 (14) all_58_30 = all_6_2 % 154.26/23.29 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (16) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | BETA: splitting (3) gives: % 154.26/23.29 | % 154.26/23.29 | Case 1: % 154.26/23.29 | | % 154.26/23.29 | | (17) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.26/23.29 | | % 154.26/23.29 | | ALPHA: (17) implies: % 154.26/23.29 | | (18) all_58_4 = e1 % 154.26/23.29 | | % 154.26/23.29 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15), % 154.26/23.29 | | (16), (18) are inconsistent by sub-proof #381. % 154.26/23.29 | | % 154.26/23.29 | Case 2: % 154.26/23.29 | | % 154.26/23.29 | | (19) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.29 | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.29 | | % 154.26/23.29 | | BETA: splitting (19) gives: % 154.26/23.29 | | % 154.26/23.29 | | Case 1: % 154.26/23.29 | | | % 154.26/23.29 | | | (20) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | ALPHA: (20) implies: % 154.26/23.29 | | | (21) all_58_13 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (10), (21) imply: % 154.26/23.29 | | | (22) e1 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (6), (22) imply: % 154.26/23.29 | | | (23) all_58_28 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (2), (4), (7), (8), (9), (11), (12), (13), (14), (15), (16), % 154.26/23.29 | | | (23) are inconsistent by sub-proof #483. % 154.26/23.29 | | | % 154.26/23.29 | | Case 2: % 154.26/23.29 | | | % 154.26/23.29 | | | (24) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | ALPHA: (24) implies: % 154.26/23.29 | | | (25) all_58_26 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (5), (25) imply: % 154.26/23.29 | | | (26) e1 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (6), (26) imply: % 154.26/23.29 | | | (27) all_58_28 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (2), (4), (7), (8), (9), (11), (12), (13), (14), (15), (16), % 154.26/23.29 | | | (27) are inconsistent by sub-proof #483. % 154.26/23.29 | | | % 154.26/23.29 | | End of split % 154.26/23.29 | | % 154.26/23.29 | End of split % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #368 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_4 = e0 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (3) ~ (e3 = e1) % 154.26/23.29 (4) all_58_26 = e1 % 154.26/23.29 (5) all_58_28 = e1 % 154.26/23.29 (6) all_58_29 = e0 % 154.26/23.29 (7) ~ (e2 = e1) % 154.26/23.29 (8) ~ (e3 = e0) % 154.26/23.29 (9) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.29 (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.29 (10) ~ (e2 = e0) % 154.26/23.29 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (12) ~ (e1 = e0) % 154.26/23.29 (13) all_58_30 = all_6_2 % 154.26/23.29 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (15) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | BETA: splitting (9) gives: % 154.26/23.29 | % 154.26/23.29 | Case 1: % 154.26/23.29 | | % 154.26/23.29 | | (16) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2 % 154.26/23.29 | | % 154.26/23.29 | | ALPHA: (16) implies: % 154.26/23.29 | | (17) all_58_4 = e1 % 154.26/23.29 | | % 154.26/23.29 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14), % 154.26/23.29 | | (15), (17) are inconsistent by sub-proof #381. % 154.26/23.29 | | % 154.26/23.29 | Case 2: % 154.26/23.29 | | % 154.26/23.29 | | (18) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0 % 154.26/23.29 | | % 154.26/23.29 | | ALPHA: (18) implies: % 154.26/23.29 | | (19) all_58_26 = e0 % 154.26/23.29 | | % 154.26/23.29 | | COMBINE_EQS: (4), (19) imply: % 154.26/23.29 | | (20) e1 = e0 % 154.26/23.29 | | % 154.26/23.29 | | COMBINE_EQS: (5), (20) imply: % 154.26/23.29 | | (21) all_58_28 = e0 % 154.26/23.29 | | % 154.26/23.29 | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), (15), (21) % 154.26/23.29 | | are inconsistent by sub-proof #483. % 154.26/23.29 | | % 154.26/23.29 | End of split % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #369 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (2) all_58_20 = e0 % 154.26/23.29 (3) ~ (e3 = e1) % 154.26/23.29 (4) all_58_28 = e1 % 154.26/23.29 (5) all_58_29 = e0 % 154.26/23.29 (6) ~ (e2 = e1) % 154.26/23.29 (7) ~ (e3 = e0) % 154.26/23.29 (8) ~ (e2 = e0) % 154.26/23.29 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (10) ~ (e1 = e0) % 154.26/23.29 (11) all_58_20 = e1 % 154.26/23.29 (12) all_58_30 = all_6_2 % 154.26/23.29 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (14) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (2), (11) imply: % 154.26/23.29 | (15) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | SIMP: (15) implies: % 154.26/23.29 | (16) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (4), (16) imply: % 154.26/23.29 | (17) all_58_28 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14), (17) are % 154.26/23.29 | inconsistent by sub-proof #483. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #370 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_6 = e2 % 154.26/23.29 (2) all_58_4 = e0 % 154.26/23.29 (3) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.29 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.26/23.29 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.26/23.29 & all_58_15 = e3 & all_58_17 = e1) % 154.26/23.29 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (5) all_58_30 = e2 % 154.26/23.29 (6) ~ (e3 = e1) % 154.26/23.29 (7) all_58_28 = e1 % 154.26/23.29 (8) all_58_29 = e0 % 154.26/23.29 (9) ~ (e2 = e1) % 154.26/23.29 (10) ~ (e3 = e0) % 154.26/23.29 (11) all_58_13 = e1 % 154.26/23.29 (12) ~ (e2 = e0) % 154.26/23.29 (13) all_58_2 = e3 % 154.26/23.29 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (15) ~ (e1 = e0) % 154.26/23.29 (16) all_58_11 = e3 % 154.26/23.29 (17) all_58_30 = all_6_2 % 154.26/23.29 (18) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (19) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | BETA: splitting (3) gives: % 154.26/23.29 | % 154.26/23.29 | Case 1: % 154.26/23.29 | | % 154.26/23.29 | | (20) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.29 | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) % 154.26/23.29 | | % 154.26/23.29 | | BETA: splitting (20) gives: % 154.26/23.29 | | % 154.26/23.29 | | Case 1: % 154.26/23.29 | | | % 154.26/23.29 | | | (21) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | ALPHA: (21) implies: % 154.26/23.29 | | | (22) all_58_13 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (11), (22) imply: % 154.26/23.29 | | | (23) e1 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (7), (23) imply: % 154.26/23.29 | | | (24) all_58_28 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (4), (6), (8), (9), (10), (12), (14), (15), (17), (18), (19), % 154.26/23.29 | | | (24) are inconsistent by sub-proof #483. % 154.26/23.29 | | | % 154.26/23.29 | | Case 2: % 154.26/23.29 | | | % 154.26/23.29 | | | (25) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (13), (19), (25) are inconsistent by sub-proof #372. % 154.26/23.29 | | | % 154.26/23.29 | | End of split % 154.26/23.29 | | % 154.26/23.29 | Case 2: % 154.26/23.29 | | % 154.26/23.29 | | (26) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.26/23.29 | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) % 154.26/23.29 | | % 154.26/23.29 | | BETA: splitting (26) gives: % 154.26/23.29 | | % 154.26/23.29 | | Case 1: % 154.26/23.29 | | | % 154.26/23.29 | | | (27) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | ALPHA: (27) implies: % 154.26/23.29 | | | (28) all_58_6 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (1), (28) imply: % 154.26/23.29 | | | (29) e2 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (5), (29) imply: % 154.26/23.29 | | | (30) all_58_30 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (12), (14), (19), (30) are % 154.26/23.29 | | | inconsistent by sub-proof #701. % 154.26/23.29 | | | % 154.26/23.29 | | Case 2: % 154.26/23.29 | | | % 154.26/23.29 | | | (31) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1 % 154.26/23.29 | | | % 154.26/23.29 | | | ALPHA: (31) implies: % 154.26/23.29 | | | (32) all_58_11 = e1 % 154.26/23.29 | | | (33) all_58_4 = e3 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (2), (33) imply: % 154.26/23.29 | | | (34) e3 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | SIMP: (34) implies: % 154.26/23.29 | | | (35) e3 = e0 % 154.26/23.29 | | | % 154.26/23.29 | | | COMBINE_EQS: (16), (32) imply: % 154.26/23.29 | | | (36) e3 = e1 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (12), (14), (15), (17), (18), % 154.26/23.29 | | | (19), (35), (36) are inconsistent by sub-proof #371. % 154.26/23.29 | | | % 154.26/23.29 | | End of split % 154.26/23.29 | | % 154.26/23.29 | End of split % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #371 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (2) ~ (e3 = e1) % 154.26/23.29 (3) e3 = e1 % 154.26/23.29 (4) all_58_28 = e1 % 154.26/23.29 (5) all_58_29 = e0 % 154.26/23.29 (6) ~ (e2 = e1) % 154.26/23.29 (7) ~ (e3 = e0) % 154.26/23.29 (8) e3 = e0 % 154.26/23.29 (9) ~ (e2 = e0) % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) ~ (e1 = e0) % 154.26/23.29 (12) all_58_30 = all_6_2 % 154.26/23.29 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (14) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (3), (8) imply: % 154.26/23.29 | (15) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | SIMP: (15) implies: % 154.26/23.29 | (16) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (4), (16) imply: % 154.26/23.29 | (17) all_58_28 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (14), (17) % 154.26/23.29 | are inconsistent by sub-proof #483. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #372 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.29 (2) all_58_2 = e3 % 154.26/23.29 (3) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (1) implies: % 154.26/23.29 | (4) all_58_2 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (2), (4) imply: % 154.26/23.29 | (5) e3 = e2 % 154.26/23.29 | % 154.26/23.29 | REDUCE: (3), (5) imply: % 154.26/23.29 | (6) $false % 154.26/23.29 | % 154.26/23.29 | CLOSE: (6) is inconsistent. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #373 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_30 = e2 % 154.26/23.29 (2) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1 % 154.26/23.29 (3) all_58_29 = e0 % 154.26/23.29 (4) ~ (e2 = e1) % 154.26/23.29 (5) all_58_31 = e3 % 154.26/23.29 (6) ~ (e2 = e0) % 154.26/23.29 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (8) all_58_2 = e3 % 154.26/23.29 (9) all_58_11 = e3 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (2) implies: % 154.26/23.29 | (10) all_58_11 = e1 % 154.26/23.29 | (11) all_58_2 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (8), (11) imply: % 154.26/23.29 | (12) e3 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (9), (10) imply: % 154.26/23.29 | (13) e3 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (12), (13) imply: % 154.26/23.29 | (14) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (13), (14) are inconsistent by % 154.26/23.29 | sub-proof #378. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #374 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_4 = e0 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (3) all_58_30 = e2 % 154.26/23.29 (4) ~ (e3 = e1) % 154.26/23.29 (5) all_58_28 = e1 % 154.26/23.29 (6) all_58_29 = e0 % 154.26/23.29 (7) ~ (e2 = e1) % 154.26/23.29 (8) ~ (e3 = e0) % 154.26/23.29 (9) ~ (e2 = e0) % 154.26/23.29 (10) all_58_2 = e3 % 154.26/23.29 (11) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3 % 154.26/23.29 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (13) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (11) implies: % 154.26/23.29 | (14) all_58_4 = e3 % 154.26/23.29 | (15) all_58_2 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (10), (15) imply: % 154.26/23.29 | (16) e3 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (1), (14) imply: % 154.26/23.29 | (17) e3 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (16), (17) are % 154.26/23.29 | inconsistent by sub-proof #375. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #375 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (2) all_58_30 = e2 % 154.26/23.29 (3) ~ (e3 = e1) % 154.26/23.29 (4) all_58_28 = e1 % 154.26/23.29 (5) all_58_29 = e0 % 154.26/23.29 (6) ~ (e2 = e1) % 154.26/23.29 (7) ~ (e3 = e0) % 154.26/23.29 (8) e3 = e0 % 154.26/23.29 (9) ~ (e2 = e0) % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) ~ (e3 = e2) % 154.26/23.29 (12) e3 = e2 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | SIMP: (8) implies: % 154.26/23.29 | (13) e3 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (12), (13) imply: % 154.26/23.29 | (14) e2 = e0 % 154.26/23.29 | % 154.26/23.29 | SIMP: (14) implies: % 154.26/23.29 | (15) e2 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (2), (15) imply: % 154.26/23.29 | (16) all_58_30 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (16) are % 154.26/23.29 | inconsistent by sub-proof #701. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #376 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2 % 154.26/23.29 (2) all_58_30 = e2 % 154.26/23.29 (3) all_58_29 = e0 % 154.26/23.29 (4) all_58_8 = e2 % 154.26/23.29 (5) ~ (e2 = e1) % 154.26/23.29 (6) all_58_13 = e1 % 154.26/23.29 (7) all_58_31 = e3 % 154.26/23.29 (8) ~ (e2 = e0) % 154.26/23.29 (9) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (1) implies: % 154.26/23.29 | (10) all_58_13 = e2 % 154.26/23.29 | (11) all_58_8 = e3 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (4), (11) imply: % 154.26/23.29 | (12) e3 = e2 % 154.26/23.29 | % 154.26/23.29 | SIMP: (12) implies: % 154.26/23.29 | (13) e3 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (6), (10) imply: % 154.26/23.29 | (14) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | SIMP: (14) implies: % 154.26/23.29 | (15) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (13), (15) imply: % 154.26/23.29 | (16) e3 = e1 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (2), (3), (5), (7), (8), (9), (15), (16) are inconsistent by % 154.26/23.29 | sub-proof #378. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #377 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_30 = e2 % 154.26/23.29 (2) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2 % 154.26/23.29 (3) all_58_29 = e0 % 154.26/23.29 (4) ~ (e2 = e1) % 154.26/23.29 (5) all_58_17 = e1 % 154.26/23.29 (6) all_58_31 = e3 % 154.26/23.29 (7) ~ (e2 = e0) % 154.26/23.29 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (9) all_58_11 = e3 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (2) implies: % 154.26/23.29 | (10) all_58_17 = e2 % 154.26/23.29 | (11) all_58_11 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (9), (11) imply: % 154.26/23.29 | (12) e3 = e2 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (5), (10) imply: % 154.26/23.29 | (13) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | SIMP: (13) implies: % 154.26/23.29 | (14) e2 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (12), (14) imply: % 154.26/23.29 | (15) e3 = e1 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (3), (4), (6), (7), (8), (14), (15) are inconsistent by % 154.26/23.29 | sub-proof #378. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #378 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_30 = e2 % 154.26/23.29 (2) e3 = e1 % 154.26/23.29 (3) all_58_29 = e0 % 154.26/23.29 (4) ~ (e2 = e1) % 154.26/23.29 (5) e2 = e1 % 154.26/23.29 (6) all_58_31 = e3 % 154.26/23.29 (7) ~ (e2 = e0) % 154.26/23.29 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (2), (6) imply: % 154.26/23.29 | (9) all_58_31 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (1), (5) imply: % 154.26/23.29 | (10) all_58_30 = e1 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (3), (4), (7), (8), (9), (10) are inconsistent by sub-proof #379. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #379 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_31 = e1 % 154.26/23.29 (2) all_58_29 = e0 % 154.26/23.29 (3) ~ (e2 = e1) % 154.26/23.29 (4) all_58_30 = e1 % 154.26/23.29 (5) ~ (e2 = e0) % 154.26/23.29 (6) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | BETA: splitting (6) gives: % 154.26/23.29 | % 154.26/23.29 | Case 1: % 154.26/23.29 | | % 154.26/23.29 | | (7) all_58_29 = e2 % 154.26/23.29 | | % 154.26/23.29 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #706. % 154.26/23.29 | | % 154.26/23.29 | Case 2: % 154.26/23.29 | | % 154.26/23.29 | | (8) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 | | % 154.26/23.29 | | BETA: splitting (8) gives: % 154.26/23.29 | | % 154.26/23.29 | | Case 1: % 154.26/23.29 | | | % 154.26/23.29 | | | (9) all_58_30 = e2 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #500. % 154.26/23.29 | | | % 154.26/23.29 | | Case 2: % 154.26/23.29 | | | % 154.26/23.29 | | | (10) all_58_31 = e2 % 154.26/23.29 | | | % 154.26/23.29 | | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #697. % 154.26/23.29 | | | % 154.26/23.29 | | End of split % 154.26/23.29 | | % 154.26/23.29 | End of split % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #380 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_6 = e2 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (3) all_58_30 = e2 % 154.26/23.29 (4) ~ (e3 = e1) % 154.26/23.29 (5) all_58_28 = e1 % 154.26/23.29 (6) all_58_29 = e0 % 154.26/23.29 (7) ~ (e2 = e1) % 154.26/23.29 (8) ~ (e3 = e0) % 154.26/23.29 (9) ~ (e2 = e0) % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0 % 154.26/23.29 (12) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | ALPHA: (11) implies: % 154.26/23.29 | (13) all_58_6 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (1), (13) imply: % 154.26/23.29 | (14) e2 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (3), (14) imply: % 154.26/23.29 | (15) all_58_30 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (15) are % 154.26/23.29 | inconsistent by sub-proof #701. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #381 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_4 = e0 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (3) ~ (e3 = e1) % 154.26/23.29 (4) all_58_28 = e1 % 154.26/23.29 (5) all_58_4 = e1 % 154.26/23.29 (6) all_58_29 = e0 % 154.26/23.29 (7) ~ (e2 = e1) % 154.26/23.29 (8) ~ (e3 = e0) % 154.26/23.29 (9) ~ (e2 = e0) % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) ~ (e1 = e0) % 154.26/23.29 (12) all_58_30 = all_6_2 % 154.26/23.29 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.29 (14) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (1), (5) imply: % 154.26/23.29 | (15) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | SIMP: (15) implies: % 154.26/23.29 | (16) e1 = e0 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (4), (16) imply: % 154.26/23.29 | (17) all_58_28 = e0 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14), (17) % 154.26/23.29 | are inconsistent by sub-proof #483. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #382 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.29 (2) ~ (e3 = e1) % 154.26/23.29 (3) all_58_28 = e1 % 154.26/23.29 (4) all_58_29 = e0 % 154.26/23.29 (5) ~ (e2 = e1) % 154.26/23.29 (6) ~ (e3 = e0) % 154.26/23.29 (7) all_58_31 = e3 % 154.26/23.29 (8) ~ (e2 = e0) % 154.26/23.29 (9) e3 = e1 % 154.26/23.29 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.29 (11) all_58_30 = all_6_2 % 154.26/23.29 (12) ~ (e3 = e2) % 154.26/23.29 % 154.26/23.29 Begin of proof % 154.26/23.29 | % 154.26/23.29 | SIMP: (9) implies: % 154.26/23.29 | (13) e3 = e1 % 154.26/23.29 | % 154.26/23.29 | COMBINE_EQS: (7), (13) imply: % 154.26/23.29 | (14) all_58_31 = e1 % 154.26/23.29 | % 154.26/23.29 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (14) are % 154.26/23.29 | inconsistent by sub-proof #383. % 154.26/23.29 | % 154.26/23.29 End of proof % 154.26/23.29 % 154.26/23.29 Sub-proof #383 shows that the following formulas are inconsistent: % 154.26/23.29 ---------------------------------------------------------------- % 154.26/23.29 (1) all_58_31 = e1 % 154.26/23.29 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.30 (3) ~ (e3 = e1) % 154.26/23.30 (4) all_58_28 = e1 % 154.26/23.30 (5) all_58_29 = e0 % 154.26/23.30 (6) ~ (e2 = e1) % 154.26/23.30 (7) ~ (e3 = e0) % 154.26/23.30 (8) ~ (e2 = e0) % 154.26/23.30 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.30 (10) all_58_30 = all_6_2 % 154.26/23.30 (11) ~ (e3 = e2) % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | BETA: splitting (9) gives: % 154.26/23.30 | % 154.26/23.30 | Case 1: % 154.26/23.30 | | % 154.26/23.30 | | (12) all_58_28 = e3 % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #857. % 154.26/23.30 | | % 154.26/23.30 | Case 2: % 154.26/23.30 | | % 154.26/23.30 | | (13) ~ (all_58_28 = e3) % 154.26/23.30 | | (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.30 | | % 154.26/23.30 | | REDUCE: (4), (13) imply: % 154.26/23.30 | | (15) ~ (e3 = e1) % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14) are % 154.26/23.30 | | inconsistent by sub-proof #384. % 154.26/23.30 | | % 154.26/23.30 | End of split % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #384 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_31 = e1 % 154.26/23.30 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.30 (3) ~ (e3 = e1) % 154.26/23.30 (4) all_58_28 = e1 % 154.26/23.30 (5) all_58_29 = e0 % 154.26/23.30 (6) ~ (e2 = e1) % 154.26/23.30 (7) ~ (e3 = e0) % 154.26/23.30 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.30 (9) ~ (e2 = e0) % 154.26/23.30 (10) all_58_30 = all_6_2 % 154.26/23.30 (11) ~ (e3 = e2) % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | BETA: splitting (2) gives: % 154.26/23.30 | % 154.26/23.30 | Case 1: % 154.26/23.30 | | % 154.26/23.30 | | (12) all_58_28 = e2 % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #856. % 154.26/23.30 | | % 154.26/23.30 | Case 2: % 154.26/23.30 | | % 154.26/23.30 | | (13) ~ (all_58_28 = e2) % 154.26/23.30 | | (14) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.30 | | % 154.26/23.30 | | REDUCE: (4), (13) imply: % 154.26/23.30 | | (15) ~ (e2 = e1) % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (14) are % 154.26/23.30 | | inconsistent by sub-proof #385. % 154.26/23.30 | | % 154.26/23.30 | End of split % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #385 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_31 = e1 % 154.26/23.30 (2) ~ (e3 = e1) % 154.26/23.30 (3) all_58_29 = e0 % 154.26/23.30 (4) ~ (e2 = e1) % 154.26/23.30 (5) ~ (e3 = e0) % 154.26/23.30 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.30 (7) ~ (e2 = e0) % 154.26/23.30 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.30 (9) all_58_30 = all_6_2 % 154.26/23.30 (10) ~ (e3 = e2) % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | BETA: splitting (6) gives: % 154.26/23.30 | % 154.26/23.30 | Case 1: % 154.26/23.30 | | % 154.26/23.30 | | (11) all_58_29 = e3 % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #707. % 154.26/23.30 | | % 154.26/23.30 | Case 2: % 154.26/23.30 | | % 154.26/23.30 | | (12) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12) are inconsistent by % 154.26/23.30 | | sub-proof #655. % 154.26/23.30 | | % 154.26/23.30 | End of split % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #386 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.30 (2) all_58_30 = e2 % 154.26/23.30 (3) ~ (e3 = e1) % 154.26/23.30 (4) all_58_28 = e1 % 154.26/23.30 (5) all_58_29 = e0 % 154.26/23.30 (6) ~ (e2 = e1) % 154.26/23.30 (7) ~ (e3 = e0) % 154.26/23.30 (8) all_58_29 = e2 % 154.26/23.30 (9) ~ (e2 = e0) % 154.26/23.30 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.30 (11) ~ (e3 = e2) % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | COMBINE_EQS: (5), (8) imply: % 154.26/23.30 | (12) e2 = e0 % 154.26/23.30 | % 154.26/23.30 | SIMP: (12) implies: % 154.26/23.30 | (13) e2 = e0 % 154.26/23.30 | % 154.26/23.30 | COMBINE_EQS: (2), (13) imply: % 154.26/23.30 | (14) all_58_30 = e0 % 154.26/23.30 | % 154.26/23.30 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (14) are % 154.26/23.30 | inconsistent by sub-proof #701. % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #387 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_56_7 = e2 % 154.26/23.30 (2) all_56_7 = e1 % 154.26/23.30 (3) ~ (e2 = e1) % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | COMBINE_EQS: (1), (2) imply: % 154.26/23.30 | (4) e2 = e1 % 154.26/23.30 | % 154.26/23.30 | SIMP: (4) implies: % 154.26/23.30 | (5) e2 = e1 % 154.26/23.30 | % 154.26/23.30 | REDUCE: (3), (5) imply: % 154.26/23.30 | (6) $false % 154.26/23.30 | % 154.26/23.30 | CLOSE: (6) is inconsistent. % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #388 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_28 = all_10_2 % 154.26/23.30 (2) all_58_28 = e2 % 154.26/23.30 (3) ~ (all_10_2 = e2) % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | COMBINE_EQS: (1), (2) imply: % 154.26/23.30 | (4) all_10_2 = e2 % 154.26/23.30 | % 154.26/23.30 | SIMP: (4) implies: % 154.26/23.30 | (5) all_10_2 = e2 % 154.26/23.30 | % 154.26/23.30 | REDUCE: (3), (5) imply: % 154.26/23.30 | (6) $false % 154.26/23.30 | % 154.26/23.30 | CLOSE: (6) is inconsistent. % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #389 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_23 = all_8_0 % 154.26/23.30 (2) all_58_31 = all_4_2 % 154.26/23.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.30 (4) all_56_15 = all_4_2 % 154.26/23.30 (5) all_56_7 = all_52_6 % 154.26/23.30 (6) ~ (all_52_6 = all_6_2) % 154.26/23.30 (7) all_56_9 = e1 % 154.26/23.30 (8) all_56_3 = e0 % 154.26/23.30 (9) ~ (all_6_2 = e0) % 154.26/23.30 (10) op(e0, e1) = all_52_11 % 154.26/23.30 (11) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.30 (12) all_56_13 = all_8_1 % 154.26/23.30 (13) ~ (all_52_2 = all_6_2) % 154.26/23.30 (14) ~ (all_52_13 = all_4_2) % 154.26/23.30 (15) all_58_19 = e0 % 154.26/23.30 (16) ~ (e3 = e1) % 154.26/23.30 (17) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.26/23.30 (18) all_56_5 = all_52_9 % 154.26/23.30 (19) all_54_14 = all_52_11 % 154.26/23.30 (20) op(e0, all_8_1) = all_8_0 % 154.26/23.30 (21) ~ (all_52_12 = e0) % 154.26/23.30 (22) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 154.26/23.30 (23) all_56_1 = all_52_4 % 154.26/23.30 (24) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.30 (25) all_58_29 = e0 % 154.26/23.30 (26) op(e2, e1) = all_52_9 % 154.26/23.30 (27) all_56_9 = all_52_12 % 154.26/23.30 (28) all_56_6 = all_52_2 % 154.26/23.30 (29) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.30 (30) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.30 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.30 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.30 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.30 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.30 (all_58_27 = e0)) % 154.26/23.30 (31) ~ (all_52_11 = all_8_1) % 154.26/23.30 (32) ~ (e3 = e0) % 154.26/23.30 (33) all_56_2 = all_52_1 % 154.26/23.30 (34) ~ (all_52_11 = e0) % 154.26/23.30 (35) op(e3, all_52_12) = all_58_5 % 154.26/23.30 (36) all_56_10 = all_52_13 % 154.26/23.30 (37) ~ (all_52_12 = all_10_2) % 154.26/23.30 (38) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.30 (39) all_56_14 = all_52_11 % 154.26/23.30 (40) all_58_28 = all_10_2 % 154.26/23.30 (41) all_14_0 = all_8_0 % 154.26/23.30 (42) all_56_12 = e0 % 154.26/23.30 (43) all_56_0 = all_10_2 % 154.26/23.30 (44) ~ (all_52_1 = e0) % 154.26/23.30 (45) ~ (all_52_12 = all_4_2) % 154.26/23.30 (46) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.26/23.30 (47) all_14_1 = all_8_1 % 154.26/23.30 (48) all_58_30 = all_6_2 % 154.26/23.30 (49) op(e2, all_52_1) = all_58_7 % 154.26/23.30 (50) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.30 (51) ~ (all_52_4 = all_52_12) % 154.26/23.30 (52) op(e3, e1) = e0 % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | COMBINE_EQS: (7), (27) imply: % 154.26/23.30 | (53) all_52_12 = e1 % 154.26/23.30 | % 154.26/23.30 | SIMP: (53) implies: % 154.26/23.30 | (54) all_52_12 = e1 % 154.26/23.30 | % 154.26/23.30 | REDUCE: (51), (54) imply: % 154.26/23.30 | (55) ~ (all_52_4 = e1) % 154.26/23.30 | % 154.26/23.30 | REDUCE: (37), (54) imply: % 154.26/23.30 | (56) ~ (all_10_2 = e1) % 154.26/23.30 | % 154.26/23.30 | SIMP: (56) implies: % 154.26/23.30 | (57) ~ (all_10_2 = e1) % 154.26/23.30 | % 154.26/23.30 | REDUCE: (45), (54) imply: % 154.26/23.30 | (58) ~ (all_4_2 = e1) % 154.26/23.30 | % 154.26/23.30 | SIMP: (58) implies: % 154.26/23.30 | (59) ~ (all_4_2 = e1) % 154.26/23.30 | % 154.26/23.30 | REDUCE: (21), (54) imply: % 154.26/23.30 | (60) ~ (e1 = e0) % 154.26/23.30 | % 154.26/23.30 | REDUCE: (35), (54) imply: % 154.26/23.30 | (61) op(e3, e1) = all_58_5 % 154.26/23.30 | % 154.26/23.30 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), % 154.26/23.30 | (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25), % 154.26/23.30 | (26), (28), (29), (30), (31), (32), (33), (34), (36), (38), (39), % 154.26/23.30 | (40), (41), (42), (43), (44), (46), (47), (48), (49), (50), (52), % 154.26/23.30 | (55), (57), (59), (60), (61) are inconsistent by sub-proof #390. % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #390 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_23 = all_8_0 % 154.26/23.30 (2) all_58_31 = all_4_2 % 154.26/23.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.30 (4) all_56_15 = all_4_2 % 154.26/23.30 (5) all_56_7 = all_52_6 % 154.26/23.30 (6) ~ (all_52_6 = all_6_2) % 154.26/23.30 (7) all_56_3 = e0 % 154.26/23.30 (8) ~ (all_6_2 = e0) % 154.26/23.30 (9) op(e0, e1) = all_52_11 % 154.26/23.30 (10) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.30 (11) all_56_13 = all_8_1 % 154.26/23.30 (12) ~ (all_52_2 = all_6_2) % 154.26/23.30 (13) ~ (all_52_13 = all_4_2) % 154.26/23.30 (14) all_58_19 = e0 % 154.26/23.30 (15) ~ (e3 = e1) % 154.26/23.30 (16) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.26/23.30 (17) all_56_5 = all_52_9 % 154.26/23.30 (18) all_54_14 = all_52_11 % 154.26/23.30 (19) op(e0, all_8_1) = all_8_0 % 154.26/23.30 (20) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 154.26/23.30 (21) all_56_1 = all_52_4 % 154.26/23.30 (22) ~ (all_10_2 = e1) % 154.26/23.30 (23) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.30 (24) all_58_29 = e0 % 154.26/23.30 (25) op(e2, e1) = all_52_9 % 154.26/23.30 (26) ~ (all_52_4 = e1) % 154.26/23.30 (27) all_56_6 = all_52_2 % 154.26/23.30 (28) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.30 (29) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.30 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.30 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.30 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.30 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.30 (all_58_27 = e0)) % 154.26/23.30 (30) ~ (all_52_11 = all_8_1) % 154.26/23.30 (31) op(e3, e1) = all_58_5 % 154.26/23.30 (32) ~ (e3 = e0) % 154.26/23.30 (33) all_56_2 = all_52_1 % 154.26/23.30 (34) ~ (all_52_11 = e0) % 154.26/23.30 (35) all_56_10 = all_52_13 % 154.26/23.30 (36) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.30 (37) all_56_14 = all_52_11 % 154.26/23.30 (38) all_58_28 = all_10_2 % 154.26/23.30 (39) all_14_0 = all_8_0 % 154.26/23.30 (40) all_56_12 = e0 % 154.26/23.30 (41) all_56_0 = all_10_2 % 154.26/23.30 (42) ~ (all_52_1 = e0) % 154.26/23.30 (43) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.26/23.30 (44) all_14_1 = all_8_1 % 154.26/23.30 (45) ~ (e1 = e0) % 154.26/23.30 (46) ~ (all_4_2 = e1) % 154.26/23.30 (47) all_58_30 = all_6_2 % 154.26/23.30 (48) op(e2, all_52_1) = all_58_7 % 154.26/23.30 (49) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.30 (50) op(e3, e1) = e0 % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | BETA: splitting (49) gives: % 154.26/23.30 | % 154.26/23.30 | Case 1: % 154.26/23.30 | | % 154.26/23.30 | | (51) all_58_28 = e1 % 154.26/23.30 | | % 154.26/23.30 | | REF_CLOSE: (22), (38), (51) are inconsistent by sub-proof #858. % 154.26/23.30 | | % 154.26/23.30 | Case 2: % 154.26/23.30 | | % 154.26/23.30 | | (52) ~ (all_58_28 = e1) % 154.26/23.30 | | (53) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.30 | | % 154.26/23.30 | | BETA: splitting (53) gives: % 154.26/23.30 | | % 154.26/23.30 | | Case 1: % 154.26/23.30 | | | % 154.26/23.30 | | | (54) all_58_29 = e1 % 154.26/23.30 | | | % 154.26/23.30 | | | COMBINE_EQS: (24), (54) imply: % 154.26/23.30 | | | (55) e1 = e0 % 154.26/23.30 | | | % 154.26/23.30 | | | REDUCE: (45), (55) imply: % 154.26/23.30 | | | (56) $false % 154.26/23.30 | | | % 154.26/23.30 | | | CLOSE: (56) is inconsistent. % 154.26/23.30 | | | % 154.26/23.30 | | Case 2: % 154.26/23.30 | | | % 154.26/23.30 | | | (57) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.30 | | | % 154.26/23.30 | | | BETA: splitting (57) gives: % 154.26/23.30 | | | % 154.26/23.30 | | | Case 1: % 154.26/23.30 | | | | % 154.26/23.30 | | | | (58) all_58_30 = e1 % 154.26/23.30 | | | | % 154.26/23.30 | | | | COMBINE_EQS: (47), (58) imply: % 154.26/23.30 | | | | (59) all_6_2 = e1 % 154.26/23.30 | | | | % 154.26/23.30 | | | | SIMP: (59) implies: % 154.26/23.30 | | | | (60) all_6_2 = e1 % 154.26/23.30 | | | | % 154.26/23.30 | | | | REDUCE: (12), (60) imply: % 154.26/23.30 | | | | (61) ~ (all_52_2 = e1) % 154.26/23.30 | | | | % 154.26/23.30 | | | | REDUCE: (6), (60) imply: % 154.26/23.30 | | | | (62) ~ (all_52_6 = e1) % 154.26/23.30 | | | | % 154.26/23.30 | | | | BETA: splitting (10) gives: % 154.26/23.30 | | | | % 154.26/23.30 | | | | Case 1: % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | (63) all_56_0 = e1 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | COMBINE_EQS: (41), (63) imply: % 154.26/23.30 | | | | | (64) all_10_2 = e1 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | SIMP: (64) implies: % 154.26/23.30 | | | | | (65) all_10_2 = e1 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | REDUCE: (22), (65) imply: % 154.26/23.30 | | | | | (66) $false % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | CLOSE: (66) is inconsistent. % 154.26/23.30 | | | | | % 154.26/23.30 | | | | Case 2: % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | (67) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | BETA: splitting (28) gives: % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | Case 1: % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | (68) all_56_1 = e1 % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | REF_CLOSE: (21), (26), (68) are inconsistent by sub-proof #394. % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | Case 2: % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | (69) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | BETA: splitting (16) gives: % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | Case 1: % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | (70) all_56_2 = e1 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | COMBINE_EQS: (33), (70) imply: % 154.26/23.30 | | | | | | | (71) all_52_1 = e1 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | SIMP: (71) implies: % 154.26/23.30 | | | | | | | (72) all_52_1 = e1 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | REDUCE: (48), (72) imply: % 154.26/23.30 | | | | | | | (73) op(e2, e1) = all_58_7 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | BETA: splitting (69) gives: % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | Case 1: % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | (74) all_56_3 = e1 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | COMBINE_EQS: (7), (74) imply: % 154.26/23.30 | | | | | | | | (75) e1 = e0 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | COMBINE_EQS: (58), (75) imply: % 154.26/23.30 | | | | | | | | (76) all_58_30 = e0 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | REF_CLOSE: (2), (45), (46), (57), (76) are inconsistent by % 154.26/23.30 | | | | | | | | sub-proof #711. % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | Case 2: % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | (77) all_56_7 = e1 | all_56_13 = e1 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | BETA: splitting (77) gives: % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | Case 1: % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | (78) all_56_7 = e1 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | REF_CLOSE: (5), (62), (78) are inconsistent by sub-proof #547. % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | Case 2: % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | (79) all_56_13 = e1 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | COMBINE_EQS: (11), (79) imply: % 154.26/23.30 | | | | | | | | | (80) all_8_1 = e1 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | SIMP: (80) implies: % 154.26/23.30 | | | | | | | | | (81) all_8_1 = e1 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | COMBINE_EQS: (44), (81) imply: % 154.26/23.30 | | | | | | | | | (82) all_14_1 = e1 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | REDUCE: (30), (81) imply: % 154.26/23.30 | | | | | | | | | (83) ~ (all_52_11 = e1) % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | REDUCE: (19), (81) imply: % 154.26/23.30 | | | | | | | | | (84) op(e0, e1) = all_8_0 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (13), (14), (15), (17), % 154.26/23.30 | | | | | | | | | (18), (20), (23), (25), (29), (31), (32), (34), % 154.26/23.30 | | | | | | | | | (35), (36), (37), (39), (40), (43), (50), (70), % 154.26/23.30 | | | | | | | | | (73), (79), (82), (83), (84) are inconsistent by % 154.26/23.30 | | | | | | | | | sub-proof #391. % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | End of split % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | End of split % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | Case 2: % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | (85) ~ (all_56_2 = e1) % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | REDUCE: (33), (85) imply: % 154.26/23.30 | | | | | | | (86) ~ (all_52_1 = e1) % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | REF_CLOSE: (27), (33), (40), (45), (61), (67), (86) are % 154.26/23.30 | | | | | | | inconsistent by sub-proof #637. % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | End of split % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | End of split % 154.26/23.30 | | | | | % 154.26/23.30 | | | | End of split % 154.26/23.30 | | | | % 154.26/23.30 | | | Case 2: % 154.26/23.30 | | | | % 154.26/23.30 | | | | (87) all_58_31 = e1 % 154.26/23.30 | | | | % 154.26/23.30 | | | | REF_CLOSE: (2), (46), (87) are inconsistent by sub-proof #712. % 154.26/23.30 | | | | % 154.26/23.30 | | | End of split % 154.26/23.30 | | | % 154.26/23.30 | | End of split % 154.26/23.30 | | % 154.26/23.30 | End of split % 154.26/23.30 | % 154.26/23.30 End of proof % 154.26/23.30 % 154.26/23.30 Sub-proof #391 shows that the following formulas are inconsistent: % 154.26/23.30 ---------------------------------------------------------------- % 154.26/23.30 (1) all_58_23 = all_8_0 % 154.26/23.30 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.30 (3) all_56_15 = all_4_2 % 154.26/23.30 (4) all_56_3 = e0 % 154.26/23.30 (5) op(e0, e1) = all_52_11 % 154.26/23.30 (6) all_56_13 = e1 % 154.26/23.30 (7) ~ (all_52_13 = all_4_2) % 154.26/23.30 (8) all_58_19 = e0 % 154.26/23.30 (9) op(e0, e1) = all_8_0 % 154.26/23.30 (10) ~ (e3 = e1) % 154.26/23.30 (11) all_56_5 = all_52_9 % 154.26/23.30 (12) all_54_14 = all_52_11 % 154.26/23.30 (13) all_56_2 = e1 % 154.26/23.30 (14) ~ (all_14_0 = e3) | ~ (all_14_1 = e1) % 154.26/23.30 (15) all_14_1 = e1 % 154.26/23.30 (16) ~ (all_52_11 = e1) % 154.26/23.30 (17) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.30 (18) op(e2, e1) = all_52_9 % 154.26/23.30 (19) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.30 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.30 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.30 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.30 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.30 (all_58_27 = e0)) % 154.26/23.30 (20) op(e3, e1) = all_58_5 % 154.26/23.30 (21) ~ (e3 = e0) % 154.26/23.30 (22) ~ (all_52_11 = e0) % 154.26/23.30 (23) all_56_10 = all_52_13 % 154.26/23.30 (24) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.30 (25) all_56_14 = all_52_11 % 154.26/23.30 (26) all_14_0 = all_8_0 % 154.26/23.30 (27) all_56_12 = e0 % 154.26/23.30 (28) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.26/23.30 (29) op(e2, e1) = all_58_7 % 154.26/23.30 (30) op(e3, e1) = e0 % 154.26/23.30 % 154.26/23.30 Begin of proof % 154.26/23.30 | % 154.26/23.30 | BETA: splitting (14) gives: % 154.26/23.30 | % 154.26/23.30 | Case 1: % 154.26/23.30 | | % 154.26/23.30 | | (31) ~ (all_14_1 = e1) % 154.26/23.30 | | % 154.26/23.30 | | REDUCE: (15), (31) imply: % 154.26/23.30 | | (32) $false % 154.26/23.30 | | % 154.26/23.30 | | CLOSE: (32) is inconsistent. % 154.26/23.30 | | % 154.26/23.30 | Case 2: % 154.26/23.30 | | % 154.26/23.30 | | (33) ~ (all_14_0 = e3) % 154.26/23.30 | | % 154.26/23.30 | | REDUCE: (26), (33) imply: % 154.26/23.30 | | (34) ~ (all_8_0 = e3) % 154.26/23.30 | | % 154.26/23.30 | | GROUND_INST: instantiating (2) with all_52_11, all_8_0, e1, e0, simplifying % 154.26/23.30 | | with (5), (9) gives: % 154.26/23.30 | | (35) all_52_11 = all_8_0 % 154.26/23.30 | | % 154.26/23.30 | | GROUND_INST: instantiating (2) with all_52_9, all_58_7, e1, e2, simplifying % 154.26/23.30 | | with (18), (29) gives: % 154.26/23.30 | | (36) all_58_7 = all_52_9 % 154.26/23.30 | | % 154.26/23.30 | | GROUND_INST: instantiating (2) with e0, all_58_5, e1, e3, simplifying with % 154.26/23.30 | | (20), (30) gives: % 154.26/23.30 | | (37) all_58_5 = e0 % 154.26/23.30 | | % 154.26/23.30 | | COMBINE_EQS: (12), (35) imply: % 154.26/23.30 | | (38) all_54_14 = all_8_0 % 154.26/23.30 | | % 154.26/23.30 | | COMBINE_EQS: (25), (35) imply: % 154.26/23.30 | | (39) all_56_14 = all_8_0 % 154.26/23.30 | | % 154.26/23.30 | | REDUCE: (16), (35) imply: % 154.26/23.30 | | (40) ~ (all_8_0 = e1) % 154.26/23.30 | | % 154.26/23.30 | | REDUCE: (22), (35) imply: % 154.26/23.30 | | (41) ~ (all_8_0 = e0) % 154.26/23.30 | | % 154.26/23.30 | | BETA: splitting (24) gives: % 154.26/23.30 | | % 154.26/23.30 | | Case 1: % 154.26/23.30 | | | % 154.26/23.30 | | | (42) all_54_14 = e0 % 154.26/23.30 | | | % 154.26/23.30 | | | COMBINE_EQS: (38), (42) imply: % 154.26/23.30 | | | (43) all_8_0 = e0 % 154.26/23.30 | | | % 154.26/23.30 | | | SIMP: (43) implies: % 154.26/23.30 | | | (44) all_8_0 = e0 % 154.26/23.30 | | | % 154.26/23.30 | | | REDUCE: (41), (44) imply: % 154.26/23.30 | | | (45) $false % 154.26/23.30 | | | % 154.26/23.30 | | | CLOSE: (45) is inconsistent. % 154.26/23.30 | | | % 154.26/23.30 | | Case 2: % 154.26/23.30 | | | % 154.26/23.30 | | | (46) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.26/23.30 | | | % 154.26/23.30 | | | BETA: splitting (17) gives: % 154.26/23.30 | | | % 154.26/23.30 | | | Case 1: % 154.26/23.30 | | | | % 154.26/23.30 | | | | (47) all_56_12 = e3 % 154.26/23.30 | | | | % 154.26/23.30 | | | | COMBINE_EQS: (27), (47) imply: % 154.26/23.30 | | | | (48) e3 = e0 % 154.26/23.30 | | | | % 154.26/23.30 | | | | REDUCE: (21), (48) imply: % 154.26/23.30 | | | | (49) $false % 154.26/23.30 | | | | % 154.26/23.30 | | | | CLOSE: (49) is inconsistent. % 154.26/23.30 | | | | % 154.26/23.30 | | | Case 2: % 154.26/23.30 | | | | % 154.26/23.30 | | | | (50) ~ (all_56_12 = e3) % 154.26/23.30 | | | | (51) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.30 | | | | % 154.26/23.30 | | | | REDUCE: (27), (50) imply: % 154.26/23.30 | | | | (52) ~ (e3 = e0) % 154.26/23.30 | | | | % 154.26/23.30 | | | | BETA: splitting (51) gives: % 154.26/23.30 | | | | % 154.26/23.30 | | | | Case 1: % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | (53) all_56_13 = e3 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | COMBINE_EQS: (6), (53) imply: % 154.26/23.30 | | | | | (54) e3 = e1 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | REDUCE: (10), (54) imply: % 154.26/23.30 | | | | | (55) $false % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | CLOSE: (55) is inconsistent. % 154.26/23.30 | | | | | % 154.26/23.30 | | | | Case 2: % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | (56) ~ (all_56_13 = e3) % 154.26/23.30 | | | | | (57) all_56_14 = e3 | all_56_15 = e3 % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | REDUCE: (6), (56) imply: % 154.26/23.30 | | | | | (58) ~ (e3 = e1) % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | BETA: splitting (46) gives: % 154.26/23.30 | | | | | % 154.26/23.30 | | | | | Case 1: % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | (59) all_54_14 = e1 % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | COMBINE_EQS: (38), (59) imply: % 154.26/23.30 | | | | | | (60) all_8_0 = e1 % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | SIMP: (60) implies: % 154.26/23.30 | | | | | | (61) all_8_0 = e1 % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | REDUCE: (40), (61) imply: % 154.26/23.30 | | | | | | (62) $false % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | CLOSE: (62) is inconsistent. % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | Case 2: % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | (63) all_54_14 = e3 | all_54_14 = e2 % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | BETA: splitting (63) gives: % 154.26/23.30 | | | | | | % 154.26/23.30 | | | | | | Case 1: % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | (64) all_54_14 = e2 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | COMBINE_EQS: (38), (64) imply: % 154.26/23.30 | | | | | | | (65) all_8_0 = e2 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | SIMP: (65) implies: % 154.26/23.30 | | | | | | | (66) all_8_0 = e2 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | COMBINE_EQS: (39), (66) imply: % 154.26/23.30 | | | | | | | (67) all_56_14 = e2 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | COMBINE_EQS: (1), (66) imply: % 154.26/23.30 | | | | | | | (68) all_58_23 = e2 % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | REDUCE: (34), (66) imply: % 154.26/23.30 | | | | | | | (69) ~ (e3 = e2) % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | SIMP: (69) implies: % 154.26/23.30 | | | | | | | (70) ~ (e3 = e2) % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | BETA: splitting (28) gives: % 154.26/23.30 | | | | | | | % 154.26/23.30 | | | | | | | Case 1: % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | (71) all_56_2 = e3 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | COMBINE_EQS: (13), (71) imply: % 154.26/23.30 | | | | | | | | (72) e3 = e1 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | REDUCE: (10), (72) imply: % 154.26/23.30 | | | | | | | | (73) $false % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | CLOSE: (73) is inconsistent. % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | Case 2: % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | (74) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | BETA: splitting (74) gives: % 154.26/23.30 | | | | | | | | % 154.26/23.30 | | | | | | | | Case 1: % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | (75) all_56_3 = e3 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | COMBINE_EQS: (4), (75) imply: % 154.26/23.30 | | | | | | | | | (76) e3 = e0 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | REDUCE: (21), (76) imply: % 154.26/23.30 | | | | | | | | | (77) $false % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | CLOSE: (77) is inconsistent. % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | Case 2: % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | (78) all_56_5 = e3 | all_56_10 = e3 % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | BETA: splitting (78) gives: % 154.26/23.30 | | | | | | | | | % 154.26/23.30 | | | | | | | | | Case 1: % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | (79) all_56_5 = e3 % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | COMBINE_EQS: (11), (79) imply: % 154.26/23.30 | | | | | | | | | | (80) all_52_9 = e3 % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | SIMP: (80) implies: % 154.26/23.30 | | | | | | | | | | (81) all_52_9 = e3 % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | COMBINE_EQS: (36), (81) imply: % 154.26/23.30 | | | | | | | | | | (82) all_58_7 = e3 % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | BETA: splitting (19) gives: % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | Case 1: % 154.26/23.30 | | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | | (83) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.26/23.30 | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.26/23.30 | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.30 | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.26/23.30 | | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | | REF_CLOSE: (37), (82), (83) are inconsistent by sub-proof % 154.26/23.30 | | | | | | | | | | | #393. % 154.26/23.30 | | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | Case 2: % 154.26/23.30 | | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | | (84) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.26/23.30 | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.30 | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.26/23.30 | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.26/23.30 | | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | | REF_CLOSE: (8), (68), (84) are inconsistent by sub-proof % 154.26/23.30 | | | | | | | | | | | #478. % 154.26/23.30 | | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | End of split % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | Case 2: % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | (85) all_56_10 = e3 % 154.26/23.30 | | | | | | | | | | % 154.26/23.30 | | | | | | | | | | COMBINE_EQS: (23), (85) imply: % 154.26/23.30 | | | | | | | | | | (86) all_52_13 = e3 % 154.26/23.31 | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | REDUCE: (7), (86) imply: % 154.26/23.31 | | | | | | | | | | (87) ~ (all_4_2 = e3) % 154.26/23.31 | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | SIMP: (87) implies: % 154.26/23.31 | | | | | | | | | | (88) ~ (all_4_2 = e3) % 154.26/23.31 | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | BETA: splitting (57) gives: % 154.26/23.31 | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | Case 1: % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | | (89) all_56_14 = e3 % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | | COMBINE_EQS: (67), (89) imply: % 154.26/23.31 | | | | | | | | | | | (90) e3 = e2 % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | | REDUCE: (70), (90) imply: % 154.26/23.31 | | | | | | | | | | | (91) $false % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | | CLOSE: (91) is inconsistent. % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | Case 2: % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | | (92) all_56_15 = e3 % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | | REF_CLOSE: (3), (88), (92) are inconsistent by sub-proof % 154.26/23.31 | | | | | | | | | | | #392. % 154.26/23.31 | | | | | | | | | | | % 154.26/23.31 | | | | | | | | | | End of split % 154.26/23.31 | | | | | | | | | | % 154.26/23.31 | | | | | | | | | End of split % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | End of split % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | End of split % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | Case 2: % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | (93) all_54_14 = e3 % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | COMBINE_EQS: (38), (93) imply: % 154.26/23.31 | | | | | | | (94) all_8_0 = e3 % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | SIMP: (94) implies: % 154.26/23.31 | | | | | | | (95) all_8_0 = e3 % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | REDUCE: (34), (95) imply: % 154.26/23.31 | | | | | | | (96) $false % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | CLOSE: (96) is inconsistent. % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | End of split % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | End of split % 154.26/23.31 | | | | | % 154.26/23.31 | | | | End of split % 154.26/23.31 | | | | % 154.26/23.31 | | | End of split % 154.26/23.31 | | | % 154.26/23.31 | | End of split % 154.26/23.31 | | % 154.26/23.31 | End of split % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #392 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_56_15 = all_4_2 % 154.26/23.31 (2) all_56_15 = e3 % 154.26/23.31 (3) ~ (all_4_2 = e3) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (1), (2) imply: % 154.26/23.31 | (4) all_4_2 = e3 % 154.26/23.31 | % 154.26/23.31 | SIMP: (4) implies: % 154.26/23.31 | (5) all_4_2 = e3 % 154.26/23.31 | % 154.26/23.31 | REDUCE: (3), (5) imply: % 154.26/23.31 | (6) $false % 154.26/23.31 | % 154.26/23.31 | CLOSE: (6) is inconsistent. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #393 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.31 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.31 (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.26/23.31 (2) all_58_5 = e0 % 154.26/23.31 (3) all_58_7 = e3 % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | BETA: splitting (1) gives: % 154.26/23.31 | % 154.26/23.31 | Case 1: % 154.26/23.31 | | % 154.26/23.31 | | (4) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.31 | | (all_58_5 = e0) % 154.26/23.31 | | % 154.26/23.31 | | ALPHA: (4) implies: % 154.26/23.31 | | (5) ~ (all_58_5 = e0) % 154.26/23.31 | | % 154.26/23.31 | | REDUCE: (2), (5) imply: % 154.26/23.31 | | (6) $false % 154.26/23.31 | | % 154.26/23.31 | | CLOSE: (6) is inconsistent. % 154.26/23.31 | | % 154.26/23.31 | Case 2: % 154.26/23.31 | | % 154.26/23.31 | | (7) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 154.26/23.31 | | (all_58_12 = e0) % 154.26/23.31 | | % 154.26/23.31 | | ALPHA: (7) implies: % 154.26/23.31 | | (8) ~ (all_58_7 = e3) % 154.26/23.31 | | % 154.26/23.31 | | REDUCE: (3), (8) imply: % 154.26/23.31 | | (9) $false % 154.26/23.31 | | % 154.26/23.31 | | CLOSE: (9) is inconsistent. % 154.26/23.31 | | % 154.26/23.31 | End of split % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #394 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_56_1 = all_52_4 % 154.26/23.31 (2) all_56_1 = e1 % 154.26/23.31 (3) ~ (all_52_4 = e1) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (1), (2) imply: % 154.26/23.31 | (4) all_52_4 = e1 % 154.26/23.31 | % 154.26/23.31 | SIMP: (4) implies: % 154.26/23.31 | (5) all_52_4 = e1 % 154.26/23.31 | % 154.26/23.31 | REDUCE: (3), (5) imply: % 154.26/23.31 | (6) $false % 154.26/23.31 | % 154.26/23.31 | CLOSE: (6) is inconsistent. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #395 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.31 (2) ~ (e3 = e1) % 154.26/23.31 (3) all_58_29 = e0 % 154.26/23.31 (4) ~ (e2 = e1) % 154.26/23.31 (5) all_54_0 = e0 % 154.26/23.31 (6) ~ (e3 = e0) % 154.26/23.31 (7) all_58_28 = all_10_2 % 154.26/23.31 (8) ~ (e2 = e0) % 154.26/23.31 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.31 (10) all_54_0 = all_10_2 % 154.26/23.31 (11) ~ (e1 = e0) % 154.26/23.31 (12) all_58_30 = all_6_2 % 154.26/23.31 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.31 (14) ~ (e3 = e2) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (5), (10) imply: % 154.26/23.31 | (15) all_10_2 = e0 % 154.26/23.31 | % 154.26/23.31 | SIMP: (15) implies: % 154.26/23.31 | (16) all_10_2 = e0 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (7), (16) imply: % 154.26/23.31 | (17) all_58_28 = e0 % 154.26/23.31 | % 154.26/23.31 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (12), (13), (14), (17) are % 154.26/23.31 | inconsistent by sub-proof #483. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #396 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_58_31 = all_4_2 % 154.26/23.31 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.31 (3) all_6_2 = e0 % 154.26/23.31 (4) ~ (e3 = e1) % 154.26/23.31 (5) all_58_29 = e0 % 154.26/23.31 (6) ~ (e2 = e1) % 154.26/23.31 (7) ~ (e3 = e0) % 154.26/23.31 (8) all_58_28 = all_10_2 % 154.26/23.31 (9) ~ (e2 = e0) % 154.26/23.31 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.31 (11) ~ (e1 = e0) % 154.26/23.31 (12) ~ (all_4_2 = e1) % 154.26/23.31 (13) all_58_30 = all_6_2 % 154.26/23.31 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.31 (15) ~ (e3 = e2) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | SIMP: (3) implies: % 154.26/23.31 | (16) all_6_2 = e0 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (13), (16) imply: % 154.26/23.31 | (17) all_58_30 = e0 % 154.26/23.31 | % 154.26/23.31 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), % 154.26/23.31 | (15), (17) are inconsistent by sub-proof #698. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #397 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_54_13 = all_8_1 % 154.26/23.31 (2) all_54_13 = e0 % 154.26/23.31 (3) ~ (all_8_1 = e0) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (1), (2) imply: % 154.26/23.31 | (4) all_8_1 = e0 % 154.26/23.31 | % 154.26/23.31 | SIMP: (4) implies: % 154.26/23.31 | (5) all_8_1 = e0 % 154.26/23.31 | % 154.26/23.31 | REDUCE: (3), (5) imply: % 154.26/23.31 | (6) $false % 154.26/23.31 | % 154.26/23.31 | CLOSE: (6) is inconsistent. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #398 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_58_31 = all_4_2 % 154.26/23.31 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.31 (3) ~ (e3 = e1) % 154.26/23.31 (4) all_56_8 = e0 % 154.26/23.31 (5) all_58_29 = e0 % 154.26/23.31 (6) ~ (e2 = e1) % 154.26/23.31 (7) ~ (e3 = e0) % 154.26/23.31 (8) all_58_28 = all_10_2 % 154.26/23.31 (9) ~ (e2 = e0) % 154.26/23.31 (10) all_56_8 = all_6_2 % 154.26/23.31 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.31 (12) ~ (e1 = e0) % 154.26/23.31 (13) ~ (all_4_2 = e1) % 154.26/23.31 (14) all_58_30 = all_6_2 % 154.26/23.31 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.31 (16) ~ (e3 = e2) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (4), (10) imply: % 154.26/23.31 | (17) all_6_2 = e0 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (14), (17) imply: % 154.26/23.31 | (18) all_58_30 = e0 % 154.26/23.31 | % 154.26/23.31 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15), % 154.26/23.31 | (16), (18) are inconsistent by sub-proof #698. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #399 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_58_31 = all_4_2 % 154.26/23.31 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.31 (3) ~ (e3 = e1) % 154.26/23.31 (4) all_58_29 = e0 % 154.26/23.31 (5) ~ (e2 = e1) % 154.26/23.31 (6) ~ (e3 = e0) % 154.26/23.31 (7) all_4_2 = e0 % 154.26/23.31 (8) ~ (e2 = e0) % 154.26/23.31 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.31 (10) ~ (e1 = e0) % 154.26/23.31 (11) all_58_30 = all_6_2 % 154.26/23.31 (12) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.31 (13) ~ (e3 = e2) % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | SIMP: (7) implies: % 154.26/23.31 | (14) all_4_2 = e0 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (1), (14) imply: % 154.26/23.31 | (15) all_58_31 = e0 % 154.26/23.31 | % 154.26/23.31 | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15) are % 154.26/23.31 | inconsistent by sub-proof #844. % 154.26/23.31 | % 154.26/23.31 End of proof % 154.26/23.31 % 154.26/23.31 Sub-proof #400 shows that the following formulas are inconsistent: % 154.26/23.31 ---------------------------------------------------------------- % 154.26/23.31 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 154.26/23.31 (2) all_58_31 = all_4_2 % 154.26/23.31 (3) ~ (all_52_8 = all_52_9) % 154.26/23.31 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.31 (5) all_26_0 = all_4_0 % 154.26/23.31 (6) all_58_28 = e0 % 154.26/23.31 (7) all_54_13 = all_52_7 % 154.26/23.31 (8) ~ (all_52_2 = all_52_3) % 154.26/23.31 (9) all_58_11 = all_52_9 % 154.26/23.31 (10) all_56_15 = all_4_2 % 154.26/23.31 (11) all_56_7 = all_52_6 % 154.26/23.31 (12) ~ (all_52_6 = all_6_2) % 154.26/23.31 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 154.26/23.31 (14) all_54_2 = all_52_8 % 154.26/23.31 (15) ~ (all_52_2 = e0) % 154.26/23.31 (16) all_54_8 = all_52_2 % 154.26/23.31 (17) op(e1, all_6_2) = all_58_18 % 154.26/23.31 (18) op(e3, all_52_4) = all_58_1 % 154.26/23.31 (19) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.26/23.31 (20) op(e3, e0) = all_58_0 % 154.26/23.31 (21) all_58_15 = all_52_2 % 154.26/23.31 (22) all_58_26 = all_52_11 % 154.26/23.31 (23) op(e1, all_52_14) = all_58_19 % 154.26/23.31 (24) ~ (all_52_8 = all_52_11) % 154.26/23.31 (25) ~ (all_52_11 = all_4_2) % 154.26/23.31 (26) all_54_7 = all_52_13 % 154.26/23.31 (27) all_58_6 = all_52_12 % 154.26/23.31 (28) ~ (all_52_6 = all_8_2) % 154.26/23.31 (29) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 154.26/23.31 (30) all_56_4 = all_52_8 % 154.26/23.31 (31) ~ (all_52_4 = all_8_2) % 154.26/23.31 (32) all_54_3 = all_52_12 % 154.26/23.31 (33) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.31 (34) all_54_1 = all_52_4 % 154.26/23.31 (35) op(e0, all_4_2) = all_58_27 % 154.26/23.31 (36) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.31 (37) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 154.26/23.31 (38) ~ (all_52_4 = all_52_6) % 154.26/23.31 (39) all_58_13 = all_52_13 % 154.26/23.31 (40) op(e2, e2) = all_8_2 % 154.26/23.31 (41) op(e0, e1) = all_52_11 % 154.26/23.31 (42) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.26/23.31 (43) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.31 (44) ~ (all_52_6 = all_52_7) % 154.26/23.31 (45) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 154.26/23.31 (46) all_54_11 = all_52_14 % 154.26/23.31 (47) op(e3, e2) = all_52_4 % 154.26/23.31 (48) all_58_20 = all_52_14 % 154.26/23.31 (49) ~ (all_52_8 = all_6_2) % 154.26/23.31 (50) ~ (all_52_12 = all_52_13) % 154.26/23.31 (51) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.26/23.31 (52) all_54_10 = all_6_2 % 154.26/23.31 (53) op(e0, all_52_3) = all_58_21 % 154.26/23.31 (54) all_56_0 = e0 % 154.26/23.31 (55) op(e0, all_52_7) = all_58_23 % 154.26/23.31 (56) all_54_5 = all_8_2 % 154.26/23.31 (57) ~ (all_52_6 = all_52_14) % 154.26/23.31 (58) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 154.26/23.31 (59) all_54_15 = all_4_2 % 154.26/23.31 (60) all_26_2 = all_4_2 % 154.26/23.31 (61) ~ (all_52_4 = all_52_7) % 154.26/23.31 (62) ~ (all_52_2 = all_6_2) % 154.26/23.31 (63) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.26/23.31 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 154.26/23.31 (64) ~ (all_26_0 = e2) | ~ (all_26_1 = e1) | ~ (all_26_2 = e3) % 154.26/23.31 (65) op(e3, all_52_8) = all_58_3 % 154.26/23.31 (66) ~ (all_52_8 = all_52_12) % 154.26/23.31 (67) all_54_9 = all_52_6 % 154.26/23.31 (68) ~ (all_52_13 = all_4_2) % 154.26/23.31 (69) op(e1, e2) = all_52_6 % 154.26/23.31 (70) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.26/23.31 (71) ~ (all_52_3 = e0) % 154.26/23.31 (72) ~ (all_52_13 = all_8_2) % 154.26/23.31 (73) op(e1, all_52_6) = all_58_16 % 154.26/23.31 (74) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.26/23.31 (75) ~ (all_18_0 = e2) | ~ (all_18_1 = e3) | ~ (all_18_2 = e0) % 154.26/23.31 (76) ~ (e3 = e1) % 154.26/23.31 (77) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 154.26/23.31 (78) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 154.26/23.31 (79) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.26/23.31 (80) ~ (all_4_0 = e1) % 154.26/23.31 (81) ~ (all_52_1 = all_52_13) % 154.26/23.31 (82) all_56_5 = all_52_9 % 154.26/23.31 (83) all_54_14 = all_52_11 % 154.26/23.31 (84) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.31 (85) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 154.26/23.31 (86) all_56_12 = all_52_3 % 154.26/23.31 (87) ~ (all_52_12 = e0) % 154.26/23.31 (88) ~ (all_52_3 = all_52_7) % 154.26/23.31 (89) all_58_2 = all_52_4 % 154.26/23.31 (90) all_20_2 = all_4_2 % 154.26/23.31 (91) all_56_11 = all_52_14 % 154.26/23.31 (92) all_56_1 = all_52_4 % 154.26/23.31 (93) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 154.26/23.31 (94) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 154.26/23.31 (95) ~ (all_52_3 = all_4_2) % 154.26/23.31 (96) op(e1, e0) = all_52_14 % 154.26/23.31 (97) op(e0, e3) = all_10_1 % 154.26/23.31 (98) ~ (all_52_9 = all_52_11) % 154.26/23.31 (99) ~ (all_52_1 = all_8_2) % 154.26/23.31 (100) all_56_3 = all_8_2 % 154.26/23.31 (101) all_58_24 = all_52_7 % 154.26/23.31 (102) ~ (all_52_13 = all_52_14) % 154.26/23.31 (103) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.31 (104) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.26/23.31 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.26/23.31 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.26/23.31 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.26/23.31 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.31 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.26/23.31 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.31 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.31 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.31 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.26/23.31 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.31 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.31 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = % 154.26/23.31 e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.26/23.31 e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.26/23.31 e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.26/23.31 e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.31 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.31 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.31 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.31 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.31 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.26/23.31 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.31 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.31 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.31 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.31 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.31 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.31 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.31 e0) % 154.26/23.31 (105) ~ (all_52_4 = all_52_8) % 154.26/23.31 (106) ~ (all_10_0 = e0) % 154.26/23.31 (107) all_56_9 = all_52_12 % 154.26/23.31 (108) all_58_29 = all_8_2 % 154.26/23.31 (109) ~ (all_52_12 = all_52_14) % 154.26/23.31 (110) all_58_8 = all_52_1 % 154.26/23.31 (111) ~ (e2 = e1) % 154.26/23.31 (112) op(e3, e0) = all_52_12 % 154.26/23.31 (113) all_56_6 = all_52_2 % 154.26/23.31 (114) ~ (all_52_2 = all_52_6) % 154.26/23.31 (115) all_18_2 = all_6_2 % 154.26/23.31 (116) all_56_13 = all_52_7 % 154.26/23.31 (117) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.26/23.31 (118) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.26/23.31 (119) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.31 (120) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.26/23.31 (121) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.31 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.31 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.31 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.31 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.31 (all_58_27 = e0)) % 154.26/23.31 (122) ~ (all_52_9 = all_52_13) % 154.26/23.31 (123) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.26/23.31 (124) op(all_6_2, e1) = all_6_1 % 154.26/23.31 (125) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.26/23.31 (126) ~ (all_52_4 = e0) % 154.26/23.31 (127) op(e2, all_52_9) = all_58_10 % 154.26/23.31 (128) ~ (all_52_11 = all_6_2) % 154.26/23.31 (129) ~ (e3 = e0) % 154.26/23.31 (130) all_56_2 = all_52_1 % 154.26/23.31 (131) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 154.26/23.31 (132) op(e0, e3) = all_52_3 % 154.26/23.31 (133) op(e3, all_52_12) = all_58_5 % 154.26/23.31 (134) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 154.26/23.31 (135) all_56_10 = all_52_13 % 154.26/23.31 (136) ~ (all_52_1 = all_52_3) % 154.26/23.31 (137) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.31 (138) ~ (all_52_9 = all_8_2) % 154.26/23.31 (139) all_56_14 = all_52_11 % 154.26/23.31 (140) all_58_28 = all_10_2 % 154.26/23.31 (141) all_58_17 = all_52_6 % 154.26/23.31 (142) ~ (all_52_1 = all_52_9) % 154.26/23.31 (143) op(e3, e1) = all_52_8 % 154.26/23.31 (144) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.26/23.31 (145) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.31 (146) ~ (all_52_7 = all_52_11) % 154.26/23.31 (147) op(all_8_2, e2) = all_8_1 % 154.26/23.31 (148) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.31 (149) ~ (e2 = e0) % 154.26/23.31 (150) ~ (all_52_9 = all_6_2) % 154.26/23.31 (151) all_56_0 = all_10_2 % 154.26/23.31 (152) op(e0, e0) = all_4_2 % 154.26/23.31 (153) ~ (all_52_1 = e0) % 154.26/23.31 (154) ~ (all_52_3 = all_52_11) % 154.26/23.31 (155) all_58_22 = all_52_3 % 154.26/23.31 (156) ~ (all_52_12 = all_4_2) % 154.26/23.31 (157) all_56_8 = all_6_2 % 154.26/23.31 (158) op(e1, e1) = all_6_2 % 154.26/23.31 (159) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.26/23.31 (160) ~ (all_52_1 = all_52_2) % 154.26/23.31 (161) ~ (all_52_7 = all_8_2) % 154.26/23.31 (162) op(all_4_2, all_4_1) = all_4_0 % 154.26/23.31 (163) op(e2, e0) = all_52_13 % 154.26/23.31 (164) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.26/23.31 (165) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.31 (166) op(e2, all_52_13) = all_58_12 % 154.26/23.31 (167) all_58_4 = all_52_8 % 154.26/23.31 (168) ~ (all_8_1 = e0) % 154.26/23.31 (169) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.31 (170) all_16_1 = all_10_1 % 154.26/23.31 (171) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.26/23.31 (172) all_16_0 = all_10_0 % 154.26/23.31 (173) ~ (all_52_2 = all_52_14) % 154.26/23.31 (174) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.31 (175) ~ (all_52_14 = all_4_2) % 154.26/23.31 (176) ~ (e1 = e0) % 154.26/23.31 (177) all_26_1 = all_4_1 % 154.26/23.31 (178) ~ (all_52_7 = all_4_2) % 154.26/23.31 (179) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 154.26/23.31 (180) ~ (all_52_8 = e0) % 154.26/23.31 (181) op(e0, all_10_1) = all_10_0 % 154.26/23.31 (182) all_58_30 = all_6_2 % 154.26/23.31 (183) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.31 (184) ~ (e3 = e2) % 154.26/23.31 (185) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.26/23.31 (186) ~ (all_52_14 = all_6_2) % 154.26/23.31 (187) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 154.26/23.31 (188) op(all_4_2, e0) = all_4_1 % 154.26/23.31 (189) ~ (all_52_4 = all_52_12) % 154.26/23.31 (190) all_54_12 = all_52_3 % 154.26/23.31 (191) op(e2, all_8_2) = all_58_9 % 154.26/23.31 (192) all_54_4 = all_52_1 % 154.26/23.31 % 154.26/23.31 Begin of proof % 154.26/23.31 | % 154.26/23.31 | GROUND_INST: instantiating (4) with all_52_3, all_10_1, e3, e0, simplifying % 154.26/23.31 | with (97), (132) gives: % 154.26/23.31 | (193) all_52_3 = all_10_1 % 154.26/23.31 | % 154.26/23.31 | GROUND_INST: instantiating (4) with all_52_12, all_58_0, e0, e3, simplifying % 154.26/23.31 | with (20), (112) gives: % 154.26/23.31 | (194) all_58_0 = all_52_12 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (190), (193) imply: % 154.26/23.31 | (195) all_54_12 = all_10_1 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (86), (193) imply: % 154.26/23.31 | (196) all_56_12 = all_10_1 % 154.26/23.31 | % 154.26/23.31 | COMBINE_EQS: (155), (193) imply: % 154.26/23.31 | (197) all_58_22 = all_10_1 % 154.26/23.31 | % 154.26/23.31 | REDUCE: (136), (193) imply: % 154.26/23.31 | (198) ~ (all_52_1 = all_10_1) % 154.26/23.31 | % 154.26/23.31 | REDUCE: (8), (193) imply: % 154.26/23.31 | (199) ~ (all_52_2 = all_10_1) % 154.26/23.31 | % 154.26/23.31 | REDUCE: (88), (193) imply: % 154.26/23.31 | (200) ~ (all_52_7 = all_10_1) % 154.26/23.31 | % 154.26/23.31 | SIMP: (200) implies: % 154.26/23.31 | (201) ~ (all_52_7 = all_10_1) % 154.26/23.31 | % 154.26/23.31 | REDUCE: (154), (193) imply: % 154.26/23.31 | (202) ~ (all_52_11 = all_10_1) % 154.26/23.31 | % 154.26/23.31 | SIMP: (202) implies: % 154.26/23.31 | (203) ~ (all_52_11 = all_10_1) % 154.26/23.31 | % 154.26/23.31 | REDUCE: (95), (193) imply: % 154.26/23.31 | (204) ~ (all_10_1 = all_4_2) % 154.26/23.31 | % 154.26/23.31 | REDUCE: (71), (193) imply: % 154.26/23.31 | (205) ~ (all_10_1 = e0) % 154.26/23.31 | % 154.26/23.31 | REDUCE: (53), (193) imply: % 154.26/23.31 | (206) op(e0, all_10_1) = all_58_21 % 154.26/23.31 | % 154.26/23.31 | GROUND_INST: instantiating (4) with all_10_0, all_58_21, all_10_1, e0, % 154.26/23.31 | simplifying with (181), (206) gives: % 154.26/23.31 | (207) all_58_21 = all_10_0 % 154.26/23.31 | % 154.26/23.31 | BETA: splitting (75) gives: % 154.26/23.31 | % 154.26/23.31 | Case 1: % 154.26/23.31 | | % 154.26/23.31 | | (208) ~ (all_18_2 = e0) % 154.26/23.31 | | % 154.26/23.31 | | REDUCE: (115), (208) imply: % 154.26/23.31 | | (209) ~ (all_6_2 = e0) % 154.26/23.31 | | % 154.26/23.31 | | BETA: splitting (144) gives: % 154.26/23.31 | | % 154.26/23.31 | | Case 1: % 154.26/23.31 | | | % 154.26/23.31 | | | (210) ~ (all_20_2 = e1) % 154.26/23.31 | | | % 154.26/23.31 | | | REDUCE: (90), (210) imply: % 154.26/23.31 | | | (211) ~ (all_4_2 = e1) % 154.26/23.31 | | | % 154.26/23.31 | | | BETA: splitting (64) gives: % 154.26/23.31 | | | % 154.26/23.31 | | | Case 1: % 154.26/23.31 | | | | % 154.26/23.31 | | | | (212) ~ (all_26_1 = e1) % 154.26/23.31 | | | | % 154.26/23.31 | | | | REDUCE: (177), (212) imply: % 154.26/23.31 | | | | (213) ~ (all_4_1 = e1) % 154.26/23.31 | | | | % 154.26/23.31 | | | | BETA: splitting (63) gives: % 154.26/23.31 | | | | % 154.26/23.31 | | | | Case 1: % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | (214) all_56_15 = e0 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | COMBINE_EQS: (10), (214) imply: % 154.26/23.31 | | | | | (215) all_4_2 = e0 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | SIMP: (215) implies: % 154.26/23.31 | | | | | (216) all_4_2 = e0 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | COMBINE_EQS: (2), (216) imply: % 154.26/23.31 | | | | | (217) all_58_31 = e0 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | REDUCE: (25), (216) imply: % 154.26/23.31 | | | | | (218) ~ (all_52_11 = e0) % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | REDUCE: (175), (216) imply: % 154.26/23.31 | | | | | (219) ~ (all_52_14 = e0) % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | REDUCE: (162), (216) imply: % 154.26/23.31 | | | | | (220) op(e0, all_4_1) = all_4_0 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | REDUCE: (188), (216) imply: % 154.26/23.31 | | | | | (221) op(e0, e0) = all_4_1 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | REDUCE: (35), (216) imply: % 154.26/23.31 | | | | | (222) op(e0, e0) = all_58_27 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | REDUCE: (152), (216) imply: % 154.26/23.31 | | | | | (223) op(e0, e0) = e0 % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | BETA: splitting (174) gives: % 154.26/23.31 | | | | | % 154.26/23.31 | | | | | Case 1: % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | (224) all_56_6 = e0 % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | COMBINE_EQS: (113), (224) imply: % 154.26/23.31 | | | | | | (225) all_52_2 = e0 % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | REDUCE: (15), (225) imply: % 154.26/23.31 | | | | | | (226) $false % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | CLOSE: (226) is inconsistent. % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | Case 2: % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | (227) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | BETA: splitting (93) gives: % 154.26/23.31 | | | | | | % 154.26/23.31 | | | | | | Case 1: % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | (228) all_56_4 = e0 % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | COMBINE_EQS: (30), (228) imply: % 154.26/23.31 | | | | | | | (229) all_52_8 = e0 % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | REDUCE: (180), (229) imply: % 154.26/23.31 | | | | | | | (230) $false % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | CLOSE: (230) is inconsistent. % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | Case 2: % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | (231) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | BETA: splitting (231) gives: % 154.26/23.31 | | | | | | | % 154.26/23.31 | | | | | | | Case 1: % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | (232) all_56_5 = e0 % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | COMBINE_EQS: (82), (232) imply: % 154.26/23.31 | | | | | | | | (233) all_52_9 = e0 % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | REDUCE: (98), (233) imply: % 154.26/23.31 | | | | | | | | (234) ~ (all_52_11 = e0) % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | REDUCE: (122), (233) imply: % 154.26/23.31 | | | | | | | | (235) ~ (all_52_13 = e0) % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | SIMP: (235) implies: % 154.26/23.31 | | | | | | | | (236) ~ (all_52_13 = e0) % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | REDUCE: (150), (233) imply: % 154.26/23.31 | | | | | | | | (237) ~ (all_6_2 = e0) % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | BETA: splitting (227) gives: % 154.26/23.31 | | | | | | | | % 154.26/23.31 | | | | | | | | Case 1: % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | | (238) all_56_7 = e0 % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | | COMBINE_EQS: (11), (238) imply: % 154.26/23.31 | | | | | | | | | (239) all_52_6 = e0 % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | | REDUCE: (44), (239) imply: % 154.26/23.31 | | | | | | | | | (240) ~ (all_52_7 = e0) % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | | SIMP: (240) implies: % 154.26/23.31 | | | | | | | | | (241) ~ (all_52_7 = e0) % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | | REDUCE: (57), (239) imply: % 154.26/23.31 | | | | | | | | | (242) ~ (all_52_14 = e0) % 154.26/23.31 | | | | | | | | | % 154.26/23.31 | | | | | | | | | REDUCE: (69), (239) imply: % 154.26/23.32 | | | | | | | | | (243) op(e1, e2) = e0 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_27, e0, e0, % 154.26/23.32 | | | | | | | | | simplifying with (221), (222) gives: % 154.26/23.32 | | | | | | | | | (244) all_58_27 = all_4_1 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_27, e0, e0, % 154.26/23.32 | | | | | | | | | simplifying with (222), (223) gives: % 154.26/23.32 | | | | | | | | | (245) all_58_27 = e0 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | COMBINE_EQS: (244), (245) imply: % 154.26/23.32 | | | | | | | | | (246) all_4_1 = e0 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | SIMP: (246) implies: % 154.26/23.32 | | | | | | | | | (247) all_4_1 = e0 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | REDUCE: (220), (247) imply: % 154.26/23.32 | | | | | | | | | (248) op(e0, e0) = all_4_0 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e0, % 154.26/23.32 | | | | | | | | | simplifying with (223), (248) gives: % 154.26/23.32 | | | | | | | | | (249) all_4_0 = e0 % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | REDUCE: (80), (249) imply: % 154.26/23.32 | | | | | | | | | (250) ~ (e1 = e0) % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | BETA: splitting (37) gives: % 154.26/23.32 | | | | | | | | | % 154.26/23.32 | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | (251) all_54_8 = e0 % 154.26/23.32 | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | REF_CLOSE: (15), (16), (251) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | #731. % 154.26/23.32 | | | | | | | | | | % 154.26/23.32 | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | (252) ~ (all_54_8 = e0) % 154.26/23.32 | | | | | | | | | | (253) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.26/23.32 | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | BETA: splitting (134) gives: % 154.26/23.32 | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | (254) all_54_12 = e0 % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | COMBINE_EQS: (195), (254) imply: % 154.26/23.32 | | | | | | | | | | | (255) all_10_1 = e0 % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | REDUCE: (205), (255) imply: % 154.26/23.32 | | | | | | | | | | | (256) $false % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | CLOSE: (256) is inconsistent. % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | (257) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | BETA: splitting (179) gives: % 154.26/23.32 | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | (258) all_54_2 = e0 % 154.26/23.32 | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | REF_CLOSE: (14), (180), (258) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | #860. % 154.26/23.32 | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | (259) ~ (all_54_2 = e0) % 154.26/23.32 | | | | | | | | | | | | (260) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.26/23.32 | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | BETA: splitting (58) gives: % 154.26/23.32 | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | (261) all_54_11 = e0 % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | COMBINE_EQS: (46), (261) imply: % 154.26/23.32 | | | | | | | | | | | | | (262) all_52_14 = e0 % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | REDUCE: (219), (262) imply: % 154.26/23.32 | | | | | | | | | | | | | (263) $false % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | CLOSE: (263) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | (264) ~ (all_54_11 = e0) % 154.26/23.32 | | | | | | | | | | | | | (265) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | BETA: splitting (187) gives: % 154.26/23.32 | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | (266) all_54_7 = e0 % 154.26/23.32 | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | REF_CLOSE: (26), (236), (266) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | #742. % 154.26/23.32 | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | (267) ~ (all_54_7 = e0) % 154.26/23.32 | | | | | | | | | | | | | | (268) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.32 | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | BETA: splitting (45) gives: % 154.26/23.32 | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | (269) all_54_13 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | COMBINE_EQS: (7), (269) imply: % 154.26/23.32 | | | | | | | | | | | | | | | (270) all_52_7 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | REDUCE: (241), (270) imply: % 154.26/23.32 | | | | | | | | | | | | | | | (271) $false % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | (272) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | BETA: splitting (13) gives: % 154.26/23.32 | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | (273) all_54_3 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | REF_CLOSE: (32), (87), (273) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | #733. % 154.26/23.32 | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | (274) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | (275) all_54_4 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (192), (275) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | #859. % 154.26/23.32 | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | (276) ~ (all_54_4 = e0) % 154.26/23.32 | | | | | | | | | | | | | | | | | (277) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | (278) all_54_1 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (126), (278) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | #798. % 154.26/23.32 | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | (279) ~ (all_54_1 = e0) % 154.26/23.32 | | | | | | | | | | | | | | | | | | (280) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | (281) all_54_14 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (218), (281) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | #517. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | (282) ~ (all_54_14 = e0) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | (283) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | (284) all_58_28 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (284) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | (285) e1 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (285) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | (286) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | (287) ~ (all_58_28 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | (288) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | (289) all_58_28 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (289) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | (290) e3 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (290) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | (291) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | (292) ~ (all_58_28 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | (293) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (292) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | (294) ~ (e3 = e0) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | (295) all_58_28 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (295) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | (296) e2 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (296) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | (297) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | (298) ~ (all_58_28 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | (299) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (298) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | (300) ~ (e2 = e0) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | (301) all_56_0 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (176), (301) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | #516. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | (302) ~ (all_56_0 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | (303) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (304) all_56_12 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (304) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (305) all_10_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (306) all_10_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (306) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (307) all_16_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (306) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_11 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (306) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (309) op(e0, e1) = all_10_0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (310) ~ (all_16_1 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (307), (310) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (311) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (311) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (312) ~ (all_16_0 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (312) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (313) ~ (all_10_0 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_11, all_10_0, e1, % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (41), (309) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_52_11 = all_10_0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (314) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_54_14 = all_10_0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (314) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_56_14 = all_10_0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (314) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (317) ~ (all_52_7 = all_10_0) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (314) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_52_8 = all_10_0) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (314) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (all_10_0 = all_6_2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (308), (314) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_10_0 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_56_12 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (321) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (322) e2 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (322) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (323) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (323) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_56_13 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (325) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_52_7 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (326) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_52_7 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (327) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) ~ (all_52_4 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (317), (327) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_10_0 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (327) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) ~ (all_8_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (all_8_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_54_14 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (332) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_10_0 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (320), (333) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_54_14 = e3 | all_54_14 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_58_29 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (331), (336) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #634. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_54_14 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (338) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_10_0 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (313), (339) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_54_14 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (341) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_10_0 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (318), (342) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_52_8 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (319), (342) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_6_2 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (344) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_6_2 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_29 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (346) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_8_2 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (347) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_8_2 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (348) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_52_4 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_56_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (350) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_52_4 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (351) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) ~ (all_52_8 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (352) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_52_8 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (49), (180), (182), (217), (260), (337), % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (353) are inconsistent by sub-proof #815. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_56_1 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (354) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) ~ (all_52_4 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (280), (328), (349), (355) are inconsistent % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (129), (182), (217), (345), (356) are inconsistent % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #768. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_56_14 = e2 | all_56_15 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (214), (313), (316), (357) are inconsistent % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #515. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (358) ~ (all_56_12 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (359) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (358) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_10_1 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_56_6 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (361) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_52_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (362) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_52_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (363) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_52_1 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (363) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (365) ~ (all_52_14 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (365) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (366) ~ (all_52_14 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (363) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (367) ~ (all_10_1 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (367) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_10_1 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (363) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_6_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (369) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (370) ~ (all_6_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_56_2 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (371) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_52_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (372) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_52_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (373) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (374) ~ (all_52_13 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (374) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_52_13 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (373) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (376) ~ (all_10_1 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (373) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (377) ~ (all_8_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (377) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (378) ~ (all_8_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_54_12 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (195), (360), (379) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | #514. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) ~ (all_54_12 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_54_12 = e3 | all_54_12 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_54_12 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (195), (368), (382) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #513. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_54_12 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (383) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_10_1 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (384) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_10_1 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (385) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ~ (all_52_7 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_29 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (378), (387) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #809. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_58_29 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (389) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_8_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_8_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (391) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_56_3 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (391) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) ~ (all_52_4 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (391) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_52_7 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (391) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_52_13 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_56_2 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (396) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) e3 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (397) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (398) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_56_1 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (400) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_52_4 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (401) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) ~ (all_52_8 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (402) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) ~ (all_52_8 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_56_9 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (404) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_52_12 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (405) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) ~ (all_52_8 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_54_2 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (407) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_52_8 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (408) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_52_8 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (409) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) ~ (all_6_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (410) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) ~ (all_6_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (182), (217), (388), (411) are inconsistent % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #512. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_54_2 = e3 | all_54_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (403), (406), (412) are inconsistent by % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #555. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_56_9 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (413) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_52_12 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_56_3 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (415) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) e3 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (416) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (417) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_56_5 = e3 | all_56_10 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_56_5 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (419) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) e3 = e0 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (420) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_56_10 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (422) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_52_13 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (423) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) ~ (all_52_14 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (424) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) ~ (all_52_14 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_54_11 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (426) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_52_14 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (427) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_52_14 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (428) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) ~ (all_52_12 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (32), (50), (268), (274), (375), (395), % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414), (429) are inconsistent by sub-proof #510. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_54_11 = e3 | all_54_11 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (366), (425), (430) are inconsistent by % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #775. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_56_1 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (431) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) ~ (all_52_4 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (34), (61), (272), (280), (386), (393), % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (432) are inconsistent by sub-proof #507. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (182), (217), (370), (433) are inconsistent % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #817. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (434) ~ (all_56_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (434) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (435) ~ (all_52_1 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (195), (198), (257), (277), (360), (364), % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (368), (435) are inconsistent by sub-proof #504. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (436) ~ (all_56_6 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (436) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_52_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_56_2 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (438) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_52_1 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (439) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_52_1 = e3 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (440) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_52_2 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (441) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (442) ~ (all_52_2 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (62), (108), (147), (168), (182), % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (243), (253), (288), (437), (442) are % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (443) ~ (all_56_2 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (443) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_52_1 = e3) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_56_1 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (445) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_52_4 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (446) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_52_4 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (189), (447) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) ~ (all_52_12 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (448) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) ~ (all_52_12 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (447) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) ~ (all_8_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (450) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) ~ (all_8_2 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_58_29 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (451), (452) are inconsistent by sub-proof % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #634. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_58_30 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (454) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_6_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (455) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_6_2 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (456) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_56_8 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (456) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) ~ (all_52_14 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_56_9 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (459) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_52_12 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (449), (460) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) $false % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (461) is inconsistent. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_58_29 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (108), (147), (168), (243), (463) are % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #794. % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_56_10 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (465) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_52_13 = e2 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (466) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) ~ (all_52_1 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (466) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) ~ (all_52_14 = e2) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_56_2 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (469) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_52_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (470) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_52_1 = e1 % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (471) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_52_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (472) implies: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) ~ (all_52_2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (444), (471) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) ~ (e3 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (467), (471) imply: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) ~ (e2 = e1) % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 154.26/23.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_56_6 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (473), (476) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #639. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (477) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_56_7 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (238), (478) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_56_8 = e1 | all_56_11 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_56_8 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (457), (480) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) e2 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (481) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_58_30 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (217), (453), (482) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #846. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_56_11 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (483) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_52_14 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) all_58_30 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (217), (453), (485) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #846. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_58_31 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (486) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) e1 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (487) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) e1 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (483), (488) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_56_11 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (149), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (479), (486), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) are inconsistent by sub-proof #495. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) ~ (all_56_2 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (490) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) ~ (all_52_1 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (277), (444), (467), (491) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #828. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_56_11 = e2 | all_56_15 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (492) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_56_11 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (458), (493) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #494. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_56_15 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (214), (494) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) e2 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (454), (495) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_58_30 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (176), (211), (464), (496) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #711. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_58_31 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (217), (497) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #855. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) ~ (all_56_1 = e2) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (498) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) ~ (all_52_4 = e2) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_56_1 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (500) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_52_4 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (501) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_52_4 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (502) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) ~ (all_52_7 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (503) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) ~ (all_52_7 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (359) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_56_13 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (504), (505) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #676. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_56_14 = e1 | all_56_15 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (506) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_56_14 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (507) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_52_11 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (508) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_52_11 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (509) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) ~ (all_6_2 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (510) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) ~ (all_6_2 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (108), (147), (168), (182), (211), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (288), (511) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #503. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_56_15 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (214), (512) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) e1 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (513) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) $false % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (514) is inconsistent. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) ~ (all_56_1 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (515) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) ~ (all_52_4 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) all_54_1 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (516), (517) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_54_1 = e3 | all_54_1 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (518) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_54_1 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (499), (519) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #740. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_54_1 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (520) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_52_4 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (521) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_52_4 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (522) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) ~ (all_8_2 = e3) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (523) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) ~ (all_8_2 = e3) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) all_58_29 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (524), (525) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #756. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_58_30 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (527) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_6_2 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (528) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_6_2 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (529) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) ~ (all_52_2 = e3) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (62), (108), (147), (168), (182), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (243), (253), (288), (437), (530) are % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_58_31 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (129), (217), (531) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #853. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | (532) all_56_8 = e0 | all_56_11 = e0 % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | REF_CLOSE: (91), (157), (209), (219), (532) are inconsistent % 154.26/23.33 | | | | | | | | | by sub-proof #763. % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | End of split % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | (533) all_56_8 = e0 | all_56_14 = e0 % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | REF_CLOSE: (139), (157), (209), (218), (533) are inconsistent by % 154.26/23.33 | | | | | | | | sub-proof #805. % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | End of split % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | End of split % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | End of split % 154.26/23.33 | | | | | % 154.26/23.33 | | | | Case 2: % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | (534) ~ (all_56_15 = e0) % 154.26/23.33 | | | | | (535) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.26/23.33 | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | ALPHA: (535) implies: % 154.26/23.33 | | | | | (536) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | REDUCE: (10), (534) imply: % 154.26/23.33 | | | | | (537) ~ (all_4_2 = e0) % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | BETA: splitting (29) gives: % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | Case 1: % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | | (538) all_54_15 = e0 % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | | REF_CLOSE: (59), (537), (538) are inconsistent by sub-proof #493. % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | Case 2: % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | | (539) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | | BETA: splitting (36) gives: % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | | Case 1: % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | (540) all_56_2 = e0 % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | COMBINE_EQS: (130), (540) imply: % 154.26/23.33 | | | | | | | (541) all_52_1 = e0 % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | REDUCE: (153), (541) imply: % 154.26/23.33 | | | | | | | (542) $false % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | CLOSE: (542) is inconsistent. % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | Case 2: % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | (543) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | BETA: splitting (123) gives: % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | (544) all_56_1 = e0 % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | COMBINE_EQS: (92), (544) imply: % 154.26/23.33 | | | | | | | | (545) all_52_4 = e0 % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | REDUCE: (126), (545) imply: % 154.26/23.33 | | | | | | | | (546) $false % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | CLOSE: (546) is inconsistent. % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | (547) ~ (all_56_1 = e0) % 154.26/23.33 | | | | | | | | (548) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | BETA: splitting (174) gives: % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | (549) all_56_6 = e0 % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | COMBINE_EQS: (113), (549) imply: % 154.26/23.33 | | | | | | | | | (550) all_52_2 = e0 % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | REDUCE: (15), (550) imply: % 154.26/23.33 | | | | | | | | | (551) $false % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | CLOSE: (551) is inconsistent. % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | (552) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | BETA: splitting (93) gives: % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | (553) all_56_4 = e0 % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | COMBINE_EQS: (30), (553) imply: % 154.26/23.33 | | | | | | | | | | (554) all_52_8 = e0 % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | REDUCE: (180), (554) imply: % 154.26/23.33 | | | | | | | | | | (555) $false % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | CLOSE: (555) is inconsistent. % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | (556) ~ (all_56_4 = e0) % 154.26/23.33 | | | | | | | | | | (557) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | BETA: splitting (134) gives: % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | (558) all_54_12 = e0 % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | COMBINE_EQS: (195), (558) imply: % 154.26/23.33 | | | | | | | | | | | (559) all_10_1 = e0 % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | REDUCE: (205), (559) imply: % 154.26/23.33 | | | | | | | | | | | (560) $false % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | CLOSE: (560) is inconsistent. % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | (561) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | BETA: splitting (131) gives: % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | (562) all_54_10 = e0 % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (52), (76), (108), (111), (129), % 154.26/23.33 | | | | | | | | | | | | (149), (169), (176), (182), (183), (184), (211), % 154.26/23.33 | | | | | | | | | | | | (562) are inconsistent by sub-proof #492. % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | (563) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | BETA: splitting (164) gives: % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | (564) all_54_1 = e0 % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | REF_CLOSE: (34), (126), (564) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | #798. % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | (565) ~ (all_54_1 = e0) % 154.26/23.33 | | | | | | | | | | | | | (566) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | BETA: splitting (187) gives: % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | (567) all_54_7 = e0 % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | COMBINE_EQS: (26), (567) imply: % 154.26/23.33 | | | | | | | | | | | | | | (568) all_52_13 = e0 % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | SIMP: (568) implies: % 154.26/23.33 | | | | | | | | | | | | | | (569) all_52_13 = e0 % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | REDUCE: (122), (569) imply: % 154.26/23.33 | | | | | | | | | | | | | | (570) ~ (all_52_9 = e0) % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | REDUCE: (102), (569) imply: % 154.26/23.33 | | | | | | | | | | | | | | (571) ~ (all_52_14 = e0) % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | SIMP: (571) implies: % 154.26/23.33 | | | | | | | | | | | | | | (572) ~ (all_52_14 = e0) % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | REDUCE: (166), (569) imply: % 154.26/23.33 | | | | | | | | | | | | | | (573) op(e2, e0) = all_58_12 % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | REDUCE: (163), (569) imply: % 154.26/23.33 | | | | | | | | | | | | | | (574) op(e2, e0) = e0 % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | BETA: splitting (557) gives: % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | (575) all_56_5 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | COMBINE_EQS: (82), (575) imply: % 154.26/23.33 | | | | | | | | | | | | | | | (576) all_52_9 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | REDUCE: (570), (576) imply: % 154.26/23.33 | | | | | | | | | | | | | | | (577) $false % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | CLOSE: (577) is inconsistent. % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | (578) all_56_8 = e0 | all_56_14 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | BETA: splitting (578) gives: % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | (579) all_56_8 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (579) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | (580) all_6_2 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | SIMP: (580) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | (581) all_6_2 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (581) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | (582) all_58_30 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (108), (111), (129), (149), % 154.26/23.33 | | | | | | | | | | | | | | | | (169), (176), (183), (184), (211), (582) are % 154.26/23.33 | | | | | | | | | | | | | | | | inconsistent by sub-proof #684. % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | (583) all_56_14 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (583) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | (584) all_52_11 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | SIMP: (584) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | (585) all_52_11 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | REDUCE: (203), (585) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | (586) ~ (all_10_1 = e0) % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | REDUCE: (128), (585) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | (587) ~ (all_6_2 = e0) % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | REDUCE: (41), (585) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | (588) op(e0, e1) = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | BETA: splitting (552) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | (589) all_56_7 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (589) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | (590) all_52_6 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | REDUCE: (44), (590) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | (591) ~ (all_52_7 = e0) % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | SIMP: (591) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | (592) ~ (all_52_7 = e0) % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e0, e2, % 154.26/23.33 | | | | | | | | | | | | | | | | | simplifying with (573), (574) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | (593) all_58_12 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | (594) all_56_12 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (594) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | (595) all_10_1 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | SIMP: (595) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | (596) all_10_1 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (106), (181), (588), (596) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | by sub-proof #491. % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | (597) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | BETA: splitting (597) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (598) all_56_13 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (598) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (599) all_52_7 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | SIMP: (599) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (600) all_52_7 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | REDUCE: (61), (600) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (601) ~ (all_52_4 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | REDUCE: (201), (600) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (602) ~ (all_10_1 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | SIMP: (602) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (603) ~ (all_10_1 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | REDUCE: (161), (600) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (604) ~ (all_8_2 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | SIMP: (604) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (605) ~ (all_8_2 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | REDUCE: (178), (600) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (606) ~ (all_4_2 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | (607) all_58_28 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (176), (607) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | #690. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | (608) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (608) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | (609) all_58_29 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (609) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | (610) all_8_2 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (610) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | (611) $false % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | CLOSE: (611) is inconsistent. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | (612) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (612) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (613) all_58_30 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (613) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (614) all_6_2 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (614) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (615) ~ (all_52_8 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (614) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (616) op(e1, e1) = all_58_18 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (614) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (617) op(e1, e1) = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (618) all_56_9 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (618) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (619) all_52_12 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (619) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (620) all_52_12 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (620) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (621) op(e3, e0) = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_58_18, e1, e1, % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (616), (617) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (622) all_58_18 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (623) all_56_12 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (623) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (624) all_10_1 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (624) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (625) all_10_1 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (204), (625) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (626) ~ (all_4_2 = e2) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (626) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (627) ~ (all_4_2 = e2) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (539) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_54_15 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (628) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_4_2 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (629) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_4_2 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (630) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_58_31 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (149), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | (169), (184), (613), (631) are inconsistent by % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #497. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_54_15 = e3 | all_54_15 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_54_15 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (627), (633) are inconsistent by sub-proof % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | #490. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_54_15 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (634) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_4_2 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (635) implies: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (636) all_4_2 = e3 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (636) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (637) op(e3, e0) = all_4_1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_4_1, e0, e3, % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (621), (637) gives: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (638) all_4_1 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (638) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (639) $false % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (639) is inconsistent. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (640) ~ (all_56_12 = e2) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (641) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (640) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (642) ~ (all_10_1 = e2) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (18), (31), (34), (47), (92), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (97), (108), (111), (121), (149), (159), (169), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (181), (195), (204), (205), (207), (561), (566), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (583), (593), (598), (601), (603), (613), (622), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | (641), (642) are inconsistent by sub-proof #488. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (643) ~ (all_56_9 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (643) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (644) ~ (all_52_12 = e1) % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (30), (54), (92), (107), (117), (176), (211), % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | (601), (612), (613), (615), (644) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #484. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (645) all_58_31 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (645) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (646) all_4_2 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (646) imply: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | (647) $false % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (647) is inconsistent. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | (648) all_56_14 = e1 | all_56_15 = e1 % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (176), (211), (583), (648) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | | | by sub-proof #582. % 154.26/23.33 | | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | (649) all_56_8 = e0 | all_56_11 = e0 % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (157), (209), (572), (649) are inconsistent % 154.26/23.33 | | | | | | | | | | | | | | | | | by sub-proof #763. % 154.26/23.33 | | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | Case 2: % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | (650) ~ (all_54_7 = e0) % 154.26/23.33 | | | | | | | | | | | | | | (651) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | REDUCE: (26), (650) imply: % 154.26/23.33 | | | | | | | | | | | | | | (652) ~ (all_52_13 = e0) % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (11), (21), (22), (23), % 154.26/23.33 | | | | | | | | | | | | | | (24), (25), (26), (27), (28), (30), (31), (33), % 154.26/23.33 | | | | | | | | | | | | | | (39), (41), (44), (48), (50), (52), (54), (55), % 154.26/23.33 | | | | | | | | | | | | | | (57), (61), (68), (72), (76), (77), (82), (83), % 154.26/23.33 | | | | | | | | | | | | | | (84), (87), (91), (92), (96), (98), (100), (101), % 154.26/23.33 | | | | | | | | | | | | | | (102), (104), (107), (108), (109), (111), (113), % 154.26/23.33 | | | | | | | | | | | | | | (116), (117), (120), (121), (122), (126), (127), % 154.26/23.33 | | | | | | | | | | | | | | (128), (129), (135), (137), (138), (139), (140), % 154.26/23.33 | | | | | | | | | | | | | | (145), (148), (149), (151), (152), (157), (163), % 154.26/23.33 | | | | | | | | | | | | | | (165), (167), (169), (170), (172), (173), (176), % 154.26/23.33 | | | | | | | | | | | | | | (178), (180), (181), (182), (183), (184), (186), % 154.26/23.33 | | | | | | | | | | | | | | (194), (196), (203), (211), (536), (543), (548), % 154.26/23.33 | | | | | | | | | | | | | | (552), (563), (651), (652) are inconsistent by % 154.26/23.33 | | | | | | | | | | | | | | sub-proof #462. % 154.26/23.33 | | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | | % 154.26/23.33 | | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | | % 154.26/23.33 | | | | | | | | | End of split % 154.26/23.33 | | | | | | | | | % 154.26/23.33 | | | | | | | | End of split % 154.26/23.33 | | | | | | | | % 154.26/23.33 | | | | | | | End of split % 154.26/23.33 | | | | | | | % 154.26/23.33 | | | | | | End of split % 154.26/23.33 | | | | | | % 154.26/23.33 | | | | | End of split % 154.26/23.33 | | | | | % 154.26/23.33 | | | | End of split % 154.26/23.33 | | | | % 154.26/23.33 | | | Case 2: % 154.26/23.33 | | | | % 154.26/23.33 | | | | (653) all_26_1 = e1 % 154.26/23.33 | | | | (654) ~ (all_26_0 = e2) | ~ (all_26_2 = e3) % 154.26/23.33 | | | | % 154.26/23.33 | | | | COMBINE_EQS: (177), (653) imply: % 154.26/23.33 | | | | (655) all_4_1 = e1 % 154.26/23.33 | | | | % 154.26/23.33 | | | | REDUCE: (162), (655) imply: % 154.26/23.33 | | | | (656) op(all_4_2, e1) = all_4_0 % 154.26/23.33 | | | | % 154.26/23.33 | | | | REDUCE: (188), (655) imply: % 154.26/23.33 | | | | (657) op(all_4_2, e0) = e1 % 154.26/23.33 | | | | % 154.26/23.33 | | | | BETA: splitting (63) gives: % 154.26/23.33 | | | | % 154.26/23.33 | | | | Case 1: % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | (658) all_56_15 = e0 % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | REF_CLOSE: (4), (10), (35), (152), (211), (657), (658) are % 154.26/23.33 | | | | | inconsistent by sub-proof #460. % 154.26/23.33 | | | | | % 154.26/23.33 | | | | Case 2: % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | (659) ~ (all_56_15 = e0) % 154.26/23.33 | | | | | (660) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.26/23.33 | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 154.26/23.33 | | | | | % 154.26/23.33 | | | | | ALPHA: (660) implies: % 154.26/23.33 | | | | | (661) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | REDUCE: (10), (659) imply: % 154.26/23.34 | | | | | (662) ~ (all_4_2 = e0) % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | BETA: splitting (29) gives: % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | Case 1: % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | (663) all_54_15 = e0 % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | REF_CLOSE: (59), (662), (663) are inconsistent by sub-proof #493. % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | Case 2: % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | (664) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | BETA: splitting (36) gives: % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | Case 1: % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | (665) all_56_2 = e0 % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | COMBINE_EQS: (130), (665) imply: % 154.26/23.34 | | | | | | | (666) all_52_1 = e0 % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | REDUCE: (153), (666) imply: % 154.26/23.34 | | | | | | | (667) $false % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | CLOSE: (667) is inconsistent. % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | Case 2: % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | (668) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | BETA: splitting (123) gives: % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | (669) all_56_1 = e0 % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | COMBINE_EQS: (92), (669) imply: % 154.26/23.34 | | | | | | | | (670) all_52_4 = e0 % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | REDUCE: (126), (670) imply: % 154.26/23.34 | | | | | | | | (671) $false % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | CLOSE: (671) is inconsistent. % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | (672) ~ (all_56_1 = e0) % 154.26/23.34 | | | | | | | | (673) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | BETA: splitting (174) gives: % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | (674) all_56_6 = e0 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | COMBINE_EQS: (113), (674) imply: % 154.26/23.34 | | | | | | | | | (675) all_52_2 = e0 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | REDUCE: (15), (675) imply: % 154.26/23.34 | | | | | | | | | (676) $false % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | CLOSE: (676) is inconsistent. % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | (677) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | BETA: splitting (93) gives: % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | (678) all_56_4 = e0 % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | COMBINE_EQS: (30), (678) imply: % 154.26/23.34 | | | | | | | | | | (679) all_52_8 = e0 % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | REDUCE: (180), (679) imply: % 154.26/23.34 | | | | | | | | | | (680) $false % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | CLOSE: (680) is inconsistent. % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | (681) ~ (all_56_4 = e0) % 154.26/23.34 | | | | | | | | | | (682) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | BETA: splitting (179) gives: % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | (683) all_54_2 = e0 % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | REF_CLOSE: (14), (180), (683) are inconsistent by sub-proof % 154.26/23.34 | | | | | | | | | | | #860. % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | (684) ~ (all_54_2 = e0) % 154.26/23.34 | | | | | | | | | | | (685) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | BETA: splitting (134) gives: % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | (686) all_54_12 = e0 % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | REF_CLOSE: (195), (205), (686) are inconsistent by sub-proof % 154.26/23.34 | | | | | | | | | | | | #459. % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | (687) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | BETA: splitting (131) gives: % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | (688) all_54_10 = e0 % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (52), (76), (108), (111), (129), % 154.26/23.34 | | | | | | | | | | | | | (149), (169), (176), (182), (183), (184), (211), % 154.26/23.34 | | | | | | | | | | | | | (688) are inconsistent by sub-proof #492. % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | (689) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | BETA: splitting (164) gives: % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | (690) all_54_1 = e0 % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | REF_CLOSE: (34), (126), (690) are inconsistent by sub-proof % 154.26/23.34 | | | | | | | | | | | | | | #798. % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | (691) ~ (all_54_1 = e0) % 154.26/23.34 | | | | | | | | | | | | | | (692) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | BETA: splitting (187) gives: % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | (693) all_54_7 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | COMBINE_EQS: (26), (693) imply: % 154.26/23.34 | | | | | | | | | | | | | | | (694) all_52_13 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | SIMP: (694) implies: % 154.26/23.34 | | | | | | | | | | | | | | | (695) all_52_13 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | REDUCE: (122), (695) imply: % 154.26/23.34 | | | | | | | | | | | | | | | (696) ~ (all_52_9 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | REDUCE: (102), (695) imply: % 154.26/23.34 | | | | | | | | | | | | | | | (697) ~ (all_52_14 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | SIMP: (697) implies: % 154.26/23.34 | | | | | | | | | | | | | | | (698) ~ (all_52_14 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | REDUCE: (166), (695) imply: % 154.26/23.34 | | | | | | | | | | | | | | | (699) op(e2, e0) = all_58_12 % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | REDUCE: (163), (695) imply: % 154.26/23.34 | | | | | | | | | | | | | | | (700) op(e2, e0) = e0 % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | BETA: splitting (682) gives: % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | (701) all_56_5 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (701) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | (702) all_52_9 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | REDUCE: (696), (702) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | (703) $false % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | CLOSE: (703) is inconsistent. % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | (704) all_56_8 = e0 | all_56_14 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | BETA: splitting (704) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | (705) all_56_8 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (705) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | (706) all_6_2 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (706) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | (707) all_58_30 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (108), (111), (129), (149), % 154.26/23.34 | | | | | | | | | | | | | | | | | (169), (176), (183), (184), (211), (707) are % 154.26/23.34 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684. % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | (708) all_56_14 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (708) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | (709) all_52_11 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | SIMP: (709) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | (710) all_52_11 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | REDUCE: (203), (710) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | (711) ~ (all_10_1 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | REDUCE: (128), (710) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | (712) ~ (all_6_2 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | REDUCE: (41), (710) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | (713) op(e0, e1) = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | BETA: splitting (677) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | (714) all_56_7 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (714) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | (715) all_52_6 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | REDUCE: (44), (715) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | (716) ~ (all_52_7 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | SIMP: (716) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | (717) ~ (all_52_7 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e0, e2, % 154.26/23.34 | | | | | | | | | | | | | | | | | | simplifying with (699), (700) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | (718) all_58_12 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | (719) all_56_12 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (719) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | (720) all_10_1 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | SIMP: (720) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | (721) all_10_1 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (106), (181), (713), (721) are inconsistent % 154.26/23.34 | | | | | | | | | | | | | | | | | | | by sub-proof #491. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | (722) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (722) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (723) all_56_13 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (723) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (724) all_52_7 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | SIMP: (724) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (725) all_52_7 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (725) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (726) ~ (all_52_4 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (725) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (727) ~ (all_10_1 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | SIMP: (727) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (728) ~ (all_10_1 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (725) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (729) ~ (all_8_2 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | SIMP: (729) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (730) ~ (all_8_2 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (178), (725) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (731) ~ (all_4_2 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | (732) all_58_28 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (176), (732) are inconsistent by sub-proof % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | #690. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | (733) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | (734) all_58_29 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (734) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | (735) all_8_2 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (730), (735) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | (736) $false % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (736) is inconsistent. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | (737) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (738) all_58_30 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (738) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (739) all_6_2 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (739) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (740) ~ (all_52_8 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (739) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (741) op(e1, e1) = all_6_1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (739) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (742) op(e1, e1) = all_58_18 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (739) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (743) op(e1, e1) = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (744) all_56_9 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (744) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (745) all_52_12 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (745) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (746) all_52_12 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (746) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (747) op(e3, e1) = all_58_5 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_6_1, all_58_18, e1, e1, % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (741), (742) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (748) all_58_18 = all_6_1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_58_18, e1, e1, % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (742), (743) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (749) all_58_18 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_8, all_58_5, e1, e3, % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (143), (747) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (750) all_58_5 = all_52_8 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (748), (749) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (751) all_6_1 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_56_12 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (752) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_10_1 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (753) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_10_1 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (204), (754) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (755) ~ (all_4_2 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (755) implies: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (756) ~ (all_4_2 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_58_28 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (149), (757) are inconsistent by sub-proof % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | #688. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (758) ~ (all_58_28 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (758) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (760) ~ (e2 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (664) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_54_15 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (761) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) all_4_2 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (762) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_58_31 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (149), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (184), (738), (763) are inconsistent by % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #497. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) ~ (all_54_15 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_54_15 = e3 | all_54_15 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_54_15 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (766) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_4_2 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (756), (767) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) $false % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (768) is inconsistent. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_54_15 = e3 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (769) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_4_2 = e3 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (770) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_26_2 = e3 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (770) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_58_31 = e3 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (656), (770) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) op(e3, e1) = all_4_0 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_58_29 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (774) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_8_2 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (775) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) ~ (all_52_4 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_56_4 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (777) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_52_8 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (778) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) op(e3, e1) = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (654), (771), (773), (779) are % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) ~ (all_56_4 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (780) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) ~ (all_52_8 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (34), (74), (92), (105), (685), (692), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726), (740), (776), (781) are inconsistent by % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #553. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (184), (737), (772), (782) are % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #457. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (783) ~ (all_56_12 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (783) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (785) ~ (all_10_1 = e2) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (18), (31), (34), (47), (92), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (97), (108), (111), (121), (149), (159), (169), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (181), (195), (204), (205), (207), (687), (692), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (708), (718), (723), (726), (728), (738), (749), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | (784), (785) are inconsistent by sub-proof #488. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (786) ~ (all_56_9 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (786) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (787) ~ (all_52_12 = e1) % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (30), (54), (92), (107), (117), (176), (211), % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | (726), (737), (738), (740), (787) are inconsistent % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #484. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (788) all_58_31 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (788) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (789) all_4_2 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (789) imply: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | (790) $false % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (790) is inconsistent. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | (791) all_56_14 = e1 | all_56_15 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (176), (211), (708), (791) are inconsistent % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | by sub-proof #582. % 154.26/23.34 | | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | (792) all_56_8 = e0 | all_56_11 = e0 % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (157), (209), (698), (792) are inconsistent % 154.26/23.34 | | | | | | | | | | | | | | | | | | by sub-proof #763. % 154.26/23.34 | | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | (793) ~ (all_54_7 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | (794) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | REDUCE: (26), (793) imply: % 154.26/23.34 | | | | | | | | | | | | | | | (795) ~ (all_52_13 = e0) % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (11), (21), (22), (23), % 154.26/23.34 | | | | | | | | | | | | | | | (24), (25), (26), (27), (28), (30), (31), (33), % 154.26/23.34 | | | | | | | | | | | | | | | (39), (41), (44), (48), (50), (52), (54), (55), % 154.26/23.34 | | | | | | | | | | | | | | | (57), (61), (68), (72), (76), (77), (82), (83), % 154.26/23.34 | | | | | | | | | | | | | | | (84), (87), (91), (92), (96), (98), (100), (101), % 154.26/23.34 | | | | | | | | | | | | | | | (102), (104), (107), (108), (109), (111), (113), % 154.26/23.34 | | | | | | | | | | | | | | | (116), (117), (120), (121), (122), (126), (127), % 154.26/23.34 | | | | | | | | | | | | | | | (128), (129), (135), (137), (138), (139), (140), % 154.26/23.34 | | | | | | | | | | | | | | | (145), (148), (149), (151), (152), (157), (163), % 154.26/23.34 | | | | | | | | | | | | | | | (165), (167), (169), (170), (172), (173), (176), % 154.26/23.34 | | | | | | | | | | | | | | | (178), (180), (181), (182), (183), (184), (186), % 154.26/23.34 | | | | | | | | | | | | | | | (194), (196), (203), (211), (661), (668), (673), % 154.26/23.34 | | | | | | | | | | | | | | | (677), (689), (794), (795) are inconsistent by % 154.26/23.34 | | | | | | | | | | | | | | | sub-proof #462. % 154.26/23.34 | | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | End of split % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | End of split % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | End of split % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | End of split % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | End of split % 154.26/23.34 | | | | | % 154.26/23.34 | | | | End of split % 154.26/23.34 | | | | % 154.26/23.34 | | | End of split % 154.26/23.34 | | | % 154.26/23.34 | | Case 2: % 154.26/23.34 | | | % 154.26/23.34 | | | (796) all_20_2 = e1 % 154.26/23.34 | | | % 154.26/23.34 | | | COMBINE_EQS: (90), (796) imply: % 154.26/23.34 | | | (797) all_4_2 = e1 % 154.26/23.34 | | | % 154.26/23.34 | | | SIMP: (797) implies: % 154.26/23.34 | | | (798) all_4_2 = e1 % 154.26/23.34 | | | % 154.26/23.34 | | | COMBINE_EQS: (10), (798) imply: % 154.26/23.34 | | | (799) all_56_15 = e1 % 154.26/23.34 | | | % 154.26/23.34 | | | COMBINE_EQS: (2), (798) imply: % 154.26/23.34 | | | (800) all_58_31 = e1 % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (178), (798) imply: % 154.26/23.34 | | | (801) ~ (all_52_7 = e1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (25), (798) imply: % 154.26/23.34 | | | (802) ~ (all_52_11 = e1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (156), (798) imply: % 154.26/23.34 | | | (803) ~ (all_52_12 = e1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (175), (798) imply: % 154.26/23.34 | | | (804) ~ (all_52_14 = e1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (204), (798) imply: % 154.26/23.34 | | | (805) ~ (all_10_1 = e1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (162), (798) imply: % 154.26/23.34 | | | (806) op(e1, all_4_1) = all_4_0 % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (188), (798) imply: % 154.26/23.34 | | | (807) op(e1, e0) = all_4_1 % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (35), (798) imply: % 154.26/23.34 | | | (808) op(e0, e1) = all_58_27 % 154.26/23.34 | | | % 154.26/23.34 | | | GROUND_INST: instantiating (4) with all_52_11, all_58_27, e1, e0, % 154.26/23.34 | | | simplifying with (41), (808) gives: % 154.26/23.34 | | | (809) all_58_27 = all_52_11 % 154.26/23.34 | | | % 154.26/23.34 | | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, % 154.26/23.34 | | | simplifying with (96), (807) gives: % 154.26/23.34 | | | (810) all_52_14 = all_4_1 % 154.26/23.34 | | | % 154.26/23.34 | | | COMBINE_EQS: (46), (810) imply: % 154.26/23.34 | | | (811) all_54_11 = all_4_1 % 154.26/23.34 | | | % 154.26/23.34 | | | COMBINE_EQS: (91), (810) imply: % 154.26/23.34 | | | (812) all_56_11 = all_4_1 % 154.26/23.34 | | | % 154.26/23.34 | | | COMBINE_EQS: (48), (810) imply: % 154.26/23.34 | | | (813) all_58_20 = all_4_1 % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (57), (810) imply: % 154.26/23.34 | | | (814) ~ (all_52_6 = all_4_1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (109), (810) imply: % 154.26/23.34 | | | (815) ~ (all_52_12 = all_4_1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (102), (810) imply: % 154.26/23.34 | | | (816) ~ (all_52_13 = all_4_1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (186), (810) imply: % 154.26/23.34 | | | (817) ~ (all_6_2 = all_4_1) % 154.26/23.34 | | | % 154.26/23.34 | | | SIMP: (817) implies: % 154.26/23.34 | | | (818) ~ (all_6_2 = all_4_1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (804), (810) imply: % 154.26/23.34 | | | (819) ~ (all_4_1 = e1) % 154.26/23.34 | | | % 154.26/23.34 | | | REDUCE: (23), (810) imply: % 154.26/23.34 | | | (820) op(e1, all_4_1) = all_58_19 % 154.26/23.34 | | | % 154.26/23.34 | | | GROUND_INST: instantiating (4) with all_4_0, all_58_19, all_4_1, e1, % 154.26/23.34 | | | simplifying with (806), (820) gives: % 154.26/23.34 | | | (821) all_58_19 = all_4_0 % 154.26/23.34 | | | % 154.26/23.34 | | | BETA: splitting (13) gives: % 154.26/23.34 | | | % 154.26/23.34 | | | Case 1: % 154.26/23.34 | | | | % 154.26/23.34 | | | | (822) all_54_3 = e0 % 154.26/23.34 | | | | % 154.26/23.34 | | | | REF_CLOSE: (32), (87), (822) are inconsistent by sub-proof #733. % 154.26/23.34 | | | | % 154.26/23.34 | | | Case 2: % 154.26/23.34 | | | | % 154.26/23.34 | | | | (823) ~ (all_54_3 = e0) % 154.26/23.34 | | | | (824) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.26/23.34 | | | | % 154.26/23.34 | | | | BETA: splitting (134) gives: % 154.26/23.34 | | | | % 154.26/23.34 | | | | Case 1: % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | (825) all_54_12 = e0 % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | COMBINE_EQS: (195), (825) imply: % 154.26/23.34 | | | | | (826) all_10_1 = e0 % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | REDUCE: (205), (826) imply: % 154.26/23.34 | | | | | (827) $false % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | CLOSE: (827) is inconsistent. % 154.26/23.34 | | | | | % 154.26/23.34 | | | | Case 2: % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | (828) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | BETA: splitting (93) gives: % 154.26/23.34 | | | | | % 154.26/23.34 | | | | | Case 1: % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | (829) all_56_4 = e0 % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | COMBINE_EQS: (30), (829) imply: % 154.26/23.34 | | | | | | (830) all_52_8 = e0 % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | REDUCE: (180), (830) imply: % 154.26/23.34 | | | | | | (831) $false % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | CLOSE: (831) is inconsistent. % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | Case 2: % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | (832) ~ (all_56_4 = e0) % 154.26/23.34 | | | | | | (833) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | BETA: splitting (123) gives: % 154.26/23.34 | | | | | | % 154.26/23.34 | | | | | | Case 1: % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | (834) all_56_1 = e0 % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | COMBINE_EQS: (92), (834) imply: % 154.26/23.34 | | | | | | | (835) all_52_4 = e0 % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | REDUCE: (126), (835) imply: % 154.26/23.34 | | | | | | | (836) $false % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | CLOSE: (836) is inconsistent. % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | Case 2: % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | (837) ~ (all_56_1 = e0) % 154.26/23.34 | | | | | | | (838) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | BETA: splitting (174) gives: % 154.26/23.34 | | | | | | | % 154.26/23.34 | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | (839) all_56_6 = e0 % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | COMBINE_EQS: (113), (839) imply: % 154.26/23.34 | | | | | | | | (840) all_52_2 = e0 % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | REDUCE: (15), (840) imply: % 154.26/23.34 | | | | | | | | (841) $false % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | CLOSE: (841) is inconsistent. % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | (842) ~ (all_56_6 = e0) % 154.26/23.34 | | | | | | | | (843) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | BETA: splitting (85) gives: % 154.26/23.34 | | | | | | | | % 154.26/23.34 | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | (844) all_54_5 = e0 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | COMBINE_EQS: (56), (844) imply: % 154.26/23.34 | | | | | | | | | (845) all_8_2 = e0 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | COMBINE_EQS: (108), (845) imply: % 154.26/23.34 | | | | | | | | | (846) all_58_29 = e0 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (169), (176), % 154.26/23.34 | | | | | | | | | (182), (183), (184), (846) are inconsistent by % 154.26/23.34 | | | | | | | | | sub-proof #483. % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | (847) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | BETA: splitting (37) gives: % 154.26/23.34 | | | | | | | | | % 154.26/23.34 | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | (848) all_54_8 = e0 % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | COMBINE_EQS: (16), (848) imply: % 154.26/23.34 | | | | | | | | | | (849) all_52_2 = e0 % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | REDUCE: (15), (849) imply: % 154.26/23.34 | | | | | | | | | | (850) $false % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | CLOSE: (850) is inconsistent. % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | (851) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | BETA: splitting (43) gives: % 154.26/23.34 | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | Case 1: % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | (852) all_56_0 = e1 % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | REF_CLOSE: (54), (176), (852) are inconsistent by sub-proof % 154.26/23.34 | | | | | | | | | | | #516. % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | Case 2: % 154.26/23.34 | | | | | | | | | | | % 154.26/23.34 | | | | | | | | | | | (853) ~ (all_56_0 = e1) % 154.26/23.34 | | | | | | | | | | | (854) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.34 | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | REDUCE: (54), (853) imply: % 154.26/23.35 | | | | | | | | | | | (855) ~ (e1 = e0) % 154.26/23.35 | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | BETA: splitting (187) gives: % 154.26/23.35 | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | (856) all_54_7 = e0 % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | COMBINE_EQS: (26), (856) imply: % 154.26/23.35 | | | | | | | | | | | | (857) all_52_13 = e0 % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | COMBINE_EQS: (135), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (858) all_56_10 = e0 % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | COMBINE_EQS: (39), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (859) all_58_13 = e0 % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | REDUCE: (122), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (860) ~ (all_52_9 = e0) % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | REDUCE: (72), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (861) ~ (all_8_2 = e0) % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | SIMP: (861) implies: % 154.26/23.35 | | | | | | | | | | | | (862) ~ (all_8_2 = e0) % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | REDUCE: (816), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (863) ~ (all_4_1 = e0) % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | SIMP: (863) implies: % 154.26/23.35 | | | | | | | | | | | | (864) ~ (all_4_1 = e0) % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | REDUCE: (166), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (865) op(e2, e0) = all_58_12 % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | REDUCE: (163), (857) imply: % 154.26/23.35 | | | | | | | | | | | | (866) op(e2, e0) = e0 % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | BETA: splitting (843) gives: % 154.26/23.35 | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | (867) all_56_7 = e0 % 154.26/23.35 | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | COMBINE_EQS: (11), (867) imply: % 154.26/23.35 | | | | | | | | | | | | | (868) all_52_6 = e0 % 154.26/23.35 | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | COMBINE_EQS: (141), (868) imply: % 154.26/23.35 | | | | | | | | | | | | | (869) all_58_17 = e0 % 154.26/23.35 | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | REDUCE: (73), (868) imply: % 154.26/23.35 | | | | | | | | | | | | | (870) op(e1, e0) = all_58_16 % 154.26/23.35 | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | BETA: splitting (833) gives: % 154.26/23.35 | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | (871) all_56_5 = e0 % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | COMBINE_EQS: (82), (871) imply: % 154.26/23.35 | | | | | | | | | | | | | | (872) all_52_9 = e0 % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | REDUCE: (860), (872) imply: % 154.26/23.35 | | | | | | | | | | | | | | (873) $false % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | CLOSE: (873) is inconsistent. % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | (874) ~ (all_56_5 = e0) % 154.26/23.35 | | | | | | | | | | | | | | (875) all_56_8 = e0 | all_56_14 = e0 % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | BETA: splitting (875) gives: % 154.26/23.35 | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | (876) all_56_8 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | REF_CLOSE: (30), (33), (36), (50), (76), (82), (84), (92), % 154.26/23.35 | | | | | | | | | | | | | | | (100), (107), (108), (111), (126), (129), (130), % 154.26/23.35 | | | | | | | | | | | | | | | (135), (140), (149), (151), (153), (157), (169), % 154.26/23.35 | | | | | | | | | | | | | | | (180), (182), (184), (800), (860), (862), (876) % 154.26/23.35 | | | | | | | | | | | | | | | are inconsistent by sub-proof #454. % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | (877) all_56_14 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | COMBINE_EQS: (139), (877) imply: % 154.26/23.35 | | | | | | | | | | | | | | | (878) all_52_11 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | SIMP: (878) implies: % 154.26/23.35 | | | | | | | | | | | | | | | (879) all_52_11 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | COMBINE_EQS: (809), (879) imply: % 154.26/23.35 | | | | | | | | | | | | | | | (880) all_58_27 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | COMBINE_EQS: (22), (879) imply: % 154.26/23.35 | | | | | | | | | | | | | | | (881) all_58_26 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | REDUCE: (146), (879) imply: % 154.26/23.35 | | | | | | | | | | | | | | | (882) ~ (all_52_7 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_1, all_58_16, e0, e1, % 154.26/23.35 | | | | | | | | | | | | | | | simplifying with (807), (870) gives: % 154.26/23.35 | | | | | | | | | | | | | | | (883) all_58_16 = all_4_1 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_12, e0, e2, % 154.26/23.35 | | | | | | | | | | | | | | | simplifying with (865), (866) gives: % 154.26/23.35 | | | | | | | | | | | | | | | (884) all_58_12 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 154.26/23.35 | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | (885) all_54_11 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (811), (885) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | (886) all_4_1 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | REDUCE: (864), (886) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | (887) $false % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | CLOSE: (887) is inconsistent. % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | (888) ~ (all_54_11 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | (889) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | (890) all_56_9 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (890) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | (891) all_52_12 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | SIMP: (891) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | (892) all_52_12 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (194), (892) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | (893) all_58_0 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | REDUCE: (815), (892) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | (894) ~ (all_4_1 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | SIMP: (894) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | (895) ~ (all_4_1 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | (896) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (884), (893), (896) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | #669. % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | (897) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | BETA: splitting (897) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (898) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | ALPHA: (898) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (899) ~ (all_58_16 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | REDUCE: (883), (899) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (900) ~ (all_4_1 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (889) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | (901) all_54_11 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (811), (819), (901) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | #545. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | (902) all_54_11 = e3 | all_54_11 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (902) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (903) all_54_11 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (811), (900), (903) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | #453. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (904) all_54_11 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (811), (895), (904) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | #544. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (905) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | ALPHA: (905) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (906) ~ (all_58_27 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | REDUCE: (880), (906) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (907) $false % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | CLOSE: (907) is inconsistent. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | End of split % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | (908) ~ (all_56_9 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | REDUCE: (107), (908) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | (909) ~ (all_52_12 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | BETA: splitting (824) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | (910) all_54_3 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (910) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | (911) all_52_12 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | REDUCE: (803), (911) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | (912) $false % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | CLOSE: (912) is inconsistent. % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | (913) all_54_3 = e3 | all_54_3 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | BETA: splitting (913) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (914) all_54_3 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (914) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (915) all_52_12 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (915) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (916) all_58_6 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | REDUCE: (189), (915) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (917) ~ (all_52_4 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | REDUCE: (66), (915) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (918) ~ (all_52_8 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | REDUCE: (815), (915) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (919) ~ (all_4_1 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | SIMP: (919) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | (920) ~ (all_4_1 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (889) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | (921) all_54_11 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (811), (819), (921) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | #545. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | (922) ~ (all_54_11 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | (923) all_54_11 = e3 | all_54_11 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (923) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (924) all_54_11 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (811), (920), (924) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | #453. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (925) all_54_11 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (811), (925) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (926) all_4_1 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | SIMP: (926) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (927) all_4_1 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (813), (927) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (928) all_58_20 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | REDUCE: (818), (927) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | (929) ~ (all_6_2 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | (930) all_58_28 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (129), (930) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | #689. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | (931) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (931) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | (932) all_58_29 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (932) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | (933) all_8_2 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (933) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | (934) all_56_3 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (933) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_52_4 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | (936) all_54_1 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (126), (936) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | #798. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | (937) ~ (all_54_1 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | (938) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_58_28 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (149), (939) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | #688. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | (940) ~ (all_58_28 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | (941) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (940) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | (942) ~ (e2 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (943) all_56_1 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (943) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_52_4 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (944) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_58_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (944) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (946) ~ (all_52_7 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (944) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (947) ~ (all_52_8 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (947) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (948) ~ (all_52_8 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (935), (944) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (949) ~ (e3 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (917), (944) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (950) ~ (e2 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_54_2 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (180), (951) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | #860. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) ~ (all_54_2 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_56_1 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (943), (954) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (955) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_56_3 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (956) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) e3 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (957) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) $false % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (958) is inconsistent. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) ~ (all_56_3 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_56_7 = e2 | all_56_13 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_56_12 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (961) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_10_1 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (962) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_10_1 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (963) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) all_58_22 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (963) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) ~ (all_52_1 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (963) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) ~ (all_52_2 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (963) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) ~ (all_52_7 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_56_4 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (968) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) all_52_8 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (969) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_58_4 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (969) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) ~ (all_52_9 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (971) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) ~ (all_52_9 = e3) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (960) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) all_56_7 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (867), (973) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) e2 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (974) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) $false % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (975) is inconsistent. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) all_56_13 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (976) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) all_52_7 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (977) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_52_7 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (978) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_58_24 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (967), (978) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) ~ (e3 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_58_31 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (800), (981) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #845. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (982) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_58_30 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (184), (800), (932), (941), (983) are % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #499. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) all_56_6 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (985) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) all_52_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (986) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) all_52_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (987) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) all_58_15 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (987) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) ~ (all_52_1 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) all_54_10 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (990) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_6_2 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (991) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) all_6_2 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (992) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_58_30 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (129), (149), (184), (800), (931), % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941), (993) are inconsistent by sub-proof #451. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) all_54_4 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (192), (995) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #859. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) ~ (all_54_4 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) all_56_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (130), (989), (998) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #450. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) ~ (all_56_2 = e1) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (941) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) all_58_29 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (184), (932), (1001) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) ~ (all_58_29 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1000) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_56_3 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (934), (1004) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #449. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_56_5 = e1 | all_56_10 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (994) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) all_54_10 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (1006) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) all_6_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1007) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_6_2 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (1008) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_58_30 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (800), (1003), (1009) are inconsistent by % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) all_54_10 = e3 | all_54_10 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1010) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) all_54_10 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (1011) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) all_6_2 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1012) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) all_6_2 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (1013) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) all_58_30 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) all_56_2 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (1015) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) all_52_1 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1016) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) all_52_1 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (1017) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) all_58_8 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1017) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) ~ (all_52_9 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1019) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) ~ (all_52_9 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1005) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_56_5 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (1021) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) all_52_9 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1022) implies: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) all_52_9 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (1023) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) all_58_11 = e1 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) all_58_29 = e2 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (184), (932), (1025) are inconsistent by sub-proof % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1026) gives: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) all_58_28 = e3 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (1027) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) e3 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1028) imply: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) all_58_29 = e0 % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1029) are inconsistent by % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) ~ (all_58_28 = e3) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1030) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) ~ (e3 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1031) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1033) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1034) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1035) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1036) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_58_8 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_58_4 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (970), (1038) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1039) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1018), (1037) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1040), (1041) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (111), (129), (149), (169), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (932), (1014), (1040), (1042) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1043) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1044) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) all_58_8 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1018), (1046) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (964), (1045) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1048) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1047), (1049) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) e2 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1049) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_58_29 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1051) are inconsistent by % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1052) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_58_8 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1018), (1054) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (869), (1053) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) e2 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1055), (1056) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1057) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) all_58_29 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1058) are inconsistent by % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1059) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1060) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1061) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_58_13 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_58_8 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1018), (1063) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (859), (1062) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) e2 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1065) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) e2 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1064), (1066) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1067) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_58_29 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1068) are inconsistent by % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1069) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_58_15 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_58_2 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (945), (1071) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1072) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (988), (1070) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (111), (129), (149), (169), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (932), (1014), (1073), (1074) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1075) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) all_58_6 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_58_2 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (945), (1078) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1079) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (916), (1077) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1081) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1080), (1082) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (111), (129), (149), (169), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (932), (1014), (1080), (1083) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (800), (869), (945), (1003), (1014), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) are inconsistent by sub-proof #445. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1085) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1086) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1087) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (800), (979), (1003), (1014), (1088) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #444. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1089) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_58_2 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (945), (1091) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1092) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1090), (1093) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (111), (129), (149), (169), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (932), (1014), (1093), (1094) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1095) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1096) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_58_15 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (988), (1098) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (932), (964), (1097), (1099) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #443. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1100) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_58_17 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_58_15 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (988), (1102) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (869), (1101) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) e1 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1103), (1104) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1105) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_58_29 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1106) are inconsistent by % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1107) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1108) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1109) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_58_26 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_58_20 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (881), (928), (931), (932), (1110), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) are inconsistent by sub-proof #441. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1112) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_58_6 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_58_4 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (970), (1114) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1115) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (916), (1113) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1117) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1116), (1118) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (111), (129), (149), (169), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (932), (1014), (1116), (1119) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1121) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_58_11 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_58_4 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (970), (1124) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1125) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1024), (1123) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) e2 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (869), (1122) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) e2 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1127), (1128) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) e1 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1126), (1129) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1130) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_58_29 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1131) are inconsistent by % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1132) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) all_58_20 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (928), (931), (932), (1133) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1134) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1135) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1136) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1137) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) all_58_4 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (970), (1138) are inconsistent by sub-proof % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #647. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1139) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1140) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) all_58_24 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_58_6 = e3 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (916), (1142) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1143) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) e3 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (979), (1141) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) e2 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1144), (1145) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1146) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) all_58_29 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (1147) are inconsistent by % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1148) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) all_58_20 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (928), (931), (932), (1149) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1150) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1151) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1152) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (932), (964), (1153) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #439. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1154) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) all_58_20 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (928), (1156) imply: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1157) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) e3 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (932), (964), (1155), (1158) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #443. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1159) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1160) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) all_58_22 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (932), (964), (1161) are % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #439. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (800), (979), (1003), (1014), (1162) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #438. % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1163) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1164) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1165) gives: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1166) implies: % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) all_58_20 = e1 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_58_17 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_58_11 = e2 % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1024), (1169) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) e2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (869), (1168) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) e2 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (928), (1167) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) e3 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1172) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) e3 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1170), (1171) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) e1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (931), (932), (1173), (1174) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1175) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) all_58_13 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (800), (859), (1003), (1014), (1176) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #437. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1177) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1178) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) all_58_20 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (928), (931), (932), (1179) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1180) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) e2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) all_58_17 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (800), (869), (1003), (1014), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181), (1182) are inconsistent by sub-proof #446. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1183) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1184) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1185) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) all_58_20 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (928), (931), (932), (1186) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1187) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) all_58_26 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) all_58_20 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (881), (928), (931), (932), (1188), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) are inconsistent by sub-proof #441. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1190) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (800), (979), (1003), (1014), (1191) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #436. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1192) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) all_58_20 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (111), (129), (149), (182), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184), (800), (928), (931), (932), (1193) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) all_56_10 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (858), (1194) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) e1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (1195) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1196) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) ~ (all_56_2 = e2) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (1197) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) ~ (all_52_1 = e2) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (965), (989), (997), (1198) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #828. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_54_10 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (1199) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_6_2 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1200) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) all_6_2 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (1201) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) all_58_30 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (184), (800), (1003), (1202) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #658. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) ~ (all_56_6 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1203) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) ~ (all_52_2 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (851) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) all_54_8 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (1204), (1205) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) ~ (all_54_8 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_54_8 = e3 | all_54_8 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1207) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) all_54_8 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (1208) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) all_52_2 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1209) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) all_52_2 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (1210) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) ~ (all_6_2 = e2) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1211) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) ~ (all_6_2 = e2) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (941) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_58_29 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (184), (932), (1213) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (182), (800), (1212), (1214) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #435. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_54_8 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (966), (1215) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #786. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) ~ (all_56_4 = e3) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (1216) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) ~ (all_52_8 = e3) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (918), (948), (953), (1217) are inconsistent % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #554. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (960) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) all_56_7 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (867), (1219) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) e2 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1220) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1221) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) all_56_13 = e2 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (129), (184), (799), (877), (1218), (1222) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #433. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) ~ (all_56_1 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (1223) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) ~ (all_52_4 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (917), (935), (938), (1224) are inconsistent % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #738. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | (1225) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (182), (800), (929), (1225) are inconsistent % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #432. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1226) all_54_3 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (1226) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1227) all_52_12 = e3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | REDUCE: (909), (1227) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1228) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | CLOSE: (1228) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | (1229) all_56_8 = e0 | all_56_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | BETA: splitting (1229) gives: % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | (1230) all_56_8 = e0 % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | REF_CLOSE: (30), (33), (36), (50), (76), (82), (84), (92), % 154.26/23.37 | | | | | | | | | | | | | | (100), (107), (108), (111), (126), (129), (130), % 154.26/23.37 | | | | | | | | | | | | | | (135), (140), (149), (151), (153), (157), (169), % 154.26/23.37 | | | | | | | | | | | | | | (180), (182), (184), (800), (860), (862), (1230) % 154.26/23.37 | | | | | | | | | | | | | | are inconsistent by sub-proof #454. % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | (1231) all_56_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | REF_CLOSE: (812), (864), (1231) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | #525. % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | (1232) ~ (all_54_7 = e0) % 154.26/23.37 | | | | | | | | | | | | (1233) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.37 | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | REDUCE: (26), (1232) imply: % 154.26/23.37 | | | | | | | | | | | | (1234) ~ (all_52_13 = e0) % 154.26/23.37 | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | BETA: splitting (63) gives: % 154.26/23.37 | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | (1235) all_56_15 = e0 % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | REF_CLOSE: (176), (799), (1235) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | #550. % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | (1236) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) % 154.26/23.37 | | | | | | | | | | | | | & (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = % 154.26/23.37 | | | | | | | | | | | | | e0) % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | ALPHA: (1236) implies: % 154.26/23.37 | | | | | | | | | | | | | (1237) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | BETA: splitting (1237) gives: % 154.26/23.37 | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | (1238) all_56_9 = e0 % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | REF_CLOSE: (87), (107), (1238) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | #521. % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | (1239) all_56_10 = e0 | all_56_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | BETA: splitting (1239) gives: % 154.26/23.37 | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | (1240) all_56_10 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | REF_CLOSE: (135), (1234), (1240) are inconsistent by % 154.26/23.37 | | | | | | | | | | | | | | | sub-proof #526. % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | (1241) all_56_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | COMBINE_EQS: (812), (1241) imply: % 154.26/23.37 | | | | | | | | | | | | | | | (1242) all_4_1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | SIMP: (1242) implies: % 154.26/23.37 | | | | | | | | | | | | | | | (1243) all_4_1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | COMBINE_EQS: (813), (1243) imply: % 154.26/23.37 | | | | | | | | | | | | | | | (1244) all_58_20 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | REDUCE: (814), (1243) imply: % 154.26/23.37 | | | | | | | | | | | | | | | (1245) ~ (all_52_6 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | REDUCE: (806), (1243) imply: % 154.26/23.37 | | | | | | | | | | | | | | | (1246) op(e1, e0) = all_4_0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | REDUCE: (807), (1243) imply: % 154.26/23.37 | | | | | | | | | | | | | | | (1247) op(e1, e0) = e0 % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | BETA: splitting (838) gives: % 154.26/23.37 | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | (1248) all_56_3 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (100), % 154.26/23.37 | | | | | | | | | | | | | | | | (107), (108), (109), (111), (126), (129), (140), % 154.26/23.37 | | | | | | | | | | | | | | | | (149), (151), (157), (169), (176), (180), (182), % 154.26/23.37 | | | | | | | | | | | | | | | | (183), (184), (209), (843), (1245), (1248) are % 154.26/23.37 | | | | | | | | | | | | | | | | inconsistent by sub-proof #480. % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | (1249) all_56_7 = e0 | all_56_13 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | BETA: splitting (1249) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | (1250) all_56_7 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (1250) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1251) all_52_6 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | REDUCE: (1245), (1251) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1252) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | CLOSE: (1252) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | (1253) all_56_13 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (1253) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1254) all_52_7 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | SIMP: (1254) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1255) all_52_7 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (1255) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1256) all_58_24 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | REDUCE: (146), (1255) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1257) ~ (all_52_11 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | SIMP: (1257) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1258) ~ (all_52_11 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | REDUCE: (201), (1255) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | (1259) ~ (all_10_1 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | BETA: splitting (833) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1260) all_56_5 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (1260) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1261) all_52_9 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (1261) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1262) all_58_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | REDUCE: (122), (1261) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1263) ~ (all_52_13 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | REDUCE: (138), (1261) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1264) ~ (all_8_2 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | SIMP: (1264) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1265) ~ (all_8_2 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | REDUCE: (150), (1261) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1266) ~ (all_6_2 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_4_0, e0, e1, % 154.26/23.37 | | | | | | | | | | | | | | | | | | simplifying with (1246), (1247) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1267) all_4_0 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (821), (1267) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | (1268) all_58_19 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1269) all_54_14 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (1269) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1270) all_52_11 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1270) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1271) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | CLOSE: (1271) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1272) ~ (all_54_14 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | (1273) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | (1274) all_54_1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (126), (1274) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | #798. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | (1275) ~ (all_54_1 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | (1276) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | (1277) all_54_9 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (1277) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | (1278) all_52_6 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1245), (1278) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | (1279) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1279) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | (1280) ~ (all_54_9 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | (1281) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1282) all_56_4 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (1282) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1283) all_52_8 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1283) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1284) all_52_8 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (1284) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1285) all_58_4 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (1284) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1286) ~ (all_52_4 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (1284) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1287) ~ (all_52_11 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (1284) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1288) ~ (all_52_12 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (65), (1284) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1289) op(e3, e1) = all_58_3 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (1284) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1290) op(e3, e1) = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_58_3, e1, e3, % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | simplifying with (1289), (1290) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | (1291) all_58_3 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | (1292) all_54_4 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (192), (1292) are inconsistent by sub-proof % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | #859. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | (1293) ~ (all_54_4 = e0) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | (1294) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1295) all_56_6 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (1295) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_52_2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1296) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_52_2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (1297) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1298) all_58_15 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1297) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1299) ~ (all_52_6 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1299) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1300) ~ (all_52_6 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (1297) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1301) ~ (all_10_1 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1302) all_56_1 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (1302) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1303) all_52_4 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1286), (1303) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1304) $false % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1304) is inconsistent. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1305) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1305) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) all_56_3 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (1306) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) all_8_2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1307) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) all_8_2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (1308) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) all_58_29 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (1308) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) ~ (all_52_1 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (1308) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) ~ (all_52_13 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (12), (19), (22), (27), (32), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (38), (39), (50), (54), (67), (74), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (76), (83), (87), (89), (92), (94), (103), (104), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (120), (126), (128), (129), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (130), (135), (139), (141), (149), (159), (165), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (176), (182), (183), (184), (189), (192), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (196), (197), (198), (203), (205), (799), (800), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (802), (803), (805), (824), (1234), (1241), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1244), (1245), (1253), (1256), (1258), (1262), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1273), (1276), (1281), (1286), (1294), (1298), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1300), (1306), (1309), (1310), (1311) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #420. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) all_56_7 = e1 | all_56_13 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (116), (801), (1300), (1312) are % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | (1313) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1313) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1314) all_56_7 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (1314) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1315) all_52_6 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (1315) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1316) all_58_17 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1315) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | (1317) ~ (all_52_2 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) all_56_2 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (1318) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) all_52_1 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1319) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) all_52_1 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (1320) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) all_58_8 = e1 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (1320) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) ~ (all_52_2 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (1320) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) ~ (all_52_13 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1323) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) ~ (all_52_13 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (1320) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) ~ (all_10_1 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (1320) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) ~ (all_8_2 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1326) implies: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) ~ (all_8_2 = e1) % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) all_58_31 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (1328) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) e1 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1314), (1329) imply: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) all_56_7 = e0 % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1317), (1330) are inconsistent by % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #418. % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) ~ (all_58_31 = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1332) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) all_58_30 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (149), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (184), (800), (1333) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #497. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1334) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) all_58_29 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (1335) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) all_8_2 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (1336) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) op(e2, e2) = all_58_9 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (1336) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) op(e2, e2) = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_58_28 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (129), (1339) are inconsistent by sub-proof % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1340) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_58_29 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (184), (1335), (1341) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #780. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1342) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) all_58_30 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (1343) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) all_6_2 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (1344) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) ~ (all_52_2 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) all_56_6 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (1346) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) all_52_2 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1347) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) all_52_2 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (1348) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) ~ (all_10_1 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1349) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) ~ (all_10_1 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) all_56_12 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (1351) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) all_10_1 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1352) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) all_10_1 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1353) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) op(e0, e3) = all_10_0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (1353) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) op(e0, e3) = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (121), (207), (1268), (1291), (1337), (1338), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354), (1355) are inconsistent by sub-proof #417. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) ~ (all_56_12 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (1356) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) ~ (all_10_1 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (195), (805), (828), (1350), (1357) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) ~ (all_56_6 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1358) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) ~ (all_52_2 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (851), (1317), (1345), (1359) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #416. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) all_58_31 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (800), (1360) are inconsistent by sub-proof % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #656. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) ~ (all_58_29 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (1361) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1363) ~ (all_8_2 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1362) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364) all_58_28 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (129), (1364) are inconsistent by sub-proof % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (847) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) all_54_5 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (1327), (1366) are inconsistent by sub-proof % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #534. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) all_54_5 = e3 | all_54_5 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1367) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_54_5 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (1363), (1368) are inconsistent by sub-proof % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #533. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) all_54_5 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (1369) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) all_8_2 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1370) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) all_8_2 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (1371) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_58_29 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (1371) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373) ~ (all_52_13 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1374) all_56_9 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (1374) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1375) all_52_12 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1375) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_52_12 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (1376) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_58_6 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (1376) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1378) ~ (all_52_13 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1379) all_56_9 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (184), (1374), (1379) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #415. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1380) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1380) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1381) all_56_10 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (1381) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1382) all_52_13 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1382) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_52_13 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (1383) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_58_13 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1373), (1383) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1385) ~ (e3 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1365) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1386) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1386) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1387) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1387) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1388) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1388) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1389) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1389) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1390) all_58_8 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1321), (1390) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1391) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1391) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1392) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (1392) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1393) $false % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1393) is inconsistent. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1394) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1394) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1395) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1396) all_58_8 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1377), (1397) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) e3 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1321), (1396) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1399) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1398), (1400) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1401) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1400), (1401) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #414. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1402) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1402) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1403) all_58_17 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1404) all_58_11 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1405) all_58_8 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1321), (1405) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1406) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1406) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1404) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408) e2 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1408) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409) e2 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1316), (1403) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1410) e2 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1410) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411) e2 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1409), (1411) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1412) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1407), (1412) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #414. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1413) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1413) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1414) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1414) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1415) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1416) all_58_24 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1256), (1416) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #413. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1417) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1417) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418) all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1321), (1418) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #412. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1419) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1420) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1420) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421) all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1321), (1421) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #412. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1422) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1423) all_58_11 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1423) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1424) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1425) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1426) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1428) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) all_58_13 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1321), (1430) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) e2 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1431) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) e2 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1384), (1429) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) e2 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1432), (1433) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #410. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1434) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1435) all_58_8 = e2 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1321), (1435) are inconsistent by % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #412. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1436) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1436) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1437) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) all_58_6 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) all_58_4 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1285), (1439) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1440) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1377), (1438) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) e3 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1441), (1442) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1441), (1443) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #414. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1444) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_58_11 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) all_58_4 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1285), (1446) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1447) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1445) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1449) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1448), (1450) are % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #414. % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1451) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1452) gives: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1453) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_58_20 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) all_58_4 = e3 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1285), (1455) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1456) implies: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) e3 = e1 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1244), (1454) imply: % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) e1 = e0 % 154.26/23.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1458) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1457), (1459) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #414. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1460) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) all_58_15 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (1461) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) all_52_2 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1317), (1462) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) $false % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1463) is inconsistent. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1464) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1465) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) all_58_11 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262), (1265), (1286), (1314), (1316), (1317), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466), (1467) are inconsistent by sub-proof #409. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_58_26 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (1469) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_52_11 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1470) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) $false % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1471) is inconsistent. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1472) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1473) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1474) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1475) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) e3 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (1476) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) $false % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1477) is inconsistent. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1478) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1479) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) all_58_13 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1384), (1480) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) e2 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1481) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) $false % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1482) is inconsistent. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1483) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) all_58_26 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (1484) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) all_52_11 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1258), (1485) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) $false % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1486) is inconsistent. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1487) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1488) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1489) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) all_58_6 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1377), (1490) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #408. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1491) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) all_58_6 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1377), (1492) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #408. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1493) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1494) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_58_6 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (33), (76), (84), (91), (92), (107), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (126), (129), (140), (149), (151), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (180), (182), (183), (184), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (843), (1245), (1372), (1377), (1495) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #408. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1496) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_58_13 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1384), (1498) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) e2 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1316), (1497) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) e2 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1500) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) e2 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1499), (1501) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1502) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1503) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1504) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1505) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1506) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) all_58_17 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_58_11 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262), (1265), (1286), (1314), (1316), (1317), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507), (1508) are inconsistent by sub-proof #409. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1509) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_58_11 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1510) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1511) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1512) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1513) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) all_58_11 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1514) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1515) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1516) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) all_58_11 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1262), (1517) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1518) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1519) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1520) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1521) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) all_58_24 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1256), (1522) are inconsistent by % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #413. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1523) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) all_58_20 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1244), (1524) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1314), (1317), (1525) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1526) gives: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1384), (1527) are inconsistent by % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #407. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1528) implies: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) e1 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1314), (1529) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) all_56_7 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (33), (76), (91), (92), (100), (108), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (116), (119), (129), (145), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (801), (804), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1286), (1317), (1530) are inconsistent by % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #418. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) all_56_11 = e2 | all_56_15 = e2 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (149), (799), (1241), (1531) are % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #423. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) ~ (all_56_9 = e3) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (32), (50), (107), (803), (824), (1233), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324), (1373), (1532) are inconsistent by % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #406. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) ~ (all_56_2 = e1) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (1533) imply: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) ~ (all_52_1 = e1) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (130), (196), (805), (854), (1317), (1534) % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #403. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_56_8 = e1 | all_56_11 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (149), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | (157), (169), (176), (182), (184), (800), (1241), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1535) are inconsistent by sub-proof #495. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | (1536) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (139), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | (149), (157), (169), (176), (182), (184), (800), % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | (802), (1260), (1536) are inconsistent by % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | sub-proof #402. % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.39 | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | (1537) all_56_8 = e0 | all_56_14 = e0 % 154.26/23.39 | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (76), (108), (111), (129), (139), % 154.26/23.39 | | | | | | | | | | | | | | | | | | (149), (157), (169), (182), (184), (800), (1258), % 154.26/23.39 | | | | | | | | | | | | | | | | | | (1537) are inconsistent by sub-proof #401. % 154.26/23.39 | | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | | % 154.26/23.39 | | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | | % 154.26/23.39 | | | | | | | | | End of split % 154.26/23.39 | | | | | | | | | % 154.26/23.39 | | | | | | | | End of split % 154.26/23.39 | | | | | | | | % 154.26/23.39 | | | | | | | End of split % 154.26/23.39 | | | | | | | % 154.26/23.39 | | | | | | End of split % 154.26/23.39 | | | | | | % 154.26/23.39 | | | | | End of split % 154.26/23.39 | | | | | % 154.26/23.39 | | | | End of split % 154.26/23.39 | | | | % 154.26/23.39 | | | End of split % 154.26/23.39 | | | % 154.26/23.39 | | End of split % 154.26/23.39 | | % 154.26/23.39 | Case 2: % 154.26/23.39 | | % 154.26/23.39 | | (1538) all_18_2 = e0 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (115), (1538) imply: % 154.26/23.39 | | (1539) all_6_2 = e0 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (182), (1539) imply: % 154.26/23.39 | | (1540) all_58_30 = e0 % 154.26/23.39 | | % 154.26/23.39 | | REF_CLOSE: (2), (6), (33), (76), (90), (108), (111), (129), (144), (149), % 154.26/23.39 | | (169), (176), (183), (184), (1540) are inconsistent by sub-proof % 154.26/23.39 | | #679. % 154.26/23.39 | | % 154.26/23.39 | End of split % 154.26/23.39 | % 154.26/23.39 End of proof % 154.26/23.39 % 154.26/23.39 Sub-proof #401 shows that the following formulas are inconsistent: % 154.26/23.39 ---------------------------------------------------------------- % 154.26/23.39 (1) all_56_8 = e0 | all_56_14 = e0 % 154.26/23.39 (2) all_58_28 = e0 % 154.26/23.39 (3) all_58_31 = e1 % 154.26/23.39 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.39 (5) ~ (e3 = e1) % 154.26/23.39 (6) all_58_29 = all_8_2 % 154.26/23.39 (7) ~ (e2 = e1) % 154.26/23.39 (8) ~ (e3 = e0) % 154.26/23.39 (9) ~ (all_52_11 = e0) % 154.26/23.39 (10) all_56_14 = all_52_11 % 154.26/23.39 (11) ~ (e2 = e0) % 154.26/23.39 (12) all_56_8 = all_6_2 % 154.26/23.39 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.39 (14) all_58_30 = all_6_2 % 154.26/23.39 (15) ~ (e3 = e2) % 154.26/23.39 % 154.26/23.39 Begin of proof % 154.26/23.39 | % 154.26/23.39 | BETA: splitting (1) gives: % 154.26/23.39 | % 154.26/23.39 | Case 1: % 154.26/23.39 | | % 154.26/23.39 | | (16) all_56_8 = e0 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (12), (16) imply: % 154.26/23.39 | | (17) all_6_2 = e0 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (14), (17) imply: % 154.26/23.39 | | (18) all_58_30 = e0 % 154.26/23.39 | | % 154.26/23.39 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (13), (15), (18) are % 154.26/23.39 | | inconsistent by sub-proof #680. % 154.26/23.39 | | % 154.26/23.39 | Case 2: % 154.26/23.39 | | % 154.26/23.39 | | (19) all_56_14 = e0 % 154.26/23.39 | | % 154.26/23.39 | | REF_CLOSE: (9), (10), (19) are inconsistent by sub-proof #806. % 154.26/23.39 | | % 154.26/23.39 | End of split % 154.26/23.39 | % 154.26/23.39 End of proof % 154.26/23.39 % 154.26/23.39 Sub-proof #402 shows that the following formulas are inconsistent: % 154.26/23.39 ---------------------------------------------------------------- % 154.26/23.39 (1) all_58_28 = e0 % 154.26/23.39 (2) all_58_31 = e1 % 154.26/23.39 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.39 (4) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.26/23.39 (5) ~ (e3 = e1) % 154.26/23.39 (6) ~ (all_52_11 = e1) % 154.26/23.39 (7) all_58_29 = all_8_2 % 154.26/23.39 (8) ~ (e2 = e1) % 154.26/23.39 (9) ~ (e3 = e0) % 154.26/23.39 (10) all_56_5 = e0 % 154.26/23.39 (11) all_56_14 = all_52_11 % 154.26/23.39 (12) ~ (e2 = e0) % 154.26/23.39 (13) all_56_8 = all_6_2 % 154.26/23.39 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.39 (15) ~ (e1 = e0) % 154.26/23.39 (16) all_58_30 = all_6_2 % 154.26/23.39 (17) ~ (e3 = e2) % 154.26/23.39 % 154.26/23.39 Begin of proof % 154.26/23.39 | % 154.26/23.39 | BETA: splitting (4) gives: % 154.26/23.39 | % 154.26/23.39 | Case 1: % 154.26/23.39 | | % 154.26/23.39 | | (18) all_56_5 = e1 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (10), (18) imply: % 154.26/23.39 | | (19) e1 = e0 % 154.26/23.39 | | % 154.26/23.39 | | REDUCE: (15), (19) imply: % 154.26/23.39 | | (20) $false % 154.26/23.39 | | % 154.26/23.39 | | CLOSE: (20) is inconsistent. % 154.26/23.39 | | % 154.26/23.39 | Case 2: % 154.26/23.39 | | % 154.26/23.39 | | (21) all_56_8 = e1 | all_56_14 = e1 % 154.26/23.39 | | % 154.26/23.39 | | BETA: splitting (21) gives: % 154.26/23.39 | | % 154.26/23.39 | | Case 1: % 154.26/23.39 | | | % 154.26/23.39 | | | (22) all_56_8 = e1 % 154.26/23.39 | | | % 154.26/23.39 | | | COMBINE_EQS: (13), (22) imply: % 154.26/23.39 | | | (23) all_6_2 = e1 % 154.26/23.39 | | | % 154.26/23.39 | | | SIMP: (23) implies: % 154.26/23.39 | | | (24) all_6_2 = e1 % 154.26/23.39 | | | % 154.26/23.39 | | | COMBINE_EQS: (16), (24) imply: % 154.26/23.39 | | | (25) all_58_30 = e1 % 154.26/23.39 | | | % 154.26/23.39 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (12), (14), (17), (25) are % 154.26/23.39 | | | inconsistent by sub-proof #497. % 154.26/23.39 | | | % 154.26/23.39 | | Case 2: % 154.26/23.39 | | | % 154.26/23.39 | | | (26) all_56_14 = e1 % 154.26/23.39 | | | % 154.26/23.39 | | | REF_CLOSE: (6), (11), (26) are inconsistent by sub-proof #811. % 154.26/23.39 | | | % 154.26/23.39 | | End of split % 154.26/23.39 | | % 154.26/23.39 | End of split % 154.26/23.39 | % 154.26/23.39 End of proof % 154.26/23.39 % 154.26/23.39 Sub-proof #403 shows that the following formulas are inconsistent: % 154.26/23.39 ---------------------------------------------------------------- % 154.26/23.39 (1) ~ (all_52_1 = e1) % 154.26/23.39 (2) all_56_12 = all_10_1 % 154.26/23.39 (3) ~ (all_52_2 = e1) % 154.26/23.39 (4) all_56_6 = all_52_2 % 154.26/23.39 (5) all_56_2 = all_52_1 % 154.26/23.39 (6) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.26/23.39 (7) ~ (all_10_1 = e1) % 154.26/23.39 % 154.26/23.39 Begin of proof % 154.26/23.39 | % 154.26/23.39 | BETA: splitting (6) gives: % 154.26/23.39 | % 154.26/23.39 | Case 1: % 154.26/23.39 | | % 154.26/23.39 | | (8) all_56_2 = e1 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (5), (8) imply: % 154.26/23.39 | | (9) all_52_1 = e1 % 154.26/23.39 | | % 154.26/23.39 | | REDUCE: (1), (9) imply: % 154.26/23.39 | | (10) $false % 154.26/23.39 | | % 154.26/23.39 | | CLOSE: (10) is inconsistent. % 154.26/23.39 | | % 154.26/23.39 | Case 2: % 154.26/23.39 | | % 154.26/23.39 | | (11) all_56_6 = e1 | all_56_12 = e1 % 154.26/23.39 | | % 154.26/23.39 | | REF_CLOSE: (2), (3), (4), (7), (11) are inconsistent by sub-proof #404. % 154.26/23.39 | | % 154.26/23.39 | End of split % 154.26/23.39 | % 154.26/23.39 End of proof % 154.26/23.39 % 154.26/23.39 Sub-proof #404 shows that the following formulas are inconsistent: % 154.26/23.39 ---------------------------------------------------------------- % 154.26/23.39 (1) all_56_12 = all_10_1 % 154.26/23.39 (2) ~ (all_52_2 = e1) % 154.26/23.39 (3) all_56_6 = all_52_2 % 154.26/23.39 (4) all_56_6 = e1 | all_56_12 = e1 % 154.26/23.39 (5) ~ (all_10_1 = e1) % 154.26/23.39 % 154.26/23.39 Begin of proof % 154.26/23.39 | % 154.26/23.39 | BETA: splitting (4) gives: % 154.26/23.39 | % 154.26/23.39 | Case 1: % 154.26/23.39 | | % 154.26/23.39 | | (6) all_56_6 = e1 % 154.26/23.39 | | % 154.26/23.39 | | COMBINE_EQS: (3), (6) imply: % 154.26/23.39 | | (7) all_52_2 = e1 % 154.26/23.39 | | % 154.26/23.39 | | REDUCE: (2), (7) imply: % 154.26/23.39 | | (8) $false % 154.26/23.39 | | % 154.26/23.39 | | CLOSE: (8) is inconsistent. % 154.26/23.39 | | % 154.26/23.39 | Case 2: % 154.26/23.39 | | % 154.26/23.39 | | (9) all_56_12 = e1 % 154.26/23.39 | | % 154.26/23.39 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #405. % 154.26/23.39 | | % 154.26/23.39 | End of split % 154.26/23.39 | % 154.26/23.39 End of proof % 154.26/23.39 % 154.26/23.39 Sub-proof #405 shows that the following formulas are inconsistent: % 154.26/23.39 ---------------------------------------------------------------- % 154.26/23.39 (1) all_56_12 = all_10_1 % 154.26/23.39 (2) all_56_12 = e1 % 154.26/23.39 (3) ~ (all_10_1 = e1) % 154.26/23.39 % 154.26/23.39 Begin of proof % 154.26/23.39 | % 154.26/23.39 | COMBINE_EQS: (1), (2) imply: % 154.26/23.39 | (4) all_10_1 = e1 % 154.26/23.39 | % 154.26/23.39 | SIMP: (4) implies: % 154.26/23.39 | (5) all_10_1 = e1 % 154.26/23.39 | % 154.26/23.39 | REDUCE: (3), (5) imply: % 154.26/23.39 | (6) $false % 154.26/23.39 | % 154.26/23.39 | CLOSE: (6) is inconsistent. % 154.26/23.39 | % 154.26/23.39 End of proof % 154.26/23.39 % 154.26/23.39 Sub-proof #406 shows that the following formulas are inconsistent: % 154.26/23.39 ---------------------------------------------------------------- % 154.26/23.39 (1) ~ (all_52_13 = e1) % 154.26/23.39 (2) all_54_7 = all_52_13 % 154.26/23.39 (3) ~ (all_56_9 = e3) % 154.26/23.39 (4) all_54_3 = all_52_12 % 154.26/23.39 (5) ~ (all_52_12 = all_52_13) % 154.26/23.39 (6) ~ (all_52_13 = e3) % 154.26/23.39 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.40 (8) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.26/23.40 (9) all_56_9 = all_52_12 % 154.26/23.40 (10) ~ (all_52_12 = e1) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | REDUCE: (3), (9) imply: % 154.26/23.40 | (11) ~ (all_52_12 = e3) % 154.26/23.40 | % 154.26/23.40 | BETA: splitting (7) gives: % 154.26/23.40 | % 154.26/23.40 | Case 1: % 154.26/23.40 | | % 154.26/23.40 | | (12) all_54_7 = e1 % 154.26/23.40 | | % 154.26/23.40 | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #605. % 154.26/23.40 | | % 154.26/23.40 | Case 2: % 154.26/23.40 | | % 154.26/23.40 | | (13) all_54_7 = e3 | all_54_7 = e2 % 154.26/23.40 | | % 154.26/23.40 | | BETA: splitting (13) gives: % 154.26/23.40 | | % 154.26/23.40 | | Case 1: % 154.26/23.40 | | | % 154.26/23.40 | | | (14) all_54_7 = e2 % 154.26/23.40 | | | % 154.26/23.40 | | | COMBINE_EQS: (2), (14) imply: % 154.26/23.40 | | | (15) all_52_13 = e2 % 154.26/23.40 | | | % 154.26/23.40 | | | SIMP: (15) implies: % 154.26/23.40 | | | (16) all_52_13 = e2 % 154.26/23.40 | | | % 154.26/23.40 | | | REDUCE: (5), (16) imply: % 154.26/23.40 | | | (17) ~ (all_52_12 = e2) % 154.26/23.40 | | | % 154.26/23.40 | | | REF_CLOSE: (4), (8), (10), (11), (17) are inconsistent by sub-proof #612. % 154.26/23.40 | | | % 154.26/23.40 | | Case 2: % 154.26/23.40 | | | % 154.26/23.40 | | | (18) all_54_7 = e3 % 154.26/23.40 | | | % 154.26/23.40 | | | REF_CLOSE: (2), (6), (18) are inconsistent by sub-proof #603. % 154.26/23.40 | | | % 154.26/23.40 | | End of split % 154.26/23.40 | | % 154.26/23.40 | End of split % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #407 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.40 (2) all_58_13 = e2 % 154.26/23.40 (3) ~ (e2 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | ALPHA: (1) implies: % 154.26/23.40 | (4) all_58_13 = e0 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (2), (4) imply: % 154.26/23.40 | (5) e2 = e0 % 154.26/23.40 | % 154.26/23.40 | REDUCE: (3), (5) imply: % 154.26/23.40 | (6) $false % 154.26/23.40 | % 154.26/23.40 | CLOSE: (6) is inconsistent. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #408 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_56_7 = all_52_6 % 154.26/23.40 (2) all_56_4 = all_52_8 % 154.26/23.40 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (4) ~ (all_6_2 = e0) % 154.26/23.40 (5) ~ (e3 = e1) % 154.26/23.40 (6) ~ (all_52_6 = e0) % 154.26/23.40 (7) all_58_6 = e0 % 154.26/23.40 (8) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.40 (9) all_56_11 = all_52_14 % 154.26/23.40 (10) all_56_1 = all_52_4 % 154.26/23.40 (11) all_56_9 = all_52_12 % 154.26/23.40 (12) all_58_29 = e3 % 154.26/23.40 (13) ~ (all_52_12 = all_52_14) % 154.26/23.40 (14) ~ (e2 = e1) % 154.26/23.40 (15) ~ (all_52_4 = e0) % 154.26/23.40 (16) ~ (e3 = e0) % 154.26/23.40 (17) all_58_6 = e3 % 154.26/23.40 (18) all_58_28 = all_10_2 % 154.26/23.40 (19) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.40 (20) ~ (e2 = e0) % 154.26/23.40 (21) all_56_0 = all_10_2 % 154.26/23.40 (22) all_56_8 = all_6_2 % 154.26/23.40 (23) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.40 (24) ~ (e1 = e0) % 154.26/23.40 (25) ~ (all_52_8 = e0) % 154.26/23.40 (26) all_58_30 = all_6_2 % 154.26/23.40 (27) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.40 (28) ~ (e3 = e2) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (7), (17) imply: % 154.26/23.40 | (29) e3 = e0 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (12), (29) imply: % 154.26/23.40 | (30) all_58_29 = e0 % 154.26/23.40 | % 154.26/23.40 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14), % 154.26/23.40 | (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 154.26/23.40 | (27), (28), (30) are inconsistent by sub-proof #481. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #409 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_31 = all_4_2 % 154.26/23.40 (2) all_58_28 = e0 % 154.26/23.40 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (4) ~ (all_52_7 = e1) % 154.26/23.40 (5) all_58_11 = e0 % 154.26/23.40 (6) ~ (all_52_14 = e1) % 154.26/23.40 (7) ~ (e3 = e1) % 154.26/23.40 (8) ~ (all_52_2 = e1) % 154.26/23.40 (9) all_56_11 = all_52_14 % 154.26/23.40 (10) all_56_1 = all_52_4 % 154.26/23.40 (11) all_58_11 = e2 % 154.26/23.40 (12) all_56_3 = all_8_2 % 154.26/23.40 (13) all_58_29 = all_8_2 % 154.26/23.40 (14) ~ (all_52_4 = e1) % 154.26/23.40 (15) ~ (e2 = e1) % 154.26/23.40 (16) all_56_6 = all_52_2 % 154.26/23.40 (17) all_56_13 = all_52_7 % 154.26/23.40 (18) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 (19) all_58_17 = e1 % 154.26/23.40 (20) ~ (e3 = e0) % 154.26/23.40 (21) all_56_7 = e1 % 154.26/23.40 (22) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.40 (23) ~ (e2 = e0) % 154.26/23.40 (24) all_56_8 = all_6_2 % 154.26/23.40 (25) all_58_17 = e2 % 154.26/23.40 (26) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.40 (27) ~ (e1 = e0) % 154.26/23.40 (28) all_58_30 = all_6_2 % 154.26/23.40 (29) ~ (e3 = e2) % 154.26/23.40 (30) ~ (all_8_2 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (5), (11) imply: % 154.26/23.40 | (31) e2 = e0 % 154.26/23.40 | % 154.26/23.40 | SIMP: (31) implies: % 154.26/23.40 | (32) e2 = e0 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (19), (25) imply: % 154.26/23.40 | (33) e2 = e1 % 154.26/23.40 | % 154.26/23.40 | SIMP: (33) implies: % 154.26/23.40 | (34) e2 = e1 % 154.26/23.40 | % 154.26/23.40 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), % 154.26/23.40 | (15), (16), (17), (18), (20), (21), (22), (23), (24), (26), (27), % 154.26/23.40 | (28), (29), (30), (32), (34) are inconsistent by sub-proof #410. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #410 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_31 = all_4_2 % 154.26/23.40 (2) all_58_28 = e0 % 154.26/23.40 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (4) ~ (all_52_7 = e1) % 154.26/23.40 (5) ~ (all_52_14 = e1) % 154.26/23.40 (6) ~ (e3 = e1) % 154.26/23.40 (7) ~ (all_52_2 = e1) % 154.26/23.40 (8) all_56_11 = all_52_14 % 154.26/23.40 (9) all_56_1 = all_52_4 % 154.26/23.40 (10) all_56_3 = all_8_2 % 154.26/23.40 (11) all_58_29 = all_8_2 % 154.26/23.40 (12) ~ (all_52_4 = e1) % 154.26/23.40 (13) ~ (e2 = e1) % 154.26/23.40 (14) e2 = e1 % 154.26/23.40 (15) all_56_6 = all_52_2 % 154.26/23.40 (16) all_56_13 = all_52_7 % 154.26/23.40 (17) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 (18) ~ (e3 = e0) % 154.26/23.40 (19) all_56_7 = e1 % 154.26/23.40 (20) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.40 (21) ~ (e2 = e0) % 154.26/23.40 (22) e2 = e0 % 154.26/23.40 (23) all_56_8 = all_6_2 % 154.26/23.40 (24) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.40 (25) ~ (e1 = e0) % 154.26/23.40 (26) all_58_30 = all_6_2 % 154.26/23.40 (27) ~ (e3 = e2) % 154.26/23.40 (28) ~ (all_8_2 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (14), (22) imply: % 154.26/23.40 | (29) e1 = e0 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (19), (29) imply: % 154.26/23.40 | (30) all_56_7 = e0 % 154.26/23.40 | % 154.26/23.40 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 154.26/23.40 | (13), (15), (16), (17), (18), (20), (21), (23), (24), (25), (26), % 154.26/23.40 | (27), (28), (30) are inconsistent by sub-proof #418. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #411 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_31 = all_4_2 % 154.26/23.40 (2) all_58_28 = e0 % 154.26/23.40 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (4) ~ (all_52_7 = e1) % 154.26/23.40 (5) ~ (all_52_14 = e1) % 154.26/23.40 (6) ~ (e3 = e1) % 154.26/23.40 (7) ~ (all_52_2 = e1) % 154.26/23.40 (8) all_56_11 = all_52_14 % 154.26/23.40 (9) all_56_1 = all_52_4 % 154.26/23.40 (10) all_56_3 = all_8_2 % 154.26/23.40 (11) all_58_29 = all_8_2 % 154.26/23.40 (12) ~ (all_52_4 = e1) % 154.26/23.40 (13) ~ (e2 = e1) % 154.26/23.40 (14) all_56_6 = all_52_2 % 154.26/23.40 (15) all_56_13 = all_52_7 % 154.26/23.40 (16) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 (17) ~ (e3 = e0) % 154.26/23.40 (18) all_56_7 = e1 % 154.26/23.40 (19) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.40 (20) ~ (e2 = e0) % 154.26/23.40 (21) all_56_8 = all_6_2 % 154.26/23.40 (22) e1 = e0 % 154.26/23.40 (23) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.40 (24) ~ (e1 = e0) % 154.26/23.40 (25) all_58_30 = all_6_2 % 154.26/23.40 (26) ~ (e3 = e2) % 154.26/23.40 (27) ~ (all_8_2 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | SIMP: (22) implies: % 154.26/23.40 | (28) e1 = e0 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (18), (28) imply: % 154.26/23.40 | (29) all_56_7 = e0 % 154.26/23.40 | % 154.26/23.40 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 154.26/23.40 | (13), (14), (15), (16), (17), (19), (20), (21), (23), (24), (25), % 154.26/23.40 | (26), (27), (29) are inconsistent by sub-proof #418. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #412 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_8 = e2 % 154.26/23.40 (2) all_58_8 = e1 % 154.26/23.40 (3) ~ (e2 = e1) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (1), (2) imply: % 154.26/23.40 | (4) e2 = e1 % 154.26/23.40 | % 154.26/23.40 | SIMP: (4) implies: % 154.26/23.40 | (5) e2 = e1 % 154.26/23.40 | % 154.26/23.40 | REDUCE: (3), (5) imply: % 154.26/23.40 | (6) $false % 154.26/23.40 | % 154.26/23.40 | CLOSE: (6) is inconsistent. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #413 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_24 = e2 % 154.26/23.40 (2) all_58_24 = e0 % 154.26/23.40 (3) ~ (e2 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (1), (2) imply: % 154.26/23.40 | (4) e2 = e0 % 154.26/23.40 | % 154.26/23.40 | SIMP: (4) implies: % 154.26/23.40 | (5) e2 = e0 % 154.26/23.40 | % 154.26/23.40 | REDUCE: (3), (5) imply: % 154.26/23.40 | (6) $false % 154.26/23.40 | % 154.26/23.40 | CLOSE: (6) is inconsistent. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #414 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_56_7 = all_52_6 % 154.26/23.40 (2) all_56_4 = all_52_8 % 154.26/23.40 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (4) ~ (all_6_2 = e0) % 154.26/23.40 (5) ~ (e3 = e1) % 154.26/23.40 (6) e3 = e1 % 154.26/23.40 (7) ~ (all_52_6 = e0) % 154.26/23.40 (8) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.40 (9) all_56_11 = all_52_14 % 154.26/23.40 (10) all_56_1 = all_52_4 % 154.26/23.40 (11) all_56_9 = all_52_12 % 154.26/23.40 (12) all_58_29 = e3 % 154.26/23.40 (13) ~ (all_52_12 = all_52_14) % 154.26/23.40 (14) ~ (e2 = e1) % 154.26/23.40 (15) ~ (all_52_4 = e0) % 154.26/23.40 (16) ~ (e3 = e0) % 154.26/23.40 (17) all_58_28 = all_10_2 % 154.26/23.40 (18) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.40 (19) ~ (e2 = e0) % 154.26/23.40 (20) all_56_0 = all_10_2 % 154.26/23.40 (21) all_56_8 = all_6_2 % 154.26/23.40 (22) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.40 (23) ~ (e1 = e0) % 154.26/23.40 (24) e1 = e0 % 154.26/23.40 (25) ~ (all_52_8 = e0) % 154.26/23.40 (26) all_58_30 = all_6_2 % 154.26/23.40 (27) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.40 (28) ~ (e3 = e2) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (6), (24) imply: % 154.26/23.40 | (29) e3 = e0 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (12), (29) imply: % 154.26/23.40 | (30) all_58_29 = e0 % 154.26/23.40 | % 154.26/23.40 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14), % 154.26/23.40 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (26), % 154.26/23.40 | (27), (28), (30) are inconsistent by sub-proof #481. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #415 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_56_9 = e3 % 154.26/23.40 (2) all_56_9 = e2 % 154.26/23.40 (3) ~ (e3 = e2) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (1), (2) imply: % 154.26/23.40 | (4) e3 = e2 % 154.26/23.40 | % 154.26/23.40 | SIMP: (4) implies: % 154.26/23.40 | (5) e3 = e2 % 154.26/23.40 | % 154.26/23.40 | REDUCE: (3), (5) imply: % 154.26/23.40 | (6) $false % 154.26/23.40 | % 154.26/23.40 | CLOSE: (6) is inconsistent. % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #416 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_54_8 = all_52_2 % 154.26/23.40 (2) ~ (all_52_2 = e1) % 154.26/23.40 (3) ~ (all_52_2 = e3) % 154.26/23.40 (4) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.26/23.40 (5) ~ (all_52_2 = e2) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | BETA: splitting (4) gives: % 154.26/23.40 | % 154.26/23.40 | Case 1: % 154.26/23.40 | | % 154.26/23.40 | | (6) all_54_8 = e1 % 154.26/23.40 | | % 154.26/23.40 | | COMBINE_EQS: (1), (6) imply: % 154.26/23.40 | | (7) all_52_2 = e1 % 154.26/23.40 | | % 154.26/23.40 | | REDUCE: (2), (7) imply: % 154.26/23.40 | | (8) $false % 154.26/23.40 | | % 154.26/23.40 | | CLOSE: (8) is inconsistent. % 154.26/23.40 | | % 154.26/23.40 | Case 2: % 154.26/23.40 | | % 154.26/23.40 | | (9) all_54_8 = e3 | all_54_8 = e2 % 154.26/23.40 | | % 154.26/23.40 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #785. % 154.26/23.40 | | % 154.26/23.40 | End of split % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #417 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.40 (2) all_58_19 = e0 % 154.26/23.40 (3) all_58_21 = all_10_0 % 154.26/23.40 (4) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.40 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.40 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.40 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.40 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.40 (all_58_27 = e0)) % 154.26/23.40 (5) op(e0, e3) = e3 % 154.26/23.40 (6) op(e0, e3) = all_10_0 % 154.26/23.40 (7) op(e2, e2) = e2 % 154.26/23.40 (8) all_58_3 = e1 % 154.26/23.40 (9) op(e2, e2) = all_58_9 % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | GROUND_INST: instantiating (1) with e3, all_10_0, e3, e0, simplifying with % 154.26/23.40 | (5), (6) gives: % 154.26/23.40 | (10) all_10_0 = e3 % 154.26/23.40 | % 154.26/23.40 | GROUND_INST: instantiating (1) with e2, all_58_9, e2, e2, simplifying with % 154.26/23.40 | (7), (9) gives: % 154.26/23.40 | (11) all_58_9 = e2 % 154.26/23.40 | % 154.26/23.40 | COMBINE_EQS: (3), (10) imply: % 154.26/23.40 | (12) all_58_21 = e3 % 154.26/23.40 | % 154.26/23.40 | BETA: splitting (4) gives: % 154.26/23.40 | % 154.26/23.40 | Case 1: % 154.26/23.40 | | % 154.26/23.40 | | (13) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.40 | | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.40 | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.26/23.40 | | % 154.26/23.40 | | BETA: splitting (13) gives: % 154.26/23.40 | | % 154.26/23.40 | | Case 1: % 154.26/23.40 | | | % 154.26/23.40 | | | (14) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.40 | | | (all_58_5 = e0) % 154.26/23.40 | | | % 154.26/23.40 | | | ALPHA: (14) implies: % 154.26/23.40 | | | (15) ~ (all_58_3 = e1) % 154.26/23.40 | | | % 154.26/23.40 | | | REDUCE: (8), (15) imply: % 154.26/23.40 | | | (16) $false % 154.26/23.40 | | | % 154.26/23.40 | | | CLOSE: (16) is inconsistent. % 154.26/23.40 | | | % 154.26/23.40 | | Case 2: % 154.26/23.40 | | | % 154.26/23.40 | | | (17) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 154.26/23.40 | | | (all_58_12 = e0) % 154.26/23.40 | | | % 154.26/23.40 | | | ALPHA: (17) implies: % 154.26/23.40 | | | (18) ~ (all_58_9 = e2) % 154.26/23.40 | | | % 154.26/23.40 | | | REDUCE: (11), (18) imply: % 154.26/23.40 | | | (19) $false % 154.26/23.40 | | | % 154.26/23.40 | | | CLOSE: (19) is inconsistent. % 154.26/23.40 | | | % 154.26/23.40 | | End of split % 154.26/23.40 | | % 154.26/23.40 | Case 2: % 154.26/23.40 | | % 154.26/23.40 | | (20) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 154.26/23.40 | | ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & % 154.26/23.40 | | ~ (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.26/23.40 | | % 154.26/23.40 | | REF_CLOSE: (2), (12), (20) are inconsistent by sub-proof #616. % 154.26/23.40 | | % 154.26/23.40 | End of split % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #418 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_31 = all_4_2 % 154.26/23.40 (2) all_58_28 = e0 % 154.26/23.40 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (4) ~ (all_52_7 = e1) % 154.26/23.40 (5) all_56_7 = e0 % 154.26/23.40 (6) ~ (all_52_14 = e1) % 154.26/23.40 (7) ~ (e3 = e1) % 154.26/23.40 (8) ~ (all_52_2 = e1) % 154.26/23.40 (9) all_56_11 = all_52_14 % 154.26/23.40 (10) all_56_1 = all_52_4 % 154.26/23.40 (11) all_56_3 = all_8_2 % 154.26/23.40 (12) all_58_29 = all_8_2 % 154.26/23.40 (13) ~ (all_52_4 = e1) % 154.26/23.40 (14) ~ (e2 = e1) % 154.26/23.40 (15) all_56_6 = all_52_2 % 154.26/23.40 (16) all_56_13 = all_52_7 % 154.26/23.40 (17) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 (18) ~ (e3 = e0) % 154.26/23.40 (19) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.40 (20) ~ (e2 = e0) % 154.26/23.40 (21) all_56_8 = all_6_2 % 154.26/23.40 (22) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.40 (23) ~ (e1 = e0) % 154.26/23.40 (24) all_58_30 = all_6_2 % 154.26/23.40 (25) ~ (e3 = e2) % 154.26/23.40 (26) ~ (all_8_2 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | BETA: splitting (19) gives: % 154.26/23.40 | % 154.26/23.40 | Case 1: % 154.26/23.40 | | % 154.26/23.40 | | (27) all_56_6 = e1 % 154.26/23.40 | | % 154.26/23.40 | | REF_CLOSE: (8), (15), (27) are inconsistent by sub-proof #639. % 154.26/23.40 | | % 154.26/23.40 | Case 2: % 154.26/23.40 | | % 154.26/23.40 | | (28) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.40 | | % 154.26/23.40 | | BETA: splitting (17) gives: % 154.26/23.40 | | % 154.26/23.40 | | Case 1: % 154.26/23.40 | | | % 154.26/23.40 | | | (29) all_56_1 = e1 % 154.26/23.40 | | | % 154.26/23.40 | | | COMBINE_EQS: (10), (29) imply: % 154.26/23.40 | | | (30) all_52_4 = e1 % 154.26/23.40 | | | % 154.26/23.40 | | | REDUCE: (13), (30) imply: % 154.26/23.40 | | | (31) $false % 154.26/23.40 | | | % 154.26/23.40 | | | CLOSE: (31) is inconsistent. % 154.26/23.40 | | | % 154.26/23.40 | | Case 2: % 154.26/23.40 | | | % 154.26/23.40 | | | (32) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 | | | % 154.26/23.40 | | | BETA: splitting (32) gives: % 154.26/23.40 | | | % 154.26/23.40 | | | Case 1: % 154.26/23.40 | | | | % 154.26/23.40 | | | | (33) all_56_3 = e1 % 154.26/23.40 | | | | % 154.26/23.40 | | | | COMBINE_EQS: (11), (33) imply: % 154.26/23.40 | | | | (34) all_8_2 = e1 % 154.26/23.40 | | | | % 154.26/23.40 | | | | COMBINE_EQS: (12), (34) imply: % 154.26/23.40 | | | | (35) all_58_29 = e1 % 154.26/23.40 | | | | % 154.26/23.40 | | | | BETA: splitting (28) gives: % 154.26/23.40 | | | | % 154.26/23.40 | | | | Case 1: % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | (36) all_56_7 = e1 % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | COMBINE_EQS: (5), (36) imply: % 154.26/23.40 | | | | | (37) e1 = e0 % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | REDUCE: (23), (37) imply: % 154.26/23.40 | | | | | (38) $false % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | CLOSE: (38) is inconsistent. % 154.26/23.40 | | | | | % 154.26/23.40 | | | | Case 2: % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | (39) all_56_8 = e1 | all_56_11 = e1 % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | BETA: splitting (39) gives: % 154.26/23.40 | | | | | % 154.26/23.40 | | | | | Case 1: % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | (40) all_56_8 = e1 % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | COMBINE_EQS: (21), (40) imply: % 154.26/23.40 | | | | | | (41) all_6_2 = e1 % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | SIMP: (41) implies: % 154.26/23.40 | | | | | | (42) all_6_2 = e1 % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | COMBINE_EQS: (24), (42) imply: % 154.26/23.40 | | | | | | (43) all_58_30 = e1 % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | REF_CLOSE: (1), (2), (3), (7), (14), (18), (20), (22), (25), (35), % 154.26/23.40 | | | | | | (43) are inconsistent by sub-proof #472. % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | Case 2: % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | (44) all_56_11 = e1 % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | | REF_CLOSE: (6), (9), (44) are inconsistent by sub-proof #580. % 154.26/23.40 | | | | | | % 154.26/23.40 | | | | | End of split % 154.26/23.40 | | | | | % 154.26/23.40 | | | | End of split % 154.26/23.40 | | | | % 154.26/23.40 | | | Case 2: % 154.26/23.40 | | | | % 154.26/23.40 | | | | (45) all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 | | | | % 154.26/23.40 | | | | REF_CLOSE: (4), (5), (16), (23), (45) are inconsistent by sub-proof % 154.26/23.40 | | | | #419. % 154.26/23.40 | | | | % 154.26/23.40 | | | End of split % 154.26/23.40 | | | % 154.26/23.40 | | End of split % 154.26/23.40 | | % 154.26/23.40 | End of split % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #419 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) ~ (all_52_7 = e1) % 154.26/23.40 (2) all_56_7 = e0 % 154.26/23.40 (3) all_56_7 = e1 | all_56_13 = e1 % 154.26/23.40 (4) all_56_13 = all_52_7 % 154.26/23.40 (5) ~ (e1 = e0) % 154.26/23.40 % 154.26/23.40 Begin of proof % 154.26/23.40 | % 154.26/23.40 | BETA: splitting (3) gives: % 154.26/23.40 | % 154.26/23.40 | Case 1: % 154.26/23.40 | | % 154.26/23.40 | | (6) all_56_7 = e1 % 154.26/23.40 | | % 154.26/23.40 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #501. % 154.26/23.40 | | % 154.26/23.40 | Case 2: % 154.26/23.40 | | % 154.26/23.40 | | (7) all_56_13 = e1 % 154.26/23.40 | | % 154.26/23.40 | | COMBINE_EQS: (4), (7) imply: % 154.26/23.40 | | (8) all_52_7 = e1 % 154.26/23.40 | | % 154.26/23.40 | | REDUCE: (1), (8) imply: % 154.26/23.40 | | (9) $false % 154.26/23.40 | | % 154.26/23.40 | | CLOSE: (9) is inconsistent. % 154.26/23.40 | | % 154.26/23.40 | End of split % 154.26/23.40 | % 154.26/23.40 End of proof % 154.26/23.40 % 154.26/23.40 Sub-proof #420 shows that the following formulas are inconsistent: % 154.26/23.40 ---------------------------------------------------------------- % 154.26/23.40 (1) all_58_31 = all_4_2 % 154.26/23.40 (2) ~ (all_52_1 = e1) % 154.26/23.40 (3) all_58_28 = e0 % 154.26/23.40 (4) all_56_7 = all_52_6 % 154.26/23.40 (5) ~ (all_52_6 = all_6_2) % 154.26/23.40 (6) ~ (all_10_1 = e0) % 154.26/23.40 (7) ~ (all_52_13 = e1) % 154.26/23.40 (8) all_58_31 = e1 % 154.26/23.40 (9) ~ (all_52_11 = all_10_1) % 154.26/23.40 (10) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.26/23.40 (11) all_58_26 = all_52_11 % 154.26/23.40 (12) all_58_6 = all_52_12 % 154.26/23.40 (13) all_58_15 = e1 % 154.26/23.40 (14) all_54_3 = all_52_12 % 154.26/23.40 (15) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.40 (16) all_54_1 = all_52_4 % 154.26/23.40 (17) ~ (all_52_4 = all_52_6) % 154.26/23.40 (18) all_58_13 = all_52_13 % 154.26/23.40 (19) all_56_12 = all_10_1 % 154.26/23.40 (20) all_58_11 = e0 % 154.26/23.40 (21) all_58_20 = e0 % 154.26/23.40 (22) ~ (all_52_6 = e1) % 154.26/23.40 (23) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.40 (24) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.26/23.40 (25) ~ (all_52_12 = all_52_13) % 154.26/23.40 (26) all_56_13 = e0 % 154.26/23.40 (27) all_56_0 = e0 % 154.26/23.40 (28) all_54_9 = all_52_6 % 154.26/23.40 (29) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.26/23.40 (30) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.26/23.40 (31) ~ (e3 = e1) % 154.26/23.40 (32) ~ (all_52_6 = e0) % 154.26/23.40 (33) all_54_14 = all_52_11 % 154.26/23.40 (34) ~ (all_52_12 = e0) % 154.26/23.40 (35) all_58_2 = all_52_4 % 154.26/23.40 (36) all_56_1 = all_52_4 % 154.26/23.40 (37) ~ (all_52_13 = e0) % 154.26/23.40 (38) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 154.26/23.40 (39) all_58_24 = e0 % 154.26/23.40 (40) ~ (all_52_1 = all_10_1) % 154.26/23.40 (41) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.26/23.40 (42) ~ (all_52_11 = e1) % 154.26/23.40 (43) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.40 (44) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.26/23.40 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.26/23.40 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.26/23.40 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.26/23.40 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.40 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.26/23.40 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.40 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.40 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.40 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.26/23.40 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.40 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.40 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.40 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.40 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.40 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.40 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.40 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.40 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.40 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.40 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.40 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.26/23.40 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.40 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.40 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.40 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.40 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.40 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.40 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.40 e0) % 154.26/23.40 (45) all_56_9 = all_52_12 % 154.26/23.40 (46) ~ (all_52_4 = e1) % 154.26/23.40 (47) all_58_8 = all_52_1 % 154.26/23.40 (48) ~ (e2 = e1) % 154.26/23.40 (49) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.26/23.40 (50) all_58_29 = e1 % 154.26/23.40 (51) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.26/23.40 (52) all_56_3 = e1 % 154.26/23.40 (53) ~ (all_52_4 = e0) % 154.26/23.40 (54) ~ (all_52_11 = all_6_2) % 154.26/23.40 (55) ~ (e3 = e0) % 154.26/23.40 (56) all_56_2 = all_52_1 % 154.26/23.40 (57) ~ (all_52_11 = e0) % 154.26/23.40 (58) all_58_22 = all_10_1 % 154.26/23.40 (59) all_56_10 = all_52_13 % 154.26/23.40 (60) ~ (all_52_12 = e1) % 154.26/23.40 (61) all_56_14 = all_52_11 % 154.26/23.40 (62) all_58_17 = all_52_6 % 154.26/23.40 (63) ~ (e2 = e0) % 154.26/23.40 (64) ~ (all_10_1 = e1) % 154.26/23.41 (65) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.26/23.41 (66) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.41 (67) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.41 (68) ~ (e1 = e0) % 154.26/23.41 (69) all_58_30 = all_6_2 % 154.26/23.41 (70) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.41 (71) all_56_11 = e0 % 154.26/23.41 (72) ~ (e3 = e2) % 154.26/23.41 (73) all_56_15 = e1 % 154.26/23.41 (74) ~ (all_52_4 = all_52_12) % 154.26/23.41 (75) all_54_4 = all_52_1 % 154.26/23.41 % 154.26/23.41 Begin of proof % 154.26/23.41 | % 154.26/23.41 | BETA: splitting (15) gives: % 154.26/23.41 | % 154.26/23.41 | Case 1: % 154.26/23.41 | | % 154.26/23.41 | | (76) all_58_28 = e2 % 154.26/23.41 | | % 154.26/23.41 | | REF_CLOSE: (3), (63), (76) are inconsistent by sub-proof #688. % 154.26/23.41 | | % 154.26/23.41 | Case 2: % 154.26/23.41 | | % 154.26/23.41 | | (77) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.41 | | % 154.26/23.41 | | BETA: splitting (77) gives: % 154.26/23.41 | | % 154.26/23.41 | | Case 1: % 154.26/23.41 | | | % 154.26/23.41 | | | (78) all_58_29 = e2 % 154.26/23.41 | | | % 154.26/23.41 | | | REF_CLOSE: (48), (50), (78) are inconsistent by sub-proof #687. % 154.26/23.41 | | | % 154.26/23.41 | | Case 2: % 154.26/23.41 | | | % 154.26/23.41 | | | (79) ~ (all_58_29 = e2) % 154.26/23.41 | | | (80) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.41 | | | % 154.26/23.41 | | | REDUCE: (50), (79) imply: % 154.26/23.41 | | | (81) ~ (e2 = e1) % 154.26/23.41 | | | % 154.26/23.41 | | | BETA: splitting (80) gives: % 154.26/23.41 | | | % 154.26/23.41 | | | Case 1: % 154.26/23.41 | | | | % 154.26/23.41 | | | | (82) all_58_30 = e2 % 154.26/23.41 | | | | % 154.26/23.41 | | | | COMBINE_EQS: (69), (82) imply: % 154.26/23.41 | | | | (83) all_6_2 = e2 % 154.26/23.41 | | | | % 154.26/23.41 | | | | REDUCE: (5), (83) imply: % 154.26/23.41 | | | | (84) ~ (all_52_6 = e2) % 154.26/23.41 | | | | % 154.26/23.41 | | | | REDUCE: (54), (83) imply: % 154.26/23.41 | | | | (85) ~ (all_52_11 = e2) % 154.26/23.41 | | | | % 154.26/23.41 | | | | BETA: splitting (65) gives: % 154.26/23.41 | | | | % 154.26/23.41 | | | | Case 1: % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | (86) all_56_1 = e2 % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | COMBINE_EQS: (36), (86) imply: % 154.26/23.41 | | | | | (87) all_52_4 = e2 % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | COMBINE_EQS: (35), (87) imply: % 154.26/23.41 | | | | | (88) all_58_2 = e2 % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | REDUCE: (17), (87) imply: % 154.26/23.41 | | | | | (89) ~ (all_52_6 = e2) % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | REDUCE: (74), (87) imply: % 154.26/23.41 | | | | | (90) ~ (all_52_12 = e2) % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | SIMP: (90) implies: % 154.26/23.41 | | | | | (91) ~ (all_52_12 = e2) % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | BETA: splitting (30) gives: % 154.26/23.41 | | | | | % 154.26/23.41 | | | | | Case 1: % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | | (92) all_56_1 = e3 % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | | REF_CLOSE: (72), (86), (92) are inconsistent by sub-proof #568. % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | Case 2: % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | | (93) ~ (all_56_1 = e3) % 154.26/23.41 | | | | | | (94) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | | REDUCE: (86), (93) imply: % 154.26/23.41 | | | | | | (95) ~ (e3 = e2) % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | | BETA: splitting (10) gives: % 154.26/23.41 | | | | | | % 154.26/23.41 | | | | | | Case 1: % 154.26/23.41 | | | | | | | % 154.26/23.41 | | | | | | | (96) all_56_9 = e2 % 154.26/23.41 | | | | | | | % 154.26/23.41 | | | | | | | REF_CLOSE: (45), (91), (96) are inconsistent by sub-proof #431. % 154.26/23.41 | | | | | | | % 154.26/23.41 | | | | | | Case 2: % 154.26/23.41 | | | | | | | % 154.26/23.41 | | | | | | | (97) ~ (all_56_9 = e2) % 154.26/23.41 | | | | | | | (98) all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.26/23.41 | | | | | | | % 154.26/23.41 | | | | | | | BETA: splitting (66) gives: % 154.26/23.41 | | | | | | | % 154.26/23.41 | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | (99) all_56_12 = e2 % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | COMBINE_EQS: (19), (99) imply: % 154.26/23.41 | | | | | | | | (100) all_10_1 = e2 % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | SIMP: (100) implies: % 154.26/23.41 | | | | | | | | (101) all_10_1 = e2 % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | COMBINE_EQS: (58), (101) imply: % 154.26/23.41 | | | | | | | | (102) all_58_22 = e2 % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | REDUCE: (40), (101) imply: % 154.26/23.41 | | | | | | | | (103) ~ (all_52_1 = e2) % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | BETA: splitting (43) gives: % 154.26/23.41 | | | | | | | | % 154.26/23.41 | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | (104) all_56_12 = e3 % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | COMBINE_EQS: (99), (104) imply: % 154.26/23.41 | | | | | | | | | (105) e3 = e2 % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | REDUCE: (72), (105) imply: % 154.26/23.41 | | | | | | | | | (106) $false % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | CLOSE: (106) is inconsistent. % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | (107) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | BETA: splitting (38) gives: % 154.26/23.41 | | | | | | | | | % 154.26/23.41 | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | (108) all_56_0 = e3 % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | REF_CLOSE: (27), (55), (108) are inconsistent by sub-proof % 154.26/23.41 | | | | | | | | | | #430. % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | (109) ~ (all_56_0 = e3) % 154.26/23.41 | | | | | | | | | | (110) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | REDUCE: (27), (109) imply: % 154.26/23.41 | | | | | | | | | | (111) ~ (e3 = e0) % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | BETA: splitting (67) gives: % 154.26/23.41 | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | (112) all_58_28 = e3 % 154.26/23.41 | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | REF_CLOSE: (3), (55), (112) are inconsistent by sub-proof % 154.26/23.41 | | | | | | | | | | | #689. % 154.26/23.41 | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | (113) ~ (all_58_28 = e3) % 154.26/23.41 | | | | | | | | | | | (114) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.41 | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | BETA: splitting (49) gives: % 154.26/23.41 | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | (115) all_54_14 = e1 % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | COMBINE_EQS: (33), (115) imply: % 154.26/23.41 | | | | | | | | | | | | (116) all_52_11 = e1 % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | REDUCE: (42), (116) imply: % 154.26/23.41 | | | | | | | | | | | | (117) $false % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | CLOSE: (117) is inconsistent. % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | (118) ~ (all_54_14 = e1) % 154.26/23.41 | | | | | | | | | | | | (119) all_54_14 = e3 | all_54_14 = e2 % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | BETA: splitting (107) gives: % 154.26/23.41 | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | (120) all_56_13 = e3 % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | COMBINE_EQS: (26), (120) imply: % 154.26/23.41 | | | | | | | | | | | | | (121) e3 = e0 % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | REDUCE: (55), (121) imply: % 154.26/23.41 | | | | | | | | | | | | | (122) $false % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | CLOSE: (122) is inconsistent. % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | (123) all_56_14 = e3 | all_56_15 = e3 % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.26/23.41 | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | (124) all_54_14 = e2 % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | COMBINE_EQS: (33), (124) imply: % 154.26/23.41 | | | | | | | | | | | | | | (125) all_52_11 = e2 % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | REDUCE: (85), (125) imply: % 154.26/23.41 | | | | | | | | | | | | | | (126) $false % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | (127) all_54_14 = e3 % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | COMBINE_EQS: (33), (127) imply: % 154.26/23.41 | | | | | | | | | | | | | | (128) all_52_11 = e3 % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | COMBINE_EQS: (61), (128) imply: % 154.26/23.41 | | | | | | | | | | | | | | (129) all_56_14 = e3 % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | COMBINE_EQS: (11), (128) imply: % 154.26/23.41 | | | | | | | | | | | | | | (130) all_58_26 = e3 % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | BETA: splitting (44) gives: % 154.26/23.41 | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | (131) all_58_31 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | COMBINE_EQS: (8), (131) imply: % 154.26/23.41 | | | | | | | | | | | | | | | (132) e1 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | COMBINE_EQS: (50), (132) imply: % 154.26/23.41 | | | | | | | | | | | | | | | (133) all_58_29 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | REF_CLOSE: (15), (31), (48), (55), (63), (67), (68), (69), % 154.26/23.41 | | | | | | | | | | | | | | | (70), (72), (131), (133) are inconsistent by % 154.26/23.41 | | | | | | | | | | | | | | | sub-proof #844. % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | (134) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.26/23.41 | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.41 | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.41 | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.41 | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.41 | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.41 | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.41 | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.41 | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.41 | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.41 | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.41 | | | | | | | | | | | | | | | e0) % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | BETA: splitting (114) gives: % 154.26/23.41 | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | (135) all_58_29 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | REF_CLOSE: (31), (50), (135) are inconsistent by sub-proof % 154.26/23.41 | | | | | | | | | | | | | | | | #686. % 154.26/23.41 | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | (136) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | BETA: splitting (110) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | (137) all_56_2 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (137) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | (138) all_52_1 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (138) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | (139) all_58_8 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | (140) all_56_9 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (140) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | (141) all_52_12 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | SIMP: (141) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | (142) all_52_12 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (142) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | (143) all_58_6 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | REDUCE: (25), (142) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | (144) ~ (all_52_13 = e3) % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | SIMP: (144) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | (145) ~ (all_52_13 = e3) % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | (146) all_56_3 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (52), (146) are inconsistent by sub-proof % 154.26/23.41 | | | | | | | | | | | | | | | | | | | #449. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | (147) ~ (all_56_3 = e3) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | (148) all_56_7 = e3 | all_56_13 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | REDUCE: (52), (147) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | (149) ~ (e3 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | (150) all_56_7 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (150) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | (151) all_52_6 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | SIMP: (151) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | (152) all_52_6 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (152) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | (153) all_58_17 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | (154) all_58_30 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (31), (48), (50), (72), (77), (114), (154) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #473. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | (155) ~ (all_58_30 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | (156) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (157) all_58_29 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (157) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (158) e2 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | SIMP: (158) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (159) e2 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (159) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (160) all_58_30 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (31), (48), (50), (72), (77), (114), (160) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #473. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (161) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | (162) all_56_10 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (162) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | (163) all_52_13 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (163) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | (164) all_52_13 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (164) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | (165) all_58_13 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | (166) all_58_28 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (166) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | (167) e3 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (55), (73), (123), (129), (167) are % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | (168) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (170) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_58_2 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (173) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (174) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (175) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) $false % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_58_6 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_58_2 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (180) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (181) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (179) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) e3 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (183) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) e2 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (184) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_58_30 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (136), (185) are % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #704. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_58_11 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (187) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) e2 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (188) are % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_24 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (55), (63), (72), (80), (82), (136), (192) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_58_15 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_8 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (195) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (194) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) e3 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (198) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) e2 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (199) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_30 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (31), (48), (50), (72), (77), (114), (200) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #473. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_58_22 = e3 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (203) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (204) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) $false % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_11 = e1 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (207) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) e1 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (208) are inconsistent by sub-proof #426. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (209) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_13 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (213) imply: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) e2 = e0 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (214) are % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_8 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (216) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) e3 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (217) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) $false % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_15 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_6 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (222) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (221) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (223), (224) are inconsistent by sub-proof % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_11 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (226) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (227) are inconsistent by sub-proof #426. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_20 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (231) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (232) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_29 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (63), (69), (72), (77), (136), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) are inconsistent by sub-proof #655. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_58_22 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (235) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) e3 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (236) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) $false % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_58_11 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (240) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) e2 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (241) are % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (243) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (55), (73), (123), (129), (244) are % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (245) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (249) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) $false % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_13 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (165), (253) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #424. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_22 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (256) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) e3 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (255) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (258) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (259) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) e2 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (260) are % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (55), (63), (72), (80), (82), (136), (264) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_58_26 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_6 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (267) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (266) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (269) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (268), (270) are inconsistent by sub-proof % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_22 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (273) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) e2 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (274) are % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_58_13 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (165), (276) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #424. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_26 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_58_17 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_11 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (283) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) e2 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) e2 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (282) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) e3 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (281) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (287) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (288) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) e2 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (289) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) e2 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (290) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (291) are inconsistent by sub-proof #426. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_58_11 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (293) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (294) are inconsistent by sub-proof #426. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_58_17 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (298) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) e3 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (297) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (299), (301) are inconsistent by sub-proof % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_11 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (303) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (304) are inconsistent by sub-proof #426. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_24 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (55), (63), (72), (80), (82), (136), (308) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_20 = e1 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (310) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (50), (63), (69), (72), (77), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (136), (311) are inconsistent by sub-proof #426. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_58_13 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (63), (72), (80), (82), (136), (165), (314) % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #424. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) e1 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (316) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_29 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (48), (63), (69), (72), (77), (136), % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) are inconsistent by sub-proof #655. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | (318) all_56_11 = e2 | all_56_15 = e2 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (63), (71), (73), (318) are inconsistent by % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #423. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | (319) all_56_13 = e3 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (319) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | (320) e3 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (320) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | (321) all_56_14 = e0 % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (55), (73), (123), (321) are inconsistent by % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | sub-proof #434. % 154.26/23.42 | | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | (322) ~ (all_56_9 = e3) % 154.26/23.42 | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | REDUCE: (45), (322) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | | (323) ~ (all_52_12 = e3) % 154.26/23.42 | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (41), (60), (91), (323) are inconsistent by % 154.26/23.42 | | | | | | | | | | | | | | | | | | sub-proof #612. % 154.26/23.42 | | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | (324) ~ (all_56_2 = e3) % 154.26/23.42 | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | REDUCE: (56), (324) imply: % 154.26/23.42 | | | | | | | | | | | | | | | | | (325) ~ (all_52_1 = e3) % 154.26/23.42 | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (24), (75), (103), (325) are inconsistent by % 154.26/23.42 | | | | | | | | | | | | | | | | | sub-proof #828. % 154.26/23.42 | | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | End of split % 154.26/23.42 | | | | | | | | % 154.26/23.42 | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | % 154.26/23.42 | | | | | | | | (326) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.42 | | | | | | | | % 154.26/23.42 | | | | | | | | BETA: splitting (326) gives: % 154.26/23.42 | | | | | | | | % 154.26/23.42 | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | (327) all_56_13 = e2 % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | COMBINE_EQS: (26), (327) imply: % 154.26/23.42 | | | | | | | | | (328) e2 = e0 % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | COMBINE_EQS: (82), (328) imply: % 154.26/23.42 | | | | | | | | | (329) all_58_30 = e0 % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | REF_CLOSE: (8), (48), (63), (80), (329) are inconsistent by % 154.26/23.42 | | | | | | | | | sub-proof #675. % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | (330) all_56_14 = e2 | all_56_15 = e2 % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | BETA: splitting (67) gives: % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | (331) all_58_28 = e3 % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | REF_CLOSE: (3), (55), (331) are inconsistent by sub-proof % 154.26/23.42 | | | | | | | | | | #689. % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | (332) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | BETA: splitting (330) gives: % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | Case 1: % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | (333) all_56_14 = e2 % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | REF_CLOSE: (61), (85), (333) are inconsistent by sub-proof % 154.26/23.42 | | | | | | | | | | | #422. % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | Case 2: % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | (334) all_56_15 = e2 % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | COMBINE_EQS: (73), (334) imply: % 154.26/23.42 | | | | | | | | | | | (335) e2 = e1 % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | COMBINE_EQS: (82), (335) imply: % 154.26/23.42 | | | | | | | | | | | (336) all_58_30 = e1 % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | | REF_CLOSE: (1), (31), (48), (50), (72), (77), (332), (336) % 154.26/23.42 | | | | | | | | | | | are inconsistent by sub-proof #473. % 154.26/23.42 | | | | | | | | | | | % 154.26/23.42 | | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | | % 154.26/23.42 | | | | | | | | | End of split % 154.26/23.42 | | | | | | | | | % 154.26/23.42 | | | | | | | | End of split % 154.26/23.42 | | | | | | | | % 154.26/23.42 | | | | | | | End of split % 154.26/23.42 | | | | | | | % 154.26/23.42 | | | | | | End of split % 154.26/23.42 | | | | | | % 154.26/23.42 | | | | | End of split % 154.26/23.42 | | | | | % 154.26/23.42 | | | | Case 2: % 154.26/23.42 | | | | | % 154.26/23.42 | | | | | (337) ~ (all_56_1 = e2) % 154.26/23.42 | | | | | % 154.26/23.42 | | | | | REDUCE: (36), (337) imply: % 154.26/23.42 | | | | | (338) ~ (all_52_4 = e2) % 154.26/23.42 | | | | | % 154.26/23.42 | | | | | REF_CLOSE: (16), (17), (22), (23), (28), (29), (46), (84), (338) are % 154.26/23.42 | | | | | inconsistent by sub-proof #421. % 154.26/23.42 | | | | | % 154.26/23.42 | | | | End of split % 154.26/23.42 | | | | % 154.26/23.42 | | | Case 2: % 154.26/23.42 | | | | % 154.26/23.42 | | | | (339) all_58_31 = e2 % 154.26/23.42 | | | | % 154.26/23.42 | | | | REF_CLOSE: (8), (48), (339) are inconsistent by sub-proof #697. % 154.26/23.42 | | | | % 154.26/23.42 | | | End of split % 154.26/23.42 | | | % 154.26/23.42 | | End of split % 154.26/23.42 | | % 154.26/23.42 | End of split % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #421 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) ~ (all_52_6 = e2) % 154.26/23.42 (2) all_54_1 = all_52_4 % 154.26/23.42 (3) ~ (all_52_4 = all_52_6) % 154.26/23.42 (4) ~ (all_52_6 = e1) % 154.26/23.42 (5) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.26/23.42 (6) all_54_9 = all_52_6 % 154.26/23.42 (7) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.26/23.42 (8) ~ (all_52_4 = e2) % 154.26/23.42 (9) ~ (all_52_4 = e1) % 154.26/23.42 % 154.26/23.42 Begin of proof % 154.26/23.42 | % 154.26/23.42 | BETA: splitting (7) gives: % 154.26/23.42 | % 154.26/23.42 | Case 1: % 154.26/23.42 | | % 154.26/23.42 | | (10) all_54_9 = e1 % 154.26/23.42 | | % 154.26/23.42 | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #622. % 154.26/23.42 | | % 154.26/23.42 | Case 2: % 154.26/23.42 | | % 154.26/23.42 | | (11) all_54_9 = e3 | all_54_9 = e2 % 154.26/23.42 | | % 154.26/23.42 | | BETA: splitting (5) gives: % 154.26/23.42 | | % 154.26/23.42 | | Case 1: % 154.26/23.42 | | | % 154.26/23.42 | | | (12) all_54_1 = e1 % 154.26/23.42 | | | % 154.26/23.42 | | | REF_CLOSE: (2), (9), (12) are inconsistent by sub-proof #741. % 154.26/23.42 | | | % 154.26/23.42 | | Case 2: % 154.26/23.42 | | | % 154.26/23.42 | | | (13) all_54_1 = e3 | all_54_1 = e2 % 154.26/23.42 | | | % 154.26/23.42 | | | BETA: splitting (11) gives: % 154.26/23.42 | | | % 154.26/23.42 | | | Case 1: % 154.26/23.42 | | | | % 154.26/23.42 | | | | (14) all_54_9 = e2 % 154.26/23.42 | | | | % 154.26/23.42 | | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #621. % 154.26/23.42 | | | | % 154.26/23.42 | | | Case 2: % 154.26/23.42 | | | | % 154.26/23.42 | | | | (15) all_54_9 = e3 % 154.26/23.42 | | | | % 154.26/23.42 | | | | COMBINE_EQS: (6), (15) imply: % 154.26/23.42 | | | | (16) all_52_6 = e3 % 154.26/23.42 | | | | % 154.26/23.42 | | | | SIMP: (16) implies: % 154.26/23.42 | | | | (17) all_52_6 = e3 % 154.26/23.42 | | | | % 154.26/23.42 | | | | REDUCE: (3), (17) imply: % 154.26/23.42 | | | | (18) ~ (all_52_4 = e3) % 154.26/23.42 | | | | % 154.26/23.42 | | | | REF_CLOSE: (2), (8), (13), (18) are inconsistent by sub-proof #722. % 154.26/23.42 | | | | % 154.26/23.42 | | | End of split % 154.26/23.42 | | | % 154.26/23.42 | | End of split % 154.26/23.42 | | % 154.26/23.42 | End of split % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #422 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) all_56_14 = all_52_11 % 154.26/23.42 (2) all_56_14 = e2 % 154.26/23.42 (3) ~ (all_52_11 = e2) % 154.26/23.42 % 154.26/23.42 Begin of proof % 154.26/23.42 | % 154.26/23.42 | COMBINE_EQS: (1), (2) imply: % 154.26/23.42 | (4) all_52_11 = e2 % 154.26/23.42 | % 154.26/23.42 | SIMP: (4) implies: % 154.26/23.42 | (5) all_52_11 = e2 % 154.26/23.42 | % 154.26/23.42 | REDUCE: (3), (5) imply: % 154.26/23.42 | (6) $false % 154.26/23.42 | % 154.26/23.42 | CLOSE: (6) is inconsistent. % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #423 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) all_56_11 = e2 | all_56_15 = e2 % 154.26/23.42 (2) ~ (e2 = e1) % 154.26/23.42 (3) ~ (e2 = e0) % 154.26/23.42 (4) all_56_11 = e0 % 154.26/23.42 (5) all_56_15 = e1 % 154.26/23.42 % 154.26/23.42 Begin of proof % 154.26/23.42 | % 154.26/23.42 | BETA: splitting (1) gives: % 154.26/23.42 | % 154.26/23.42 | Case 1: % 154.26/23.42 | | % 154.26/23.42 | | (6) all_56_11 = e2 % 154.26/23.42 | | % 154.26/23.42 | | COMBINE_EQS: (4), (6) imply: % 154.26/23.42 | | (7) e2 = e0 % 154.26/23.42 | | % 154.26/23.42 | | REDUCE: (3), (7) imply: % 154.26/23.42 | | (8) $false % 154.26/23.42 | | % 154.26/23.42 | | CLOSE: (8) is inconsistent. % 154.26/23.42 | | % 154.26/23.42 | Case 2: % 154.26/23.42 | | % 154.26/23.42 | | (9) all_56_15 = e2 % 154.26/23.42 | | % 154.26/23.42 | | COMBINE_EQS: (5), (9) imply: % 154.26/23.42 | | (10) e2 = e1 % 154.26/23.42 | | % 154.26/23.42 | | REDUCE: (2), (10) imply: % 154.26/23.42 | | (11) $false % 154.26/23.42 | | % 154.26/23.42 | | CLOSE: (11) is inconsistent. % 154.26/23.42 | | % 154.26/23.42 | End of split % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #424 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) all_58_13 = e0 % 154.26/23.42 (2) all_58_30 = e2 % 154.26/23.42 (3) ~ (e3 = e0) % 154.26/23.42 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.42 (5) all_58_13 = e2 % 154.26/23.42 (6) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.42 (7) ~ (e2 = e0) % 154.26/23.42 (8) ~ (e3 = e2) % 154.26/23.42 % 154.26/23.42 Begin of proof % 154.26/23.42 | % 154.26/23.42 | COMBINE_EQS: (1), (5) imply: % 154.26/23.42 | (9) e2 = e0 % 154.26/23.42 | % 154.26/23.42 | COMBINE_EQS: (2), (9) imply: % 154.26/23.42 | (10) all_58_30 = e0 % 154.26/23.42 | % 154.26/23.42 | REF_CLOSE: (3), (4), (6), (7), (8), (10) are inconsistent by sub-proof #704. % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #425 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) all_58_31 = e1 % 154.26/23.42 (2) ~ (e3 = e1) % 154.26/23.42 (3) e3 = e1 % 154.26/23.42 (4) ~ (e2 = e1) % 154.26/23.42 (5) all_58_29 = e1 % 154.26/23.42 (6) e3 = e0 % 154.26/23.42 (7) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.42 (8) ~ (e2 = e0) % 154.26/23.42 (9) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.42 (10) all_58_30 = all_6_2 % 154.26/23.42 (11) ~ (e3 = e2) % 154.26/23.42 % 154.26/23.42 Begin of proof % 154.26/23.42 | % 154.26/23.42 | COMBINE_EQS: (3), (6) imply: % 154.26/23.42 | (12) e1 = e0 % 154.26/23.42 | % 154.26/23.42 | COMBINE_EQS: (5), (12) imply: % 154.26/23.42 | (13) all_58_29 = e0 % 154.26/23.42 | % 154.26/23.42 | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (13) are inconsistent by % 154.26/23.42 | sub-proof #655. % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #426 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) all_58_31 = e1 % 154.26/23.42 (2) ~ (e3 = e1) % 154.26/23.42 (3) ~ (e2 = e1) % 154.26/23.42 (4) all_58_29 = e1 % 154.26/23.42 (5) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.42 (6) ~ (e2 = e0) % 154.26/23.42 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.42 (8) e1 = e0 % 154.26/23.42 (9) all_58_30 = all_6_2 % 154.26/23.42 (10) ~ (e3 = e2) % 154.26/23.42 % 154.26/23.42 Begin of proof % 154.26/23.42 | % 154.26/23.42 | SIMP: (8) implies: % 154.26/23.42 | (11) e1 = e0 % 154.26/23.42 | % 154.26/23.42 | COMBINE_EQS: (4), (11) imply: % 154.26/23.42 | (12) all_58_29 = e0 % 154.26/23.42 | % 154.26/23.42 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (12) are inconsistent by % 154.26/23.42 | sub-proof #655. % 154.26/23.42 | % 154.26/23.42 End of proof % 154.26/23.42 % 154.26/23.42 Sub-proof #427 shows that the following formulas are inconsistent: % 154.26/23.42 ---------------------------------------------------------------- % 154.26/23.42 (1) all_58_30 = e2 % 154.26/23.42 (2) all_58_24 = e0 % 154.26/23.42 (3) ~ (e3 = e0) % 154.26/23.42 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.42 (5) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.42 (6) ~ (e2 = e0) % 154.26/23.43 (7) all_58_24 = e2 % 154.26/23.43 (8) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (7) imply: % 154.26/23.43 | (9) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (9) imply: % 154.26/23.43 | (10) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (3), (4), (5), (6), (8), (10) are inconsistent by sub-proof #704. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #428 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) e2 = e0 % 154.26/23.43 (2) all_58_30 = e2 % 154.26/23.43 (3) ~ (e3 = e0) % 154.26/23.43 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (5) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (6) ~ (e2 = e0) % 154.26/23.43 (7) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | SIMP: (1) implies: % 154.26/23.43 | (8) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (8) imply: % 154.26/23.43 | (9) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (3), (4), (5), (6), (7), (9) are inconsistent by sub-proof #704. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #429 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_14 = e3 % 154.26/23.43 (2) all_56_14 = e3 | all_56_15 = e3 % 154.26/23.43 (3) ~ (e3 = e1) % 154.26/23.43 (4) ~ (e3 = e0) % 154.26/23.43 (5) e3 = e0 % 154.26/23.43 (6) all_56_15 = e1 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | SIMP: (5) implies: % 154.26/23.43 | (7) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (7) imply: % 154.26/23.43 | (8) all_56_14 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (2), (3), (4), (6), (8) are inconsistent by sub-proof #434. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #430 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_0 = e3 % 154.26/23.43 (2) all_56_0 = e0 % 154.26/23.43 (3) ~ (e3 = e0) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (2) imply: % 154.26/23.43 | (4) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | SIMP: (4) implies: % 154.26/23.43 | (5) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | REDUCE: (3), (5) imply: % 154.26/23.43 | (6) $false % 154.26/23.43 | % 154.26/23.43 | CLOSE: (6) is inconsistent. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #431 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_9 = all_52_12 % 154.26/23.43 (2) all_56_9 = e2 % 154.26/23.43 (3) ~ (all_52_12 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (2) imply: % 154.26/23.43 | (4) all_52_12 = e2 % 154.26/23.43 | % 154.26/23.43 | SIMP: (4) implies: % 154.26/23.43 | (5) all_52_12 = e2 % 154.26/23.43 | % 154.26/23.43 | REDUCE: (3), (5) imply: % 154.26/23.43 | (6) $false % 154.26/23.43 | % 154.26/23.43 | CLOSE: (6) is inconsistent. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #432 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) ~ (e3 = e1) % 154.26/23.43 (3) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (4) ~ (all_6_2 = e3) % 154.26/23.43 (5) all_58_30 = all_6_2 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (3) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (6) all_58_30 = e3 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (5), (6) imply: % 154.26/23.43 | | (7) all_6_2 = e3 % 154.26/23.43 | | % 154.26/23.43 | | REDUCE: (4), (7) imply: % 154.26/23.43 | | (8) $false % 154.26/23.43 | | % 154.26/23.43 | | CLOSE: (8) is inconsistent. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (9) all_58_31 = e3 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #656. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #433 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_14 = e0 % 154.26/23.43 (2) all_56_13 = e2 % 154.26/23.43 (3) ~ (e3 = e1) % 154.26/23.43 (4) ~ (e3 = e0) % 154.26/23.43 (5) ~ (e3 = e2) % 154.26/23.43 (6) all_56_15 = e1 % 154.26/23.43 (7) all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (7) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (8) all_56_13 = e3 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (2), (8) imply: % 154.26/23.43 | | (9) e3 = e2 % 154.26/23.43 | | % 154.26/23.43 | | REDUCE: (5), (9) imply: % 154.26/23.43 | | (10) $false % 154.26/23.43 | | % 154.26/23.43 | | CLOSE: (10) is inconsistent. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (11) all_56_14 = e3 | all_56_15 = e3 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (1), (3), (4), (6), (11) are inconsistent by sub-proof #434. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #434 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_14 = e0 % 154.26/23.43 (2) all_56_14 = e3 | all_56_15 = e3 % 154.26/23.43 (3) ~ (e3 = e1) % 154.26/23.43 (4) ~ (e3 = e0) % 154.26/23.43 (5) all_56_15 = e1 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (2) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (6) all_56_14 = e3 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (1), (6) imply: % 154.26/23.43 | | (7) e3 = e0 % 154.26/23.43 | | % 154.26/23.43 | | REDUCE: (4), (7) imply: % 154.26/23.43 | | (8) $false % 154.26/23.43 | | % 154.26/23.43 | | CLOSE: (8) is inconsistent. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (9) all_56_15 = e3 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (5), (9) imply: % 154.26/23.43 | | (10) e3 = e1 % 154.26/23.43 | | % 154.26/23.43 | | REDUCE: (3), (10) imply: % 154.26/23.43 | | (11) $false % 154.26/23.43 | | % 154.26/23.43 | | CLOSE: (11) is inconsistent. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #435 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) ~ (e2 = e1) % 154.26/23.43 (3) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) ~ (all_6_2 = e2) % 154.26/23.43 (5) all_58_30 = all_6_2 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (3) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (6) all_58_30 = e2 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (5), (6) imply: % 154.26/23.43 | | (7) all_6_2 = e2 % 154.26/23.43 | | % 154.26/23.43 | | REDUCE: (4), (7) imply: % 154.26/23.43 | | (8) $false % 154.26/23.43 | | % 154.26/23.43 | | CLOSE: (8) is inconsistent. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (9) all_58_31 = e2 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #697. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #436 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_58_30 = e2 % 154.26/23.43 (3) ~ (e2 = e1) % 154.26/23.43 (4) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.43 (5) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (6) ~ (e2 = e0) % 154.26/23.43 (7) all_58_24 = e2 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | ALPHA: (4) implies: % 154.26/23.43 | (8) all_58_24 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (7), (8) imply: % 154.26/23.43 | (9) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (9) imply: % 154.26/23.43 | (10) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #675. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #437 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_58_13 = e0 % 154.26/23.43 (3) all_58_30 = e2 % 154.26/23.43 (4) ~ (e2 = e1) % 154.26/23.43 (5) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (6) all_58_13 = e2 % 154.26/23.43 (7) ~ (e2 = e0) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (6) imply: % 154.26/23.43 | (8) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | SIMP: (8) implies: % 154.26/23.43 | (9) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (3), (9) imply: % 154.26/23.43 | (10) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (4), (5), (7), (10) are inconsistent by sub-proof #675. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #438 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_58_30 = e2 % 154.26/23.43 (3) ~ (e2 = e1) % 154.26/23.43 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (5) ~ (e2 = e0) % 154.26/23.43 (6) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0 % 154.26/23.43 (7) all_58_24 = e2 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | ALPHA: (6) implies: % 154.26/23.43 | (8) all_58_24 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (7), (8) imply: % 154.26/23.43 | (9) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (9) imply: % 154.26/23.43 | (10) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #675. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #439 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_28 = e0 % 154.26/23.43 (2) all_58_22 = e0 % 154.26/23.43 (3) all_58_31 = e1 % 154.26/23.43 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (5) ~ (e3 = e1) % 154.26/23.43 (6) all_58_29 = e3 % 154.26/23.43 (7) ~ (e2 = e1) % 154.26/23.43 (8) ~ (e3 = e0) % 154.26/23.43 (9) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (10) ~ (e2 = e0) % 154.26/23.43 (11) all_58_30 = all_6_2 % 154.26/23.43 (12) ~ (e3 = e2) % 154.26/23.43 (13) all_58_22 = e3 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (13) imply: % 154.26/23.43 | (14) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | SIMP: (14) implies: % 154.26/23.43 | (15) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (6), (15) imply: % 154.26/23.43 | (16) all_58_29 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (16) are % 154.26/23.43 | inconsistent by sub-proof #654. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #440 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_28 = e0 % 154.26/23.43 (2) all_58_31 = e1 % 154.26/23.43 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) all_58_20 = e0 % 154.26/23.43 (5) ~ (e3 = e1) % 154.26/23.43 (6) all_58_29 = e3 % 154.26/23.43 (7) ~ (e2 = e1) % 154.26/23.43 (8) ~ (e3 = e0) % 154.26/23.43 (9) all_58_20 = e3 % 154.26/23.43 (10) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (11) ~ (e2 = e0) % 154.26/23.43 (12) all_58_30 = all_6_2 % 154.26/23.43 (13) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (4), (9) imply: % 154.26/23.43 | (14) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | SIMP: (14) implies: % 154.26/23.43 | (15) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (6), (15) imply: % 154.26/23.43 | (16) all_58_29 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (13), (16) are % 154.26/23.43 | inconsistent by sub-proof #654. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #441 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_28 = e0 % 154.26/23.43 (2) all_58_31 = e1 % 154.26/23.43 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) ~ (e3 = e1) % 154.26/23.43 (5) all_58_26 = e1 % 154.26/23.43 (6) all_58_29 = e3 % 154.26/23.43 (7) ~ (e2 = e1) % 154.26/23.43 (8) all_58_26 = e0 % 154.26/23.43 (9) ~ (e3 = e0) % 154.26/23.43 (10) all_58_20 = e3 % 154.26/23.43 (11) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (12) ~ (e2 = e0) % 154.26/23.43 (13) all_58_20 = e1 % 154.26/23.43 (14) all_58_30 = all_6_2 % 154.26/23.43 (15) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (10), (13) imply: % 154.26/23.43 | (16) e3 = e1 % 154.26/23.43 | % 154.26/23.43 | SIMP: (16) implies: % 154.26/23.43 | (17) e3 = e1 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (5), (8) imply: % 154.26/23.43 | (18) e1 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (12), (14), (15), (17), % 154.26/23.43 | (18) are inconsistent by sub-proof #442. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #442 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_28 = e0 % 154.26/23.43 (2) all_58_31 = e1 % 154.26/23.43 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) ~ (e3 = e1) % 154.26/23.43 (5) e3 = e1 % 154.26/23.43 (6) all_58_29 = e3 % 154.26/23.43 (7) ~ (e2 = e1) % 154.26/23.43 (8) ~ (e3 = e0) % 154.26/23.43 (9) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (10) ~ (e2 = e0) % 154.26/23.43 (11) e1 = e0 % 154.26/23.43 (12) all_58_30 = all_6_2 % 154.26/23.43 (13) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | SIMP: (11) implies: % 154.26/23.43 | (14) e1 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (5), (14) imply: % 154.26/23.43 | (15) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (6), (15) imply: % 154.26/23.43 | (16) all_58_29 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (16) are % 154.26/23.43 | inconsistent by sub-proof #654. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #443 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_28 = e0 % 154.26/23.43 (2) all_58_22 = e0 % 154.26/23.43 (3) all_58_31 = e1 % 154.26/23.43 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (5) ~ (e3 = e1) % 154.26/23.43 (6) e3 = e1 % 154.26/23.43 (7) all_58_29 = e3 % 154.26/23.43 (8) ~ (e2 = e1) % 154.26/23.43 (9) ~ (e3 = e0) % 154.26/23.43 (10) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (11) ~ (e2 = e0) % 154.26/23.43 (12) all_58_30 = all_6_2 % 154.26/23.43 (13) ~ (e3 = e2) % 154.26/23.43 (14) all_58_22 = e3 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (14) imply: % 154.26/23.43 | (15) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | SIMP: (15) implies: % 154.26/23.43 | (16) e3 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (6), (16) imply: % 154.26/23.43 | (17) e1 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (7), (16) imply: % 154.26/23.43 | (18) all_58_29 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (12), (13), (18) are % 154.26/23.43 | inconsistent by sub-proof #654. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #444 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_58_30 = e2 % 154.26/23.43 (3) ~ (e2 = e1) % 154.26/23.43 (4) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (5) ~ (e2 = e0) % 154.26/23.43 (6) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0 % 154.26/23.43 (7) all_58_24 = e2 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | ALPHA: (6) implies: % 154.26/23.43 | (8) all_58_24 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (7), (8) imply: % 154.26/23.43 | (9) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (9) imply: % 154.26/23.43 | (10) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #675. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #445 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_58_17 = e0 % 154.26/23.43 (3) all_58_30 = e2 % 154.26/23.43 (4) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1 % 154.26/23.43 (5) ~ (e2 = e1) % 154.26/23.43 (6) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (7) ~ (e2 = e0) % 154.26/23.43 (8) all_58_2 = e1 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | ALPHA: (4) implies: % 154.26/23.43 | (9) all_58_17 = e1 % 154.26/23.43 | (10) all_58_2 = e2 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (8), (10) imply: % 154.26/23.43 | (11) e2 = e1 % 154.26/23.43 | % 154.26/23.43 | SIMP: (11) implies: % 154.26/23.43 | (12) e2 = e1 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (12) are inconsistent by % 154.26/23.43 | sub-proof #446. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #446 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_58_17 = e0 % 154.26/23.43 (3) all_58_30 = e2 % 154.26/23.43 (4) ~ (e2 = e1) % 154.26/23.43 (5) e2 = e1 % 154.26/23.43 (6) all_58_17 = e1 % 154.26/23.43 (7) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (8) ~ (e2 = e0) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (2), (6) imply: % 154.26/23.43 | (9) e1 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (5), (9) imply: % 154.26/23.43 | (10) e2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (3), (10) imply: % 154.26/23.43 | (11) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (4), (7), (8), (11) are inconsistent by sub-proof #675. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #447 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = all_4_2 % 154.26/23.43 (2) all_58_28 = e0 % 154.26/23.43 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) all_58_30 = e2 % 154.26/23.43 (5) ~ (e3 = e1) % 154.26/23.43 (6) e3 = e1 % 154.26/23.43 (7) all_58_29 = e3 % 154.26/23.43 (8) ~ (e2 = e1) % 154.26/23.43 (9) e2 = e1 % 154.26/23.43 (10) ~ (e3 = e0) % 154.26/23.43 (11) ~ (e2 = e0) % 154.26/23.43 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (13) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (4), (9) imply: % 154.26/23.43 | (14) all_58_30 = e1 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (6), (7) imply: % 154.26/23.43 | (15) all_58_29 = e1 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (2), (3), (5), (8), (10), (11), (12), (13), (14), (15) are % 154.26/23.43 | inconsistent by sub-proof #472. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #448 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (2) all_58_30 = e1 % 154.26/23.43 (3) ~ (e2 = e1) % 154.26/23.43 (4) all_58_31 = e1 % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (1) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (5) all_58_30 = e2 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #500. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (6) all_58_31 = e2 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #697. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #449 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_3 = e3 % 154.26/23.43 (2) all_56_3 = e1 % 154.26/23.43 (3) ~ (e3 = e1) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (2) imply: % 154.26/23.43 | (4) e3 = e1 % 154.26/23.43 | % 154.26/23.43 | SIMP: (4) implies: % 154.26/23.43 | (5) e3 = e1 % 154.26/23.43 | % 154.26/23.43 | REDUCE: (3), (5) imply: % 154.26/23.43 | (6) $false % 154.26/23.43 | % 154.26/23.43 | CLOSE: (6) is inconsistent. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #450 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_2 = all_52_1 % 154.26/23.43 (2) all_56_2 = e1 % 154.26/23.43 (3) ~ (all_52_1 = e1) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (2) imply: % 154.26/23.43 | (4) all_52_1 = e1 % 154.26/23.43 | % 154.26/23.43 | SIMP: (4) implies: % 154.26/23.43 | (5) all_52_1 = e1 % 154.26/23.43 | % 154.26/23.43 | REDUCE: (3), (5) imply: % 154.26/23.43 | (6) $false % 154.26/23.43 | % 154.26/23.43 | CLOSE: (6) is inconsistent. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #451 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) ~ (e3 = e1) % 154.26/23.43 (3) all_58_30 = e0 % 154.26/23.43 (4) ~ (e2 = e1) % 154.26/23.43 (5) ~ (e3 = e0) % 154.26/23.43 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (7) ~ (e2 = e0) % 154.26/23.43 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (9) ~ (e3 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (6) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (10) all_58_29 = e3 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10) are inconsistent by sub-proof % 154.26/23.43 | | #683. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (11) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (1), (2), (3), (5), (11) are inconsistent by sub-proof #694. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #452 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_1 = e2 % 154.26/23.43 (2) all_56_1 = e1 % 154.26/23.43 (3) ~ (e2 = e1) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (2) imply: % 154.26/23.43 | (4) e2 = e1 % 154.26/23.43 | % 154.26/23.43 | SIMP: (4) implies: % 154.26/23.43 | (5) e2 = e1 % 154.26/23.43 | % 154.26/23.43 | REDUCE: (3), (5) imply: % 154.26/23.43 | (6) $false % 154.26/23.43 | % 154.26/23.43 | CLOSE: (6) is inconsistent. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #453 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_54_11 = all_4_1 % 154.26/23.43 (2) all_54_11 = e2 % 154.26/23.43 (3) ~ (all_4_1 = e2) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (1), (2) imply: % 154.26/23.43 | (4) all_4_1 = e2 % 154.26/23.43 | % 154.26/23.43 | SIMP: (4) implies: % 154.26/23.43 | (5) all_4_1 = e2 % 154.26/23.43 | % 154.26/23.43 | REDUCE: (3), (5) imply: % 154.26/23.43 | (6) $false % 154.26/23.43 | % 154.26/23.43 | CLOSE: (6) is inconsistent. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #454 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_56_4 = all_52_8 % 154.26/23.43 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.43 (5) ~ (all_52_12 = all_52_13) % 154.26/23.43 (6) ~ (e3 = e1) % 154.26/23.43 (7) all_56_8 = e0 % 154.26/23.43 (8) all_56_5 = all_52_9 % 154.26/23.43 (9) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.43 (10) all_56_1 = all_52_4 % 154.26/23.43 (11) ~ (all_52_9 = e0) % 154.26/23.43 (12) all_56_3 = all_8_2 % 154.26/23.43 (13) all_56_9 = all_52_12 % 154.26/23.43 (14) all_58_29 = all_8_2 % 154.26/23.43 (15) ~ (e2 = e1) % 154.26/23.43 (16) ~ (all_52_4 = e0) % 154.26/23.43 (17) ~ (e3 = e0) % 154.26/23.43 (18) all_56_2 = all_52_1 % 154.26/23.43 (19) all_56_10 = all_52_13 % 154.26/23.43 (20) all_58_28 = all_10_2 % 154.26/23.43 (21) ~ (e2 = e0) % 154.26/23.43 (22) all_56_0 = all_10_2 % 154.26/23.43 (23) ~ (all_52_1 = e0) % 154.26/23.43 (24) all_56_8 = all_6_2 % 154.26/23.43 (25) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (26) ~ (all_52_8 = e0) % 154.26/23.43 (27) all_58_30 = all_6_2 % 154.26/23.43 (28) ~ (e3 = e2) % 154.26/23.43 (29) ~ (all_8_2 = e0) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (7), (24) imply: % 154.26/23.43 | (30) all_6_2 = e0 % 154.26/23.43 | % 154.26/23.43 | SIMP: (30) implies: % 154.26/23.43 | (31) all_6_2 = e0 % 154.26/23.43 | % 154.26/23.43 | COMBINE_EQS: (27), (31) imply: % 154.26/23.43 | (32) all_58_30 = e0 % 154.26/23.43 | % 154.26/23.43 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), % 154.26/23.43 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), % 154.26/23.43 | (26), (28), (29), (32) are inconsistent by sub-proof #455. % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #455 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_58_31 = e1 % 154.26/23.43 (2) all_56_4 = all_52_8 % 154.26/23.43 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.43 (4) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.43 (5) ~ (all_52_12 = all_52_13) % 154.26/23.43 (6) ~ (e3 = e1) % 154.26/23.43 (7) all_56_5 = all_52_9 % 154.26/23.43 (8) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.43 (9) all_56_1 = all_52_4 % 154.26/23.43 (10) ~ (all_52_9 = e0) % 154.26/23.43 (11) all_56_3 = all_8_2 % 154.26/23.43 (12) all_56_9 = all_52_12 % 154.26/23.43 (13) all_58_29 = all_8_2 % 154.26/23.43 (14) all_58_30 = e0 % 154.26/23.43 (15) ~ (e2 = e1) % 154.26/23.43 (16) ~ (all_52_4 = e0) % 154.26/23.43 (17) ~ (e3 = e0) % 154.26/23.43 (18) all_56_2 = all_52_1 % 154.26/23.43 (19) all_56_10 = all_52_13 % 154.26/23.43 (20) all_58_28 = all_10_2 % 154.26/23.43 (21) ~ (e2 = e0) % 154.26/23.43 (22) all_56_0 = all_10_2 % 154.26/23.43 (23) ~ (all_52_1 = e0) % 154.26/23.43 (24) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.43 (25) ~ (all_52_8 = e0) % 154.26/23.43 (26) ~ (e3 = e2) % 154.26/23.43 (27) ~ (all_8_2 = e0) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (8) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (28) all_56_0 = e0 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (22), (28) imply: % 154.26/23.43 | | (29) all_10_2 = e0 % 154.26/23.43 | | % 154.26/23.43 | | SIMP: (29) implies: % 154.26/23.43 | | (30) all_10_2 = e0 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (20), (30) imply: % 154.26/23.43 | | (31) all_58_28 = e0 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (1), (3), (6), (13), (14), (15), (17), (21), (24), (26), (31) are % 154.26/23.43 | | inconsistent by sub-proof #680. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (32) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.43 | | % 154.26/23.43 | | REF_CLOSE: (2), (4), (5), (7), (9), (10), (11), (12), (16), (18), (19), % 154.26/23.43 | | (23), (25), (27), (32) are inconsistent by sub-proof #456. % 154.26/23.43 | | % 154.26/23.43 | End of split % 154.26/23.43 | % 154.26/23.43 End of proof % 154.26/23.43 % 154.26/23.43 Sub-proof #456 shows that the following formulas are inconsistent: % 154.26/23.43 ---------------------------------------------------------------- % 154.26/23.43 (1) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.43 (2) all_56_4 = all_52_8 % 154.26/23.43 (3) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.43 (4) ~ (all_52_12 = all_52_13) % 154.26/23.43 (5) all_56_5 = all_52_9 % 154.26/23.43 (6) all_56_1 = all_52_4 % 154.26/23.43 (7) ~ (all_52_9 = e0) % 154.26/23.43 (8) all_56_3 = all_8_2 % 154.26/23.43 (9) all_56_9 = all_52_12 % 154.26/23.43 (10) ~ (all_52_4 = e0) % 154.26/23.43 (11) all_56_2 = all_52_1 % 154.26/23.43 (12) all_56_10 = all_52_13 % 154.26/23.43 (13) ~ (all_52_1 = e0) % 154.26/23.43 (14) ~ (all_52_8 = e0) % 154.26/23.43 (15) ~ (all_8_2 = e0) % 154.26/23.43 % 154.26/23.43 Begin of proof % 154.26/23.43 | % 154.26/23.43 | BETA: splitting (3) gives: % 154.26/23.43 | % 154.26/23.43 | Case 1: % 154.26/23.43 | | % 154.26/23.43 | | (16) all_56_2 = e0 % 154.26/23.43 | | % 154.26/23.43 | | COMBINE_EQS: (11), (16) imply: % 154.26/23.43 | | (17) all_52_1 = e0 % 154.26/23.43 | | % 154.26/23.43 | | REDUCE: (13), (17) imply: % 154.26/23.43 | | (18) $false % 154.26/23.43 | | % 154.26/23.43 | | CLOSE: (18) is inconsistent. % 154.26/23.43 | | % 154.26/23.43 | Case 2: % 154.26/23.43 | | % 154.26/23.43 | | (19) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.43 | | % 154.26/23.43 | | BETA: splitting (1) gives: % 154.26/23.43 | | % 154.26/23.43 | | Case 1: % 154.26/23.43 | | | % 154.26/23.43 | | | (20) all_56_1 = e0 % 154.26/23.43 | | | % 154.26/23.43 | | | COMBINE_EQS: (6), (20) imply: % 154.26/23.43 | | | (21) all_52_4 = e0 % 154.26/23.43 | | | % 154.26/23.43 | | | REDUCE: (10), (21) imply: % 154.26/23.43 | | | (22) $false % 154.26/23.43 | | | % 154.26/23.43 | | | CLOSE: (22) is inconsistent. % 154.26/23.43 | | | % 154.26/23.43 | | Case 2: % 154.26/23.43 | | | % 154.26/23.43 | | | (23) all_56_4 = e0 | all_56_9 = e0 % 154.26/23.43 | | | % 154.26/23.43 | | | BETA: splitting (23) gives: % 154.26/23.43 | | | % 154.26/23.43 | | | Case 1: % 154.26/23.43 | | | | % 154.26/23.43 | | | | (24) all_56_4 = e0 % 154.26/23.43 | | | | % 154.26/23.43 | | | | COMBINE_EQS: (2), (24) imply: % 154.26/23.43 | | | | (25) all_52_8 = e0 % 154.26/23.43 | | | | % 154.26/23.43 | | | | REDUCE: (14), (25) imply: % 154.26/23.43 | | | | (26) $false % 154.26/23.43 | | | | % 154.26/23.43 | | | | CLOSE: (26) is inconsistent. % 154.26/23.43 | | | | % 154.26/23.43 | | | Case 2: % 154.26/23.43 | | | | % 154.26/23.43 | | | | (27) all_56_9 = e0 % 154.26/23.43 | | | | % 154.26/23.43 | | | | COMBINE_EQS: (9), (27) imply: % 154.26/23.43 | | | | (28) all_52_12 = e0 % 154.26/23.43 | | | | % 154.26/23.43 | | | | REDUCE: (4), (28) imply: % 154.26/23.43 | | | | (29) ~ (all_52_13 = e0) % 154.26/23.43 | | | | % 154.26/23.43 | | | | SIMP: (29) implies: % 154.26/23.44 | | | | (30) ~ (all_52_13 = e0) % 154.26/23.44 | | | | % 154.26/23.44 | | | | REF_CLOSE: (5), (7), (8), (12), (15), (19), (30) are inconsistent by % 154.26/23.44 | | | | sub-proof #573. % 154.26/23.44 | | | | % 154.26/23.44 | | | End of split % 154.26/23.44 | | | % 154.26/23.44 | | End of split % 154.26/23.44 | | % 154.26/23.44 | End of split % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #457 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) ~ (e3 = e1) % 154.26/23.44 (2) ~ (e2 = e1) % 154.26/23.44 (3) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.44 (4) all_58_31 = e3 % 154.26/23.44 (5) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.44 (6) ~ (e3 = e2) % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | BETA: splitting (3) gives: % 154.26/23.44 | % 154.26/23.44 | Case 1: % 154.26/23.44 | | % 154.26/23.44 | | (7) all_58_30 = e2 % 154.26/23.44 | | % 154.26/23.44 | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #458. % 154.26/23.44 | | % 154.26/23.44 | Case 2: % 154.26/23.44 | | % 154.26/23.44 | | (8) all_58_31 = e2 % 154.26/23.44 | | % 154.26/23.44 | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #585. % 154.26/23.44 | | % 154.26/23.44 | End of split % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #458 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) all_58_30 = e2 % 154.26/23.44 (2) ~ (e3 = e1) % 154.26/23.44 (3) ~ (e2 = e1) % 154.26/23.44 (4) all_58_31 = e3 % 154.26/23.44 (5) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | BETA: splitting (5) gives: % 154.26/23.44 | % 154.26/23.44 | Case 1: % 154.26/23.44 | | % 154.26/23.44 | | (6) all_58_30 = e1 % 154.26/23.44 | | % 154.26/23.44 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #500. % 154.26/23.44 | | % 154.26/23.44 | Case 2: % 154.26/23.44 | | % 154.26/23.44 | | (7) all_58_31 = e1 % 154.26/23.44 | | % 154.26/23.44 | | COMBINE_EQS: (4), (7) imply: % 154.26/23.44 | | (8) e3 = e1 % 154.26/23.44 | | % 154.26/23.44 | | REDUCE: (2), (8) imply: % 154.26/23.44 | | (9) $false % 154.26/23.44 | | % 154.26/23.44 | | CLOSE: (9) is inconsistent. % 154.26/23.44 | | % 154.26/23.44 | End of split % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #459 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) all_54_12 = all_10_1 % 154.26/23.44 (2) all_54_12 = e0 % 154.26/23.44 (3) ~ (all_10_1 = e0) % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | COMBINE_EQS: (1), (2) imply: % 154.26/23.44 | (4) all_10_1 = e0 % 154.26/23.44 | % 154.26/23.44 | SIMP: (4) implies: % 154.26/23.44 | (5) all_10_1 = e0 % 154.26/23.44 | % 154.26/23.44 | REDUCE: (3), (5) imply: % 154.26/23.44 | (6) $false % 154.26/23.44 | % 154.26/23.44 | CLOSE: (6) is inconsistent. % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #460 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.44 (2) all_56_15 = all_4_2 % 154.26/23.44 (3) op(e0, all_4_2) = all_58_27 % 154.26/23.44 (4) op(all_4_2, e0) = e1 % 154.26/23.44 (5) all_56_15 = e0 % 154.26/23.44 (6) op(e0, e0) = all_4_2 % 154.26/23.44 (7) ~ (all_4_2 = e1) % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | COMBINE_EQS: (2), (5) imply: % 154.26/23.44 | (8) all_4_2 = e0 % 154.26/23.44 | % 154.26/23.44 | SIMP: (8) implies: % 154.26/23.44 | (9) all_4_2 = e0 % 154.26/23.44 | % 154.26/23.44 | REDUCE: (7), (9) imply: % 154.26/23.44 | (10) ~ (e1 = e0) % 154.26/23.44 | % 154.26/23.44 | SIMP: (10) implies: % 154.26/23.44 | (11) ~ (e1 = e0) % 154.26/23.44 | % 154.26/23.44 | REDUCE: (4), (9) imply: % 154.26/23.44 | (12) op(e0, e0) = e1 % 154.26/23.44 | % 154.26/23.44 | REDUCE: (3), (9) imply: % 154.26/23.44 | (13) op(e0, e0) = all_58_27 % 154.26/23.44 | % 154.26/23.44 | REDUCE: (6), (9) imply: % 154.26/23.44 | (14) op(e0, e0) = e0 % 154.26/23.44 | % 154.26/23.44 | REF_CLOSE: (1), (11), (12), (13), (14) are inconsistent by sub-proof #461. % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #461 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.44 (2) op(e0, e0) = all_58_27 % 154.26/23.44 (3) op(e0, e0) = e0 % 154.26/23.44 (4) op(e0, e0) = e1 % 154.26/23.44 (5) ~ (e1 = e0) % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | GROUND_INST: instantiating (1) with e1, all_58_27, e0, e0, simplifying with % 154.26/23.44 | (2), (4) gives: % 154.26/23.44 | (6) all_58_27 = e1 % 154.26/23.44 | % 154.26/23.44 | GROUND_INST: instantiating (1) with e0, all_58_27, e0, e0, simplifying with % 154.26/23.44 | (2), (3) gives: % 154.26/23.44 | (7) all_58_27 = e0 % 154.26/23.44 | % 154.26/23.44 | COMBINE_EQS: (6), (7) imply: % 154.26/23.44 | (8) e1 = e0 % 154.26/23.44 | % 154.26/23.44 | SIMP: (8) implies: % 154.26/23.44 | (9) e1 = e0 % 154.26/23.44 | % 154.26/23.44 | REDUCE: (5), (9) imply: % 154.26/23.44 | (10) $false % 154.26/23.44 | % 154.26/23.44 | CLOSE: (10) is inconsistent. % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #462 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) all_58_31 = all_4_2 % 154.26/23.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.44 (3) all_58_28 = e0 % 154.26/23.44 (4) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.44 (5) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 154.26/23.44 (6) all_58_11 = all_52_9 % 154.26/23.44 (7) all_56_15 = all_4_2 % 154.26/23.44 (8) all_56_7 = all_52_6 % 154.26/23.44 (9) ~ (all_52_11 = all_10_1) % 154.26/23.44 (10) all_58_15 = all_52_2 % 154.26/23.44 (11) all_58_26 = all_52_11 % 154.26/23.44 (12) op(e1, all_52_14) = all_58_19 % 154.26/23.44 (13) ~ (all_52_8 = all_52_11) % 154.26/23.44 (14) ~ (all_52_11 = all_4_2) % 154.26/23.44 (15) all_54_7 = all_52_13 % 154.26/23.44 (16) all_58_6 = all_52_12 % 154.26/23.44 (17) ~ (all_52_6 = all_8_2) % 154.26/23.44 (18) all_56_4 = all_52_8 % 154.26/23.44 (19) ~ (all_52_4 = all_8_2) % 154.26/23.44 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.44 (21) all_58_13 = all_52_13 % 154.26/23.44 (22) op(e0, e1) = all_52_11 % 154.26/23.44 (23) all_56_12 = all_10_1 % 154.26/23.44 (24) ~ (all_52_6 = all_52_7) % 154.26/23.44 (25) all_58_20 = all_52_14 % 154.26/23.44 (26) ~ (all_52_12 = all_52_13) % 154.26/23.44 (27) all_54_10 = all_6_2 % 154.26/23.44 (28) all_56_0 = e0 % 154.26/23.44 (29) op(e0, all_52_7) = all_58_23 % 154.26/23.44 (30) ~ (all_52_6 = all_52_14) % 154.26/23.44 (31) ~ (all_52_4 = all_52_7) % 154.26/23.44 (32) ~ (all_52_13 = all_4_2) % 154.26/23.44 (33) ~ (all_52_13 = all_8_2) % 154.26/23.44 (34) ~ (e3 = e1) % 154.26/23.44 (35) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 154.26/23.44 (36) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.44 (37) all_56_5 = all_52_9 % 154.26/23.44 (38) all_54_14 = all_52_11 % 154.26/23.44 (39) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.44 (40) ~ (all_52_12 = e0) % 154.26/23.44 (41) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.44 (42) all_56_11 = all_52_14 % 154.26/23.44 (43) all_58_0 = all_52_12 % 154.26/23.44 (44) all_56_1 = all_52_4 % 154.26/23.44 (45) ~ (all_52_13 = e0) % 154.26/23.44 (46) op(e1, e0) = all_52_14 % 154.26/23.44 (47) ~ (all_52_9 = all_52_11) % 154.26/23.44 (48) all_56_3 = all_8_2 % 154.26/23.44 (49) all_58_24 = all_52_7 % 154.26/23.44 (50) ~ (all_52_13 = all_52_14) % 154.26/23.44 (51) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.26/23.44 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.26/23.44 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.26/23.44 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.26/23.44 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.44 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.26/23.44 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.44 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.44 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.44 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.26/23.44 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.44 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.44 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.44 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.44 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.44 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.44 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.44 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.44 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.44 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.44 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.44 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.26/23.44 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.44 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.44 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.44 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.44 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.44 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.44 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.44 e0) % 154.26/23.44 (52) all_56_9 = all_52_12 % 154.26/23.44 (53) all_58_29 = all_8_2 % 154.26/23.44 (54) ~ (all_52_12 = all_52_14) % 154.26/23.44 (55) ~ (e2 = e1) % 154.26/23.44 (56) all_56_6 = all_52_2 % 154.26/23.44 (57) all_56_13 = all_52_7 % 154.26/23.44 (58) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.26/23.44 (59) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.26/23.44 (60) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.44 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.44 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.44 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.44 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.44 (all_58_27 = e0)) % 154.26/23.44 (61) ~ (all_52_9 = all_52_13) % 154.26/23.44 (62) ~ (all_52_4 = e0) % 154.26/23.44 (63) op(e2, all_52_9) = all_58_10 % 154.26/23.44 (64) ~ (all_52_11 = all_6_2) % 154.26/23.44 (65) ~ (e3 = e0) % 154.26/23.44 (66) all_56_10 = all_52_13 % 154.26/23.44 (67) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.44 (68) ~ (all_52_9 = all_8_2) % 154.26/23.44 (69) all_56_14 = all_52_11 % 154.26/23.44 (70) all_58_28 = all_10_2 % 154.26/23.44 (71) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.44 (72) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.44 (73) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.44 (74) ~ (e2 = e0) % 154.26/23.44 (75) all_56_0 = all_10_2 % 154.26/23.44 (76) op(e0, e0) = all_4_2 % 154.26/23.44 (77) all_56_8 = all_6_2 % 154.26/23.44 (78) op(e2, e0) = all_52_13 % 154.26/23.44 (79) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.44 (80) all_58_4 = all_52_8 % 154.26/23.44 (81) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.44 (82) all_16_1 = all_10_1 % 154.26/23.44 (83) all_16_0 = all_10_0 % 154.26/23.44 (84) ~ (all_52_2 = all_52_14) % 154.26/23.44 (85) ~ (e1 = e0) % 154.26/23.44 (86) ~ (all_52_7 = all_4_2) % 154.26/23.44 (87) ~ (all_4_2 = e1) % 154.26/23.44 (88) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.26/23.44 (89) ~ (all_52_8 = e0) % 154.26/23.44 (90) op(e0, all_10_1) = all_10_0 % 154.26/23.44 (91) all_58_30 = all_6_2 % 154.26/23.44 (92) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.44 (93) ~ (e3 = e2) % 154.26/23.44 (94) ~ (all_52_14 = all_6_2) % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | BETA: splitting (5) gives: % 154.26/23.44 | % 154.26/23.44 | Case 1: % 154.26/23.44 | | % 154.26/23.44 | | (95) all_56_9 = e0 % 154.26/23.44 | | % 154.26/23.44 | | REF_CLOSE: (40), (52), (95) are inconsistent by sub-proof #521. % 154.26/23.44 | | % 154.26/23.44 | Case 2: % 154.26/23.44 | | % 154.26/23.44 | | (96) all_56_10 = e0 | all_56_11 = e0 % 154.26/23.44 | | % 154.26/23.44 | | BETA: splitting (96) gives: % 154.26/23.44 | | % 154.26/23.44 | | Case 1: % 154.26/23.44 | | | % 154.26/23.44 | | | (97) all_56_10 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | REF_CLOSE: (45), (66), (97) are inconsistent by sub-proof #526. % 154.26/23.44 | | | % 154.26/23.44 | | Case 2: % 154.26/23.44 | | | % 154.26/23.44 | | | (98) all_56_11 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | COMBINE_EQS: (42), (98) imply: % 154.26/23.44 | | | (99) all_52_14 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | SIMP: (99) implies: % 154.26/23.44 | | | (100) all_52_14 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | COMBINE_EQS: (25), (100) imply: % 154.26/23.44 | | | (101) all_58_20 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (84), (100) imply: % 154.26/23.44 | | | (102) ~ (all_52_2 = e0) % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (30), (100) imply: % 154.26/23.44 | | | (103) ~ (all_52_6 = e0) % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (94), (100) imply: % 154.26/23.44 | | | (104) ~ (all_6_2 = e0) % 154.26/23.44 | | | % 154.26/23.44 | | | SIMP: (104) implies: % 154.26/23.44 | | | (105) ~ (all_6_2 = e0) % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (12), (100) imply: % 154.26/23.44 | | | (106) op(e1, e0) = all_58_19 % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (46), (100) imply: % 154.26/23.44 | | | (107) op(e1, e0) = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), % 154.26/23.44 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 154.26/23.44 | | | (26), (27), (28), (29), (31), (32), (33), (34), (35), (36), % 154.26/23.44 | | | (37), (38), (39), (41), (42), (43), (44), (45), (47), (48), % 154.26/23.44 | | | (49), (51), (52), (53), (54), (55), (56), (57), (58), (59), % 154.26/23.44 | | | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), % 154.26/23.44 | | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 154.26/23.44 | | | (80), (81), (82), (83), (85), (86), (87), (88), (89), (90), % 154.26/23.44 | | | (91), (92), (93), (98), (101), (102), (103), (105), (106), % 154.26/23.44 | | | (107) are inconsistent by sub-proof #463. % 154.26/23.44 | | | % 154.26/23.44 | | End of split % 154.26/23.44 | | % 154.26/23.44 | End of split % 154.26/23.44 | % 154.26/23.44 End of proof % 154.26/23.44 % 154.26/23.44 Sub-proof #463 shows that the following formulas are inconsistent: % 154.26/23.44 ---------------------------------------------------------------- % 154.26/23.44 (1) all_58_31 = all_4_2 % 154.26/23.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.44 (3) all_58_28 = e0 % 154.26/23.44 (4) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.26/23.44 (5) all_58_11 = all_52_9 % 154.26/23.44 (6) all_56_15 = all_4_2 % 154.26/23.44 (7) all_56_7 = all_52_6 % 154.26/23.44 (8) ~ (all_52_2 = e0) % 154.26/23.44 (9) op(e1, e0) = e0 % 154.26/23.44 (10) ~ (all_52_11 = all_10_1) % 154.26/23.44 (11) all_58_15 = all_52_2 % 154.26/23.44 (12) all_58_26 = all_52_11 % 154.26/23.44 (13) ~ (all_52_8 = all_52_11) % 154.26/23.44 (14) ~ (all_52_11 = all_4_2) % 154.26/23.44 (15) all_54_7 = all_52_13 % 154.26/23.44 (16) all_58_6 = all_52_12 % 154.26/23.44 (17) ~ (all_52_6 = all_8_2) % 154.26/23.44 (18) all_56_4 = all_52_8 % 154.26/23.44 (19) ~ (all_52_4 = all_8_2) % 154.26/23.44 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.44 (21) ~ (all_6_2 = e0) % 154.26/23.44 (22) all_58_13 = all_52_13 % 154.26/23.44 (23) op(e0, e1) = all_52_11 % 154.26/23.44 (24) all_56_12 = all_10_1 % 154.26/23.44 (25) ~ (all_52_6 = all_52_7) % 154.26/23.44 (26) all_58_20 = e0 % 154.26/23.44 (27) ~ (all_52_12 = all_52_13) % 154.26/23.44 (28) all_54_10 = all_6_2 % 154.26/23.44 (29) all_56_0 = e0 % 154.26/23.44 (30) op(e0, all_52_7) = all_58_23 % 154.26/23.44 (31) ~ (all_52_4 = all_52_7) % 154.26/23.44 (32) ~ (all_52_13 = all_4_2) % 154.26/23.44 (33) ~ (all_52_13 = all_8_2) % 154.26/23.44 (34) ~ (e3 = e1) % 154.26/23.44 (35) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 154.26/23.44 (36) ~ (all_52_6 = e0) % 154.26/23.44 (37) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.44 (38) all_56_5 = all_52_9 % 154.26/23.44 (39) all_54_14 = all_52_11 % 154.26/23.44 (40) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.26/23.44 (41) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.44 (42) all_56_11 = all_52_14 % 154.26/23.44 (43) all_58_0 = all_52_12 % 154.26/23.44 (44) all_56_1 = all_52_4 % 154.26/23.44 (45) ~ (all_52_13 = e0) % 154.26/23.44 (46) ~ (all_52_9 = all_52_11) % 154.26/23.44 (47) all_56_3 = all_8_2 % 154.26/23.44 (48) all_58_24 = all_52_7 % 154.26/23.44 (49) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.26/23.44 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.26/23.44 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.26/23.44 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.26/23.44 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.44 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.26/23.44 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.44 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.44 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.44 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.26/23.44 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.44 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.44 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.44 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.44 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.44 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.44 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.44 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.44 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.44 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.44 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.44 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.26/23.44 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.44 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.44 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.44 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.44 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.44 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.44 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.44 e0) % 154.26/23.44 (50) all_56_9 = all_52_12 % 154.26/23.44 (51) all_58_29 = all_8_2 % 154.26/23.44 (52) ~ (all_52_12 = all_52_14) % 154.26/23.44 (53) ~ (e2 = e1) % 154.26/23.44 (54) all_56_6 = all_52_2 % 154.26/23.44 (55) all_56_13 = all_52_7 % 154.26/23.44 (56) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.26/23.44 (57) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.26/23.44 (58) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.44 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.44 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.44 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.44 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.44 (all_58_27 = e0)) % 154.26/23.44 (59) ~ (all_52_9 = all_52_13) % 154.26/23.44 (60) ~ (all_52_4 = e0) % 154.26/23.44 (61) op(e2, all_52_9) = all_58_10 % 154.26/23.44 (62) ~ (all_52_11 = all_6_2) % 154.26/23.44 (63) ~ (e3 = e0) % 154.26/23.44 (64) all_56_10 = all_52_13 % 154.26/23.44 (65) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.44 (66) ~ (all_52_9 = all_8_2) % 154.26/23.44 (67) all_56_14 = all_52_11 % 154.26/23.44 (68) all_58_28 = all_10_2 % 154.26/23.44 (69) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.26/23.44 (70) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.44 (71) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.44 (72) ~ (e2 = e0) % 154.26/23.44 (73) all_56_0 = all_10_2 % 154.26/23.44 (74) op(e0, e0) = all_4_2 % 154.26/23.44 (75) all_56_8 = all_6_2 % 154.26/23.44 (76) op(e2, e0) = all_52_13 % 154.26/23.44 (77) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.44 (78) op(e1, e0) = all_58_19 % 154.26/23.44 (79) all_58_4 = all_52_8 % 154.26/23.44 (80) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.44 (81) all_16_1 = all_10_1 % 154.26/23.44 (82) all_16_0 = all_10_0 % 154.26/23.44 (83) ~ (e1 = e0) % 154.26/23.44 (84) ~ (all_52_7 = all_4_2) % 154.26/23.44 (85) ~ (all_4_2 = e1) % 154.26/23.44 (86) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.26/23.44 (87) ~ (all_52_8 = e0) % 154.26/23.44 (88) op(e0, all_10_1) = all_10_0 % 154.26/23.44 (89) all_58_30 = all_6_2 % 154.26/23.44 (90) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.44 (91) all_56_11 = e0 % 154.26/23.44 (92) ~ (e3 = e2) % 154.26/23.44 % 154.26/23.44 Begin of proof % 154.26/23.44 | % 154.26/23.44 | BETA: splitting (86) gives: % 154.26/23.44 | % 154.26/23.44 | Case 1: % 154.26/23.44 | | % 154.26/23.44 | | (93) all_56_3 = e0 % 154.26/23.44 | | % 154.26/23.44 | | REF_CLOSE: (7), (18), (20), (21), (34), (36), (40), (42), (44), (47), (50), % 154.26/23.44 | | (51), (52), (53), (60), (63), (68), (69), (72), (73), (75), (80), % 154.26/23.44 | | (83), (87), (89), (90), (92), (93) are inconsistent by sub-proof % 154.26/23.44 | | #480. % 154.26/23.44 | | % 154.26/23.44 | Case 2: % 154.26/23.44 | | % 154.26/23.44 | | (94) all_56_7 = e0 | all_56_13 = e0 % 154.26/23.44 | | % 154.26/23.44 | | BETA: splitting (94) gives: % 154.26/23.44 | | % 154.26/23.44 | | Case 1: % 154.26/23.44 | | | % 154.26/23.44 | | | (95) all_56_7 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | COMBINE_EQS: (7), (95) imply: % 154.26/23.44 | | | (96) all_52_6 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (36), (96) imply: % 154.26/23.44 | | | (97) $false % 154.26/23.44 | | | % 154.26/23.44 | | | CLOSE: (97) is inconsistent. % 154.26/23.44 | | | % 154.26/23.44 | | Case 2: % 154.26/23.44 | | | % 154.26/23.44 | | | (98) all_56_13 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | COMBINE_EQS: (55), (98) imply: % 154.26/23.44 | | | (99) all_52_7 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | SIMP: (99) implies: % 154.26/23.44 | | | (100) all_52_7 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | COMBINE_EQS: (48), (100) imply: % 154.26/23.44 | | | (101) all_58_24 = e0 % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (84), (100) imply: % 154.26/23.44 | | | (102) ~ (all_4_2 = e0) % 154.26/23.44 | | | % 154.26/23.44 | | | SIMP: (102) implies: % 154.26/23.44 | | | (103) ~ (all_4_2 = e0) % 154.26/23.44 | | | % 154.26/23.44 | | | REDUCE: (30), (100) imply: % 154.26/23.44 | | | (104) op(e0, e0) = all_58_23 % 154.26/23.44 | | | % 154.26/23.44 | | | BETA: splitting (4) gives: % 154.26/23.44 | | | % 154.26/23.44 | | | Case 1: % 154.26/23.44 | | | | % 154.26/23.44 | | | | (105) all_56_3 = e0 % 154.26/23.44 | | | | % 154.26/23.44 | | | | REF_CLOSE: (7), (18), (20), (21), (34), (36), (40), (42), (44), (47), % 154.26/23.44 | | | | (50), (51), (52), (53), (60), (63), (68), (69), (72), (73), % 154.26/23.44 | | | | (75), (80), (83), (87), (89), (90), (92), (105) are % 154.26/23.44 | | | | inconsistent by sub-proof #480. % 154.26/23.44 | | | | % 154.26/23.44 | | | Case 2: % 154.26/23.44 | | | | % 154.26/23.44 | | | | (106) all_56_5 = e0 | all_56_10 = e0 % 154.26/23.44 | | | | % 154.26/23.44 | | | | BETA: splitting (106) gives: % 154.26/23.44 | | | | % 154.26/23.44 | | | | Case 1: % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | (107) all_56_5 = e0 % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | COMBINE_EQS: (38), (107) imply: % 154.26/23.44 | | | | | (108) all_52_9 = e0 % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | COMBINE_EQS: (5), (108) imply: % 154.26/23.44 | | | | | (109) all_58_11 = e0 % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | REDUCE: (46), (108) imply: % 154.26/23.44 | | | | | (110) ~ (all_52_11 = e0) % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | SIMP: (110) implies: % 154.26/23.44 | | | | | (111) ~ (all_52_11 = e0) % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | REDUCE: (59), (108) imply: % 154.26/23.44 | | | | | (112) ~ (all_52_13 = e0) % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | REDUCE: (66), (108) imply: % 154.26/23.44 | | | | | (113) ~ (all_8_2 = e0) % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | SIMP: (113) implies: % 154.26/23.44 | | | | | (114) ~ (all_8_2 = e0) % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | REDUCE: (61), (108) imply: % 154.26/23.44 | | | | | (115) op(e2, e0) = all_58_10 % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | GROUND_INST: instantiating (2) with all_4_2, all_58_23, e0, e0, % 154.26/23.44 | | | | | simplifying with (74), (104) gives: % 154.26/23.44 | | | | | (116) all_58_23 = all_4_2 % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | GROUND_INST: instantiating (2) with e0, all_58_19, e0, e1, simplifying % 154.26/23.44 | | | | | with (9), (78) gives: % 154.26/23.44 | | | | | (117) all_58_19 = e0 % 154.26/23.44 | | | | | % 154.26/23.44 | | | | | GROUND_INST: instantiating (2) with all_52_13, all_58_10, e0, e2, % 154.26/23.44 | | | | | simplifying with (76), (115) gives: % 154.26/23.44 | | | | | (118) all_58_10 = all_52_13 % 154.26/23.44 | | | | | % 154.26/23.45 | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), % 154.26/23.45 | | | | | (15), (16), (17), (18), (19), (20), (22), (23), (24), (26), % 154.26/23.45 | | | | | (27), (28), (29), (32), (33), (34), (35), (37), (39), (41), % 154.26/23.45 | | | | | (43), (44), (45), (49), (50), (51), (53), (54), (56), (57), % 154.26/23.45 | | | | | (58), (62), (63), (64), (65), (67), (70), (71), (72), (75), % 154.26/23.45 | | | | | (77), (79), (80), (81), (82), (83), (85), (88), (89), (90), % 154.26/23.45 | | | | | (91), (92), (98), (101), (103), (109), (111), (114), (116), % 154.26/23.45 | | | | | (117), (118) are inconsistent by sub-proof #464. % 154.26/23.45 | | | | | % 154.26/23.45 | | | | Case 2: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | (119) all_56_10 = e0 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | REF_CLOSE: (45), (64), (119) are inconsistent by sub-proof #526. % 154.26/23.45 | | | | | % 154.26/23.45 | | | | End of split % 154.26/23.45 | | | | % 154.26/23.45 | | | End of split % 154.26/23.45 | | | % 154.26/23.45 | | End of split % 154.26/23.45 | | % 154.26/23.45 | End of split % 154.26/23.45 | % 154.26/23.45 End of proof % 154.26/23.45 % 154.26/23.45 Sub-proof #464 shows that the following formulas are inconsistent: % 154.26/23.45 ---------------------------------------------------------------- % 154.26/23.45 (1) all_58_31 = all_4_2 % 154.26/23.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.26/23.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.26/23.45 (3) all_58_28 = e0 % 154.26/23.45 (4) all_56_15 = all_4_2 % 154.26/23.45 (5) all_56_7 = all_52_6 % 154.26/23.45 (6) ~ (all_52_2 = e0) % 154.26/23.45 (7) ~ (all_52_11 = all_10_1) % 154.26/23.45 (8) all_58_15 = all_52_2 % 154.26/23.45 (9) all_58_26 = all_52_11 % 154.26/23.45 (10) ~ (all_52_8 = all_52_11) % 154.26/23.45 (11) ~ (all_52_11 = all_4_2) % 154.26/23.45 (12) all_54_7 = all_52_13 % 154.26/23.45 (13) all_58_6 = all_52_12 % 154.26/23.45 (14) ~ (all_52_6 = all_8_2) % 154.26/23.45 (15) all_56_4 = all_52_8 % 154.26/23.45 (16) ~ (all_52_4 = all_8_2) % 154.26/23.45 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.45 (18) all_58_13 = all_52_13 % 154.26/23.45 (19) op(e0, e1) = all_52_11 % 154.26/23.45 (20) all_56_12 = all_10_1 % 154.26/23.45 (21) all_58_11 = e0 % 154.26/23.45 (22) all_58_20 = e0 % 154.26/23.45 (23) ~ (all_52_12 = all_52_13) % 154.26/23.45 (24) all_54_10 = all_6_2 % 154.26/23.45 (25) all_56_13 = e0 % 154.26/23.45 (26) all_56_0 = e0 % 154.26/23.45 (27) ~ (all_52_13 = all_4_2) % 154.26/23.45 (28) all_58_19 = e0 % 154.26/23.45 (29) ~ (all_52_13 = all_8_2) % 154.26/23.45 (30) ~ (e3 = e1) % 154.26/23.45 (31) ~ (all_16_0 = e2) | ~ (all_16_1 = e1) % 154.26/23.45 (32) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.26/23.45 (33) all_54_14 = all_52_11 % 154.26/23.45 (34) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.45 (35) all_58_0 = all_52_12 % 154.26/23.45 (36) all_56_1 = all_52_4 % 154.26/23.45 (37) ~ (all_52_13 = e0) % 154.26/23.45 (38) all_58_24 = e0 % 154.26/23.45 (39) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.26/23.45 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.26/23.45 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.26/23.45 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.26/23.45 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.45 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.26/23.45 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.45 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.45 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.45 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.26/23.45 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.26/23.45 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.45 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.26/23.45 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.45 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.45 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.45 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.45 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.45 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.45 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.45 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.26/23.45 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.26/23.45 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.45 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.45 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.45 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.45 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.26/23.45 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.45 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.26/23.45 e0) % 154.26/23.45 (40) all_56_9 = all_52_12 % 154.26/23.45 (41) all_58_29 = all_8_2 % 154.26/23.45 (42) ~ (e2 = e1) % 154.26/23.45 (43) all_56_6 = all_52_2 % 154.26/23.45 (44) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.26/23.45 (45) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.26/23.45 (46) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.26/23.45 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.45 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.26/23.45 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.45 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.26/23.45 (all_58_27 = e0)) % 154.26/23.45 (47) ~ (all_52_11 = all_6_2) % 154.26/23.45 (48) ~ (e3 = e0) % 154.26/23.45 (49) ~ (all_52_11 = e0) % 154.26/23.45 (50) all_56_10 = all_52_13 % 154.26/23.45 (51) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 154.26/23.45 (52) all_56_14 = all_52_11 % 154.26/23.45 (53) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.45 (54) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.45 (55) ~ (e2 = e0) % 154.26/23.45 (56) ~ (all_4_2 = e0) % 154.26/23.45 (57) all_58_23 = all_4_2 % 154.26/23.45 (58) all_56_8 = all_6_2 % 154.26/23.45 (59) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.45 (60) all_58_4 = all_52_8 % 154.26/23.45 (61) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.45 (62) all_16_1 = all_10_1 % 154.26/23.45 (63) all_16_0 = all_10_0 % 154.26/23.45 (64) ~ (e1 = e0) % 154.26/23.45 (65) all_58_10 = all_52_13 % 154.26/23.45 (66) ~ (all_4_2 = e1) % 154.26/23.45 (67) op(e0, all_10_1) = all_10_0 % 154.26/23.45 (68) all_58_30 = all_6_2 % 154.26/23.45 (69) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.45 (70) all_56_11 = e0 % 154.26/23.45 (71) ~ (e3 = e2) % 154.26/23.45 (72) ~ (all_8_2 = e0) % 154.26/23.45 % 154.26/23.45 Begin of proof % 154.26/23.45 | % 154.26/23.45 | BETA: splitting (54) gives: % 154.26/23.45 | % 154.26/23.45 | Case 1: % 154.26/23.45 | | % 154.26/23.45 | | (73) all_56_12 = e1 % 154.26/23.45 | | % 154.26/23.45 | | COMBINE_EQS: (20), (73) imply: % 154.26/23.45 | | (74) all_10_1 = e1 % 154.26/23.45 | | % 154.26/23.45 | | SIMP: (74) implies: % 154.26/23.45 | | (75) all_10_1 = e1 % 154.26/23.45 | | % 154.26/23.45 | | COMBINE_EQS: (62), (75) imply: % 154.26/23.45 | | (76) all_16_1 = e1 % 154.26/23.45 | | % 154.26/23.45 | | REDUCE: (7), (75) imply: % 154.26/23.45 | | (77) ~ (all_52_11 = e1) % 154.26/23.45 | | % 154.26/23.45 | | REDUCE: (67), (75) imply: % 154.26/23.45 | | (78) op(e0, e1) = all_10_0 % 154.26/23.45 | | % 154.26/23.45 | | BETA: splitting (31) gives: % 154.26/23.45 | | % 154.26/23.45 | | Case 1: % 154.26/23.45 | | | % 154.26/23.45 | | | (79) ~ (all_16_1 = e1) % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (76), (79) imply: % 154.26/23.45 | | | (80) $false % 154.26/23.45 | | | % 154.26/23.45 | | | CLOSE: (80) is inconsistent. % 154.26/23.45 | | | % 154.26/23.45 | | Case 2: % 154.26/23.45 | | | % 154.26/23.45 | | | (81) ~ (all_16_0 = e2) % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (63), (81) imply: % 154.26/23.45 | | | (82) ~ (all_10_0 = e2) % 154.26/23.45 | | | % 154.26/23.45 | | | GROUND_INST: instantiating (2) with all_52_11, all_10_0, e1, e0, % 154.26/23.45 | | | simplifying with (19), (78) gives: % 154.26/23.45 | | | (83) all_52_11 = all_10_0 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (33), (83) imply: % 154.26/23.45 | | | (84) all_54_14 = all_10_0 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (52), (83) imply: % 154.26/23.45 | | | (85) all_56_14 = all_10_0 % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (47), (83) imply: % 154.26/23.45 | | | (86) ~ (all_10_0 = all_6_2) % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (11), (83) imply: % 154.26/23.45 | | | (87) ~ (all_10_0 = all_4_2) % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (77), (83) imply: % 154.26/23.45 | | | (88) ~ (all_10_0 = e1) % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (49), (83) imply: % 154.26/23.45 | | | (89) ~ (all_10_0 = e0) % 154.26/23.45 | | | % 154.26/23.45 | | | BETA: splitting (51) gives: % 154.26/23.45 | | | % 154.26/23.45 | | | Case 1: % 154.26/23.45 | | | | % 154.26/23.45 | | | | (90) all_54_14 = e0 % 154.26/23.45 | | | | % 154.26/23.45 | | | | REF_CLOSE: (84), (89), (90) are inconsistent by sub-proof #479. % 154.26/23.45 | | | | % 154.26/23.45 | | | Case 2: % 154.26/23.45 | | | | % 154.26/23.45 | | | | (91) ~ (all_54_14 = e0) % 154.26/23.45 | | | | (92) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 % 154.26/23.45 | | | | % 154.26/23.45 | | | | BETA: splitting (59) gives: % 154.26/23.45 | | | | % 154.26/23.45 | | | | Case 1: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | (93) all_56_12 = e2 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | COMBINE_EQS: (73), (93) imply: % 154.26/23.45 | | | | | (94) e2 = e1 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | REDUCE: (42), (94) imply: % 154.26/23.45 | | | | | (95) $false % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | CLOSE: (95) is inconsistent. % 154.26/23.45 | | | | | % 154.26/23.45 | | | | Case 2: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | (96) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | BETA: splitting (96) gives: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | Case 1: % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | (97) all_56_13 = e2 % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | COMBINE_EQS: (25), (97) imply: % 154.26/23.45 | | | | | | (98) e2 = e0 % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | REDUCE: (55), (98) imply: % 154.26/23.45 | | | | | | (99) $false % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | CLOSE: (99) is inconsistent. % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | Case 2: % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | (100) all_56_14 = e2 | all_56_15 = e2 % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | BETA: splitting (100) gives: % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | Case 1: % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | (101) all_56_14 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | COMBINE_EQS: (85), (101) imply: % 154.26/23.45 | | | | | | | (102) all_10_0 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | SIMP: (102) implies: % 154.26/23.45 | | | | | | | (103) all_10_0 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | REDUCE: (82), (103) imply: % 154.26/23.45 | | | | | | | (104) $false % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | CLOSE: (104) is inconsistent. % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | Case 2: % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | (105) all_56_15 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | COMBINE_EQS: (4), (105) imply: % 154.26/23.45 | | | | | | | (106) all_4_2 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | SIMP: (106) implies: % 154.26/23.45 | | | | | | | (107) all_4_2 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | COMBINE_EQS: (1), (107) imply: % 154.26/23.45 | | | | | | | (108) all_58_31 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | COMBINE_EQS: (57), (107) imply: % 154.26/23.45 | | | | | | | (109) all_58_23 = e2 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | REDUCE: (27), (107) imply: % 154.26/23.45 | | | | | | | (110) ~ (all_52_13 = e2) % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | BETA: splitting (92) gives: % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | (111) all_54_14 = e1 % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | COMBINE_EQS: (84), (111) imply: % 154.26/23.45 | | | | | | | | (112) all_10_0 = e1 % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | REDUCE: (88), (112) imply: % 154.26/23.45 | | | | | | | | (113) $false % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | CLOSE: (113) is inconsistent. % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | (114) ~ (all_54_14 = e1) % 154.26/23.45 | | | | | | | | (115) all_54_14 = e3 | all_54_14 = e2 % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | BETA: splitting (115) gives: % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | (116) all_54_14 = e2 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | COMBINE_EQS: (84), (116) imply: % 154.26/23.45 | | | | | | | | | (117) all_10_0 = e2 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | REDUCE: (82), (117) imply: % 154.26/23.45 | | | | | | | | | (118) $false % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | CLOSE: (118) is inconsistent. % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | (119) all_54_14 = e3 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | COMBINE_EQS: (84), (119) imply: % 154.26/23.45 | | | | | | | | | (120) all_10_0 = e3 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | REDUCE: (86), (120) imply: % 154.26/23.45 | | | | | | | | | (121) ~ (all_6_2 = e3) % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | SIMP: (121) implies: % 154.26/23.45 | | | | | | | | | (122) ~ (all_6_2 = e3) % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | BETA: splitting (61) gives: % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | (123) all_58_28 = e3 % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | REF_CLOSE: (3), (48), (123) are inconsistent by sub-proof % 154.26/23.45 | | | | | | | | | | #689. % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | (124) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | BETA: splitting (124) gives: % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | (125) all_58_29 = e3 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | COMBINE_EQS: (41), (125) imply: % 154.26/23.45 | | | | | | | | | | | (126) all_8_2 = e3 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | REDUCE: (29), (126) imply: % 154.26/23.45 | | | | | | | | | | | (127) ~ (all_52_13 = e3) % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | BETA: splitting (45) gives: % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | (128) all_56_9 = e3 % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | COMBINE_EQS: (40), (128) imply: % 154.26/23.45 | | | | | | | | | | | | (129) all_52_12 = e3 % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | SIMP: (129) implies: % 154.26/23.45 | | | | | | | | | | | | (130) all_52_12 = e3 % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | COMBINE_EQS: (35), (130) imply: % 154.26/23.45 | | | | | | | | | | | | (131) all_58_0 = e3 % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | REDUCE: (23), (130) imply: % 154.26/23.45 | | | | | | | | | | | | (132) ~ (all_52_13 = e3) % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | BETA: splitting (46) gives: % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | (133) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.26/23.45 | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.26/23.45 | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.45 | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | BETA: splitting (133) gives: % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | (134) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.26/23.45 | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0) % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | ALPHA: (134) implies: % 154.26/23.45 | | | | | | | | | | | | | | (135) ~ (all_58_0 = e3) % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | REDUCE: (131), (135) imply: % 154.26/23.45 | | | | | | | | | | | | | | (136) $false % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | CLOSE: (136) is inconsistent. % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | (137) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.26/23.45 | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0) % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | ALPHA: (137) implies: % 154.26/23.45 | | | | | | | | | | | | | | (138) ~ (all_58_10 = e1) % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | REDUCE: (65), (138) imply: % 154.26/23.45 | | | | | | | | | | | | | | (139) ~ (all_52_13 = e1) % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | REF_CLOSE: (12), (32), (110), (127), (139) are inconsistent % 154.26/23.45 | | | | | | | | | | | | | | by sub-proof #601. % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | (140) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.26/23.45 | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.26/23.45 | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.26/23.45 | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | REF_CLOSE: (28), (109), (140) are inconsistent by sub-proof % 154.26/23.45 | | | | | | | | | | | | | #478. % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | (141) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | BETA: splitting (141) gives: % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | (142) all_56_10 = e3 % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | REF_CLOSE: (50), (127), (142) are inconsistent by sub-proof % 154.26/23.45 | | | | | | | | | | | | | #477. % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | (143) all_56_11 = e3 | all_56_15 = e3 % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | BETA: splitting (143) gives: % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | (144) all_56_11 = e3 % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | COMBINE_EQS: (70), (144) imply: % 154.26/23.45 | | | | | | | | | | | | | | (145) e3 = e0 % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | COMBINE_EQS: (125), (145) imply: % 154.26/23.45 | | | | | | | | | | | | | | (146) all_58_29 = e0 % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | BETA: splitting (124) gives: % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | | REF_CLOSE: (48), (125), (146) are inconsistent by sub-proof % 154.26/23.45 | | | | | | | | | | | | | | | #707. % 154.26/23.45 | | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | | (147) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.45 | | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | | REF_CLOSE: (24), (30), (34), (68), (71), (108), (122), (147) % 154.26/23.45 | | | | | | | | | | | | | | | are inconsistent by sub-proof #475. % 154.26/23.45 | | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | (148) all_56_15 = e3 % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | COMBINE_EQS: (105), (148) imply: % 154.26/23.45 | | | | | | | | | | | | | | (149) e3 = e2 % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | REDUCE: (71), (149) imply: % 154.26/23.45 | | | | | | | | | | | | | | (150) $false % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 154.26/23.45 | | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | (151) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | REF_CLOSE: (24), (30), (34), (68), (71), (108), (122), (151) % 154.26/23.45 | | | | | | | | | | | are inconsistent by sub-proof #475. % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | End of split % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | End of split % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | End of split % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | End of split % 154.26/23.45 | | | | | % 154.26/23.45 | | | | End of split % 154.26/23.45 | | | | % 154.26/23.45 | | | End of split % 154.26/23.45 | | | % 154.26/23.45 | | End of split % 154.26/23.45 | | % 154.26/23.45 | Case 2: % 154.26/23.45 | | % 154.26/23.45 | | (152) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.26/23.45 | | % 154.26/23.45 | | BETA: splitting (152) gives: % 154.26/23.45 | | % 154.26/23.45 | | Case 1: % 154.26/23.45 | | | % 154.26/23.45 | | | (153) all_56_13 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (25), (153) imply: % 154.26/23.45 | | | (154) e1 = e0 % 154.26/23.45 | | | % 154.26/23.45 | | | REDUCE: (64), (154) imply: % 154.26/23.45 | | | (155) $false % 154.26/23.45 | | | % 154.26/23.45 | | | CLOSE: (155) is inconsistent. % 154.26/23.45 | | | % 154.26/23.45 | | Case 2: % 154.26/23.45 | | | % 154.26/23.45 | | | (156) all_56_14 = e1 | all_56_15 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | BETA: splitting (156) gives: % 154.26/23.45 | | | % 154.26/23.45 | | | Case 1: % 154.26/23.45 | | | | % 154.26/23.45 | | | | (157) all_56_14 = e1 % 154.26/23.45 | | | | % 154.26/23.45 | | | | COMBINE_EQS: (52), (157) imply: % 154.26/23.45 | | | | (158) all_52_11 = e1 % 154.26/23.45 | | | | % 154.26/23.45 | | | | SIMP: (158) implies: % 154.26/23.45 | | | | (159) all_52_11 = e1 % 154.26/23.45 | | | | % 154.26/23.45 | | | | COMBINE_EQS: (9), (159) imply: % 154.26/23.45 | | | | (160) all_58_26 = e1 % 154.26/23.45 | | | | % 154.26/23.45 | | | | REDUCE: (10), (159) imply: % 154.26/23.45 | | | | (161) ~ (all_52_8 = e1) % 154.26/23.45 | | | | % 154.26/23.45 | | | | REDUCE: (47), (159) imply: % 154.26/23.45 | | | | (162) ~ (all_6_2 = e1) % 154.26/23.45 | | | | % 154.26/23.45 | | | | SIMP: (162) implies: % 154.26/23.45 | | | | (163) ~ (all_6_2 = e1) % 154.26/23.45 | | | | % 154.26/23.45 | | | | REDUCE: (11), (159) imply: % 154.26/23.45 | | | | (164) ~ (all_4_2 = e1) % 154.26/23.45 | | | | % 154.26/23.45 | | | | BETA: splitting (69) gives: % 154.26/23.45 | | | | % 154.26/23.45 | | | | Case 1: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | (165) all_58_28 = e1 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | COMBINE_EQS: (3), (165) imply: % 154.26/23.45 | | | | | (166) e1 = e0 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | REF_CLOSE: (4), (64), (66), (156), (157), (166) are inconsistent by % 154.26/23.45 | | | | | sub-proof #581. % 154.26/23.45 | | | | | % 154.26/23.45 | | | | Case 2: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | (167) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | BETA: splitting (167) gives: % 154.26/23.45 | | | | | % 154.26/23.45 | | | | | Case 1: % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | (168) all_58_29 = e1 % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | COMBINE_EQS: (41), (168) imply: % 154.26/23.45 | | | | | | (169) all_8_2 = e1 % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | REDUCE: (16), (169) imply: % 154.26/23.45 | | | | | | (170) ~ (all_52_4 = e1) % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | REDUCE: (14), (169) imply: % 154.26/23.45 | | | | | | (171) ~ (all_52_6 = e1) % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | BETA: splitting (44) gives: % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | Case 1: % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | (172) all_56_0 = e1 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | COMBINE_EQS: (26), (172) imply: % 154.26/23.45 | | | | | | | (173) e1 = e0 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | REF_CLOSE: (1), (4), (11), (47), (49), (52), (66), (68), (156), % 154.26/23.45 | | | | | | | (167), (168), (173) are inconsistent by sub-proof #670. % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | Case 2: % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | (174) ~ (all_56_0 = e1) % 154.26/23.45 | | | | | | | (175) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | REDUCE: (26), (174) imply: % 154.26/23.45 | | | | | | | (176) ~ (e1 = e0) % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | BETA: splitting (175) gives: % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | (177) all_56_1 = e1 % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | COMBINE_EQS: (36), (177) imply: % 154.26/23.45 | | | | | | | | (178) all_52_4 = e1 % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | REDUCE: (170), (178) imply: % 154.26/23.45 | | | | | | | | (179) $false % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | CLOSE: (179) is inconsistent. % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | (180) all_56_4 = e1 | all_56_9 = e1 % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | BETA: splitting (53) gives: % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | (181) all_56_6 = e1 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | COMBINE_EQS: (43), (181) imply: % 154.26/23.45 | | | | | | | | | (182) all_52_2 = e1 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | SIMP: (182) implies: % 154.26/23.45 | | | | | | | | | (183) all_52_2 = e1 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | COMBINE_EQS: (8), (183) imply: % 154.26/23.45 | | | | | | | | | (184) all_58_15 = e1 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | BETA: splitting (39) gives: % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | (185) all_58_31 = e0 % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | COMBINE_EQS: (1), (185) imply: % 154.26/23.45 | | | | | | | | | | (186) all_4_2 = e0 % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | REDUCE: (56), (186) imply: % 154.26/23.45 | | | | | | | | | | (187) $false % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | CLOSE: (187) is inconsistent. % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | (188) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.26/23.45 | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.45 | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.26/23.45 | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.26/23.45 | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = % 154.26/23.45 | | | | | | | | | | e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 % 154.26/23.45 | | | | | | | | | | = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 154.26/23.45 | | | | | | | | | | all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.26/23.45 | | | | | | | | | | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.45 | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.26/23.45 | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.26/23.45 | | | | | | | | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.26/23.45 | | | | | | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.45 | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.45 | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.26/23.45 | | | | | | | | | | & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = % 154.26/23.45 | | | | | | | | | | e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 % 154.26/23.45 | | | | | | | | | | = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.45 | | | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 % 154.26/23.45 | | | | | | | | | | & all_58_11 = e2 & all_58_15 = e1 & all_58_17 = % 154.26/23.45 | | | | | | | | | | e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 % 154.26/23.45 | | | | | | | | | | = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 154.26/23.45 | | | | | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.26/23.45 | | | | | | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) % 154.26/23.45 | | | | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 % 154.26/23.45 | | | | | | | | | | & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.26/23.45 | | | | | | | | | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 % 154.26/23.45 | | | | | | | | | | = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.45 | | | | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 % 154.26/23.45 | | | | | | | | | | & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.45 | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.26/23.45 | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.26/23.45 | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.45 | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.45 | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.26/23.45 | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.45 | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.26/23.45 | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.45 | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.26/23.45 | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.45 | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | BETA: splitting (180) gives: % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | Case 1: % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | (189) all_56_4 = e1 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | COMBINE_EQS: (15), (189) imply: % 154.26/23.45 | | | | | | | | | | | (190) all_52_8 = e1 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | REDUCE: (161), (190) imply: % 154.26/23.45 | | | | | | | | | | | (191) $false % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | CLOSE: (191) is inconsistent. % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | (192) all_56_9 = e1 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | COMBINE_EQS: (40), (192) imply: % 154.26/23.45 | | | | | | | | | | | (193) all_52_12 = e1 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | SIMP: (193) implies: % 154.26/23.45 | | | | | | | | | | | (194) all_52_12 = e1 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | COMBINE_EQS: (13), (194) imply: % 154.26/23.45 | | | | | | | | | | | (195) all_58_6 = e1 % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | | REF_CLOSE: (1), (3), (17), (18), (21), (22), (30), (37), % 154.26/23.45 | | | | | | | | | | | (38), (42), (48), (55), (60), (61), (64), (66), % 154.26/23.45 | | | | | | | | | | | (68), (71), (160), (161), (167), (168), (184), % 154.26/23.45 | | | | | | | | | | | (188), (195) are inconsistent by sub-proof #466. % 154.26/23.45 | | | | | | | | | | | % 154.26/23.45 | | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | | % 154.26/23.45 | | | | | | | | | End of split % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | Case 2: % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | (196) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | | REF_CLOSE: (1), (3), (5), (17), (30), (42), (48), (55), (58), % 154.26/23.45 | | | | | | | | | (61), (64), (66), (68), (70), (71), (163), (167), % 154.26/23.45 | | | | | | | | | (168), (171), (196) are inconsistent by sub-proof % 154.26/23.45 | | | | | | | | | #465. % 154.26/23.45 | | | | | | | | | % 154.26/23.45 | | | | | | | | End of split % 154.26/23.45 | | | | | | | | % 154.26/23.45 | | | | | | | End of split % 154.26/23.45 | | | | | | | % 154.26/23.45 | | | | | | End of split % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | Case 2: % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | (197) all_58_30 = e1 | all_58_31 = e1 % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | | REF_CLOSE: (1), (66), (68), (163), (197) are inconsistent by % 154.26/23.45 | | | | | | sub-proof #673. % 154.26/23.45 | | | | | | % 154.26/23.45 | | | | | End of split % 154.26/23.45 | | | | | % 154.26/23.45 | | | | End of split % 154.26/23.45 | | | | % 154.26/23.45 | | | Case 2: % 154.26/23.45 | | | | % 154.26/23.45 | | | | (198) all_56_15 = e1 % 154.26/23.45 | | | | % 154.26/23.45 | | | | REF_CLOSE: (4), (66), (198) are inconsistent by sub-proof #671. % 154.26/23.45 | | | | % 154.26/23.45 | | | End of split % 154.26/23.45 | | | % 154.26/23.45 | | End of split % 154.26/23.45 | | % 154.26/23.45 | End of split % 154.26/23.45 | % 154.26/23.45 End of proof % 154.26/23.45 % 154.26/23.45 Sub-proof #465 shows that the following formulas are inconsistent: % 154.26/23.45 ---------------------------------------------------------------- % 154.26/23.45 (1) all_58_31 = all_4_2 % 154.26/23.45 (2) all_58_28 = e0 % 154.26/23.45 (3) all_56_7 = all_52_6 % 154.26/23.45 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.45 (5) ~ (all_52_6 = e1) % 154.26/23.45 (6) ~ (e3 = e1) % 154.26/23.45 (7) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.45 (8) ~ (e2 = e1) % 154.26/23.45 (9) all_58_29 = e1 % 154.26/23.45 (10) ~ (e3 = e0) % 154.26/23.45 (11) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.26/23.45 (12) ~ (e2 = e0) % 154.26/23.45 (13) all_56_8 = all_6_2 % 154.26/23.45 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.45 (15) ~ (e1 = e0) % 154.26/23.45 (16) ~ (all_6_2 = e1) % 154.26/23.45 (17) ~ (all_4_2 = e1) % 154.26/23.45 (18) all_58_30 = all_6_2 % 154.26/23.45 (19) all_56_11 = e0 % 154.26/23.45 (20) ~ (e3 = e2) % 154.26/23.45 % 154.26/23.45 Begin of proof % 154.26/23.45 | % 154.26/23.45 | BETA: splitting (11) gives: % 154.26/23.45 | % 154.26/23.45 | Case 1: % 154.26/23.45 | | % 154.26/23.45 | | (21) all_56_7 = e1 % 154.26/23.45 | | % 154.26/23.45 | | REF_CLOSE: (3), (5), (21) are inconsistent by sub-proof #547. % 154.26/23.45 | | % 154.26/23.45 | Case 2: % 154.26/23.45 | | % 154.26/23.45 | | (22) all_56_8 = e1 | all_56_11 = e1 % 154.26/23.45 | | % 154.26/23.45 | | BETA: splitting (22) gives: % 154.26/23.45 | | % 154.26/23.45 | | Case 1: % 154.26/23.45 | | | % 154.26/23.45 | | | (23) all_56_8 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (13), (23) imply: % 154.26/23.45 | | | (24) all_6_2 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | SIMP: (24) implies: % 154.26/23.45 | | | (25) all_6_2 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (18), (25) imply: % 154.26/23.45 | | | (26) all_58_30 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (12), (14), (20), (26) are % 154.26/23.45 | | | inconsistent by sub-proof #472. % 154.26/23.45 | | | % 154.26/23.45 | | Case 2: % 154.26/23.45 | | | % 154.26/23.45 | | | (27) all_56_11 = e1 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (19), (27) imply: % 154.26/23.45 | | | (28) e1 = e0 % 154.26/23.45 | | | % 154.26/23.45 | | | COMBINE_EQS: (9), (28) imply: % 154.26/23.45 | | | (29) all_58_29 = e0 % 154.26/23.45 | | | % 154.26/23.45 | | | REF_CLOSE: (1), (7), (15), (16), (17), (18), (29) are inconsistent by % 154.26/23.45 | | | sub-proof #672. % 154.26/23.45 | | | % 154.26/23.45 | | End of split % 154.26/23.45 | | % 154.26/23.45 | End of split % 154.26/23.45 | % 154.26/23.45 End of proof % 154.26/23.45 % 154.26/23.45 Sub-proof #466 shows that the following formulas are inconsistent: % 154.26/23.45 ---------------------------------------------------------------- % 154.26/23.46 (1) all_58_31 = all_4_2 % 154.26/23.46 (2) all_58_28 = e0 % 154.26/23.46 (3) all_58_15 = e1 % 154.26/23.46 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.46 (5) all_58_13 = all_52_13 % 154.26/23.46 (6) all_58_11 = e0 % 154.26/23.46 (7) all_58_20 = e0 % 154.26/23.46 (8) ~ (e3 = e1) % 154.26/23.46 (9) all_58_26 = e1 % 154.26/23.46 (10) ~ (all_52_13 = e0) % 154.26/23.46 (11) all_58_24 = e0 % 154.26/23.46 (12) all_58_6 = e1 % 154.26/23.46 (13) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.46 (14) ~ (e2 = e1) % 154.26/23.46 (15) all_58_29 = e1 % 154.26/23.46 (16) ~ (e3 = e0) % 154.26/23.46 (17) ~ (all_52_8 = e1) % 154.26/23.46 (18) ~ (e2 = e0) % 154.26/23.46 (19) all_58_4 = all_52_8 % 154.26/23.46 (20) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.46 (21) ~ (e1 = e0) % 154.26/23.46 (22) ~ (all_4_2 = e1) % 154.26/23.46 (23) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = e3 & % 154.26/23.46 all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 154.26/23.46 all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.26/23.46 all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.46 all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & % 154.26/23.46 all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.46 all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.46 all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.26/23.46 all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.26/23.46 all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 % 154.26/23.46 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = % 154.26/23.46 e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = % 154.26/23.46 e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 % 154.26/23.46 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.46 all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.46 all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.26/23.46 (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.46 (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.26/23.46 (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.26/23.46 (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.26/23.46 (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.46 = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.26/23.46 = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.26/23.46 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.26/23.46 = e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.26/23.46 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.46 all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.46 all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.46 (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.46 (24) all_58_30 = all_6_2 % 154.26/23.46 (25) ~ (e3 = e2) % 154.26/23.46 % 154.26/23.46 Begin of proof % 154.26/23.46 | % 154.26/23.46 | BETA: splitting (23) gives: % 154.26/23.46 | % 154.26/23.46 | Case 1: % 154.26/23.46 | | % 154.26/23.46 | | (26) all_58_30 = e1 % 154.26/23.46 | | % 154.26/23.46 | | REF_CLOSE: (1), (2), (4), (8), (14), (15), (16), (18), (20), (25), (26) are % 154.26/23.46 | | inconsistent by sub-proof #472. % 154.26/23.46 | | % 154.26/23.46 | Case 2: % 154.26/23.46 | | % 154.26/23.46 | | (27) ~ (all_58_30 = e1) % 154.26/23.46 | | (28) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 = e1 & % 154.26/23.46 | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.26/23.46 | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.46 | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 % 154.26/23.46 | | & all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = % 154.26/23.46 | | e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 154.26/23.46 | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = % 154.26/23.46 | | e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 % 154.26/23.46 | | = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.26/23.46 | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.26/23.46 | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 % 154.26/23.46 | | & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.26/23.46 | | e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 % 154.26/23.46 | | = e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.26/23.46 | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 % 154.26/23.46 | | & all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.26/23.46 | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.26/23.46 | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.26/23.46 | | & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.26/23.46 | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 % 154.26/23.46 | | = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.46 | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.46 | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = % 154.26/23.46 | | e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.26/23.46 | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.46 | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.46 | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.46 | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.46 | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.46 | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.26/23.46 | | all_58_26 = e0 & e1 = e0) % 154.26/23.46 | | % 154.26/23.46 | | REDUCE: (24), (27) imply: % 154.26/23.46 | | (29) ~ (all_6_2 = e1) % 154.26/23.46 | | % 154.26/23.46 | | BETA: splitting (28) gives: % 154.26/23.46 | | % 154.26/23.46 | | Case 1: % 154.26/23.46 | | | % 154.26/23.46 | | | (30) all_58_29 = e2 % 154.26/23.46 | | | % 154.26/23.46 | | | REF_CLOSE: (14), (15), (30) are inconsistent by sub-proof #687. % 154.26/23.46 | | | % 154.26/23.46 | | Case 2: % 154.26/23.46 | | | % 154.26/23.46 | | | (31) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.46 | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 % 154.26/23.46 | | | & all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = % 154.26/23.46 | | | e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.46 | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = % 154.26/23.46 | | | e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 % 154.26/23.46 | | | = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.46 | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.26/23.46 | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.46 | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.46 | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.46 | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.46 | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) % 154.26/23.46 | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 154.26/23.46 | | | e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.46 | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = % 154.26/23.46 | | | e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.26/23.46 | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.46 | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = % 154.26/23.46 | | | e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.26/23.46 | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.26/23.46 | | | e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.46 | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.26/23.46 | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = % 154.26/23.46 | | | e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.26/23.46 | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.26/23.46 | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.46 | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.26/23.46 | | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.26/23.46 | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.26/23.46 | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.26/23.46 | | | all_58_26 = e0 & e1 = e0) % 154.26/23.46 | | | % 154.26/23.46 | | | BETA: splitting (31) gives: % 154.26/23.46 | | | % 154.26/23.46 | | | Case 1: % 154.26/23.46 | | | | % 154.26/23.46 | | | | (32) all_58_28 = e3 % 154.26/23.46 | | | | % 154.26/23.46 | | | | REF_CLOSE: (2), (16), (32) are inconsistent by sub-proof #689. % 154.26/23.46 | | | | % 154.26/23.46 | | | Case 2: % 154.26/23.46 | | | | % 154.26/23.46 | | | | (33) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.26/23.46 | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.26/23.46 | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.46 | | | | all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = % 154.26/23.46 | | | | e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.46 | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = % 154.26/23.46 | | | | e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.26/23.46 | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = % 154.26/23.46 | | | | e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.26/23.46 | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.26/23.46 | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.26/23.46 | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.26/23.46 | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.26/23.46 | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.46 | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 % 154.26/23.46 | | | | = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.46 | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 % 154.26/23.46 | | | | = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 % 154.26/23.46 | | | | = e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.46 | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 % 154.26/23.46 | | | | = e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 154.26/23.46 | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 % 154.26/23.46 | | | | = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.46 | | | | = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 154.26/23.46 | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 % 154.26/23.46 | | | | = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.26/23.46 | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 154.26/23.46 | | | | e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 % 154.26/23.46 | | | | = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.46 | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = % 154.26/23.46 | | | | e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 % 154.26/23.46 | | | | = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.46 | | | | % 154.26/23.46 | | | | BETA: splitting (33) gives: % 154.26/23.46 | | | | % 154.26/23.46 | | | | Case 1: % 154.26/23.46 | | | | | % 154.26/23.46 | | | | | (34) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.26/23.46 | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.46 | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.26/23.46 | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.46 | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = e2 & all_58_4 % 154.26/23.46 | | | | | = e3 & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.46 | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 % 154.26/23.46 | | | | | = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.26/23.46 | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = % 154.26/23.46 | | | | | e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 % 154.26/23.46 | | | | | = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.26/23.46 | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = % 154.26/23.46 | | | | | e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.46 | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 % 154.26/23.46 | | | | | = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.26/23.46 | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 154.26/23.46 | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.26/23.46 | | | | | % 154.26/23.46 | | | | | BETA: splitting (34) gives: % 154.26/23.46 | | | | | % 154.26/23.46 | | | | | Case 1: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | (35) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.26/23.46 | | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.46 | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.46 | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.26/23.46 | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.26/23.46 | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.26/23.46 | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.46 | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.46 | | | | | | all_58_11 = e1 & all_58_17 = e1) % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | BETA: splitting (35) gives: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | Case 1: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (36) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 % 154.26/23.46 | | | | | | | = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.46 | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.46 | | | | | | | all_58_11 = e2 & all_58_17 = e2) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (36) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (37) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.26/23.46 | | | | | | | | all_58_15 = e1 % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | ALPHA: (37) implies: % 154.26/23.46 | | | | | | | | (38) all_58_4 = e1 % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | COMBINE_EQS: (19), (38) imply: % 154.26/23.46 | | | | | | | | (39) all_52_8 = e1 % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | REDUCE: (17), (39) imply: % 154.26/23.46 | | | | | | | | (40) $false % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | CLOSE: (40) is inconsistent. % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (41) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.46 | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.26/23.46 | | | | | | | | all_58_11 = e2 & all_58_17 = e2) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (41) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (42) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.26/23.46 | | | | | | | | | all_58_22 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (42) implies: % 154.26/23.46 | | | | | | | | | (43) all_58_6 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (12), (43) imply: % 154.26/23.46 | | | | | | | | | (44) e1 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (15), (44) imply: % 154.26/23.46 | | | | | | | | | (45) all_58_29 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (13), (21), (22), (24), (29), (45) are % 154.26/23.46 | | | | | | | | | inconsistent by sub-proof #672. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (46) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.26/23.46 | | | | | | | | | all_58_17 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (46) implies: % 154.26/23.46 | | | | | | | | | (47) all_58_11 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (6), (18), (47) are inconsistent by sub-proof #471. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | Case 2: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (48) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.46 | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.46 | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.26/23.46 | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.26/23.46 | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.46 | | | | | | | all_58_17 = e1) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (48) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (49) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.46 | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.26/23.46 | | | | | | | | all_58_8 = e2 & all_58_15 = e3) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (49) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (50) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.26/23.46 | | | | | | | | | all_58_24 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (11), (18), (50) are inconsistent by sub-proof % 154.26/23.46 | | | | | | | | | #599. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (51) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.26/23.46 | | | | | | | | | all_58_15 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (51) implies: % 154.26/23.46 | | | | | | | | | (52) all_58_15 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (3), (52) imply: % 154.26/23.46 | | | | | | | | | (53) e3 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REDUCE: (8), (53) imply: % 154.26/23.46 | | | | | | | | | (54) $false % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | CLOSE: (54) is inconsistent. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (55) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.46 | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.26/23.46 | | | | | | | | all_58_11 = e1 & all_58_17 = e1) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (55) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (56) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.26/23.46 | | | | | | | | | all_58_22 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (56) implies: % 154.26/23.46 | | | | | | | | | (57) all_58_6 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (8), (12), (57) are inconsistent by sub-proof #470. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (58) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.26/23.46 | | | | | | | | | all_58_17 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (58) implies: % 154.26/23.46 | | | | | | | | | (59) all_58_11 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (6), (13), (15), (21), (22), (24), (29), (59) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #469. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | End of split % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | Case 2: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | (60) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 % 154.26/23.46 | | | | | | = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.26/23.46 | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 % 154.26/23.46 | | | | | | = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.46 | | | | | | all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.26/23.46 | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & % 154.26/23.46 | | | | | | all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 154.26/23.46 | | | | | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.26/23.46 | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.46 | | | | | | all_58_26 = e0) % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | BETA: splitting (60) gives: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | Case 1: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (61) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.46 | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 154.26/23.46 | | | | | | | e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.46 | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.26/23.46 | | | | | | | all_58_15 = e3 & all_58_17 = e1) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (61) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (62) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.46 | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 % 154.26/23.46 | | | | | | | | = e2) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (62) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (63) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.26/23.46 | | | | | | | | | all_58_24 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (63) implies: % 154.26/23.46 | | | | | | | | | (64) all_58_13 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (5), (64) imply: % 154.26/23.46 | | | | | | | | | (65) all_52_13 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REDUCE: (10), (65) imply: % 154.26/23.46 | | | | | | | | | (66) $false % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | CLOSE: (66) is inconsistent. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (67) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (67) implies: % 154.26/23.46 | | | | | | | | | (68) e3 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REDUCE: (25), (68) imply: % 154.26/23.46 | | | | | | | | | (69) $false % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | CLOSE: (69) is inconsistent. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (70) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.46 | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.26/23.46 | | | | | | | | all_58_15 = e3 & all_58_17 = e1) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (70) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (71) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.26/23.46 | | | | | | | | | all_58_22 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (71) implies: % 154.26/23.46 | | | | | | | | | (72) all_58_6 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (12), (72) imply: % 154.26/23.46 | | | | | | | | | (73) e1 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (15), (73) imply: % 154.26/23.46 | | | | | | | | | (74) all_58_29 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (13), (21), (22), (24), (29), (74) are % 154.26/23.46 | | | | | | | | | inconsistent by sub-proof #672. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (75) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.26/23.46 | | | | | | | | | all_58_17 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (75) implies: % 154.26/23.46 | | | | | | | | | (76) all_58_11 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (6), (13), (15), (21), (22), (24), (29), (76) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #469. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | Case 2: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (77) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.46 | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.26/23.46 | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.26/23.46 | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.46 | | | | | | | all_58_26 = e0) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (77) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (78) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.26/23.46 | | | | | | | | all_58_15 = e1 & all_58_22 = e3) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (78) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (79) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | | | all_58_26 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (79) implies: % 154.26/23.46 | | | | | | | | | (80) all_58_20 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (7), (13), (15), (21), (22), (24), (29), (80) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #468. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (81) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.26/23.46 | | | | | | | | | all_58_22 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (81) implies: % 154.26/23.46 | | | | | | | | | (82) all_58_6 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (8), (12), (82) are inconsistent by sub-proof #470. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (83) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.46 | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.26/23.46 | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (83) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (84) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.26/23.46 | | | | | | | | | all_58_17 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (84) implies: % 154.26/23.46 | | | | | | | | | (85) all_58_11 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (6), (18), (85) are inconsistent by sub-proof #471. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (86) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.26/23.46 | | | | | | | | | all_58_26 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (86) implies: % 154.26/23.46 | | | | | | | | | (87) all_58_26 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (9), (13), (15), (21), (22), (24), (29), (87) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #467. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | End of split % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | End of split % 154.26/23.46 | | | | | % 154.26/23.46 | | | | Case 2: % 154.26/23.46 | | | | | % 154.26/23.46 | | | | | (88) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.26/23.46 | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.46 | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = % 154.26/23.46 | | | | | e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.46 | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.46 | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 % 154.26/23.46 | | | | | & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 154.26/23.46 | | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.26/23.46 | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.26/23.46 | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.46 | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.26/23.46 | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.46 | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.46 | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 % 154.26/23.46 | | | | | & e1 = e0) % 154.26/23.46 | | | | | % 154.26/23.46 | | | | | BETA: splitting (88) gives: % 154.26/23.46 | | | | | % 154.26/23.46 | | | | | Case 1: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | (89) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.26/23.46 | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.46 | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.26/23.46 | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.46 | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.46 | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = % 154.26/23.46 | | | | | | e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | BETA: splitting (89) gives: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | Case 1: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (90) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = % 154.26/23.46 | | | | | | | e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.26/23.46 | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.46 | | | | | | | all_58_26 = e0) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (90) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (91) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | ALPHA: (91) implies: % 154.26/23.46 | | | | | | | | (92) e3 = e1 % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | REDUCE: (8), (92) imply: % 154.26/23.46 | | | | | | | | (93) $false % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | CLOSE: (93) is inconsistent. % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (94) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.46 | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.26/23.46 | | | | | | | | all_58_22 = e3 & all_58_26 = e0) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (94) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (95) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.26/23.46 | | | | | | | | | all_58_24 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (95) implies: % 154.26/23.46 | | | | | | | | | (96) all_58_6 = e3 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (8), (12), (96) are inconsistent by sub-proof #470. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (97) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.26/23.46 | | | | | | | | | all_58_26 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (97) implies: % 154.26/23.46 | | | | | | | | | (98) all_58_26 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (9), (13), (15), (21), (22), (24), (29), (98) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #467. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | Case 2: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (99) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.46 | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.26/23.46 | | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.26/23.46 | | | | | | | = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (99) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (100) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.46 | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | | all_58_22 = e0 & all_58_26 = e1) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (100) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (101) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.26/23.46 | | | | | | | | | all_58_24 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (101) implies: % 154.26/23.46 | | | | | | | | | (102) all_58_6 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (12), (102) imply: % 154.26/23.46 | | | | | | | | | (103) e1 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (15), (103) imply: % 154.26/23.46 | | | | | | | | | (104) all_58_29 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (13), (21), (22), (24), (29), (104) are % 154.26/23.46 | | | | | | | | | inconsistent by sub-proof #672. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (105) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.26/23.46 | | | | | | | | | all_58_26 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (105) implies: % 154.26/23.46 | | | | | | | | | (106) all_58_20 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (7), (13), (15), (21), (22), (24), (29), (106) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #468. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (107) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 % 154.26/23.46 | | | | | | | | = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.26/23.46 | | | | | | | | e0) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (107) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (108) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (108) implies: % 154.26/23.46 | | | | | | | | | (109) all_58_6 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (12), (109) imply: % 154.26/23.46 | | | | | | | | | (110) e1 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (15), (110) imply: % 154.26/23.46 | | | | | | | | | (111) all_58_29 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (13), (21), (22), (24), (29), (111) are % 154.26/23.46 | | | | | | | | | inconsistent by sub-proof #672. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (112) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.26/23.46 | | | | | | | | | all_58_24 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (112) implies: % 154.26/23.46 | | | | | | | | | (113) all_58_11 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (6), (18), (113) are inconsistent by sub-proof % 154.26/23.46 | | | | | | | | | #471. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | End of split % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | Case 2: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | (114) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.46 | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.46 | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.26/23.46 | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.46 | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = % 154.26/23.46 | | | | | | e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.26/23.46 | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.46 | | | | | | all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.26/23.46 | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | BETA: splitting (114) gives: % 154.26/23.46 | | | | | | % 154.26/23.46 | | | | | | Case 1: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (115) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.46 | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.26/23.46 | | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.26/23.46 | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (115) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (116) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.26/23.46 | | | | | | | | all_58_17 = e1 & all_58_24 = e2) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (116) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (117) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | | | all_58_26 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (117) implies: % 154.26/23.46 | | | | | | | | | (118) all_58_20 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (7), (118) imply: % 154.26/23.46 | | | | | | | | | (119) e1 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | COMBINE_EQS: (15), (119) imply: % 154.26/23.46 | | | | | | | | | (120) all_58_29 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (13), (21), (22), (24), (29), (120) are % 154.26/23.46 | | | | | | | | | inconsistent by sub-proof #672. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (121) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.26/23.46 | | | | | | | | | all_58_24 = e2 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (121) implies: % 154.26/23.46 | | | | | | | | | (122) all_58_11 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (6), (13), (15), (21), (22), (24), (29), (122) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #469. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (123) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.46 | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & % 154.26/23.46 | | | | | | | | e2 = e1) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (123) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (124) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.26/23.46 | | | | | | | | | all_58_26 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (124) implies: % 154.26/23.46 | | | | | | | | | (125) all_58_26 = e0 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (9), (13), (15), (21), (22), (24), (29), (125) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #467. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | Case 2: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (126) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | ALPHA: (126) implies: % 154.26/23.46 | | | | | | | | | (127) all_58_11 = e1 % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | REF_CLOSE: (1), (6), (13), (15), (21), (22), (24), (29), (127) % 154.26/23.46 | | | | | | | | | are inconsistent by sub-proof #469. % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | End of split % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | End of split % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | Case 2: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | (128) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.46 | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.26/23.46 | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 % 154.26/23.46 | | | | | | | = e0 & e1 = e0) % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | BETA: splitting (128) gives: % 154.26/23.46 | | | | | | | % 154.26/23.46 | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | (129) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.46 | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.26/23.46 | | | | | | | | all_58_24 = e0 & all_58_26 = e1) % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | BETA: splitting (129) gives: % 154.26/23.46 | | | | | | | | % 154.26/23.46 | | | | | | | | Case 1: % 154.26/23.46 | | | | | | | | | % 154.26/23.46 | | | | | | | | | (130) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.26/23.46 | | | | | | | | | all_58_26 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | ALPHA: (130) implies: % 154.26/23.47 | | | | | | | | | (131) all_58_26 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | REF_CLOSE: (1), (9), (13), (15), (21), (22), (24), (29), (131) % 154.26/23.47 | | | | | | | | | are inconsistent by sub-proof #467. % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | Case 2: % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | (132) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.26/23.47 | | | | | | | | | all_58_26 = e1 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | ALPHA: (132) implies: % 154.26/23.47 | | | | | | | | | (133) all_58_20 = e1 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | REF_CLOSE: (1), (7), (13), (15), (21), (22), (24), (29), (133) % 154.26/23.47 | | | | | | | | | are inconsistent by sub-proof #468. % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | End of split % 154.26/23.47 | | | | | | | | % 154.26/23.47 | | | | | | | Case 2: % 154.26/23.47 | | | | | | | | % 154.26/23.47 | | | | | | | | (134) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.26/23.47 | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.26/23.47 | | | | | | | | % 154.26/23.47 | | | | | | | | BETA: splitting (134) gives: % 154.26/23.47 | | | | | | | | % 154.26/23.47 | | | | | | | | Case 1: % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | (135) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | ALPHA: (135) implies: % 154.26/23.47 | | | | | | | | | (136) e2 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | REDUCE: (18), (136) imply: % 154.26/23.47 | | | | | | | | | (137) $false % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | CLOSE: (137) is inconsistent. % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | Case 2: % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | (138) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | ALPHA: (138) implies: % 154.26/23.47 | | | | | | | | | (139) all_58_26 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | COMBINE_EQS: (9), (139) imply: % 154.26/23.47 | | | | | | | | | (140) e1 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | COMBINE_EQS: (15), (140) imply: % 154.26/23.47 | | | | | | | | | (141) all_58_29 = e0 % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | | REF_CLOSE: (1), (13), (21), (22), (24), (29), (141) are % 154.26/23.47 | | | | | | | | | inconsistent by sub-proof #672. % 154.26/23.47 | | | | | | | | | % 154.26/23.47 | | | | | | | | End of split % 154.26/23.47 | | | | | | | | % 154.26/23.47 | | | | | | | End of split % 154.26/23.47 | | | | | | | % 154.26/23.47 | | | | | | End of split % 154.26/23.47 | | | | | | % 154.26/23.47 | | | | | End of split % 154.26/23.47 | | | | | % 154.26/23.47 | | | | End of split % 154.26/23.47 | | | | % 154.26/23.47 | | | End of split % 154.26/23.47 | | | % 154.26/23.47 | | End of split % 154.26/23.47 | | % 154.26/23.47 | End of split % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #467 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = all_4_2 % 154.26/23.47 (2) all_58_26 = e1 % 154.26/23.47 (3) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.47 (4) all_58_29 = e1 % 154.26/23.47 (5) all_58_26 = e0 % 154.26/23.47 (6) ~ (e1 = e0) % 154.26/23.47 (7) ~ (all_6_2 = e1) % 154.26/23.47 (8) ~ (all_4_2 = e1) % 154.26/23.47 (9) all_58_30 = all_6_2 % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (2), (5) imply: % 154.26/23.47 | (10) e1 = e0 % 154.26/23.47 | % 154.26/23.47 | SIMP: (10) implies: % 154.26/23.47 | (11) e1 = e0 % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (4), (11) imply: % 154.26/23.47 | (12) all_58_29 = e0 % 154.26/23.47 | % 154.26/23.47 | REF_CLOSE: (1), (3), (6), (7), (8), (9), (12) are inconsistent by sub-proof % 154.26/23.47 | #672. % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #468 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = all_4_2 % 154.26/23.47 (2) all_58_20 = e0 % 154.26/23.47 (3) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.47 (4) all_58_29 = e1 % 154.26/23.47 (5) ~ (e1 = e0) % 154.26/23.47 (6) ~ (all_6_2 = e1) % 154.26/23.47 (7) all_58_20 = e1 % 154.26/23.47 (8) ~ (all_4_2 = e1) % 154.26/23.47 (9) all_58_30 = all_6_2 % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (2), (7) imply: % 154.26/23.47 | (10) e1 = e0 % 154.26/23.47 | % 154.26/23.47 | SIMP: (10) implies: % 154.26/23.47 | (11) e1 = e0 % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (4), (11) imply: % 154.26/23.47 | (12) all_58_29 = e0 % 154.26/23.47 | % 154.26/23.47 | REF_CLOSE: (1), (3), (5), (6), (8), (9), (12) are inconsistent by sub-proof % 154.26/23.47 | #672. % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #469 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = all_4_2 % 154.26/23.47 (2) all_58_11 = e0 % 154.26/23.47 (3) all_58_11 = e1 % 154.26/23.47 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.26/23.47 (5) all_58_29 = e1 % 154.26/23.47 (6) ~ (e1 = e0) % 154.26/23.47 (7) ~ (all_6_2 = e1) % 154.26/23.47 (8) ~ (all_4_2 = e1) % 154.26/23.47 (9) all_58_30 = all_6_2 % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (2), (3) imply: % 154.26/23.47 | (10) e1 = e0 % 154.26/23.47 | % 154.26/23.47 | SIMP: (10) implies: % 154.26/23.47 | (11) e1 = e0 % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (5), (11) imply: % 154.26/23.47 | (12) all_58_29 = e0 % 154.26/23.47 | % 154.26/23.47 | REF_CLOSE: (1), (4), (6), (7), (8), (9), (12) are inconsistent by sub-proof % 154.26/23.47 | #672. % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #470 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_6 = e3 % 154.26/23.47 (2) all_58_6 = e1 % 154.26/23.47 (3) ~ (e3 = e1) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (1), (2) imply: % 154.26/23.47 | (4) e3 = e1 % 154.26/23.47 | % 154.26/23.47 | SIMP: (4) implies: % 154.26/23.47 | (5) e3 = e1 % 154.26/23.47 | % 154.26/23.47 | REDUCE: (3), (5) imply: % 154.26/23.47 | (6) $false % 154.26/23.47 | % 154.26/23.47 | CLOSE: (6) is inconsistent. % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #471 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_11 = e2 % 154.26/23.47 (2) all_58_11 = e0 % 154.26/23.47 (3) ~ (e2 = e0) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (1), (2) imply: % 154.26/23.47 | (4) e2 = e0 % 154.26/23.47 | % 154.26/23.47 | SIMP: (4) implies: % 154.26/23.47 | (5) e2 = e0 % 154.26/23.47 | % 154.26/23.47 | REDUCE: (3), (5) imply: % 154.26/23.47 | (6) $false % 154.26/23.47 | % 154.26/23.47 | CLOSE: (6) is inconsistent. % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #472 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = all_4_2 % 154.26/23.47 (2) all_58_28 = e0 % 154.26/23.47 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.47 (4) ~ (e3 = e1) % 154.26/23.47 (5) ~ (e2 = e1) % 154.26/23.47 (6) all_58_29 = e1 % 154.26/23.47 (7) ~ (e3 = e0) % 154.26/23.47 (8) all_58_30 = e1 % 154.26/23.47 (9) ~ (e2 = e0) % 154.26/23.47 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 (11) ~ (e3 = e2) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | BETA: splitting (10) gives: % 154.26/23.47 | % 154.26/23.47 | Case 1: % 154.26/23.47 | | % 154.26/23.47 | | (12) all_58_28 = e3 % 154.26/23.47 | | % 154.26/23.47 | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #689. % 154.26/23.47 | | % 154.26/23.47 | Case 2: % 154.26/23.47 | | % 154.26/23.47 | | (13) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 | | % 154.26/23.47 | | BETA: splitting (3) gives: % 154.26/23.47 | | % 154.26/23.47 | | Case 1: % 154.26/23.47 | | | % 154.26/23.47 | | | (14) all_58_28 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #688. % 154.26/23.47 | | | % 154.26/23.47 | | Case 2: % 154.26/23.47 | | | % 154.26/23.47 | | | (15) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | REF_CLOSE: (1), (4), (5), (6), (8), (11), (13), (15) are inconsistent by % 154.26/23.47 | | | sub-proof #473. % 154.26/23.47 | | | % 154.26/23.47 | | End of split % 154.26/23.47 | | % 154.26/23.47 | End of split % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #473 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = all_4_2 % 154.26/23.47 (2) ~ (e3 = e1) % 154.26/23.47 (3) ~ (e2 = e1) % 154.26/23.47 (4) all_58_29 = e1 % 154.26/23.47 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 (6) all_58_30 = e1 % 154.26/23.47 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.26/23.47 (8) ~ (e3 = e2) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | BETA: splitting (7) gives: % 154.26/23.47 | % 154.26/23.47 | Case 1: % 154.26/23.47 | | % 154.26/23.47 | | (9) all_58_29 = e2 % 154.26/23.47 | | % 154.26/23.47 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #687. % 154.26/23.47 | | % 154.26/23.47 | Case 2: % 154.26/23.47 | | % 154.26/23.47 | | (10) ~ (all_58_29 = e2) % 154.26/23.47 | | (11) all_58_30 = e2 | all_58_31 = e2 % 154.26/23.47 | | % 154.26/23.47 | | REDUCE: (4), (10) imply: % 154.26/23.47 | | (12) ~ (e2 = e1) % 154.26/23.47 | | % 154.26/23.47 | | BETA: splitting (11) gives: % 154.26/23.47 | | % 154.26/23.47 | | Case 1: % 154.26/23.47 | | | % 154.26/23.47 | | | (13) all_58_30 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #500. % 154.26/23.47 | | | % 154.26/23.47 | | Case 2: % 154.26/23.47 | | | % 154.26/23.47 | | | (14) all_58_31 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | COMBINE_EQS: (1), (14) imply: % 154.26/23.47 | | | (15) all_4_2 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | REF_CLOSE: (2), (4), (5), (6), (8), (14) are inconsistent by sub-proof % 154.26/23.47 | | | #474. % 154.26/23.47 | | | % 154.26/23.47 | | End of split % 154.26/23.47 | | % 154.26/23.47 | End of split % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #474 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = e2 % 154.26/23.47 (2) ~ (e3 = e1) % 154.26/23.47 (3) all_58_29 = e1 % 154.26/23.47 (4) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 (5) all_58_30 = e1 % 154.26/23.47 (6) ~ (e3 = e2) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | BETA: splitting (4) gives: % 154.26/23.47 | % 154.26/23.47 | Case 1: % 154.26/23.47 | | % 154.26/23.47 | | (7) all_58_29 = e3 % 154.26/23.47 | | % 154.26/23.47 | | COMBINE_EQS: (3), (7) imply: % 154.26/23.47 | | (8) e3 = e1 % 154.26/23.47 | | % 154.26/23.47 | | REDUCE: (2), (8) imply: % 154.26/23.47 | | (9) $false % 154.26/23.47 | | % 154.26/23.47 | | CLOSE: (9) is inconsistent. % 154.26/23.47 | | % 154.26/23.47 | Case 2: % 154.26/23.47 | | % 154.26/23.47 | | (10) ~ (all_58_29 = e3) % 154.26/23.47 | | (11) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 | | % 154.26/23.47 | | REDUCE: (3), (10) imply: % 154.26/23.47 | | (12) ~ (e3 = e1) % 154.26/23.47 | | % 154.26/23.47 | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #664. % 154.26/23.47 | | % 154.26/23.47 | End of split % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #475 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_31 = e2 % 154.26/23.47 (2) all_54_10 = all_6_2 % 154.26/23.47 (3) ~ (e3 = e1) % 154.26/23.47 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 % 154.26/23.47 (5) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 (6) ~ (all_6_2 = e3) % 154.26/23.47 (7) all_58_30 = all_6_2 % 154.26/23.47 (8) ~ (e3 = e2) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | BETA: splitting (4) gives: % 154.26/23.47 | % 154.26/23.47 | Case 1: % 154.26/23.47 | | % 154.26/23.47 | | (9) all_54_10 = e1 % 154.26/23.47 | | % 154.26/23.47 | | COMBINE_EQS: (2), (9) imply: % 154.26/23.47 | | (10) all_6_2 = e1 % 154.26/23.47 | | % 154.26/23.47 | | SIMP: (10) implies: % 154.26/23.47 | | (11) all_6_2 = e1 % 154.26/23.47 | | % 154.26/23.47 | | COMBINE_EQS: (7), (11) imply: % 154.26/23.47 | | (12) all_58_30 = e1 % 154.26/23.47 | | % 154.26/23.47 | | REF_CLOSE: (1), (3), (5), (8), (12) are inconsistent by sub-proof #664. % 154.26/23.47 | | % 154.26/23.47 | Case 2: % 154.26/23.47 | | % 154.26/23.47 | | (13) all_54_10 = e3 | all_54_10 = e2 % 154.26/23.47 | | % 154.26/23.47 | | BETA: splitting (13) gives: % 154.26/23.47 | | % 154.26/23.47 | | Case 1: % 154.26/23.47 | | | % 154.26/23.47 | | | (14) all_54_10 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | COMBINE_EQS: (2), (14) imply: % 154.26/23.47 | | | (15) all_6_2 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | SIMP: (15) implies: % 154.26/23.47 | | | (16) all_6_2 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | COMBINE_EQS: (7), (16) imply: % 154.26/23.47 | | | (17) all_58_30 = e2 % 154.26/23.47 | | | % 154.26/23.47 | | | REDUCE: (6), (16) imply: % 154.26/23.47 | | | (18) ~ (e3 = e2) % 154.26/23.47 | | | % 154.26/23.47 | | | REF_CLOSE: (1), (5), (8), (17) are inconsistent by sub-proof #476. % 154.26/23.47 | | | % 154.26/23.47 | | Case 2: % 154.26/23.47 | | | % 154.26/23.47 | | | (19) all_54_10 = e3 % 154.26/23.47 | | | % 154.26/23.47 | | | COMBINE_EQS: (2), (19) imply: % 154.26/23.47 | | | (20) all_6_2 = e3 % 154.26/23.47 | | | % 154.26/23.47 | | | SIMP: (20) implies: % 154.26/23.47 | | | (21) all_6_2 = e3 % 154.26/23.47 | | | % 154.26/23.47 | | | REDUCE: (6), (21) imply: % 154.26/23.47 | | | (22) $false % 154.26/23.47 | | | % 154.26/23.47 | | | CLOSE: (22) is inconsistent. % 154.26/23.47 | | | % 154.26/23.47 | | End of split % 154.26/23.47 | | % 154.26/23.47 | End of split % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #476 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_58_30 = e3 | all_58_31 = e3 % 154.26/23.47 (2) all_58_30 = e2 % 154.26/23.47 (3) ~ (e3 = e2) % 154.26/23.47 (4) all_58_31 = e2 % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | BETA: splitting (1) gives: % 154.26/23.47 | % 154.26/23.47 | Case 1: % 154.26/23.47 | | % 154.26/23.47 | | (5) all_58_30 = e3 % 154.26/23.47 | | % 154.26/23.47 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #659. % 154.26/23.47 | | % 154.26/23.47 | Case 2: % 154.26/23.47 | | % 154.26/23.47 | | (6) all_58_31 = e3 % 154.26/23.47 | | % 154.26/23.47 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #585. % 154.26/23.47 | | % 154.26/23.47 | End of split % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #477 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) all_56_10 = all_52_13 % 154.26/23.47 (2) all_56_10 = e3 % 154.26/23.47 (3) ~ (all_52_13 = e3) % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | COMBINE_EQS: (1), (2) imply: % 154.26/23.47 | (4) all_52_13 = e3 % 154.26/23.47 | % 154.26/23.47 | SIMP: (4) implies: % 154.26/23.47 | (5) all_52_13 = e3 % 154.26/23.47 | % 154.26/23.47 | REDUCE: (3), (5) imply: % 154.26/23.47 | (6) $false % 154.26/23.47 | % 154.26/23.47 | CLOSE: (6) is inconsistent. % 154.26/23.47 | % 154.26/23.47 End of proof % 154.26/23.47 % 154.26/23.47 Sub-proof #478 shows that the following formulas are inconsistent: % 154.26/23.47 ---------------------------------------------------------------- % 154.26/23.47 (1) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.26/23.47 (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.26/23.47 (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.26/23.47 (2) all_58_19 = e0 % 154.26/23.47 (3) all_58_23 = e2 % 154.26/23.47 % 154.26/23.47 Begin of proof % 154.26/23.47 | % 154.26/23.47 | BETA: splitting (1) gives: % 154.26/23.47 | % 154.26/23.47 | Case 1: % 154.26/23.47 | | % 154.26/23.47 | | (4) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.26/23.47 | | (all_58_19 = e0) % 154.26/23.47 | | % 154.26/23.47 | | ALPHA: (4) implies: % 154.26/23.47 | | (5) ~ (all_58_19 = e0) % 154.52/23.47 | | % 154.52/23.47 | | REDUCE: (2), (5) imply: % 154.52/23.47 | | (6) $false % 154.52/23.47 | | % 154.52/23.47 | | CLOSE: (6) is inconsistent. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (7) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.52/23.47 | | (all_58_27 = e0) % 154.52/23.47 | | % 154.52/23.47 | | ALPHA: (7) implies: % 154.52/23.47 | | (8) ~ (all_58_23 = e2) % 154.52/23.47 | | % 154.52/23.47 | | REDUCE: (3), (8) imply: % 154.52/23.47 | | (9) $false % 154.52/23.47 | | % 154.52/23.47 | | CLOSE: (9) is inconsistent. % 154.52/23.47 | | % 154.52/23.47 | End of split % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #479 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_54_14 = all_10_0 % 154.52/23.47 (2) all_54_14 = e0 % 154.52/23.47 (3) ~ (all_10_0 = e0) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | COMBINE_EQS: (1), (2) imply: % 154.52/23.47 | (4) all_10_0 = e0 % 154.52/23.47 | % 154.52/23.47 | SIMP: (4) implies: % 154.52/23.47 | (5) all_10_0 = e0 % 154.52/23.47 | % 154.52/23.47 | REDUCE: (3), (5) imply: % 154.52/23.47 | (6) $false % 154.52/23.47 | % 154.52/23.47 | CLOSE: (6) is inconsistent. % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #480 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_56_7 = all_52_6 % 154.52/23.47 (2) all_56_3 = e0 % 154.52/23.47 (3) all_56_4 = all_52_8 % 154.52/23.47 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.47 (5) ~ (all_6_2 = e0) % 154.52/23.47 (6) ~ (e3 = e1) % 154.52/23.47 (7) ~ (all_52_6 = e0) % 154.52/23.47 (8) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.52/23.47 (9) all_56_11 = all_52_14 % 154.52/23.47 (10) all_56_1 = all_52_4 % 154.52/23.47 (11) all_56_3 = all_8_2 % 154.52/23.47 (12) all_56_9 = all_52_12 % 154.52/23.47 (13) all_58_29 = all_8_2 % 154.52/23.47 (14) ~ (all_52_12 = all_52_14) % 154.52/23.47 (15) ~ (e2 = e1) % 154.52/23.47 (16) ~ (all_52_4 = e0) % 154.52/23.47 (17) ~ (e3 = e0) % 154.52/23.47 (18) all_58_28 = all_10_2 % 154.52/23.47 (19) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.52/23.47 (20) ~ (e2 = e0) % 154.52/23.47 (21) all_56_0 = all_10_2 % 154.52/23.47 (22) all_56_8 = all_6_2 % 154.52/23.47 (23) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.47 (24) ~ (e1 = e0) % 154.52/23.47 (25) ~ (all_52_8 = e0) % 154.52/23.47 (26) all_58_30 = all_6_2 % 154.52/23.47 (27) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.47 (28) ~ (e3 = e2) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | COMBINE_EQS: (2), (11) imply: % 154.52/23.47 | (29) all_8_2 = e0 % 154.52/23.47 | % 154.52/23.47 | COMBINE_EQS: (13), (29) imply: % 154.52/23.47 | (30) all_58_29 = e0 % 154.52/23.47 | % 154.52/23.47 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15), % 154.52/23.47 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 154.52/23.47 | (27), (28), (30) are inconsistent by sub-proof #481. % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #481 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_56_7 = all_52_6 % 154.52/23.47 (2) all_56_4 = all_52_8 % 154.52/23.47 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.47 (4) ~ (all_6_2 = e0) % 154.52/23.47 (5) ~ (e3 = e1) % 154.52/23.47 (6) ~ (all_52_6 = e0) % 154.52/23.47 (7) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.52/23.47 (8) all_56_11 = all_52_14 % 154.52/23.47 (9) all_56_1 = all_52_4 % 154.52/23.47 (10) all_58_29 = e0 % 154.52/23.47 (11) all_56_9 = all_52_12 % 154.52/23.47 (12) ~ (all_52_12 = all_52_14) % 154.52/23.47 (13) ~ (e2 = e1) % 154.52/23.47 (14) ~ (all_52_4 = e0) % 154.52/23.47 (15) ~ (e3 = e0) % 154.52/23.47 (16) all_58_28 = all_10_2 % 154.52/23.47 (17) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.52/23.47 (18) ~ (e2 = e0) % 154.52/23.47 (19) all_56_0 = all_10_2 % 154.52/23.47 (20) all_56_8 = all_6_2 % 154.52/23.47 (21) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.47 (22) ~ (e1 = e0) % 154.52/23.47 (23) ~ (all_52_8 = e0) % 154.52/23.47 (24) all_58_30 = all_6_2 % 154.52/23.47 (25) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.47 (26) ~ (e3 = e2) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | BETA: splitting (7) gives: % 154.52/23.47 | % 154.52/23.47 | Case 1: % 154.52/23.47 | | % 154.52/23.47 | | (27) all_56_0 = e0 % 154.52/23.47 | | % 154.52/23.47 | | COMBINE_EQS: (19), (27) imply: % 154.52/23.47 | | (28) all_10_2 = e0 % 154.52/23.47 | | % 154.52/23.47 | | COMBINE_EQS: (16), (28) imply: % 154.52/23.47 | | (29) all_58_28 = e0 % 154.52/23.47 | | % 154.52/23.47 | | REF_CLOSE: (3), (5), (10), (13), (15), (18), (21), (22), (24), (25), (26), % 154.52/23.47 | | (29) are inconsistent by sub-proof #483. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (30) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.52/23.47 | | % 154.52/23.47 | | BETA: splitting (30) gives: % 154.52/23.47 | | % 154.52/23.47 | | Case 1: % 154.52/23.47 | | | % 154.52/23.47 | | | (31) all_56_1 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | COMBINE_EQS: (9), (31) imply: % 154.52/23.47 | | | (32) all_52_4 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (14), (32) imply: % 154.52/23.47 | | | (33) $false % 154.52/23.47 | | | % 154.52/23.47 | | | CLOSE: (33) is inconsistent. % 154.52/23.47 | | | % 154.52/23.47 | | Case 2: % 154.52/23.47 | | | % 154.52/23.47 | | | (34) all_56_4 = e0 | all_56_9 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | REF_CLOSE: (1), (2), (4), (6), (8), (11), (12), (17), (20), (23), (34) are % 154.52/23.47 | | | inconsistent by sub-proof #482. % 154.52/23.47 | | | % 154.52/23.47 | | End of split % 154.52/23.47 | | % 154.52/23.47 | End of split % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #482 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_56_7 = all_52_6 % 154.52/23.47 (2) all_56_4 = all_52_8 % 154.52/23.47 (3) ~ (all_6_2 = e0) % 154.52/23.47 (4) all_56_4 = e0 | all_56_9 = e0 % 154.52/23.47 (5) ~ (all_52_6 = e0) % 154.52/23.47 (6) all_56_11 = all_52_14 % 154.52/23.47 (7) all_56_9 = all_52_12 % 154.52/23.47 (8) ~ (all_52_12 = all_52_14) % 154.52/23.47 (9) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 154.52/23.47 (10) all_56_8 = all_6_2 % 154.52/23.47 (11) ~ (all_52_8 = e0) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | BETA: splitting (9) gives: % 154.52/23.47 | % 154.52/23.47 | Case 1: % 154.52/23.47 | | % 154.52/23.47 | | (12) all_56_7 = e0 % 154.52/23.47 | | % 154.52/23.47 | | COMBINE_EQS: (1), (12) imply: % 154.52/23.47 | | (13) all_52_6 = e0 % 154.52/23.47 | | % 154.52/23.47 | | REDUCE: (5), (13) imply: % 154.52/23.47 | | (14) $false % 154.52/23.47 | | % 154.52/23.47 | | CLOSE: (14) is inconsistent. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (15) all_56_8 = e0 | all_56_11 = e0 % 154.52/23.47 | | % 154.52/23.47 | | BETA: splitting (15) gives: % 154.52/23.47 | | % 154.52/23.47 | | Case 1: % 154.52/23.47 | | | % 154.52/23.47 | | | (16) all_56_8 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | REF_CLOSE: (3), (10), (16) are inconsistent by sub-proof #764. % 154.52/23.47 | | | % 154.52/23.47 | | Case 2: % 154.52/23.47 | | | % 154.52/23.47 | | | (17) all_56_11 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | COMBINE_EQS: (6), (17) imply: % 154.52/23.47 | | | (18) all_52_14 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | SIMP: (18) implies: % 154.52/23.47 | | | (19) all_52_14 = e0 % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (8), (19) imply: % 154.52/23.47 | | | (20) ~ (all_52_12 = e0) % 154.52/23.47 | | | % 154.52/23.47 | | | REF_CLOSE: (2), (4), (7), (11), (20) are inconsistent by sub-proof #520. % 154.52/23.47 | | | % 154.52/23.47 | | End of split % 154.52/23.47 | | % 154.52/23.47 | End of split % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #483 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_58_28 = e0 % 154.52/23.47 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.47 (3) ~ (e3 = e1) % 154.52/23.47 (4) all_58_29 = e0 % 154.52/23.47 (5) ~ (e2 = e1) % 154.52/23.47 (6) ~ (e3 = e0) % 154.52/23.47 (7) ~ (e2 = e0) % 154.52/23.47 (8) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.47 (9) ~ (e1 = e0) % 154.52/23.47 (10) all_58_30 = all_6_2 % 154.52/23.47 (11) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.47 (12) ~ (e3 = e2) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | BETA: splitting (11) gives: % 154.52/23.47 | % 154.52/23.47 | Case 1: % 154.52/23.47 | | % 154.52/23.47 | | (13) all_58_28 = e1 % 154.52/23.47 | | % 154.52/23.47 | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #690. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (14) ~ (all_58_28 = e1) % 154.52/23.47 | | (15) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.47 | | % 154.52/23.47 | | REDUCE: (1), (14) imply: % 154.52/23.47 | | (16) ~ (e1 = e0) % 154.52/23.47 | | % 154.52/23.47 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (15) are % 154.52/23.47 | | inconsistent by sub-proof #651. % 154.52/23.47 | | % 154.52/23.47 | End of split % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #484 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_58_31 = all_4_2 % 154.52/23.47 (2) all_56_4 = all_52_8 % 154.52/23.47 (3) all_56_0 = e0 % 154.52/23.47 (4) all_56_1 = all_52_4 % 154.52/23.47 (5) all_56_9 = all_52_12 % 154.52/23.47 (6) ~ (all_52_4 = e1) % 154.52/23.47 (7) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.52/23.47 (8) ~ (all_52_12 = e1) % 154.52/23.47 (9) all_58_30 = e1 % 154.52/23.47 (10) ~ (all_52_8 = e1) % 154.52/23.47 (11) all_58_30 = e1 | all_58_31 = e1 % 154.52/23.47 (12) ~ (e1 = e0) % 154.52/23.47 (13) ~ (all_4_2 = e1) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | BETA: splitting (7) gives: % 154.52/23.47 | % 154.52/23.47 | Case 1: % 154.52/23.47 | | % 154.52/23.47 | | (14) all_56_0 = e1 % 154.52/23.47 | | % 154.52/23.47 | | COMBINE_EQS: (3), (14) imply: % 154.52/23.47 | | (15) e1 = e0 % 154.52/23.47 | | % 154.52/23.47 | | REF_CLOSE: (1), (9), (11), (12), (13), (15) are inconsistent by sub-proof % 154.52/23.47 | | #487. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (16) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.52/23.47 | | % 154.52/23.47 | | BETA: splitting (16) gives: % 154.52/23.47 | | % 154.52/23.47 | | Case 1: % 154.52/23.47 | | | % 154.52/23.47 | | | (17) all_56_1 = e1 % 154.52/23.47 | | | % 154.52/23.47 | | | COMBINE_EQS: (4), (17) imply: % 154.52/23.47 | | | (18) all_52_4 = e1 % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (6), (18) imply: % 154.52/23.47 | | | (19) $false % 154.52/23.47 | | | % 154.52/23.47 | | | CLOSE: (19) is inconsistent. % 154.52/23.47 | | | % 154.52/23.47 | | Case 2: % 154.52/23.47 | | | % 154.52/23.47 | | | (20) all_56_4 = e1 | all_56_9 = e1 % 154.52/23.47 | | | % 154.52/23.47 | | | REF_CLOSE: (2), (5), (8), (10), (20) are inconsistent by sub-proof #485. % 154.52/23.47 | | | % 154.52/23.47 | | End of split % 154.52/23.47 | | % 154.52/23.47 | End of split % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #485 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_56_4 = all_52_8 % 154.52/23.47 (2) all_56_9 = all_52_12 % 154.52/23.47 (3) all_56_4 = e1 | all_56_9 = e1 % 154.52/23.47 (4) ~ (all_52_12 = e1) % 154.52/23.47 (5) ~ (all_52_8 = e1) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | BETA: splitting (3) gives: % 154.52/23.47 | % 154.52/23.47 | Case 1: % 154.52/23.47 | | % 154.52/23.47 | | (6) all_56_4 = e1 % 154.52/23.47 | | % 154.52/23.47 | | COMBINE_EQS: (1), (6) imply: % 154.52/23.47 | | (7) all_52_8 = e1 % 154.52/23.47 | | % 154.52/23.47 | | REDUCE: (5), (7) imply: % 154.52/23.47 | | (8) $false % 154.52/23.47 | | % 154.52/23.47 | | CLOSE: (8) is inconsistent. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (9) all_56_9 = e1 % 154.52/23.47 | | % 154.52/23.47 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #486. % 154.52/23.47 | | % 154.52/23.47 | End of split % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #486 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_56_9 = all_52_12 % 154.52/23.47 (2) all_56_9 = e1 % 154.52/23.47 (3) ~ (all_52_12 = e1) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | COMBINE_EQS: (1), (2) imply: % 154.52/23.47 | (4) all_52_12 = e1 % 154.52/23.47 | % 154.52/23.47 | SIMP: (4) implies: % 154.52/23.47 | (5) all_52_12 = e1 % 154.52/23.47 | % 154.52/23.47 | REDUCE: (3), (5) imply: % 154.52/23.47 | (6) $false % 154.52/23.47 | % 154.52/23.47 | CLOSE: (6) is inconsistent. % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #487 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_58_31 = all_4_2 % 154.52/23.47 (2) all_58_30 = e1 % 154.52/23.47 (3) all_58_30 = e1 | all_58_31 = e1 % 154.52/23.47 (4) e1 = e0 % 154.52/23.47 (5) ~ (e1 = e0) % 154.52/23.47 (6) ~ (all_4_2 = e1) % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | SIMP: (4) implies: % 154.52/23.47 | (7) e1 = e0 % 154.52/23.47 | % 154.52/23.47 | COMBINE_EQS: (2), (7) imply: % 154.52/23.47 | (8) all_58_30 = e0 % 154.52/23.47 | % 154.52/23.47 | REF_CLOSE: (1), (3), (5), (6), (8) are inconsistent by sub-proof #711. % 154.52/23.47 | % 154.52/23.47 End of proof % 154.52/23.47 % 154.52/23.47 Sub-proof #488 shows that the following formulas are inconsistent: % 154.52/23.47 ---------------------------------------------------------------- % 154.52/23.47 (1) all_58_12 = e0 % 154.52/23.47 (2) all_58_31 = all_4_2 % 154.52/23.47 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.52/23.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.52/23.47 (4) all_58_28 = e0 % 154.52/23.47 (5) all_56_14 = e0 % 154.52/23.47 (6) all_56_15 = all_4_2 % 154.52/23.47 (7) ~ (all_10_1 = e0) % 154.52/23.47 (8) op(e3, all_52_4) = all_58_1 % 154.52/23.47 (9) ~ (all_52_4 = all_8_2) % 154.52/23.47 (10) all_54_1 = all_52_4 % 154.52/23.47 (11) ~ (all_10_1 = all_4_2) % 154.52/23.47 (12) all_56_13 = e1 % 154.52/23.47 (13) op(e3, e2) = all_52_4 % 154.52/23.47 (14) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.52/23.47 (15) all_54_12 = all_10_1 % 154.52/23.47 (16) all_56_1 = all_52_4 % 154.52/23.47 (17) ~ (all_10_1 = e2) % 154.52/23.47 (18) op(e0, e3) = all_10_1 % 154.52/23.47 (19) all_58_21 = all_10_0 % 154.52/23.47 (20) all_58_29 = all_8_2 % 154.52/23.47 (21) ~ (all_52_4 = e1) % 154.52/23.47 (22) ~ (e2 = e1) % 154.52/23.47 (23) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.52/23.47 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.52/23.47 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.52/23.47 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.52/23.47 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.52/23.47 (all_58_27 = e0)) % 154.52/23.47 (24) all_58_18 = e1 % 154.52/23.47 (25) all_58_30 = e1 % 154.52/23.47 (26) ~ (e2 = e0) % 154.52/23.47 (27) ~ (all_10_1 = e1) % 154.52/23.47 (28) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.52/23.47 (29) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.52/23.47 (30) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.47 (31) op(e0, all_10_1) = all_10_0 % 154.52/23.47 (32) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.52/23.47 % 154.52/23.47 Begin of proof % 154.52/23.47 | % 154.52/23.47 | BETA: splitting (32) gives: % 154.52/23.47 | % 154.52/23.47 | Case 1: % 154.52/23.47 | | % 154.52/23.47 | | (33) all_54_12 = e1 % 154.52/23.47 | | % 154.52/23.47 | | REF_CLOSE: (15), (27), (33) are inconsistent by sub-proof #514. % 154.52/23.47 | | % 154.52/23.47 | Case 2: % 154.52/23.47 | | % 154.52/23.47 | | (34) ~ (all_54_12 = e1) % 154.52/23.47 | | (35) all_54_12 = e3 | all_54_12 = e2 % 154.52/23.47 | | % 154.52/23.47 | | BETA: splitting (35) gives: % 154.52/23.47 | | % 154.52/23.47 | | Case 1: % 154.52/23.47 | | | % 154.52/23.47 | | | (36) all_54_12 = e2 % 154.52/23.47 | | | % 154.52/23.47 | | | REF_CLOSE: (15), (17), (36) are inconsistent by sub-proof #513. % 154.52/23.47 | | | % 154.52/23.47 | | Case 2: % 154.52/23.47 | | | % 154.52/23.47 | | | (37) all_54_12 = e3 % 154.52/23.47 | | | % 154.52/23.47 | | | COMBINE_EQS: (15), (37) imply: % 154.52/23.47 | | | (38) all_10_1 = e3 % 154.52/23.47 | | | % 154.52/23.47 | | | SIMP: (38) implies: % 154.52/23.47 | | | (39) all_10_1 = e3 % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (11), (39) imply: % 154.52/23.47 | | | (40) ~ (all_4_2 = e3) % 154.52/23.47 | | | % 154.52/23.47 | | | SIMP: (40) implies: % 154.52/23.47 | | | (41) ~ (all_4_2 = e3) % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (27), (39) imply: % 154.52/23.47 | | | (42) ~ (e3 = e1) % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (7), (39) imply: % 154.52/23.47 | | | (43) ~ (e3 = e0) % 154.52/23.47 | | | % 154.52/23.47 | | | REDUCE: (31), (39) imply: % 154.52/23.48 | | | (44) op(e0, e3) = all_10_0 % 154.52/23.48 | | | % 154.52/23.48 | | | REDUCE: (18), (39) imply: % 154.52/23.48 | | | (45) op(e0, e3) = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | BETA: splitting (29) gives: % 154.52/23.48 | | | % 154.52/23.48 | | | Case 1: % 154.52/23.48 | | | | % 154.52/23.48 | | | | (46) all_56_13 = e2 % 154.52/23.48 | | | | % 154.52/23.48 | | | | COMBINE_EQS: (12), (46) imply: % 154.52/23.48 | | | | (47) e2 = e1 % 154.52/23.48 | | | | % 154.52/23.48 | | | | REDUCE: (22), (47) imply: % 154.52/23.48 | | | | (48) $false % 154.52/23.48 | | | | % 154.52/23.48 | | | | CLOSE: (48) is inconsistent. % 154.52/23.48 | | | | % 154.52/23.48 | | | Case 2: % 154.52/23.48 | | | | % 154.52/23.48 | | | | (49) all_56_14 = e2 | all_56_15 = e2 % 154.52/23.48 | | | | % 154.52/23.48 | | | | BETA: splitting (49) gives: % 154.52/23.48 | | | | % 154.52/23.48 | | | | Case 1: % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | (50) all_56_14 = e2 % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | COMBINE_EQS: (5), (50) imply: % 154.52/23.48 | | | | | (51) e2 = e0 % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | REDUCE: (26), (51) imply: % 154.52/23.48 | | | | | (52) $false % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | CLOSE: (52) is inconsistent. % 154.52/23.48 | | | | | % 154.52/23.48 | | | | Case 2: % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | (53) all_56_15 = e2 % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | COMBINE_EQS: (6), (53) imply: % 154.52/23.48 | | | | | (54) all_4_2 = e2 % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | SIMP: (54) implies: % 154.52/23.48 | | | | | (55) all_4_2 = e2 % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | COMBINE_EQS: (2), (55) imply: % 154.52/23.48 | | | | | (56) all_58_31 = e2 % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | REDUCE: (41), (55) imply: % 154.52/23.48 | | | | | (57) ~ (e3 = e2) % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | SIMP: (57) implies: % 154.52/23.48 | | | | | (58) ~ (e3 = e2) % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | BETA: splitting (30) gives: % 154.52/23.48 | | | | | % 154.52/23.48 | | | | | Case 1: % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | | (59) all_58_28 = e3 % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | | REF_CLOSE: (4), (43), (59) are inconsistent by sub-proof #689. % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | Case 2: % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | | (60) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | | BETA: splitting (60) gives: % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | | Case 1: % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | (61) all_58_29 = e3 % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | COMBINE_EQS: (20), (61) imply: % 154.52/23.48 | | | | | | | (62) all_8_2 = e3 % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | REDUCE: (9), (62) imply: % 154.52/23.48 | | | | | | | (63) ~ (all_52_4 = e3) % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | BETA: splitting (28) gives: % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | Case 1: % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | (64) all_56_1 = e2 % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | COMBINE_EQS: (16), (64) imply: % 154.52/23.48 | | | | | | | | (65) all_52_4 = e2 % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | SIMP: (65) implies: % 154.52/23.48 | | | | | | | | (66) all_52_4 = e2 % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | REDUCE: (8), (66) imply: % 154.52/23.48 | | | | | | | | (67) op(e3, e2) = all_58_1 % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | REDUCE: (13), (66) imply: % 154.52/23.48 | | | | | | | | (68) op(e3, e2) = e2 % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | REF_CLOSE: (1), (3), (19), (23), (24), (44), (45), (67), (68) % 154.52/23.48 | | | | | | | | are inconsistent by sub-proof #489. % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | Case 2: % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | (69) ~ (all_56_1 = e2) % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | REDUCE: (16), (69) imply: % 154.52/23.48 | | | | | | | | (70) ~ (all_52_4 = e2) % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | | REF_CLOSE: (10), (14), (21), (63), (70) are inconsistent by % 154.52/23.48 | | | | | | | | sub-proof #738. % 154.52/23.48 | | | | | | | | % 154.52/23.48 | | | | | | | End of split % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | Case 2: % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | (71) all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | | REF_CLOSE: (25), (42), (56), (58), (71) are inconsistent by % 154.52/23.48 | | | | | | | sub-proof #664. % 154.52/23.48 | | | | | | | % 154.52/23.48 | | | | | | End of split % 154.52/23.48 | | | | | | % 154.52/23.48 | | | | | End of split % 154.52/23.48 | | | | | % 154.52/23.48 | | | | End of split % 154.52/23.48 | | | | % 154.52/23.48 | | | End of split % 154.52/23.48 | | | % 154.52/23.48 | | End of split % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #489 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_12 = e0 % 154.52/23.48 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.52/23.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.52/23.48 (3) all_58_21 = all_10_0 % 154.52/23.48 (4) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.52/23.48 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.52/23.48 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.52/23.48 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.52/23.48 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.52/23.48 (all_58_27 = e0)) % 154.52/23.48 (5) op(e3, e2) = e2 % 154.52/23.48 (6) op(e3, e2) = all_58_1 % 154.52/23.48 (7) op(e0, e3) = e3 % 154.52/23.48 (8) all_58_18 = e1 % 154.52/23.48 (9) op(e0, e3) = all_10_0 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | GROUND_INST: instantiating (2) with e3, all_10_0, e3, e0, simplifying with % 154.52/23.48 | (7), (9) gives: % 154.52/23.48 | (10) all_10_0 = e3 % 154.52/23.48 | % 154.52/23.48 | GROUND_INST: instantiating (2) with e2, all_58_1, e2, e3, simplifying with % 154.52/23.48 | (5), (6) gives: % 154.52/23.48 | (11) all_58_1 = e2 % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (3), (10) imply: % 154.52/23.48 | (12) all_58_21 = e3 % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (4) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (13) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.52/23.48 | | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.52/23.48 | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (11), (13) are inconsistent by sub-proof #617. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (14) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 154.52/23.48 | | ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & % 154.52/23.48 | | ~ (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.52/23.48 | | % 154.52/23.48 | | BETA: splitting (14) gives: % 154.52/23.48 | | % 154.52/23.48 | | Case 1: % 154.52/23.48 | | | % 154.52/23.48 | | | (15) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 154.52/23.48 | | | ~ (all_58_19 = e0) % 154.52/23.48 | | | % 154.52/23.48 | | | ALPHA: (15) implies: % 154.52/23.48 | | | (16) ~ (all_58_18 = e1) % 154.52/23.48 | | | % 154.52/23.48 | | | REDUCE: (8), (16) imply: % 154.52/23.48 | | | (17) $false % 154.52/23.48 | | | % 154.52/23.48 | | | CLOSE: (17) is inconsistent. % 154.52/23.48 | | | % 154.52/23.48 | | Case 2: % 154.52/23.48 | | | % 154.52/23.48 | | | (18) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & % 154.52/23.48 | | | ~ (all_58_27 = e0) % 154.52/23.48 | | | % 154.52/23.48 | | | ALPHA: (18) implies: % 154.52/23.48 | | | (19) ~ (all_58_21 = e3) % 154.52/23.48 | | | % 154.52/23.48 | | | REDUCE: (12), (19) imply: % 154.52/23.48 | | | (20) $false % 154.52/23.48 | | | % 154.52/23.48 | | | CLOSE: (20) is inconsistent. % 154.52/23.48 | | | % 154.52/23.48 | | End of split % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #490 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_15 = all_4_2 % 154.52/23.48 (2) all_54_15 = e2 % 154.52/23.48 (3) ~ (all_4_2 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (1), (2) imply: % 154.52/23.48 | (4) all_4_2 = e2 % 154.52/23.48 | % 154.52/23.48 | SIMP: (4) implies: % 154.52/23.48 | (5) all_4_2 = e2 % 154.52/23.48 | % 154.52/23.48 | REDUCE: (3), (5) imply: % 154.52/23.48 | (6) $false % 154.52/23.48 | % 154.52/23.48 | CLOSE: (6) is inconsistent. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #491 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.52/23.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.52/23.48 (2) ~ (all_10_0 = e0) % 154.52/23.48 (3) op(e0, e1) = e0 % 154.52/23.48 (4) all_10_1 = e1 % 154.52/23.48 (5) op(e0, all_10_1) = all_10_0 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | REDUCE: (4), (5) imply: % 154.52/23.48 | (6) op(e0, e1) = all_10_0 % 154.52/23.48 | % 154.52/23.48 | GROUND_INST: instantiating (1) with e0, all_10_0, e1, e0, simplifying with % 154.52/23.48 | (3), (6) gives: % 154.52/23.48 | (7) all_10_0 = e0 % 154.52/23.48 | % 154.52/23.48 | REDUCE: (2), (7) imply: % 154.52/23.48 | (8) $false % 154.52/23.48 | % 154.52/23.48 | CLOSE: (8) is inconsistent. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #492 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_31 = all_4_2 % 154.52/23.48 (2) all_58_28 = e0 % 154.52/23.48 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 (4) all_54_10 = all_6_2 % 154.52/23.48 (5) ~ (e3 = e1) % 154.52/23.48 (6) all_58_29 = all_8_2 % 154.52/23.48 (7) ~ (e2 = e1) % 154.52/23.48 (8) ~ (e3 = e0) % 154.52/23.48 (9) ~ (e2 = e0) % 154.52/23.48 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 (11) ~ (e1 = e0) % 154.52/23.48 (12) all_54_10 = e0 % 154.52/23.48 (13) ~ (all_4_2 = e1) % 154.52/23.48 (14) all_58_30 = all_6_2 % 154.52/23.48 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.48 (16) ~ (e3 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (4), (12) imply: % 154.52/23.48 | (17) all_6_2 = e0 % 154.52/23.48 | % 154.52/23.48 | SIMP: (17) implies: % 154.52/23.48 | (18) all_6_2 = e0 % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (14), (18) imply: % 154.52/23.48 | (19) all_58_30 = e0 % 154.52/23.48 | % 154.52/23.48 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (15), % 154.52/23.48 | (16), (19) are inconsistent by sub-proof #684. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #493 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_15 = all_4_2 % 154.52/23.48 (2) all_54_15 = e0 % 154.52/23.48 (3) ~ (all_4_2 = e0) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (1), (2) imply: % 154.52/23.48 | (4) all_4_2 = e0 % 154.52/23.48 | % 154.52/23.48 | SIMP: (4) implies: % 154.52/23.48 | (5) all_4_2 = e0 % 154.52/23.48 | % 154.52/23.48 | REDUCE: (3), (5) imply: % 154.52/23.48 | (6) $false % 154.52/23.48 | % 154.52/23.48 | CLOSE: (6) is inconsistent. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #494 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_56_11 = all_52_14 % 154.52/23.48 (2) all_56_11 = e2 % 154.52/23.48 (3) ~ (all_52_14 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (1), (2) imply: % 154.52/23.48 | (4) all_52_14 = e2 % 154.52/23.48 | % 154.52/23.48 | SIMP: (4) implies: % 154.52/23.48 | (5) all_52_14 = e2 % 154.52/23.48 | % 154.52/23.48 | REDUCE: (3), (5) imply: % 154.52/23.48 | (6) $false % 154.52/23.48 | % 154.52/23.48 | CLOSE: (6) is inconsistent. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #495 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_56_8 = e1 | all_56_11 = e1 % 154.52/23.48 (2) all_58_28 = e0 % 154.52/23.48 (3) all_58_31 = e1 % 154.52/23.48 (4) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 (5) ~ (e3 = e1) % 154.52/23.48 (6) all_58_29 = all_8_2 % 154.52/23.48 (7) ~ (e2 = e1) % 154.52/23.48 (8) ~ (e3 = e0) % 154.52/23.48 (9) ~ (e2 = e0) % 154.52/23.48 (10) all_56_8 = all_6_2 % 154.52/23.48 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 (12) ~ (e1 = e0) % 154.52/23.48 (13) all_58_30 = all_6_2 % 154.52/23.48 (14) all_56_11 = e0 % 154.52/23.48 (15) ~ (e3 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (1) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (16) all_56_8 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (15), % 154.52/23.48 | | (16) are inconsistent by sub-proof #496. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (17) all_56_11 = e1 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (14), (17) imply: % 154.52/23.48 | | (18) e1 = e0 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (12), (18) imply: % 154.52/23.48 | | (19) $false % 154.52/23.48 | | % 154.52/23.48 | | CLOSE: (19) is inconsistent. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #496 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_28 = e0 % 154.52/23.48 (2) all_58_31 = e1 % 154.52/23.48 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 (4) all_56_8 = e1 % 154.52/23.48 (5) ~ (e3 = e1) % 154.52/23.48 (6) all_58_29 = all_8_2 % 154.52/23.48 (7) ~ (e2 = e1) % 154.52/23.48 (8) ~ (e3 = e0) % 154.52/23.48 (9) ~ (e2 = e0) % 154.52/23.48 (10) all_56_8 = all_6_2 % 154.52/23.48 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 (12) all_58_30 = all_6_2 % 154.52/23.48 (13) ~ (e3 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (4), (10) imply: % 154.52/23.48 | (14) all_6_2 = e1 % 154.52/23.48 | % 154.52/23.48 | SIMP: (14) implies: % 154.52/23.48 | (15) all_6_2 = e1 % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (12), (15) imply: % 154.52/23.48 | (16) all_58_30 = e1 % 154.52/23.48 | % 154.52/23.48 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (13), (16) are % 154.52/23.48 | inconsistent by sub-proof #497. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #497 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_28 = e0 % 154.52/23.48 (2) all_58_31 = e1 % 154.52/23.48 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 (4) ~ (e3 = e1) % 154.52/23.48 (5) all_58_29 = all_8_2 % 154.52/23.48 (6) ~ (e2 = e1) % 154.52/23.48 (7) ~ (e3 = e0) % 154.52/23.48 (8) all_58_30 = e1 % 154.52/23.48 (9) ~ (e2 = e0) % 154.52/23.48 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 (11) ~ (e3 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (10) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (12) all_58_28 = e3 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #689. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (13) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 | | % 154.52/23.48 | | BETA: splitting (13) gives: % 154.52/23.48 | | % 154.52/23.48 | | Case 1: % 154.52/23.48 | | | % 154.52/23.48 | | | (14) all_58_29 = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | COMBINE_EQS: (5), (14) imply: % 154.52/23.48 | | | (15) all_8_2 = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | BETA: splitting (3) gives: % 154.52/23.48 | | | % 154.52/23.48 | | | Case 1: % 154.52/23.48 | | | | % 154.52/23.48 | | | | (16) all_58_28 = e2 % 154.52/23.48 | | | | % 154.52/23.48 | | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #688. % 154.52/23.48 | | | | % 154.52/23.48 | | | Case 2: % 154.52/23.48 | | | | % 154.52/23.48 | | | | (17) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 | | | | % 154.52/23.48 | | | | REF_CLOSE: (2), (6), (8), (11), (14), (17) are inconsistent by sub-proof % 154.52/23.48 | | | | #499. % 154.52/23.48 | | | | % 154.52/23.48 | | | End of split % 154.52/23.48 | | | % 154.52/23.48 | | Case 2: % 154.52/23.48 | | | % 154.52/23.48 | | | (18) all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | REF_CLOSE: (2), (4), (8), (18) are inconsistent by sub-proof #498. % 154.52/23.48 | | | % 154.52/23.48 | | End of split % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #498 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_30 = e3 | all_58_31 = e3 % 154.52/23.48 (2) all_58_30 = e1 % 154.52/23.48 (3) ~ (e3 = e1) % 154.52/23.48 (4) all_58_31 = e1 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (1) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (5) all_58_30 = e3 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (2), (5) imply: % 154.52/23.48 | | (6) e3 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (3), (6) imply: % 154.52/23.48 | | (7) $false % 154.52/23.48 | | % 154.52/23.48 | | CLOSE: (7) is inconsistent. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (8) all_58_31 = e3 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (4), (8) imply: % 154.52/23.48 | | (9) e3 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (3), (9) imply: % 154.52/23.48 | | (10) $false % 154.52/23.48 | | % 154.52/23.48 | | CLOSE: (10) is inconsistent. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #499 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_31 = e1 % 154.52/23.48 (2) all_58_29 = e3 % 154.52/23.48 (3) ~ (e2 = e1) % 154.52/23.48 (4) all_58_30 = e1 % 154.52/23.48 (5) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 (6) ~ (e3 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (5) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (7) all_58_29 = e2 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (2), (7) imply: % 154.52/23.48 | | (8) e3 = e2 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (6), (8) imply: % 154.52/23.48 | | (9) $false % 154.52/23.48 | | % 154.52/23.48 | | CLOSE: (9) is inconsistent. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (10) all_58_30 = e2 | all_58_31 = e2 % 154.52/23.48 | | % 154.52/23.48 | | BETA: splitting (10) gives: % 154.52/23.48 | | % 154.52/23.48 | | Case 1: % 154.52/23.48 | | | % 154.52/23.48 | | | (11) all_58_30 = e2 % 154.52/23.48 | | | % 154.52/23.48 | | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #500. % 154.52/23.48 | | | % 154.52/23.48 | | Case 2: % 154.52/23.48 | | | % 154.52/23.48 | | | (12) all_58_31 = e2 % 154.52/23.48 | | | % 154.52/23.48 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #697. % 154.52/23.48 | | | % 154.52/23.48 | | End of split % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #500 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_30 = e2 % 154.52/23.48 (2) all_58_30 = e1 % 154.52/23.48 (3) ~ (e2 = e1) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (1), (2) imply: % 154.52/23.48 | (4) e2 = e1 % 154.52/23.48 | % 154.52/23.48 | SIMP: (4) implies: % 154.52/23.48 | (5) e2 = e1 % 154.52/23.48 | % 154.52/23.48 | REDUCE: (3), (5) imply: % 154.52/23.48 | (6) $false % 154.52/23.48 | % 154.52/23.48 | CLOSE: (6) is inconsistent. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #501 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_56_7 = e1 % 154.52/23.48 (2) all_56_7 = e0 % 154.52/23.48 (3) ~ (e1 = e0) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | COMBINE_EQS: (1), (2) imply: % 154.52/23.48 | (4) e1 = e0 % 154.52/23.48 | % 154.52/23.48 | SIMP: (4) implies: % 154.52/23.48 | (5) e1 = e0 % 154.52/23.48 | % 154.52/23.48 | REDUCE: (3), (5) imply: % 154.52/23.48 | (6) $false % 154.52/23.48 | % 154.52/23.48 | CLOSE: (6) is inconsistent. % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #502 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_31 = all_4_2 % 154.52/23.48 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.52/23.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.52/23.48 (3) all_54_8 = all_52_2 % 154.52/23.48 (4) ~ (all_52_2 = all_6_2) % 154.52/23.48 (5) all_58_29 = all_8_2 % 154.52/23.48 (6) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.48 (7) op(all_8_2, e2) = all_8_1 % 154.52/23.48 (8) ~ (all_52_2 = e3) % 154.52/23.48 (9) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.52/23.48 (10) ~ (all_8_1 = e0) % 154.52/23.48 (11) op(e1, e2) = e0 % 154.52/23.48 (12) ~ (all_4_2 = e1) % 154.52/23.48 (13) all_58_30 = all_6_2 % 154.52/23.48 (14) ~ (all_52_2 = e2) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (9) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (15) all_54_8 = e1 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (3), (15) imply: % 154.52/23.48 | | (16) all_52_2 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (4), (16) imply: % 154.52/23.48 | | (17) ~ (all_6_2 = e1) % 154.52/23.48 | | % 154.52/23.48 | | SIMP: (17) implies: % 154.52/23.48 | | (18) ~ (all_6_2 = e1) % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (13), (18) are % 154.52/23.48 | | inconsistent by sub-proof #503. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (19) all_54_8 = e3 | all_54_8 = e2 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (3), (8), (14), (19) are inconsistent by sub-proof #785. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #503 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_58_31 = all_4_2 % 154.52/23.48 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.52/23.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.52/23.48 (3) all_58_29 = all_8_2 % 154.52/23.48 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.48 (5) op(all_8_2, e2) = all_8_1 % 154.52/23.48 (6) ~ (all_8_1 = e0) % 154.52/23.48 (7) op(e1, e2) = e0 % 154.52/23.48 (8) ~ (all_6_2 = e1) % 154.52/23.48 (9) ~ (all_4_2 = e1) % 154.52/23.48 (10) all_58_30 = all_6_2 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (4) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (11) all_58_29 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (2), (3), (5), (6), (7), (11) are inconsistent by sub-proof #794. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (12) all_58_30 = e1 | all_58_31 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (8), (9), (10), (12) are inconsistent by sub-proof #673. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #504 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) ~ (all_52_1 = e1) % 154.52/23.48 (2) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.52/23.48 (3) all_54_12 = all_10_1 % 154.52/23.48 (4) ~ (all_10_1 = e2) % 154.52/23.48 (5) ~ (all_52_1 = all_10_1) % 154.52/23.48 (6) ~ (all_10_1 = e1) % 154.52/23.48 (7) ~ (all_52_1 = e2) % 154.52/23.48 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.52/23.48 (9) all_54_4 = all_52_1 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (2) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (10) all_54_4 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (9), (10) are inconsistent by sub-proof #832. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (11) all_54_4 = e3 | all_54_4 = e2 % 154.52/23.48 | | % 154.52/23.48 | | BETA: splitting (11) gives: % 154.52/23.48 | | % 154.52/23.48 | | Case 1: % 154.52/23.48 | | | % 154.52/23.48 | | | (12) all_54_4 = e2 % 154.52/23.48 | | | % 154.52/23.48 | | | REF_CLOSE: (7), (9), (12) are inconsistent by sub-proof #831. % 154.52/23.48 | | | % 154.52/23.48 | | Case 2: % 154.52/23.48 | | | % 154.52/23.48 | | | (13) all_54_4 = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | COMBINE_EQS: (9), (13) imply: % 154.52/23.48 | | | (14) all_52_1 = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | SIMP: (14) implies: % 154.52/23.48 | | | (15) all_52_1 = e3 % 154.52/23.48 | | | % 154.52/23.48 | | | REDUCE: (5), (15) imply: % 154.52/23.48 | | | (16) ~ (all_10_1 = e3) % 154.52/23.48 | | | % 154.52/23.48 | | | SIMP: (16) implies: % 154.52/23.48 | | | (17) ~ (all_10_1 = e3) % 154.52/23.48 | | | % 154.52/23.48 | | | REF_CLOSE: (3), (4), (6), (8), (17) are inconsistent by sub-proof #505. % 154.52/23.48 | | | % 154.52/23.48 | | End of split % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #505 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_12 = all_10_1 % 154.52/23.48 (2) ~ (all_10_1 = e2) % 154.52/23.48 (3) ~ (all_10_1 = e3) % 154.52/23.48 (4) ~ (all_10_1 = e1) % 154.52/23.48 (5) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (5) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (6) all_54_12 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #514. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (7) all_54_12 = e3 | all_54_12 = e2 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #506. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #506 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_12 = e3 | all_54_12 = e2 % 154.52/23.48 (2) all_54_12 = all_10_1 % 154.52/23.48 (3) ~ (all_10_1 = e2) % 154.52/23.48 (4) ~ (all_10_1 = e3) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (1) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (5) all_54_12 = e2 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (2), (5) imply: % 154.52/23.48 | | (6) all_10_1 = e2 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (3), (6) imply: % 154.52/23.48 | | (7) $false % 154.52/23.48 | | % 154.52/23.48 | | CLOSE: (7) is inconsistent. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (8) all_54_12 = e3 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (2), (8) imply: % 154.52/23.48 | | (9) all_10_1 = e3 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (4), (9) imply: % 154.52/23.48 | | (10) $false % 154.52/23.48 | | % 154.52/23.48 | | CLOSE: (10) is inconsistent. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #507 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_13 = all_52_7 % 154.52/23.48 (2) all_54_1 = all_52_4 % 154.52/23.48 (3) ~ (all_52_4 = e3) % 154.52/23.48 (4) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.52/23.48 (5) ~ (all_52_4 = all_52_7) % 154.52/23.48 (6) ~ (all_52_7 = e2) % 154.52/23.48 (7) ~ (all_52_4 = e2) % 154.52/23.48 (8) ~ (all_52_7 = e3) % 154.52/23.48 (9) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (4) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (10) all_54_1 = e1 % 154.52/23.48 | | % 154.52/23.48 | | COMBINE_EQS: (2), (10) imply: % 154.52/23.48 | | (11) all_52_4 = e1 % 154.52/23.48 | | % 154.52/23.48 | | SIMP: (11) implies: % 154.52/23.48 | | (12) all_52_4 = e1 % 154.52/23.48 | | % 154.52/23.48 | | REDUCE: (5), (12) imply: % 154.52/23.48 | | (13) ~ (all_52_7 = e1) % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (1), (6), (8), (9), (13) are inconsistent by sub-proof #509. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (14) all_54_1 = e3 | all_54_1 = e2 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (2), (3), (7), (14) are inconsistent by sub-proof #508. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #508 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_1 = e3 | all_54_1 = e2 % 154.52/23.48 (2) all_54_1 = all_52_4 % 154.52/23.48 (3) ~ (all_52_4 = e2) % 154.52/23.48 (4) ~ (all_52_4 = e3) % 154.52/23.48 % 154.52/23.48 Begin of proof % 154.52/23.48 | % 154.52/23.48 | BETA: splitting (1) gives: % 154.52/23.48 | % 154.52/23.48 | Case 1: % 154.52/23.48 | | % 154.52/23.48 | | (5) all_54_1 = e2 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #740. % 154.52/23.48 | | % 154.52/23.48 | Case 2: % 154.52/23.48 | | % 154.52/23.48 | | (6) all_54_1 = e3 % 154.52/23.48 | | % 154.52/23.48 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #739. % 154.52/23.48 | | % 154.52/23.48 | End of split % 154.52/23.48 | % 154.52/23.48 End of proof % 154.52/23.48 % 154.52/23.48 Sub-proof #509 shows that the following formulas are inconsistent: % 154.52/23.48 ---------------------------------------------------------------- % 154.52/23.48 (1) all_54_13 = all_52_7 % 154.52/23.49 (2) ~ (all_52_7 = e2) % 154.52/23.49 (3) ~ (all_52_7 = e3) % 154.52/23.49 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 154.52/23.49 (5) ~ (all_52_7 = e1) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | SIMP: (5) implies: % 154.52/23.49 | (6) ~ (all_52_7 = e1) % 154.52/23.49 | % 154.52/23.49 | BETA: splitting (4) gives: % 154.52/23.49 | % 154.52/23.49 | Case 1: % 154.52/23.49 | | % 154.52/23.49 | | (7) all_54_13 = e1 % 154.52/23.49 | | % 154.52/23.49 | | COMBINE_EQS: (1), (7) imply: % 154.52/23.49 | | (8) all_52_7 = e1 % 154.52/23.49 | | % 154.52/23.49 | | REDUCE: (6), (8) imply: % 154.52/23.49 | | (9) $false % 154.52/23.49 | | % 154.52/23.49 | | CLOSE: (9) is inconsistent. % 154.52/23.49 | | % 154.52/23.49 | Case 2: % 154.52/23.49 | | % 154.52/23.49 | | (10) all_54_13 = e3 | all_54_13 = e2 % 154.52/23.49 | | % 154.52/23.49 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #730. % 154.52/23.49 | | % 154.52/23.49 | End of split % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #510 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) ~ (all_52_13 = e1) % 154.52/23.49 (2) all_54_7 = all_52_13 % 154.52/23.49 (3) all_54_3 = all_52_12 % 154.52/23.49 (4) ~ (all_52_12 = all_52_13) % 154.52/23.49 (5) ~ (all_52_13 = e2) % 154.52/23.49 (6) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.52/23.49 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.52/23.49 (8) ~ (all_52_12 = e1) % 154.52/23.49 (9) ~ (all_52_12 = e2) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | BETA: splitting (6) gives: % 154.52/23.49 | % 154.52/23.49 | Case 1: % 154.52/23.49 | | % 154.52/23.49 | | (10) all_54_7 = e1 % 154.52/23.49 | | % 154.52/23.49 | | COMBINE_EQS: (2), (10) imply: % 154.52/23.49 | | (11) all_52_13 = e1 % 154.52/23.49 | | % 154.52/23.49 | | REDUCE: (1), (11) imply: % 154.52/23.49 | | (12) $false % 154.52/23.49 | | % 154.52/23.49 | | CLOSE: (12) is inconsistent. % 154.52/23.49 | | % 154.52/23.49 | Case 2: % 154.52/23.49 | | % 154.52/23.49 | | (13) all_54_7 = e3 | all_54_7 = e2 % 154.52/23.49 | | % 154.52/23.49 | | BETA: splitting (7) gives: % 154.52/23.49 | | % 154.52/23.49 | | Case 1: % 154.52/23.49 | | | % 154.52/23.49 | | | (14) all_54_3 = e1 % 154.52/23.49 | | | % 154.52/23.49 | | | COMBINE_EQS: (3), (14) imply: % 154.52/23.49 | | | (15) all_52_12 = e1 % 154.52/23.49 | | | % 154.52/23.49 | | | REDUCE: (8), (15) imply: % 154.52/23.49 | | | (16) $false % 154.52/23.49 | | | % 154.52/23.49 | | | CLOSE: (16) is inconsistent. % 154.52/23.49 | | | % 154.52/23.49 | | Case 2: % 154.52/23.49 | | | % 154.52/23.49 | | | (17) all_54_3 = e3 | all_54_3 = e2 % 154.52/23.49 | | | % 154.52/23.49 | | | BETA: splitting (17) gives: % 154.52/23.49 | | | % 154.52/23.49 | | | Case 1: % 154.52/23.49 | | | | % 154.52/23.49 | | | | (18) all_54_3 = e2 % 154.52/23.49 | | | | % 154.52/23.49 | | | | COMBINE_EQS: (3), (18) imply: % 154.52/23.49 | | | | (19) all_52_12 = e2 % 154.52/23.49 | | | | % 154.52/23.49 | | | | REDUCE: (9), (19) imply: % 154.52/23.49 | | | | (20) $false % 154.52/23.49 | | | | % 154.52/23.49 | | | | CLOSE: (20) is inconsistent. % 154.52/23.49 | | | | % 154.52/23.49 | | | Case 2: % 154.52/23.49 | | | | % 154.52/23.49 | | | | (21) all_54_3 = e3 % 154.52/23.49 | | | | % 154.52/23.49 | | | | COMBINE_EQS: (3), (21) imply: % 154.52/23.49 | | | | (22) all_52_12 = e3 % 154.52/23.49 | | | | % 154.52/23.49 | | | | REDUCE: (4), (22) imply: % 154.52/23.49 | | | | (23) ~ (all_52_13 = e3) % 154.52/23.49 | | | | % 154.52/23.49 | | | | SIMP: (23) implies: % 154.52/23.49 | | | | (24) ~ (all_52_13 = e3) % 154.52/23.49 | | | | % 154.52/23.49 | | | | REF_CLOSE: (2), (5), (13), (24) are inconsistent by sub-proof #511. % 154.52/23.49 | | | | % 154.52/23.49 | | | End of split % 154.52/23.49 | | | % 154.52/23.49 | | End of split % 154.52/23.49 | | % 154.52/23.49 | End of split % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #511 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_54_7 = e3 | all_54_7 = e2 % 154.52/23.49 (2) all_54_7 = all_52_13 % 154.52/23.49 (3) ~ (all_52_13 = e2) % 154.52/23.49 (4) ~ (all_52_13 = e3) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | BETA: splitting (1) gives: % 154.52/23.49 | % 154.52/23.49 | Case 1: % 154.52/23.49 | | % 154.52/23.49 | | (5) all_54_7 = e2 % 154.52/23.49 | | % 154.52/23.49 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #604. % 154.52/23.49 | | % 154.52/23.49 | Case 2: % 154.52/23.49 | | % 154.52/23.49 | | (6) all_54_7 = e3 % 154.52/23.49 | | % 154.52/23.49 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #603. % 154.52/23.49 | | % 154.52/23.49 | End of split % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #512 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_58_31 = e0 % 154.52/23.49 (2) all_58_30 = e1 | all_58_31 = e1 % 154.52/23.49 (3) ~ (e1 = e0) % 154.52/23.49 (4) ~ (all_6_2 = e1) % 154.52/23.49 (5) all_58_30 = all_6_2 % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | BETA: splitting (2) gives: % 154.52/23.49 | % 154.52/23.49 | Case 1: % 154.52/23.49 | | % 154.52/23.49 | | (6) all_58_30 = e1 % 154.52/23.49 | | % 154.52/23.49 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #825. % 154.52/23.49 | | % 154.52/23.49 | Case 2: % 154.52/23.49 | | % 154.52/23.49 | | (7) all_58_31 = e1 % 154.52/23.49 | | % 154.52/23.49 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #845. % 154.52/23.49 | | % 154.52/23.49 | End of split % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #513 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_54_12 = all_10_1 % 154.52/23.49 (2) all_54_12 = e2 % 154.52/23.49 (3) ~ (all_10_1 = e2) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | COMBINE_EQS: (1), (2) imply: % 154.52/23.49 | (4) all_10_1 = e2 % 154.52/23.49 | % 154.52/23.49 | SIMP: (4) implies: % 154.52/23.49 | (5) all_10_1 = e2 % 154.52/23.49 | % 154.52/23.49 | REDUCE: (3), (5) imply: % 154.52/23.49 | (6) $false % 154.52/23.49 | % 154.52/23.49 | CLOSE: (6) is inconsistent. % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #514 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_54_12 = all_10_1 % 154.52/23.49 (2) all_54_12 = e1 % 154.52/23.49 (3) ~ (all_10_1 = e1) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | COMBINE_EQS: (1), (2) imply: % 154.52/23.49 | (4) all_10_1 = e1 % 154.52/23.49 | % 154.52/23.49 | SIMP: (4) implies: % 154.52/23.49 | (5) all_10_1 = e1 % 154.52/23.49 | % 154.52/23.49 | REDUCE: (3), (5) imply: % 154.52/23.49 | (6) $false % 154.52/23.49 | % 154.52/23.49 | CLOSE: (6) is inconsistent. % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #515 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) ~ (all_10_0 = e2) % 154.52/23.49 (2) all_56_14 = e2 | all_56_15 = e2 % 154.52/23.49 (3) all_56_14 = all_10_0 % 154.52/23.49 (4) all_56_15 = e0 % 154.52/23.49 (5) ~ (e2 = e0) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | BETA: splitting (2) gives: % 154.52/23.49 | % 154.52/23.49 | Case 1: % 154.52/23.49 | | % 154.52/23.49 | | (6) all_56_14 = e2 % 154.52/23.49 | | % 154.52/23.49 | | COMBINE_EQS: (3), (6) imply: % 154.52/23.49 | | (7) all_10_0 = e2 % 154.52/23.49 | | % 154.52/23.49 | | REDUCE: (1), (7) imply: % 154.52/23.49 | | (8) $false % 154.52/23.49 | | % 154.52/23.49 | | CLOSE: (8) is inconsistent. % 154.52/23.49 | | % 154.52/23.49 | Case 2: % 154.52/23.49 | | % 154.52/23.49 | | (9) all_56_15 = e2 % 154.52/23.49 | | % 154.52/23.49 | | COMBINE_EQS: (4), (9) imply: % 154.52/23.49 | | (10) e2 = e0 % 154.52/23.49 | | % 154.52/23.49 | | REDUCE: (5), (10) imply: % 154.52/23.49 | | (11) $false % 154.52/23.49 | | % 154.52/23.49 | | CLOSE: (11) is inconsistent. % 154.52/23.49 | | % 154.52/23.49 | End of split % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #516 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_56_0 = e1 % 154.52/23.49 (2) all_56_0 = e0 % 154.52/23.49 (3) ~ (e1 = e0) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | COMBINE_EQS: (1), (2) imply: % 154.52/23.49 | (4) e1 = e0 % 154.52/23.49 | % 154.52/23.49 | SIMP: (4) implies: % 154.52/23.49 | (5) e1 = e0 % 154.52/23.49 | % 154.52/23.49 | REDUCE: (3), (5) imply: % 154.52/23.49 | (6) $false % 154.52/23.49 | % 154.52/23.49 | CLOSE: (6) is inconsistent. % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #517 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_54_14 = all_52_11 % 154.52/23.49 (2) all_54_14 = e0 % 154.52/23.49 (3) ~ (all_52_11 = e0) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | COMBINE_EQS: (1), (2) imply: % 154.52/23.49 | (4) all_52_11 = e0 % 154.52/23.49 | % 154.52/23.49 | SIMP: (4) implies: % 154.52/23.49 | (5) all_52_11 = e0 % 154.52/23.49 | % 154.52/23.49 | REDUCE: (3), (5) imply: % 154.52/23.49 | (6) $false % 154.52/23.49 | % 154.52/23.49 | CLOSE: (6) is inconsistent. % 154.52/23.49 | % 154.52/23.49 End of proof % 154.52/23.49 % 154.52/23.49 Sub-proof #518 shows that the following formulas are inconsistent: % 154.52/23.49 ---------------------------------------------------------------- % 154.52/23.49 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 154.52/23.49 (2) all_58_31 = all_4_2 % 154.52/23.49 (3) ~ (all_52_8 = all_52_9) % 154.52/23.49 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.52/23.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.52/23.49 (5) all_26_0 = all_4_0 % 154.52/23.49 (6) ~ (all_52_2 = all_52_3) % 154.52/23.49 (7) all_58_11 = all_52_9 % 154.52/23.49 (8) all_56_15 = all_4_2 % 154.52/23.49 (9) all_56_7 = all_52_6 % 154.52/23.49 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 154.52/23.49 (11) all_54_2 = all_52_8 % 154.52/23.49 (12) ~ (all_52_2 = e0) % 154.52/23.49 (13) all_54_8 = all_52_2 % 154.52/23.49 (14) op(e3, all_52_4) = all_58_1 % 154.52/23.49 (15) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.52/23.49 (16) ~ (all_52_8 = all_10_2) % 154.52/23.49 (17) all_58_15 = all_52_2 % 154.52/23.49 (18) all_58_26 = all_52_11 % 154.52/23.49 (19) all_44_1 = all_4_1 % 154.52/23.49 (20) op(e1, all_52_14) = all_58_19 % 154.52/23.49 (21) ~ (all_52_8 = all_52_11) % 154.52/23.49 (22) ~ (all_52_11 = all_4_2) % 154.52/23.49 (23) all_54_7 = all_52_13 % 154.52/23.49 (24) all_58_6 = all_52_12 % 154.52/23.49 (25) ~ (all_52_6 = all_8_2) % 154.52/23.49 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 154.52/23.49 (27) all_56_4 = all_52_8 % 154.52/23.49 (28) ~ (all_52_4 = all_8_2) % 154.52/23.49 (29) ~ (all_34_0 = e3) | ~ (all_34_1 = e2) | ~ (all_34_2 = e1) % 154.52/23.49 (30) all_54_3 = all_52_12 % 154.52/23.49 (31) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.49 (32) all_54_1 = all_52_4 % 154.52/23.49 (33) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.52/23.49 (34) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 154.52/23.49 (35) ~ (all_52_4 = all_52_6) % 154.52/23.49 (36) ~ (all_44_0 = e3) | ~ (all_44_1 = e1) | ~ (all_44_2 = e2) % 154.52/23.49 (37) all_58_13 = all_52_13 % 154.52/23.49 (38) op(e2, e2) = all_8_2 % 154.52/23.49 (39) all_20_1 = all_4_1 % 154.52/23.49 (40) op(e0, e1) = all_52_11 % 154.52/23.49 (41) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.52/23.49 (42) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.52/23.49 (43) all_34_0 = all_4_0 % 154.52/23.49 (44) ~ (all_52_6 = all_52_7) % 154.52/23.49 (45) op(all_10_2, all_10_1) = all_10_0 % 154.52/23.49 (46) all_54_11 = all_52_14 % 154.52/23.49 (47) op(e3, e2) = all_52_4 % 154.52/23.49 (48) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.52/23.49 (49) all_58_20 = all_52_14 % 154.52/23.49 (50) ~ (all_52_12 = all_52_13) % 154.52/23.49 (51) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.52/23.49 (52) op(e0, all_52_3) = all_58_21 % 154.52/23.49 (53) op(e0, all_52_7) = all_58_23 % 154.52/23.49 (54) all_54_5 = all_8_2 % 154.52/23.49 (55) ~ (all_52_6 = all_52_14) % 154.52/23.49 (56) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 154.52/23.49 (57) all_54_6 = all_52_9 % 154.52/23.49 (58) all_54_15 = all_4_2 % 154.52/23.49 (59) all_26_2 = all_4_2 % 154.52/23.49 (60) ~ (all_52_4 = all_52_7) % 154.52/23.49 (61) all_56_15 = e0 | ((all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.52/23.49 (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0)) % 154.52/23.49 (62) ~ (all_26_0 = e2) | ~ (all_26_1 = e1) | ~ (all_26_2 = e3) % 154.52/23.49 (63) op(e3, e3) = all_10_2 % 154.52/23.49 (64) ~ (all_52_8 = all_52_12) % 154.52/23.49 (65) all_54_9 = all_52_6 % 154.52/23.49 (66) ~ (all_52_13 = all_4_2) % 154.52/23.49 (67) op(e1, e2) = all_52_6 % 154.52/23.49 (68) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.52/23.49 (69) ~ (all_52_13 = all_8_2) % 154.52/23.49 (70) op(e1, all_52_6) = all_58_16 % 154.52/23.49 (71) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.52/23.49 (72) ~ (e3 = e1) % 154.52/23.49 (73) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 154.52/23.49 (74) all_56_8 = e0 % 154.52/23.49 (75) ~ (all_52_6 = e0) % 154.52/23.49 (76) all_56_2 = e1 | all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.52/23.49 (77) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 154.52/23.49 (78) ~ (all_52_1 = all_52_13) % 154.52/23.49 (79) all_56_5 = all_52_9 % 154.52/23.49 (80) all_56_0 = e0 | all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.52/23.49 (81) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 154.52/23.49 (82) all_56_12 = all_52_3 % 154.52/23.49 (83) ~ (all_52_3 = all_52_7) % 154.52/23.49 (84) all_58_2 = all_52_4 % 154.52/23.49 (85) all_20_2 = all_4_2 % 154.52/23.49 (86) all_56_11 = all_52_14 % 154.52/23.49 (87) all_56_1 = all_52_4 % 154.52/23.49 (88) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 154.52/23.49 (89) ~ (all_52_3 = all_4_2) % 154.52/23.49 (90) op(e1, e3) = all_52_2 % 154.52/23.49 (91) op(e0, all_52_11) = all_58_25 % 154.52/23.49 (92) op(e1, e0) = all_52_14 % 154.52/23.49 (93) ~ (all_52_9 = all_52_11) % 154.52/23.49 (94) ~ (all_52_9 = e0) % 154.52/23.49 (95) ~ (all_52_1 = all_8_2) % 154.52/23.49 (96) all_56_3 = all_8_2 % 154.52/23.49 (97) all_58_24 = all_52_7 % 154.52/23.49 (98) ~ (all_52_13 = all_52_14) % 154.52/23.49 (99) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 154.52/23.49 (100) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.52/23.49 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.52/23.49 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.52/23.49 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.52/23.49 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.52/23.49 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.52/23.49 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.52/23.49 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.52/23.49 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.52/23.49 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.52/23.49 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.52/23.49 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.52/23.49 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = % 154.52/23.49 e3 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.52/23.49 e2 & all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.52/23.49 e1 & all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.52/23.49 e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.52/23.49 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.52/23.49 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.52/23.49 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.52/23.49 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.52/23.49 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.52/23.49 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.52/23.49 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.52/23.49 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.52/23.49 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.52/23.49 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.52/23.49 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.52/23.49 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.52/23.49 e0) % 154.52/23.49 (101) ~ (all_52_4 = all_52_8) % 154.52/23.49 (102) op(e1, all_52_2) = all_58_14 % 154.52/23.49 (103) op(e2, e1) = all_52_9 % 154.52/23.49 (104) all_56_9 = all_52_12 % 154.52/23.49 (105) all_58_29 = all_8_2 % 154.52/23.49 (106) ~ (all_52_12 = all_52_14) % 154.52/23.49 (107) all_58_30 = e0 % 154.52/23.49 (108) all_58_8 = all_52_1 % 154.52/23.49 (109) ~ (e2 = e1) % 154.52/23.49 (110) op(e3, e0) = all_52_12 % 154.52/23.49 (111) all_20_0 = all_4_0 % 154.52/23.49 (112) all_56_6 = all_52_2 % 154.52/23.49 (113) all_34_1 = all_4_1 % 154.52/23.49 (114) ~ (all_52_2 = all_52_6) % 154.52/23.49 (115) all_56_13 = all_52_7 % 154.52/23.49 (116) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.52/23.49 (117) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.52/23.49 (118) all_56_1 = e1 | all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.52/23.49 (119) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.52/23.49 (120) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.52/23.49 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.52/23.49 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.52/23.49 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.52/23.49 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.52/23.49 (all_58_27 = e0)) % 154.52/23.49 (121) ~ (all_52_9 = all_52_13) % 154.52/23.49 (122) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.52/23.49 (123) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.52/23.49 (124) all_34_2 = all_4_2 % 154.52/23.49 (125) ~ (all_52_11 = all_6_2) % 154.52/23.49 (126) op(e3, all_10_2) = all_58_0 % 154.52/23.49 (127) all_44_2 = all_4_2 % 154.52/23.49 (128) op(e1, e1) = e0 % 154.52/23.49 (129) ~ (e3 = e0) % 154.52/23.49 (130) all_56_2 = all_52_1 % 154.52/23.49 (131) ~ (all_52_11 = e0) % 154.52/23.49 (132) op(e3, all_52_12) = all_58_5 % 154.52/23.49 (133) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 154.52/23.49 (134) all_56_10 = all_52_13 % 154.52/23.49 (135) ~ (all_52_12 = all_10_2) % 154.52/23.49 (136) ~ (all_52_1 = all_52_3) % 154.52/23.49 (137) op(e0, e1) = all_6_1 % 154.52/23.49 (138) ~ (all_52_9 = all_8_2) % 154.52/23.49 (139) all_56_14 = all_52_11 % 154.52/23.49 (140) all_58_28 = all_10_2 % 154.52/23.49 (141) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.52/23.49 (142) all_58_17 = all_52_6 % 154.52/23.49 (143) ~ (all_52_1 = all_52_9) % 154.52/23.49 (144) op(e3, e1) = all_52_8 % 154.52/23.49 (145) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.52/23.49 (146) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.52/23.49 (147) ~ (all_52_7 = all_52_11) % 154.52/23.49 (148) op(all_8_2, e2) = all_8_1 % 154.52/23.49 (149) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.52/23.49 (150) ~ (e2 = e0) % 154.52/23.49 (151) ~ (all_52_2 = all_10_2) % 154.52/23.49 (152) all_56_0 = all_10_2 % 154.52/23.49 (153) op(e0, e0) = all_4_2 % 154.52/23.49 (154) ~ (all_52_3 = all_52_11) % 154.52/23.49 (155) all_58_22 = all_52_3 % 154.52/23.49 (156) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 154.52/23.49 (157) ~ (all_52_12 = all_4_2) % 154.52/23.49 (158) ~ (all_52_3 = all_10_2) % 154.52/23.49 (159) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.52/23.49 (160) ~ (all_52_1 = all_52_2) % 154.52/23.49 (161) ~ (all_52_7 = all_8_2) % 154.52/23.49 (162) op(all_4_2, all_4_1) = all_4_0 % 154.52/23.49 (163) op(e2, e0) = all_52_13 % 154.52/23.49 (164) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 154.52/23.49 (165) all_56_12 = e2 | all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.52/23.49 (166) op(e2, all_52_13) = all_58_12 % 154.52/23.49 (167) all_58_4 = all_52_8 % 154.52/23.49 (168) ~ (all_8_1 = e0) % 154.52/23.49 (169) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.49 (170) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.52/23.49 (171) all_54_0 = all_10_2 % 154.52/23.49 (172) ~ (all_52_2 = all_52_14) % 154.52/23.49 (173) ~ (all_52_14 = all_4_2) % 154.52/23.49 (174) ~ (e1 = e0) % 154.52/23.49 (175) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 154.52/23.49 (176) all_26_1 = all_4_1 % 154.52/23.49 (177) ~ (all_52_7 = all_4_2) % 154.52/23.49 (178) ~ (all_52_14 = e0) % 154.52/23.49 (179) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 154.52/23.49 (180) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 154.52/23.49 (181) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 154.52/23.49 (182) ~ (all_52_8 = e0) % 154.52/23.49 (183) ~ (all_52_4 = all_10_2) % 154.52/23.49 (184) all_44_0 = all_4_0 % 154.52/23.49 (185) all_58_30 = all_6_2 % 154.52/23.49 (186) op(e2, all_52_1) = all_58_7 % 154.52/23.49 (187) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.52/23.49 (188) ~ (e3 = e2) % 154.52/23.49 (189) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.52/23.49 (190) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 154.52/23.49 (191) op(all_4_2, e0) = all_4_1 % 154.52/23.49 (192) op(all_10_2, e3) = all_10_1 % 154.52/23.49 (193) op(e1, e0) = all_58_18 % 154.52/23.49 (194) ~ (all_8_2 = e0) % 154.52/23.49 (195) op(e0, all_6_1) = all_6_0 % 154.52/23.49 (196) ~ (all_52_4 = all_52_12) % 154.52/23.49 (197) all_54_12 = all_52_3 % 154.52/23.49 (198) op(e2, all_8_2) = all_58_9 % 154.52/23.49 (199) all_54_4 = all_52_1 % 154.52/23.49 (200) ~ (all_52_1 = all_10_2) % 154.52/23.49 % 154.52/23.49 Begin of proof % 154.52/23.49 | % 154.52/23.49 | GROUND_INST: instantiating (4) with all_52_11, all_6_1, e1, e0, simplifying % 154.52/23.49 | with (40), (137) gives: % 154.52/23.49 | (201) all_52_11 = all_6_1 % 154.52/23.49 | % 154.52/23.49 | GROUND_INST: instantiating (4) with all_52_14, all_58_18, e0, e1, simplifying % 154.52/23.49 | with (92), (193) gives: % 154.52/23.49 | (202) all_58_18 = all_52_14 % 154.52/23.49 | % 154.52/23.49 | COMBINE_EQS: (139), (201) imply: % 154.52/23.49 | (203) all_56_14 = all_6_1 % 154.52/23.49 | % 154.52/23.49 | COMBINE_EQS: (18), (201) imply: % 154.52/23.49 | (204) all_58_26 = all_6_1 % 154.52/23.49 | % 154.52/23.49 | REDUCE: (154), (201) imply: % 154.52/23.49 | (205) ~ (all_52_3 = all_6_1) % 154.52/23.49 | % 154.52/23.49 | REDUCE: (147), (201) imply: % 154.52/23.49 | (206) ~ (all_52_7 = all_6_1) % 154.52/23.49 | % 154.52/23.49 | REDUCE: (21), (201) imply: % 154.52/23.49 | (207) ~ (all_52_8 = all_6_1) % 154.52/23.49 | % 154.52/23.49 | REDUCE: (93), (201) imply: % 154.52/23.49 | (208) ~ (all_52_9 = all_6_1) % 154.52/23.49 | % 154.52/23.49 | REDUCE: (22), (201) imply: % 154.52/23.49 | (209) ~ (all_6_1 = all_4_2) % 154.52/23.49 | % 154.52/23.49 | REDUCE: (131), (201) imply: % 154.52/23.49 | (210) ~ (all_6_1 = e0) % 154.52/23.49 | % 154.52/23.49 | REDUCE: (91), (201) imply: % 154.52/23.49 | (211) op(e0, all_6_1) = all_58_25 % 154.52/23.49 | % 154.52/23.49 | GROUND_INST: instantiating (4) with all_6_0, all_58_25, all_6_1, e0, % 154.52/23.49 | simplifying with (195), (211) gives: % 154.52/23.49 | (212) all_58_25 = all_6_0 % 154.52/23.49 | % 154.52/23.49 | BETA: splitting (145) gives: % 154.52/23.49 | % 154.52/23.49 | Case 1: % 154.52/23.49 | | % 154.52/23.49 | | (213) ~ (all_20_2 = e1) % 154.52/23.49 | | % 154.52/23.49 | | REDUCE: (85), (213) imply: % 154.52/23.49 | | (214) ~ (all_4_2 = e1) % 154.52/23.49 | | % 154.52/23.49 | | BETA: splitting (62) gives: % 154.52/23.49 | | % 154.52/23.49 | | Case 1: % 154.52/23.49 | | | % 154.52/23.49 | | | (215) ~ (all_26_1 = e1) % 154.52/23.49 | | | % 154.52/23.49 | | | REDUCE: (176), (215) imply: % 154.52/23.49 | | | (216) ~ (all_4_1 = e1) % 154.52/23.49 | | | % 154.52/23.49 | | | BETA: splitting (61) gives: % 154.52/23.49 | | | % 154.52/23.49 | | | Case 1: % 154.52/23.49 | | | | % 154.52/23.49 | | | | (217) all_56_15 = e0 % 154.52/23.49 | | | | % 154.52/23.49 | | | | REF_CLOSE: (2), (8), (31), (72), (107), (109), (129), (150), (169), % 154.52/23.49 | | | | (174), (187), (188), (214), (217) are inconsistent by % 154.52/23.49 | | | | sub-proof #709. % 154.52/23.49 | | | | % 154.52/23.49 | | | Case 2: % 154.52/23.49 | | | | % 154.52/23.49 | | | | (218) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & (all_56_12 % 154.52/23.49 | | | | = e0 | all_56_13 = e0 | all_56_14 = e0) % 154.52/23.49 | | | | % 154.52/23.49 | | | | ALPHA: (218) implies: % 154.52/23.49 | | | | (219) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 154.52/23.49 | | | | % 154.52/23.49 | | | | BETA: splitting (26) gives: % 154.52/23.49 | | | | % 154.52/23.49 | | | | Case 1: % 154.52/23.49 | | | | | % 154.52/23.49 | | | | | (220) all_54_15 = e0 % 154.52/23.49 | | | | | % 154.52/23.49 | | | | | REF_CLOSE: (2), (31), (58), (72), (107), (109), (129), (150), (169), % 154.52/23.49 | | | | | (174), (187), (188), (214), (220) are inconsistent by % 154.52/23.49 | | | | | sub-proof #708. % 154.52/23.49 | | | | | % 154.52/23.49 | | | | Case 2: % 154.52/23.49 | | | | | % 154.52/23.49 | | | | | (221) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.52/23.49 | | | | | % 154.52/23.49 | | | | | BETA: splitting (122) gives: % 154.52/23.49 | | | | | % 154.52/23.49 | | | | | Case 1: % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | (222) all_56_1 = e0 % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | COMBINE_EQS: (87), (222) imply: % 154.52/23.49 | | | | | | (223) all_52_4 = e0 % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | COMBINE_EQS: (84), (223) imply: % 154.52/23.49 | | | | | | (224) all_58_2 = e0 % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | REDUCE: (35), (223) imply: % 154.52/23.49 | | | | | | (225) ~ (all_52_6 = e0) % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | REDUCE: (60), (223) imply: % 154.52/23.49 | | | | | | (226) ~ (all_52_7 = e0) % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | SIMP: (226) implies: % 154.52/23.49 | | | | | | (227) ~ (all_52_7 = e0) % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | REDUCE: (14), (223) imply: % 154.52/23.49 | | | | | | (228) op(e3, e0) = all_58_1 % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (13), (15), % 154.52/23.49 | | | | | | (16), (17), (20), (22), (24), (25), (27), (30), (31), % 154.52/23.49 | | | | | | (33), (34), (37), (42), (48), (49), (50), (51), (52), % 154.52/23.49 | | | | | | (55), (57), (58), (63), (64), (65), (66), (67), (69), % 154.52/23.49 | | | | | | (70), (72), (73), (74), (75), (77), (78), (79), (82), % 154.52/23.49 | | | | | | (83), (85), (86), (94), (95), (96), (97), (98), (100), % 154.52/23.49 | | | | | | (104), (105), (106), (107), (108), (109), (110), (112), % 154.52/23.49 | | | | | | (114), (115), (117), (120), (121), (123), (125), (126), % 154.52/23.49 | | | | | | (128), (129), (130), (131), (134), (135), (136), (137), % 154.52/23.49 | | | | | | (138), (139), (140), (142), (143), (145), (146), (148), % 154.52/23.49 | | | | | | (149), (150), (151), (152), (153), (155), (157), (159), % 154.52/23.49 | | | | | | (160), (161), (163), (166), (167), (169), (170), (171), % 154.52/23.49 | | | | | | (172), (173), (174), (175), (177), (180), (181), (185), % 154.52/23.49 | | | | | | (187), (188), (189), (195), (199), (200), (203), (204), % 154.52/23.49 | | | | | | (208), (209), (212), (214), (219), (221), (222), (224), % 154.52/23.49 | | | | | | (227), (228) are inconsistent by sub-proof #608. % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | Case 2: % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | (229) ~ (all_56_1 = e0) % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | REDUCE: (87), (229) imply: % 154.52/23.49 | | | | | | (230) ~ (all_52_4 = e0) % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | BETA: splitting (80) gives: % 154.52/23.49 | | | | | | % 154.52/23.49 | | | | | | Case 1: % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | (231) all_56_0 = e0 % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | COMBINE_EQS: (152), (231) imply: % 154.52/23.49 | | | | | | | (232) all_10_2 = e0 % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | COMBINE_EQS: (140), (232) imply: % 154.52/23.49 | | | | | | | (233) all_58_28 = e0 % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.52/23.49 | | | | | | | (145), (150), (169), (174), (187), (188), (233) are % 154.52/23.49 | | | | | | | inconsistent by sub-proof #679. % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | Case 2: % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | (234) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | BETA: splitting (234) gives: % 154.52/23.49 | | | | | | | % 154.52/23.49 | | | | | | | Case 1: % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | (235) all_56_1 = e0 % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | COMBINE_EQS: (87), (235) imply: % 154.52/23.49 | | | | | | | | (236) all_52_4 = e0 % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | REDUCE: (230), (236) imply: % 154.52/23.49 | | | | | | | | (237) $false % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | CLOSE: (237) is inconsistent. % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | Case 2: % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | (238) all_56_4 = e0 | all_56_9 = e0 % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | BETA: splitting (238) gives: % 154.52/23.49 | | | | | | | | % 154.52/23.49 | | | | | | | | Case 1: % 154.52/23.49 | | | | | | | | | % 154.52/23.49 | | | | | | | | | (239) all_56_4 = e0 % 154.52/23.49 | | | | | | | | | % 154.52/23.49 | | | | | | | | | COMBINE_EQS: (27), (239) imply: % 154.52/23.49 | | | | | | | | | (240) all_52_8 = e0 % 154.52/23.49 | | | | | | | | | % 154.52/23.49 | | | | | | | | | REDUCE: (182), (240) imply: % 154.52/23.50 | | | | | | | | | (241) $false % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | CLOSE: (241) is inconsistent. % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | (242) all_56_9 = e0 % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | COMBINE_EQS: (104), (242) imply: % 154.52/23.50 | | | | | | | | | (243) all_52_12 = e0 % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | SIMP: (243) implies: % 154.52/23.50 | | | | | | | | | (244) all_52_12 = e0 % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | COMBINE_EQS: (24), (244) imply: % 154.52/23.50 | | | | | | | | | (245) all_58_6 = e0 % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | REDUCE: (50), (244) imply: % 154.52/23.50 | | | | | | | | | (246) ~ (all_52_13 = e0) % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | SIMP: (246) implies: % 154.52/23.50 | | | | | | | | | (247) ~ (all_52_13 = e0) % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | REDUCE: (106), (244) imply: % 154.52/23.50 | | | | | | | | | (248) ~ (all_52_14 = e0) % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | REDUCE: (132), (244) imply: % 154.52/23.50 | | | | | | | | | (249) op(e3, e0) = all_58_5 % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | REDUCE: (110), (244) imply: % 154.52/23.50 | | | | | | | | | (250) op(e3, e0) = e0 % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | BETA: splitting (33) gives: % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | (251) all_56_2 = e0 % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | COMBINE_EQS: (130), (251) imply: % 154.52/23.50 | | | | | | | | | | (252) all_52_1 = e0 % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | COMBINE_EQS: (108), (252) imply: % 154.52/23.50 | | | | | | | | | | (253) all_58_8 = e0 % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | REDUCE: (160), (252) imply: % 154.52/23.50 | | | | | | | | | | (254) ~ (all_52_2 = e0) % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | REDUCE: (136), (252) imply: % 154.52/23.50 | | | | | | | | | | (255) ~ (all_52_3 = e0) % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | SIMP: (255) implies: % 154.52/23.50 | | | | | | | | | | (256) ~ (all_52_3 = e0) % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | REDUCE: (200), (252) imply: % 154.52/23.50 | | | | | | | | | | (257) ~ (all_10_2 = e0) % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | SIMP: (257) implies: % 154.52/23.50 | | | | | | | | | | (258) ~ (all_10_2 = e0) % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | REDUCE: (186), (252) imply: % 154.52/23.50 | | | | | | | | | | (259) op(e2, e0) = all_58_7 % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | BETA: splitting (219) gives: % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | (260) all_56_12 = e0 % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | REF_CLOSE: (82), (256), (260) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | #607. % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | (261) all_56_13 = e0 | all_56_14 = e0 % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | BETA: splitting (261) gives: % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | (262) all_56_13 = e0 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | COMBINE_EQS: (115), (262) imply: % 154.52/23.50 | | | | | | | | | | | | (263) all_52_7 = e0 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | SIMP: (263) implies: % 154.52/23.50 | | | | | | | | | | | | (264) all_52_7 = e0 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | COMBINE_EQS: (97), (264) imply: % 154.52/23.50 | | | | | | | | | | | | (265) all_58_24 = e0 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | REDUCE: (161), (264) imply: % 154.52/23.50 | | | | | | | | | | | | (266) ~ (all_8_2 = e0) % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | REDUCE: (206), (264) imply: % 154.52/23.50 | | | | | | | | | | | | (267) ~ (all_6_1 = e0) % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | REDUCE: (53), (264) imply: % 154.52/23.50 | | | | | | | | | | | | (268) op(e0, e0) = all_58_23 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_23, e0, e0, % 154.52/23.50 | | | | | | | | | | | | simplifying with (153), (268) gives: % 154.52/23.50 | | | | | | | | | | | | (269) all_58_23 = all_4_2 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, all_58_7, e0, % 154.52/23.50 | | | | | | | | | | | | e2, simplifying with (163), (259) gives: % 154.52/23.50 | | | | | | | | | | | | (270) all_58_7 = all_52_13 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_5, e0, e3, % 154.52/23.50 | | | | | | | | | | | | simplifying with (249), (250) gives: % 154.52/23.50 | | | | | | | | | | | | (271) all_58_5 = e0 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | BETA: splitting (34) gives: % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | (272) all_54_8 = e0 % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | REF_CLOSE: (12), (13), (272) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | #731. % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | (273) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | BETA: splitting (123) gives: % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | (274) all_56_9 = e1 % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | COMBINE_EQS: (242), (274) imply: % 154.52/23.50 | | | | | | | | | | | | | | (275) e1 = e0 % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | REDUCE: (174), (275) imply: % 154.52/23.50 | | | | | | | | | | | | | | (276) $false % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | CLOSE: (276) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | (277) ~ (all_56_9 = e1) % 154.52/23.50 | | | | | | | | | | | | | | (278) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | REDUCE: (242), (277) imply: % 154.52/23.50 | | | | | | | | | | | | | | (279) ~ (e1 = e0) % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | BETA: splitting (133) gives: % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | (280) all_54_12 = e0 % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | REF_CLOSE: (197), (256), (280) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | #762. % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | (281) ~ (all_54_12 = e0) % 154.52/23.50 | | | | | | | | | | | | | | | (282) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | (283) all_56_12 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (17), (23), (27), (28), (31), (37), % 154.52/23.50 | | | | | | | | | | | | | | | | (49), (66), (69), (72), (82), (86), (87), (89), % 154.52/23.50 | | | | | | | | | | | | | | | | (98), (100), (105), (107), (109), (116), (120), % 154.52/23.50 | | | | | | | | | | | | | | | | (129), (134), (140), (150), (152), (155), (158), % 154.52/23.50 | | | | | | | | | | | | | | | | (167), (169), (172), (173), (178), (182), (187), % 154.52/23.50 | | | | | | | | | | | | | | | | (188), (190), (202), (204), (207), (242), (245), % 154.52/23.50 | | | | | | | | | | | | | | | | (247), (253), (256), (265), (269), (270), (271), % 154.52/23.50 | | | | | | | | | | | | | | | | (278), (283) are inconsistent by sub-proof #589. % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | (284) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | (285) all_56_13 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (285) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | (286) e1 = e0 % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | REDUCE: (174), (286) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | (287) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | (288) all_56_14 = e1 | all_56_15 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | (289) all_56_14 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (289) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (290) all_6_1 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | SIMP: (290) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (291) all_6_1 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | REDUCE: (205), (291) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (292) ~ (all_52_3 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | REDUCE: (208), (291) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (293) ~ (all_52_9 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | REDUCE: (209), (291) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (294) ~ (all_4_2 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | REDUCE: (195), (291) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (295) op(e0, e1) = all_6_0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | REDUCE: (137), (291) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (296) op(e0, e1) = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, all_6_0, e1, e0, % 154.52/23.50 | | | | | | | | | | | | | | | | | | simplifying with (295), (296) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (297) all_6_0 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (297) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | (298) all_58_25 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (299) all_56_0 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (299) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (300) all_10_2 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (300) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (301) all_58_28 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REDUCE: (151), (300) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (302) ~ (all_52_2 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REDUCE: (45), (300) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (303) op(e1, all_10_1) = all_10_0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REDUCE: (192), (300) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (304) op(e1, e3) = all_10_1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_2, all_10_1, e3, e1, % 154.52/23.50 | | | | | | | | | | | | | | | | | | | simplifying with (90), (304) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (305) all_52_2 = all_10_1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (305) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (306) all_54_8 = all_10_1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REDUCE: (6), (305) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (307) ~ (all_52_3 = all_10_1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | SIMP: (307) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_3 = all_10_1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REDUCE: (302), (305) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (309) ~ (all_10_1 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REDUCE: (102), (305) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (310) op(e1, all_10_1) = all_58_14 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_10_0, all_58_14, % 154.52/23.50 | | | | | | | | | | | | | | | | | | | all_10_1, e1, simplifying with (303), (310) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (311) all_58_14 = all_10_0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (312) all_56_12 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (312) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (313) all_52_3 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | SIMP: (313) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (314) all_52_3 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (314) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (315) ~ (all_4_2 = e3) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (316) ~ (all_4_2 = e3) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (317) all_56_12 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (312), (317) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | #588. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (318) ~ (all_56_12 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (319) all_56_13 = e2 | all_56_14 = e2 | all_56_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (320) all_56_13 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (320) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (321) e2 = e0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (321) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (322) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (323) ~ (all_56_13 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (324) all_56_14 = e2 | all_56_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (262), (323) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (325) ~ (e2 = e0) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | (326) all_54_15 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (214), (326) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | #587. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | (327) all_54_15 = e3 | all_54_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_28 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (301), (328) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | #857. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_58_28 = e3) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | (330) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (329) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | (331) ~ (e3 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_29 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (332) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_8_2 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (333) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_56_3 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_56_2 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (335) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (336) e1 = e0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (336) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (337) e1 = e0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (337) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_58_28 = e0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (338) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_56_3 = e1 | all_56_5 = e1 | all_56_10 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_56_3 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (340) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) e3 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (341) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (342) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_56_5 = e1 | all_56_10 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_56_14 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (344) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) e2 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (345) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (346) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_56_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (347) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_4_2 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_4_2 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (349) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) op(e2, e0) = all_4_1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_56_5 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (351) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_52_9 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (293), (352) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (353) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_56_10 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (354) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_52_13 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (355) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_52_13 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (356) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) op(e2, e0) = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (216), (350), (357) are inconsistent by % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #586. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_30 = e3 | all_58_31 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_54_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (359) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_4_2 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_4_2 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (361) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_31 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (361) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (e3 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (358) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_30 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (129), (364) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | #755. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_58_31 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (362), (365) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | #585. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_54_15 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (366) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_4_2 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (367) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_4_2 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (368) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (369) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (369) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (370) ~ (all_56_12 = e3) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (370) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | (371) ~ (all_52_3 = e3) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (372) all_54_12 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (372) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (373) all_52_3 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (292), (373) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (374) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_54_12 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | (376) all_54_12 = e3 | all_54_12 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (377) all_54_12 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (377) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (378) all_52_3 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (308), (378) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (379) ~ (all_10_1 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (379) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (380) ~ (all_10_1 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (378) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (381) ~ (all_4_2 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (381) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (382) ~ (all_4_2 = e2) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | (383) all_54_8 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (383) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | (384) all_10_1 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (384) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | (385) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (385) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | (386) all_54_8 = e3 | all_54_8 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | (387) all_58_28 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (301), (387) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | #856. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | (388) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_54_15 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (389) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_4_2 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (390) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (391) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (391) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_54_15 = e3 | all_54_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_54_15 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (393) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_4_2 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (394) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (395) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (395) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_54_15 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (396) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_4_2 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (397) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_58_31 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) all_54_8 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (380), (399) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | #727. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_54_8 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (306), (400) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_10_1 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_10_1 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (303), (402) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) op(e1, e3) = all_10_0 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (304), (402) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) op(e1, e3) = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_58_29 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (405) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) all_8_2 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (406) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) op(e2, e2) = all_58_9 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (406) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) op(e2, e2) = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e3, all_10_0, e3, e1, % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (403), (404) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_10_0 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e2, all_58_9, e2, e2, % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (407), (408) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_58_9 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (409) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_58_14 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (410), (412) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #584. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (298), (411), (413) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #583. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_58_30 = e2 | all_58_31 = e2 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (150), (188), (398), (414) are inconsistent % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #705. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (415) all_54_12 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (415) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (416) all_52_3 = e3 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (416) imply: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | (417) $false % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (417) is inconsistent. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (418) ~ (all_56_0 = e1) % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (419) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (66), (69), (82), (86), (105), (107), % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (112), (134), (140), (152), (172), (174), (187), % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (214), (247), (251), (278), (288), (289), (292), % 154.52/23.50 | | | | | | | | | | | | | | | | | | | (418), (419) are inconsistent by sub-proof #576. % 154.52/23.50 | | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | (420) all_56_15 = e1 % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (214), (420) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | | | | | | | #671. % 154.52/23.50 | | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | (421) all_56_14 = e0 % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | | REF_CLOSE: (203), (210), (421) are inconsistent by sub-proof % 154.52/23.50 | | | | | | | | | | | | #575. % 154.52/23.50 | | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | Case 2: % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | (422) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | | REF_CLOSE: (79), (94), (96), (134), (194), (247), (422) are % 154.52/23.50 | | | | | | | | | | inconsistent by sub-proof #573. % 154.52/23.50 | | | | | | | | | | % 154.52/23.50 | | | | | | | | | End of split % 154.52/23.50 | | | | | | | | | % 154.52/23.50 | | | | | | | | End of split % 154.52/23.50 | | | | | | | | % 154.52/23.50 | | | | | | | End of split % 154.52/23.50 | | | | | | | % 154.52/23.50 | | | | | | End of split % 154.52/23.50 | | | | | | % 154.52/23.50 | | | | | End of split % 154.52/23.50 | | | | | % 154.52/23.50 | | | | End of split % 154.52/23.50 | | | | % 154.52/23.50 | | | End of split % 154.52/23.50 | | | % 154.52/23.50 | | Case 2: % 154.52/23.50 | | | % 154.52/23.50 | | | (423) all_26_1 = e1 % 154.52/23.50 | | | (424) ~ (all_26_0 = e2) | ~ (all_26_2 = e3) % 154.52/23.50 | | | % 154.52/23.50 | | | COMBINE_EQS: (176), (423) imply: % 154.52/23.50 | | | (425) all_4_1 = e1 % 154.52/23.50 | | | % 154.52/23.50 | | | SIMP: (425) implies: % 154.52/23.50 | | | (426) all_4_1 = e1 % 154.52/23.50 | | | % 154.52/23.50 | | | COMBINE_EQS: (19), (426) imply: % 154.52/23.50 | | | (427) all_44_1 = e1 % 154.52/23.50 | | | % 154.52/23.50 | | | REDUCE: (162), (426) imply: % 154.52/23.50 | | | (428) op(all_4_2, e1) = all_4_0 % 154.52/23.50 | | | % 154.52/23.50 | | | BETA: splitting (36) gives: % 154.52/23.50 | | | % 154.52/23.50 | | | Case 1: % 154.52/23.50 | | | | % 154.52/23.50 | | | | (429) ~ (all_44_1 = e1) % 154.52/23.50 | | | | % 154.52/23.50 | | | | REDUCE: (427), (429) imply: % 154.52/23.50 | | | | (430) $false % 154.52/23.50 | | | | % 154.52/23.50 | | | | CLOSE: (430) is inconsistent. % 154.52/23.50 | | | | % 154.52/23.50 | | | Case 2: % 154.52/23.50 | | | | % 154.52/23.50 | | | | (431) ~ (all_44_0 = e3) | ~ (all_44_2 = e2) % 154.52/23.50 | | | | % 154.52/23.50 | | | | BETA: splitting (61) gives: % 154.52/23.50 | | | | % 154.52/23.50 | | | | Case 1: % 154.52/23.50 | | | | | % 154.52/23.50 | | | | | (432) all_56_15 = e0 % 154.52/23.50 | | | | | % 154.52/23.50 | | | | | REF_CLOSE: (2), (8), (31), (72), (107), (109), (129), (150), (169), % 154.52/23.50 | | | | | (174), (187), (188), (214), (432) are inconsistent by % 154.52/23.50 | | | | | sub-proof #709. % 154.52/23.50 | | | | | % 154.52/23.50 | | | | Case 2: % 154.52/23.50 | | | | | % 154.52/23.50 | | | | | (433) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.52/23.50 | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 154.52/23.50 | | | | | % 154.52/23.50 | | | | | ALPHA: (433) implies: % 154.52/23.50 | | | | | (434) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 154.52/23.50 | | | | | % 154.52/23.50 | | | | | BETA: splitting (26) gives: % 154.52/23.50 | | | | | % 154.52/23.50 | | | | | Case 1: % 154.52/23.50 | | | | | | % 154.52/23.50 | | | | | | (435) all_54_15 = e0 % 154.52/23.50 | | | | | | % 154.52/23.51 | | | | | | REF_CLOSE: (2), (31), (58), (72), (107), (109), (129), (150), (169), % 154.52/23.51 | | | | | | (174), (187), (188), (214), (435) are inconsistent by % 154.52/23.51 | | | | | | sub-proof #708. % 154.52/23.51 | | | | | | % 154.52/23.51 | | | | | Case 2: % 154.52/23.51 | | | | | | % 154.52/23.51 | | | | | | (436) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.52/23.51 | | | | | | % 154.52/23.51 | | | | | | BETA: splitting (122) gives: % 154.52/23.51 | | | | | | % 154.52/23.51 | | | | | | Case 1: % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | (437) all_56_1 = e0 % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | COMBINE_EQS: (87), (437) imply: % 154.52/23.51 | | | | | | | (438) all_52_4 = e0 % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | COMBINE_EQS: (84), (438) imply: % 154.52/23.51 | | | | | | | (439) all_58_2 = e0 % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | REDUCE: (35), (438) imply: % 154.52/23.51 | | | | | | | (440) ~ (all_52_6 = e0) % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | REDUCE: (60), (438) imply: % 154.52/23.51 | | | | | | | (441) ~ (all_52_7 = e0) % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | SIMP: (441) implies: % 154.52/23.51 | | | | | | | (442) ~ (all_52_7 = e0) % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | REDUCE: (14), (438) imply: % 154.52/23.51 | | | | | | | (443) op(e3, e0) = all_58_1 % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (13), (15), % 154.52/23.51 | | | | | | | (16), (17), (20), (22), (24), (25), (27), (30), (31), % 154.52/23.51 | | | | | | | (33), (34), (37), (42), (48), (49), (50), (51), (52), % 154.52/23.51 | | | | | | | (55), (57), (58), (63), (64), (65), (66), (67), (69), % 154.52/23.51 | | | | | | | (70), (72), (73), (74), (75), (77), (78), (79), (82), % 154.52/23.51 | | | | | | | (83), (85), (86), (94), (95), (96), (97), (98), (100), % 154.52/23.51 | | | | | | | (104), (105), (106), (107), (108), (109), (110), (112), % 154.52/23.51 | | | | | | | (114), (115), (117), (120), (121), (123), (125), (126), % 154.52/23.51 | | | | | | | (128), (129), (130), (131), (134), (135), (136), (137), % 154.52/23.51 | | | | | | | (138), (139), (140), (142), (143), (145), (146), (148), % 154.52/23.51 | | | | | | | (149), (150), (151), (152), (153), (155), (157), (159), % 154.52/23.51 | | | | | | | (160), (161), (163), (166), (167), (169), (170), (171), % 154.52/23.51 | | | | | | | (172), (173), (174), (175), (177), (180), (181), (185), % 154.52/23.51 | | | | | | | (187), (188), (189), (195), (199), (200), (203), (204), % 154.52/23.51 | | | | | | | (208), (209), (212), (214), (434), (436), (437), (439), % 154.52/23.51 | | | | | | | (442), (443) are inconsistent by sub-proof #608. % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | Case 2: % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | (444) ~ (all_56_1 = e0) % 154.52/23.51 | | | | | | | (445) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | REDUCE: (87), (444) imply: % 154.52/23.51 | | | | | | | (446) ~ (all_52_4 = e0) % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | BETA: splitting (80) gives: % 154.52/23.51 | | | | | | | % 154.52/23.51 | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | (447) all_56_0 = e0 % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | COMBINE_EQS: (152), (447) imply: % 154.52/23.51 | | | | | | | | (448) all_10_2 = e0 % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | COMBINE_EQS: (140), (448) imply: % 154.52/23.51 | | | | | | | | (449) all_58_28 = e0 % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.52/23.51 | | | | | | | | (145), (150), (169), (174), (187), (188), (449) are % 154.52/23.51 | | | | | | | | inconsistent by sub-proof #679. % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | (450) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | BETA: splitting (450) gives: % 154.52/23.51 | | | | | | | | % 154.52/23.51 | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | (451) all_56_1 = e0 % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | COMBINE_EQS: (87), (451) imply: % 154.52/23.51 | | | | | | | | | (452) all_52_4 = e0 % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | REDUCE: (446), (452) imply: % 154.52/23.51 | | | | | | | | | (453) $false % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | CLOSE: (453) is inconsistent. % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | (454) all_56_4 = e0 | all_56_9 = e0 % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | BETA: splitting (445) gives: % 154.52/23.51 | | | | | | | | | % 154.52/23.51 | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | (455) all_56_3 = e0 % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | COMBINE_EQS: (96), (455) imply: % 154.52/23.51 | | | | | | | | | | (456) all_8_2 = e0 % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | COMBINE_EQS: (105), (456) imply: % 154.52/23.51 | | | | | | | | | | (457) all_58_29 = e0 % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (107), (109), (129), (140), % 154.52/23.51 | | | | | | | | | | (145), (150), (169), (174), (187), (188), (457) % 154.52/23.51 | | | | | | | | | | are inconsistent by sub-proof #691. % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | (458) all_56_7 = e0 | all_56_13 = e0 % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | BETA: splitting (458) gives: % 154.52/23.51 | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | (459) all_56_7 = e0 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | COMBINE_EQS: (9), (459) imply: % 154.52/23.51 | | | | | | | | | | | (460) all_52_6 = e0 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | REDUCE: (75), (460) imply: % 154.52/23.51 | | | | | | | | | | | (461) $false % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | CLOSE: (461) is inconsistent. % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | (462) all_56_13 = e0 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | COMBINE_EQS: (115), (462) imply: % 154.52/23.51 | | | | | | | | | | | (463) all_52_7 = e0 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | SIMP: (463) implies: % 154.52/23.51 | | | | | | | | | | | (464) all_52_7 = e0 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | COMBINE_EQS: (97), (464) imply: % 154.52/23.51 | | | | | | | | | | | (465) all_58_24 = e0 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | REDUCE: (161), (464) imply: % 154.52/23.51 | | | | | | | | | | | (466) ~ (all_8_2 = e0) % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | REDUCE: (206), (464) imply: % 154.52/23.51 | | | | | | | | | | | (467) ~ (all_6_1 = e0) % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | REDUCE: (53), (464) imply: % 154.52/23.51 | | | | | | | | | | | (468) op(e0, e0) = all_58_23 % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | BETA: splitting (454) gives: % 154.52/23.51 | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | (469) all_56_4 = e0 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | COMBINE_EQS: (27), (469) imply: % 154.52/23.51 | | | | | | | | | | | | (470) all_52_8 = e0 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | REDUCE: (182), (470) imply: % 154.52/23.51 | | | | | | | | | | | | (471) $false % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | CLOSE: (471) is inconsistent. % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | (472) all_56_9 = e0 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | COMBINE_EQS: (104), (472) imply: % 154.52/23.51 | | | | | | | | | | | | (473) all_52_12 = e0 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | COMBINE_EQS: (24), (473) imply: % 154.52/23.51 | | | | | | | | | | | | (474) all_58_6 = e0 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | REDUCE: (50), (473) imply: % 154.52/23.51 | | | | | | | | | | | | (475) ~ (all_52_13 = e0) % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | SIMP: (475) implies: % 154.52/23.51 | | | | | | | | | | | | (476) ~ (all_52_13 = e0) % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | REDUCE: (106), (473) imply: % 154.52/23.51 | | | | | | | | | | | | (477) ~ (all_52_14 = e0) % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | REDUCE: (132), (473) imply: % 154.52/23.51 | | | | | | | | | | | | (478) op(e3, e0) = all_58_5 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | REDUCE: (110), (473) imply: % 154.52/23.51 | | | | | | | | | | | | (479) op(e3, e0) = e0 % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | BETA: splitting (33) gives: % 154.52/23.51 | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | (480) all_56_2 = e0 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | COMBINE_EQS: (130), (480) imply: % 154.52/23.51 | | | | | | | | | | | | | (481) all_52_1 = e0 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | COMBINE_EQS: (108), (481) imply: % 154.52/23.51 | | | | | | | | | | | | | (482) all_58_8 = e0 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | REDUCE: (160), (481) imply: % 154.52/23.51 | | | | | | | | | | | | | (483) ~ (all_52_2 = e0) % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | REDUCE: (136), (481) imply: % 154.52/23.51 | | | | | | | | | | | | | (484) ~ (all_52_3 = e0) % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | SIMP: (484) implies: % 154.52/23.51 | | | | | | | | | | | | | (485) ~ (all_52_3 = e0) % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | REDUCE: (143), (481) imply: % 154.52/23.51 | | | | | | | | | | | | | (486) ~ (all_52_9 = e0) % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | REDUCE: (200), (481) imply: % 154.52/23.51 | | | | | | | | | | | | | (487) ~ (all_10_2 = e0) % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | SIMP: (487) implies: % 154.52/23.51 | | | | | | | | | | | | | (488) ~ (all_10_2 = e0) % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | REDUCE: (186), (481) imply: % 154.52/23.51 | | | | | | | | | | | | | (489) op(e2, e0) = all_58_7 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, all_58_23, e0, e0, % 154.52/23.51 | | | | | | | | | | | | | simplifying with (153), (468) gives: % 154.52/23.51 | | | | | | | | | | | | | (490) all_58_23 = all_4_2 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_13, all_58_7, e0, % 154.52/23.51 | | | | | | | | | | | | | e2, simplifying with (163), (489) gives: % 154.52/23.51 | | | | | | | | | | | | | (491) all_58_7 = all_52_13 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_58_5, e0, e3, % 154.52/23.51 | | | | | | | | | | | | | simplifying with (478), (479) gives: % 154.52/23.51 | | | | | | | | | | | | | (492) all_58_5 = e0 % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | BETA: splitting (56) gives: % 154.52/23.51 | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | (493) all_54_11 = e0 % 154.52/23.51 | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | REF_CLOSE: (46), (178), (493) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | #743. % 154.52/23.51 | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | (494) ~ (all_54_11 = e0) % 154.52/23.51 | | | | | | | | | | | | | | (495) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.52/23.51 | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | BETA: splitting (123) gives: % 154.52/23.51 | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | (496) all_56_9 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | COMBINE_EQS: (472), (496) imply: % 154.52/23.51 | | | | | | | | | | | | | | | (497) e1 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | REDUCE: (174), (497) imply: % 154.52/23.51 | | | | | | | | | | | | | | | (498) $false % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | CLOSE: (498) is inconsistent. % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | (499) ~ (all_56_9 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | (500) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | REDUCE: (472), (499) imply: % 154.52/23.51 | | | | | | | | | | | | | | | (501) ~ (e1 = e0) % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 154.52/23.51 | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | (502) all_54_6 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | REF_CLOSE: (57), (94), (502) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | #797. % 154.52/23.51 | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | (503) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | (504) all_54_9 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (75), (504) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | | #572. % 154.52/23.51 | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | (505) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | (506) all_54_8 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (506) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | | | #731. % 154.52/23.51 | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | (507) ~ (all_54_8 = e0) % 154.52/23.51 | | | | | | | | | | | | | | | | | | (508) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | (509) all_54_2 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (182), (509) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | | | | #860. % 154.52/23.51 | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | (510) ~ (all_54_2 = e0) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | (511) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | (512) all_54_1 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (446), (512) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | #798. % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | (513) ~ (all_54_1 = e0) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | (514) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | (515) all_54_12 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (485), (515) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | #762. % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | (516) ~ (all_54_12 = e0) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | (517) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | (518) all_54_7 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (476), (518) are inconsistent by sub-proof % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | #742. % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | (519) ~ (all_54_7 = e0) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | (520) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (521) all_56_12 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (17), (23), (27), (28), (31), (37), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (49), (66), (69), (72), (82), (86), (87), (89), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (98), (100), (105), (107), (109), (116), (120), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (129), (134), (140), (150), (152), (155), (158), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (167), (169), (172), (173), (178), (182), (187), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (188), (190), (202), (204), (207), (465), (472), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (474), (476), (482), (485), (490), (491), (492), % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (500), (521) are inconsistent by sub-proof #589. % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | (522) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | (523) all_56_13 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (523) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | (524) e1 = e0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (524) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | (525) $false % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (525) is inconsistent. % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | (526) all_56_14 = e1 | all_56_15 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_56_14 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (527) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_6_1 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (528) implies: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_6_1 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (529) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_58_26 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (529) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (531) ~ (all_52_3 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (529) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (532) ~ (all_52_9 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (529) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | (533) ~ (all_4_2 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_56_0 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (534) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_10_2 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (535) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_58_28 = e1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (535) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (537) ~ (all_52_2 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (535) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (538) ~ (all_52_4 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (535) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (539) ~ (all_52_8 = e1) % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (535) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (540) op(e1, e3) = all_10_1 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (535) imply: % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (541) op(e3, e1) = all_58_0 % 154.52/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_2, all_10_1, e3, e1, % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (90), (540) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_52_2 = all_10_1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_8, all_58_0, e1, e3, % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (144), (541) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_58_0 = all_52_8 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (544) all_54_8 = all_10_1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_56_6 = all_10_1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_58_15 = all_10_1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (547) ~ (all_52_3 = all_10_1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (547) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (548) ~ (all_52_3 = all_10_1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (549) ~ (all_52_6 = all_10_1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (549) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (550) ~ (all_52_6 = all_10_1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (551) ~ (all_52_14 = all_10_1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (551) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (552) ~ (all_52_14 = all_10_1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (537), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (553) ~ (all_10_1 = e1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (542) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (554) ~ (all_10_1 = e0) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_56_4 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (555) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_52_8 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (556) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_52_8 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (557) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) ~ (all_52_4 = e2) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (557) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) ~ (all_52_9 = e2) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (559) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) ~ (all_52_9 = e2) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (557) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) op(e3, e1) = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_54_1 = e1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (562) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_52_4 = e1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (563) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) $false % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (564) is inconsistent. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) ~ (all_54_1 = e1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_54_1 = e3 | all_54_1 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_54_1 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (567) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_52_4 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (568) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) $false % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (569) is inconsistent. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_54_1 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (570) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_52_4 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (571) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) ~ (all_8_2 = e3) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (572) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) ~ (all_8_2 = e3) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_58_31 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (72), (107), (109), (129), (150), (169), % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188), (536), (574) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #715. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (575) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_58_30 = e1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (576) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) e1 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (577) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) e1 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (578) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_58_28 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (579) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_58_29 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (581) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) all_8_2 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (582) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) ~ (e3 = e2) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_58_28 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (536), (584) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #857. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (585) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_58_29 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (581), (586) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_58_30 = e3 | all_58_31 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (587) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_58_30 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (129), (588) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #755. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_58_31 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (589) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_4_2 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (590) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_26_2 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (428), (590) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) op(e3, e1) = all_4_0 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (424), (561), (591), (592) are % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) ~ (all_58_29 = e2) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (593) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) ~ (all_8_2 = e2) % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_54_6 = e1 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (532), (595) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_54_6 = e3 | all_54_6 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_58_28 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (536), (597) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #856. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (596) gives: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) all_54_6 = e2 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (560), (599) are inconsistent by sub-proof % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #773. % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_54_6 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (600) imply: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_52_9 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (601) implies: % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_52_9 = e3 % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (602) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) op(e2, e1) = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_58_29 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (604) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_8_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (605) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) $false % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (606) is inconsistent. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (607) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_58_30 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (150), (608) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #718. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_58_31 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (609) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_4_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (127), (184), (428), (431), (603), (610) are % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #570. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) ~ (all_56_4 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (611) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) ~ (all_52_8 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_54_2 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (539), (614) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #819. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) ~ (all_54_2 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_54_2 = e3 | all_54_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_56_0 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (534), (617) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #796. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (612) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_56_5 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (619) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_52_9 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (620) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_52_9 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (621) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_58_11 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_56_1 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (623) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_52_4 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (624) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_58_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (624) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) ~ (all_8_2 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (626) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) ~ (all_8_2 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_56_0 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (534), (628) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #569. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_56_1 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (623), (630) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #568. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_56_4 = e3 | all_56_9 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_56_4 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (632) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_52_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (633) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_52_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (634) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_58_4 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) all_58_28 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (536), (636) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #856. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (637) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) all_58_29 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (638) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_8_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (627), (639) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) $false % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (640) is inconsistent. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) ~ (all_58_29 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_58_30 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (150), (643) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #718. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_58_31 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (644) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_4_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (645) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) ~ (all_52_3 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (645) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) ~ (all_52_13 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_56_6 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (545), (648) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_10_1 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (649) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_10_1 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (650) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_58_15 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (650) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) ~ (all_52_6 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (650) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) ~ (all_52_14 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) all_56_12 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (654) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_52_3 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (655) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_52_3 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (656) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_58_22 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_58_28 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (536), (658) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #857. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (659) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_58_29 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (660) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_8_2 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (661) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) ~ (all_52_6 = e3) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (661) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) ~ (all_52_13 = e3) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_54_9 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (664) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_52_6 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (665) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_52_6 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (666) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_58_17 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (520) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_54_7 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (668) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_52_13 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (669) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_52_13 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (670) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_58_13 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (98), (670) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) ~ (all_52_14 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (672) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) ~ (all_52_14 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (663), (670) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) ~ (e3 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (647), (670) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) ~ (e2 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) all_54_11 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (673), (676) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_54_11 = e3 | all_54_11 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (677) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_54_11 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (653), (678) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #777. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_54_11 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (679) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_52_14 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (680) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_52_14 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (681) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_58_20 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_58_31 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (150), (642), (683) are inconsistent by % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #717. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) ~ (all_58_31 = e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (685) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_58_30 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (686) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) e1 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (687) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_58_28 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (688) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) ~ (all_58_30 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (690) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_58_29 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (660), (691) are inconsistent by sub-proof % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_58_28 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (693) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) e3 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (660), (694) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_58_29 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (150), (188), (642), (659), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) are inconsistent by sub-proof #685. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) ~ (all_58_28 = e3) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (698) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (699) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (700) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (701) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_58_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_4 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_58_2 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (625), (704) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (705) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (703) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) e3 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (707) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) e3 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (702) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) e3 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (706), (709) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) e2 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (706), (708) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) e2 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (710), (711) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) e1 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (712) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_58_28 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (713) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (715) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_58_22 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (107), (109), (129), (150), (188), (536), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657), (659), (660), (716) are inconsistent by % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #566. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (717) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_58_17 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) all_58_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_58_2 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (625), (720) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (721) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (719) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) e3 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (667), (718) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) e2 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (722), (723) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) e2 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (725) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) e2 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (724), (726) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) e1 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (727) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_58_28 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (728) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (731) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_58_13 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_58_8 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) all_58_2 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (625), (734) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (735) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (733) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) e3 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (671), (732) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) e2 = e1 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (736), (737) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) e2 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (739) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) e2 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738), (740) are inconsistent by sub-proof #565. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (741) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_58_15 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_58_8 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (743) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) e2 = e0 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (651), (742) imply: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) e3 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (107), (109), (129), (150), (188), (536), % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659), (660), (744), (745) are inconsistent by % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #564. % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (746) gives: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (747) implies: % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) all_58_6 = e3 % 154.64/23.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (748) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) e3 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (660), (749) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) all_58_29 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (107), (109), (129), (150), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659), (750) are inconsistent by sub-proof #702. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (751) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) all_58_11 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_58_8 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (753) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (752) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754), (755) are inconsistent by sub-proof #565. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (757) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (759) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) all_58_13 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (760) are inconsistent by sub-proof #563. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) e3 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_58_8 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (763) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (107), (109), (129), (150), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659), (660), (762), (764) are inconsistent by % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #564. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) all_58_22 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (107), (109), (129), (150), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657), (659), (660), (767) are inconsistent by % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #566. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (768) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_58_15 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_58_11 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (770) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (651), (769) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) e3 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (771), (772) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (660), (773) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) all_58_29 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (150), (188), (642), (659), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) are inconsistent by sub-proof #685. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (775) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (777) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) all_58_20 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (682), (778) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (150), (188), (642), (659), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660), (779) are inconsistent by sub-proof #562. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (780) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_58_6 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_58_4 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (782) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (783) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (474), (781) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) e3 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (784), (785) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) e1 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (786) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) all_58_28 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (787) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (789) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_58_4 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (790) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (150), (188), (642), (659), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660), (791) are inconsistent by sub-proof #562. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_58_20 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_58_4 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (794) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (795) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (682), (793) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) e3 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796), (797) are inconsistent by sub-proof #561. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (798) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (799) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (801) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_58_4 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (802) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (150), (188), (642), (659), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660), (803) are inconsistent by sub-proof #562. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (804) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (805) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_58_13 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (806) are inconsistent by sub-proof #563. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (530), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536), (808) are inconsistent by sub-proof #560. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (809) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) all_58_13 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (671), (813) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (465), (812) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814), (815) are inconsistent by sub-proof #565. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (816) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_58_22 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_58_20 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (682), (818) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (819) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (657), (817) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) e3 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820), (821) are inconsistent by sub-proof #561. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (822) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (823) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) all_58_22 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (107), (109), (129), (150), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657), (659), (660), (824) are inconsistent by % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #566. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (825) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_58_13 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (826) are inconsistent by sub-proof #563. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (827) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (828) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (829) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (830) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) all_58_20 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (682), (831) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) e3 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (150), (188), (642), (659), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660), (832) are inconsistent by sub-proof #562. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (833) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) all_58_13 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (671), (835) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (465), (834) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (836), (837) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) e1 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (838) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_58_28 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (839) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (840) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (841) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (842) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) e1 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (843) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) all_58_28 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (844) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (845) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) all_58_11 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (846) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (644), (847) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_58_31 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (109), (150), (642), (848) are inconsistent % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #675. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (849) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (850) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (851) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_58_24 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) all_58_13 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (671), (853) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) e2 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (465), (852) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (855) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854), (856) are inconsistent by sub-proof #565. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (857) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) all_58_13 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (858) are inconsistent by sub-proof #563. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (860) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_58_13 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (536), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (861) are inconsistent by sub-proof #563. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (862) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) all_58_26 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (530), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536), (863) are inconsistent by sub-proof #560. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) all_54_7 = e3 | all_54_7 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (647), (663), (864) are inconsistent by % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #602. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_54_9 = e3 | all_54_9 = e2 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (652), (662), (865) are inconsistent by % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #559. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_58_30 = e3 | all_58_31 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (866) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_58_30 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (129), (867) are inconsistent by sub-proof % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #755. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_58_31 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (644), (868) are inconsistent by sub-proof % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #585. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) ~ (all_56_12 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (869) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) ~ (all_52_3 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (517), (531), (646), (870) are inconsistent % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #557. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) ~ (all_56_6 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (545), (871) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) ~ (all_10_1 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_56_12 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (873) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_52_3 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (874) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_52_3 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (875) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) ~ (all_10_1 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (876) implies: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) ~ (all_10_1 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (508), (544), (553), (872), (877) are inconsistent % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #725. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) ~ (all_56_12 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (878) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) ~ (all_52_3 = e3) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (517), (531), (646), (879) are inconsistent % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #557. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) all_56_9 = e3 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (880) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) e3 = e0 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (881) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) $false % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (882) is inconsistent. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) ~ (all_56_1 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (87), (883) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) ~ (all_52_4 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (32), (71), (87), (101), (511), (514), % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538), (539), (613), (884) are inconsistent by % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #553. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) ~ (all_56_5 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (885) imply: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) ~ (all_52_9 = e2) % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) all_54_6 = e1 % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (532), (887) are inconsistent by sub-proof % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774. % 154.64/23.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_54_6 = e3 | all_54_6 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_54_2 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (613), (889) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #556. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_54_2 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (890) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_52_8 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (891) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) all_52_8 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (892) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) ~ (all_52_9 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (893) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) ~ (all_52_9 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (886), (888), (894) are inconsistent by % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #552. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (895) ~ (all_56_0 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (66), (69), (82), (86), (105), (107), % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (134), (140), (152), (172), (174), (187), % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (476), (480), (500), (526), (527), (531), % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (895), (896) are inconsistent by sub-proof #576. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_56_15 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (214), (897) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | #671. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | (898) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | REF_CLOSE: (79), (94), (96), (134), (194), (476), (898) are % 154.64/23.54 | | | | | | | | | | | | | inconsistent by sub-proof #573. % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | End of split % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | End of split % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | End of split % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | End of split % 154.64/23.54 | | | | | % 154.64/23.54 | | | | End of split % 154.64/23.54 | | | | % 154.64/23.54 | | | End of split % 154.64/23.54 | | | % 154.64/23.54 | | End of split % 154.64/23.54 | | % 154.64/23.54 | Case 2: % 154.64/23.54 | | % 154.64/23.54 | | (899) all_20_2 = e1 % 154.64/23.54 | | (900) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (85), (899) imply: % 154.64/23.54 | | (901) all_4_2 = e1 % 154.64/23.54 | | % 154.64/23.54 | | SIMP: (901) implies: % 154.64/23.54 | | (902) all_4_2 = e1 % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (124), (902) imply: % 154.64/23.54 | | (903) all_34_2 = e1 % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (8), (902) imply: % 154.64/23.54 | | (904) all_56_15 = e1 % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (2), (902) imply: % 154.64/23.54 | | (905) all_58_31 = e1 % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (89), (902) imply: % 154.64/23.54 | | (906) ~ (all_52_3 = e1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (177), (902) imply: % 154.64/23.54 | | (907) ~ (all_52_7 = e1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (157), (902) imply: % 154.64/23.54 | | (908) ~ (all_52_12 = e1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (66), (902) imply: % 154.64/23.54 | | (909) ~ (all_52_13 = e1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (209), (902) imply: % 154.64/23.54 | | (910) ~ (all_6_1 = e1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (162), (902) imply: % 154.64/23.54 | | (911) op(e1, all_4_1) = all_4_0 % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (191), (902) imply: % 154.64/23.54 | | (912) op(e1, e0) = all_4_1 % 154.64/23.54 | | % 154.64/23.54 | | GROUND_INST: instantiating (4) with all_52_14, all_4_1, e0, e1, simplifying % 154.64/23.54 | | with (92), (912) gives: % 154.64/23.54 | | (913) all_52_14 = all_4_1 % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (46), (913) imply: % 154.64/23.54 | | (914) all_54_11 = all_4_1 % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (86), (913) imply: % 154.64/23.54 | | (915) all_56_11 = all_4_1 % 154.64/23.54 | | % 154.64/23.54 | | COMBINE_EQS: (49), (913) imply: % 154.64/23.54 | | (916) all_58_20 = all_4_1 % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (172), (913) imply: % 154.64/23.54 | | (917) ~ (all_52_2 = all_4_1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (55), (913) imply: % 154.64/23.54 | | (918) ~ (all_52_6 = all_4_1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (106), (913) imply: % 154.64/23.54 | | (919) ~ (all_52_12 = all_4_1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (98), (913) imply: % 154.64/23.54 | | (920) ~ (all_52_13 = all_4_1) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (178), (913) imply: % 154.64/23.54 | | (921) ~ (all_4_1 = e0) % 154.64/23.54 | | % 154.64/23.54 | | REDUCE: (20), (913) imply: % 154.64/23.54 | | (922) op(e1, all_4_1) = all_58_19 % 154.64/23.54 | | % 154.64/23.54 | | GROUND_INST: instantiating (4) with all_4_0, all_58_19, all_4_1, e1, % 154.64/23.54 | | simplifying with (911), (922) gives: % 154.64/23.54 | | (923) all_58_19 = all_4_0 % 154.64/23.54 | | % 154.64/23.54 | | BETA: splitting (29) gives: % 154.64/23.54 | | % 154.64/23.54 | | Case 1: % 154.64/23.54 | | | % 154.64/23.54 | | | (924) ~ (all_34_2 = e1) % 154.64/23.54 | | | % 154.64/23.54 | | | REDUCE: (903), (924) imply: % 154.64/23.54 | | | (925) $false % 154.64/23.54 | | | % 154.64/23.54 | | | CLOSE: (925) is inconsistent. % 154.64/23.54 | | | % 154.64/23.54 | | Case 2: % 154.64/23.54 | | | % 154.64/23.54 | | | (926) ~ (all_34_0 = e3) | ~ (all_34_1 = e2) % 154.64/23.54 | | | % 154.64/23.54 | | | BETA: splitting (56) gives: % 154.64/23.54 | | | % 154.64/23.54 | | | Case 1: % 154.64/23.54 | | | | % 154.64/23.54 | | | | (927) all_54_11 = e0 % 154.64/23.54 | | | | % 154.64/23.54 | | | | REF_CLOSE: (914), (921), (927) are inconsistent by sub-proof #551. % 154.64/23.54 | | | | % 154.64/23.54 | | | Case 2: % 154.64/23.54 | | | | % 154.64/23.54 | | | | (928) ~ (all_54_11 = e0) % 154.64/23.54 | | | | (929) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 154.64/23.54 | | | | % 154.64/23.54 | | | | BETA: splitting (33) gives: % 154.64/23.54 | | | | % 154.64/23.54 | | | | Case 1: % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | (930) all_56_2 = e0 % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | COMBINE_EQS: (130), (930) imply: % 154.64/23.54 | | | | | (931) all_52_1 = e0 % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | COMBINE_EQS: (108), (931) imply: % 154.64/23.54 | | | | | (932) all_58_8 = e0 % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | REDUCE: (160), (931) imply: % 154.64/23.54 | | | | | (933) ~ (all_52_2 = e0) % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | REDUCE: (143), (931) imply: % 154.64/23.54 | | | | | (934) ~ (all_52_9 = e0) % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | REDUCE: (78), (931) imply: % 154.64/23.54 | | | | | (935) ~ (all_52_13 = e0) % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | SIMP: (935) implies: % 154.64/23.54 | | | | | (936) ~ (all_52_13 = e0) % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | BETA: splitting (61) gives: % 154.64/23.54 | | | | | % 154.64/23.54 | | | | | Case 1: % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | | (937) all_56_15 = e0 % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | | REF_CLOSE: (174), (904), (937) are inconsistent by sub-proof #550. % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | Case 2: % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | | (938) (all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0) & % 154.64/23.54 | | | | | | (all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0) % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | | ALPHA: (938) implies: % 154.64/23.54 | | | | | | (939) all_56_9 = e0 | all_56_10 = e0 | all_56_11 = e0 % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | | BETA: splitting (939) gives: % 154.64/23.54 | | | | | | % 154.64/23.54 | | | | | | Case 1: % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | (940) all_56_9 = e0 % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | COMBINE_EQS: (104), (940) imply: % 154.64/23.54 | | | | | | | (941) all_52_12 = e0 % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | SIMP: (941) implies: % 154.64/23.54 | | | | | | | (942) all_52_12 = e0 % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | COMBINE_EQS: (24), (942) imply: % 154.64/23.54 | | | | | | | (943) all_58_6 = e0 % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | REDUCE: (196), (942) imply: % 154.64/23.54 | | | | | | | (944) ~ (all_52_4 = e0) % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | REDUCE: (919), (942) imply: % 154.64/23.54 | | | | | | | (945) ~ (all_4_1 = e0) % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | REDUCE: (908), (942) imply: % 154.64/23.54 | | | | | | | (946) ~ (e1 = e0) % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | BETA: splitting (122) gives: % 154.64/23.54 | | | | | | | % 154.64/23.54 | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | (947) all_56_1 = e0 % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | COMBINE_EQS: (87), (947) imply: % 154.64/23.54 | | | | | | | | (948) all_52_4 = e0 % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | REDUCE: (944), (948) imply: % 154.64/23.54 | | | | | | | | (949) $false % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | CLOSE: (949) is inconsistent. % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | (950) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | BETA: splitting (950) gives: % 154.64/23.54 | | | | | | | | % 154.64/23.54 | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | (951) all_56_3 = e0 % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | COMBINE_EQS: (96), (951) imply: % 154.64/23.54 | | | | | | | | | (952) all_8_2 = e0 % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | COMBINE_EQS: (105), (952) imply: % 154.64/23.54 | | | | | | | | | (953) all_58_29 = e0 % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (107), (109), (129), (140), % 154.64/23.54 | | | | | | | | | (145), (150), (169), (174), (187), (188), (953) are % 154.64/23.54 | | | | | | | | | inconsistent by sub-proof #691. % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | (954) all_56_7 = e0 | all_56_13 = e0 % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | BETA: splitting (954) gives: % 154.64/23.54 | | | | | | | | | % 154.64/23.54 | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | (955) all_56_7 = e0 % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | COMBINE_EQS: (9), (955) imply: % 154.64/23.54 | | | | | | | | | | (956) all_52_6 = e0 % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | REDUCE: (75), (956) imply: % 154.64/23.54 | | | | | | | | | | (957) $false % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | CLOSE: (957) is inconsistent. % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | (958) all_56_13 = e0 % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | COMBINE_EQS: (115), (958) imply: % 154.64/23.54 | | | | | | | | | | (959) all_52_7 = e0 % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | SIMP: (959) implies: % 154.64/23.54 | | | | | | | | | | (960) all_52_7 = e0 % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | COMBINE_EQS: (97), (960) imply: % 154.64/23.54 | | | | | | | | | | (961) all_58_24 = e0 % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | REDUCE: (83), (960) imply: % 154.64/23.54 | | | | | | | | | | (962) ~ (all_52_3 = e0) % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | REDUCE: (206), (960) imply: % 154.64/23.54 | | | | | | | | | | (963) ~ (all_6_1 = e0) % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | BETA: splitting (133) gives: % 154.64/23.54 | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | (964) all_54_12 = e0 % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | COMBINE_EQS: (197), (964) imply: % 154.64/23.54 | | | | | | | | | | | (965) all_52_3 = e0 % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | REDUCE: (962), (965) imply: % 154.64/23.54 | | | | | | | | | | | (966) $false % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | CLOSE: (966) is inconsistent. % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | (967) ~ (all_54_12 = e0) % 154.64/23.54 | | | | | | | | | | | (968) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | BETA: splitting (42) gives: % 154.64/23.54 | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | (969) all_56_0 = e1 % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | COMBINE_EQS: (152), (969) imply: % 154.64/23.54 | | | | | | | | | | | | (970) all_10_2 = e1 % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | COMBINE_EQS: (140), (970) imply: % 154.64/23.54 | | | | | | | | | | | | (971) all_58_28 = e1 % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | BETA: splitting (169) gives: % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | (972) all_58_28 = e3 % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | REF_CLOSE: (72), (971), (972) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | #857. % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | (973) ~ (all_58_28 = e3) % 154.64/23.54 | | | | | | | | | | | | | (974) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | REDUCE: (971), (973) imply: % 154.64/23.54 | | | | | | | | | | | | | (975) ~ (e3 = e1) % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | BETA: splitting (974) gives: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | (976) all_58_29 = e3 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | COMBINE_EQS: (105), (976) imply: % 154.64/23.54 | | | | | | | | | | | | | | (977) all_8_2 = e3 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | (978) all_58_28 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | COMBINE_EQS: (971), (978) imply: % 154.64/23.54 | | | | | | | | | | | | | | | (979) e2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | REDUCE: (109), (979) imply: % 154.64/23.54 | | | | | | | | | | | | | | | (980) $false % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | CLOSE: (980) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | (981) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | REF_CLOSE: (107), (109), (150), (188), (905), (976), (981) % 154.64/23.54 | | | | | | | | | | | | | | | are inconsistent by sub-proof #683. % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | (982) all_58_30 = e3 | all_58_31 = e3 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (905), (982) are inconsistent % 154.64/23.54 | | | | | | | | | | | | | | by sub-proof #694. % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | (983) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | BETA: splitting (983) gives: % 154.64/23.54 | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | (984) all_56_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | REF_CLOSE: (174), (930), (984) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | #549. % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | (985) all_56_6 = e1 | all_56_12 = e1 % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | BETA: splitting (985) gives: % 154.64/23.54 | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | (986) all_56_6 = e1 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | COMBINE_EQS: (112), (986) imply: % 154.64/23.54 | | | | | | | | | | | | | | (987) all_52_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | SIMP: (987) implies: % 154.64/23.54 | | | | | | | | | | | | | | (988) all_52_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | COMBINE_EQS: (17), (988) imply: % 154.64/23.54 | | | | | | | | | | | | | | (989) all_58_15 = e1 % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | REDUCE: (6), (988) imply: % 154.64/23.54 | | | | | | | | | | | | | | (990) ~ (all_52_3 = e1) % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | REDUCE: (114), (988) imply: % 154.64/23.54 | | | | | | | | | | | | | | (991) ~ (all_52_6 = e1) % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | SIMP: (991) implies: % 154.64/23.54 | | | | | | | | | | | | | | (992) ~ (all_52_6 = e1) % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | REDUCE: (917), (988) imply: % 154.64/23.54 | | | | | | | | | | | | | | (993) ~ (all_4_1 = e1) % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | SIMP: (993) implies: % 154.64/23.54 | | | | | | | | | | | | | | (994) ~ (all_4_1 = e1) % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | BETA: splitting (77) gives: % 154.64/23.54 | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | (995) all_54_0 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.54 | | | | | | | | | | | | | | | (140), (145), (150), (169), (171), (174), (187), % 154.64/23.54 | | | | | | | | | | | | | | | (188), (995) are inconsistent by sub-proof #678. % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | (996) ~ (all_54_0 = e0) % 154.64/23.54 | | | | | | | | | | | | | | | (997) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | REDUCE: (171), (996) imply: % 154.64/23.54 | | | | | | | | | | | | | | | (998) ~ (all_10_2 = e0) % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 154.64/23.54 | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | (999) all_54_9 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | REF_CLOSE: (65), (75), (999) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | | | | #572. % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | (1000) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | (1001) all_56_4 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (1001) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | (1002) all_52_8 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | SIMP: (1002) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | (1003) all_52_8 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | REDUCE: (101), (1003) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | (1004) ~ (all_52_4 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1005) all_56_1 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (1005) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1006) all_52_4 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | REDUCE: (1004), (1006) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1007) $false % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | CLOSE: (1007) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1008) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | BETA: splitting (1008) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1009) all_56_3 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (1009) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1010) all_8_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | SIMP: (1010) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1011) all_8_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (1011) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1012) all_58_29 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1013) all_58_28 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (107), (129), (169), (188), (905), (1012), % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1013) are inconsistent by sub-proof #548. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1014) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1014) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1015) all_58_29 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1012), (1015) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1016) e2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (1016) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1017) $false % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1017) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1018) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (109), (150), (905), (1018) are % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #696. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1019) all_56_7 = e1 | all_56_13 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (115), (907), (992), (1019) are inconsistent % 154.64/23.54 | | | | | | | | | | | | | | | | | | | by sub-proof #546. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | (1020) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | BETA: splitting (1020) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1021) all_56_5 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (1021) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1022) all_52_9 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | SIMP: (1022) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1023) all_52_9 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (1023) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1024) all_58_11 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | REDUCE: (121), (1023) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1025) ~ (all_52_13 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | REDUCE: (138), (1023) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1026) ~ (all_8_2 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | SIMP: (1026) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1027) ~ (all_8_2 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | REDUCE: (208), (1023) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | (1028) ~ (all_6_1 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1029) all_56_1 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (1029) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1030) all_52_4 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (1030) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1031) all_58_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | REDUCE: (101), (1030) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1032) ~ (all_52_8 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | SIMP: (1032) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1033) ~ (all_52_8 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | REDUCE: (183), (1030) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1034) ~ (all_10_2 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | SIMP: (1034) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | (1035) ~ (all_10_2 = e1) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1036) all_54_5 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (1036) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1037) all_8_2 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (1037) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1038) all_58_29 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (107), (109), (129), (140), % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (145), (150), (169), (174), (187), (188), (1038) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #691. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1039) ~ (all_54_5 = e0) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | (1040) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1041) all_54_2 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (1041) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1042) all_52_8 = e0 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (1042) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1043) $false % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1043) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1044) ~ (all_54_2 = e0) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | (1045) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1046) all_56_12 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (1046) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1047) all_52_3 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1047) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1048) all_52_3 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (1048) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1049) ~ (all_10_2 = e2) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1049) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1050) ~ (all_10_2 = e2) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | (1051) all_56_0 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (1051) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | (1052) all_10_2 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (1052) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | (1053) all_58_28 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_58_28 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1053), (1054) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | (1055) e3 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (1055) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | (1056) $false % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1056) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1057) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1058) all_58_29 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (1058) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1059) all_8_2 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (1059) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1060) ~ (all_52_6 = e2) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (929) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_54_11 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (914), (994), (1061) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | #545. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_54_11 = e3 | all_54_11 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1000) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_54_9 = e1 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (992), (1063) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_54_9 = e3 | all_54_9 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1064) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) all_54_9 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (1060), (1065) are inconsistent by sub-proof % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #621. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_54_9 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (1066) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) all_52_6 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1067) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_52_6 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (918), (1068) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) ~ (all_4_1 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1069) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) ~ (all_4_1 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (1068) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) op(e1, e2) = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1062) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) all_54_11 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (914), (1072) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_4_1 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1073) implies: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_4_1 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (1074) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_34_1 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (911), (1074) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) op(e1, e2) = all_4_0 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (926) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) ~ (all_34_1 = e2) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1075), (1077) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) $false % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1078) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) ~ (all_34_0 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1079) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) ~ (all_4_0 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e3, all_4_0, e2, e1, % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1071), (1076) gives: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) all_4_0 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1080), (1081) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) $false % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1082) is inconsistent. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_54_11 = e3 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (914), (1070), (1083) are inconsistent by % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #544. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (109), (150), (905), (1084) are % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #696. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | (1085) ~ (all_56_0 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (1085) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | (1086) ~ (all_10_2 = e3) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (997), (1035), (1050), (1086) are % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #813. % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1087) ~ (all_56_12 = e2) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (1087) imply: % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | (1088) ~ (all_52_3 = e2) % 154.64/23.54 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (11), (16), (25), (27), (31), (37), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (41), (54), (65), (68), (69), (71), (74), (82), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (96), (100), (105), (107), (134), (140), (141), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (142), (152), (155), (158), (167), (169), (171), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (174), (180), (182), (194), (197), (203), (204), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (207), (210), (905), (906), (909), (910), (915), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (916), (920), (921), (930), (932), (936), (943), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (961), (968), (985), (986), (989), (992), (994), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (997), (998), (1000), (1021), (1024), (1027), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1029), (1031), (1033), (1035), (1040), (1045), % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1088) are inconsistent by sub-proof #530. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | (1089) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (96), (174), (958), (992), (1027), (1089) are % 154.64/23.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #528. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | (1090) all_56_8 = e1 | all_56_14 = e1 % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (174), (203), (910), (1090) are inconsistent % 154.64/23.55 | | | | | | | | | | | | | | | | | | by sub-proof #527. % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | (1091) all_56_12 = e1 % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | REF_CLOSE: (82), (906), (1091) are inconsistent by sub-proof % 154.64/23.55 | | | | | | | | | | | | | | #577. % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | End of split % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | End of split % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | Case 2: % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | (1092) all_56_10 = e0 | all_56_11 = e0 % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | REF_CLOSE: (134), (915), (921), (936), (1092) are inconsistent by % 154.64/23.55 | | | | | | | sub-proof #524. % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | End of split % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | End of split % 154.64/23.55 | | | | | % 154.64/23.55 | | | | Case 2: % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | (1093) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | BETA: splitting (156) gives: % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | Case 1: % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | (1094) all_56_0 = e0 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | COMBINE_EQS: (152), (1094) imply: % 154.64/23.55 | | | | | | (1095) all_10_2 = e0 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | COMBINE_EQS: (140), (1095) imply: % 154.64/23.55 | | | | | | (1096) all_58_28 = e0 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), (145), % 154.64/23.55 | | | | | | (150), (169), (174), (187), (188), (1096) are % 154.64/23.55 | | | | | | inconsistent by sub-proof #679. % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | Case 2: % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | (1097) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | BETA: splitting (1093) gives: % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | Case 1: % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | (1098) all_56_3 = e0 % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | COMBINE_EQS: (96), (1098) imply: % 154.64/23.55 | | | | | | | (1099) all_8_2 = e0 % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | COMBINE_EQS: (105), (1099) imply: % 154.64/23.55 | | | | | | | (1100) all_58_29 = e0 % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | REF_CLOSE: (2), (31), (72), (85), (107), (109), (129), (140), % 154.64/23.55 | | | | | | | (145), (150), (169), (174), (187), (188), (1100) are % 154.64/23.55 | | | | | | | inconsistent by sub-proof #691. % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | Case 2: % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | (1101) all_56_5 = e0 | all_56_10 = e0 % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | BETA: splitting (1101) gives: % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | (1102) all_56_5 = e0 % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | COMBINE_EQS: (79), (1102) imply: % 154.64/23.55 | | | | | | | | (1103) all_52_9 = e0 % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | REDUCE: (94), (1103) imply: % 154.64/23.55 | | | | | | | | (1104) $false % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | CLOSE: (1104) is inconsistent. % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | (1105) all_56_10 = e0 % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | COMBINE_EQS: (134), (1105) imply: % 154.64/23.55 | | | | | | | | (1106) all_52_13 = e0 % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | SIMP: (1106) implies: % 154.64/23.55 | | | | | | | | (1107) all_52_13 = e0 % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | REDUCE: (78), (1107) imply: % 154.64/23.55 | | | | | | | | (1108) ~ (all_52_1 = e0) % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | REDUCE: (50), (1107) imply: % 154.64/23.55 | | | | | | | | (1109) ~ (all_52_12 = e0) % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | REDUCE: (909), (1107) imply: % 154.64/23.55 | | | | | | | | (1110) ~ (e1 = e0) % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | BETA: splitting (80) gives: % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | (1111) all_56_0 = e0 % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | COMBINE_EQS: (152), (1111) imply: % 154.64/23.55 | | | | | | | | | (1112) all_10_2 = e0 % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | COMBINE_EQS: (140), (1112) imply: % 154.64/23.55 | | | | | | | | | (1113) all_58_28 = e0 % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | REF_CLOSE: (2), (31), (72), (85), (105), (107), (109), (129), % 154.64/23.55 | | | | | | | | | (145), (150), (169), (174), (187), (188), (1113) % 154.64/23.55 | | | | | | | | | are inconsistent by sub-proof #679. % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | (1114) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | BETA: splitting (1097) gives: % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | (1115) all_56_2 = e0 % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | COMBINE_EQS: (130), (1115) imply: % 154.64/23.55 | | | | | | | | | | (1116) all_52_1 = e0 % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | REDUCE: (1108), (1116) imply: % 154.64/23.55 | | | | | | | | | | (1117) $false % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | CLOSE: (1117) is inconsistent. % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | (1118) all_56_6 = e0 | all_56_12 = e0 % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | BETA: splitting (1118) gives: % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | (1119) all_56_6 = e0 % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | COMBINE_EQS: (112), (1119) imply: % 154.64/23.55 | | | | | | | | | | | (1120) all_52_2 = e0 % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | REDUCE: (12), (1120) imply: % 154.64/23.55 | | | | | | | | | | | (1121) $false % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | CLOSE: (1121) is inconsistent. % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | (1122) all_56_12 = e0 % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | BETA: splitting (122) gives: % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | (1123) all_56_1 = e0 % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | COMBINE_EQS: (87), (1123) imply: % 154.64/23.55 | | | | | | | | | | | | (1124) all_52_4 = e0 % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | REDUCE: (196), (1124) imply: % 154.64/23.55 | | | | | | | | | | | | (1125) ~ (all_52_12 = e0) % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | REDUCE: (28), (1124) imply: % 154.64/23.55 | | | | | | | | | | | | (1126) ~ (all_8_2 = e0) % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | REDUCE: (47), (1124) imply: % 154.64/23.55 | | | | | | | | | | | | (1127) op(e3, e2) = e0 % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | BETA: splitting (10) gives: % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | (1128) all_54_3 = e0 % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | REF_CLOSE: (30), (1109), (1128) are inconsistent by sub-proof % 154.64/23.55 | | | | | | | | | | | | | #733. % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | (1129) ~ (all_54_3 = e0) % 154.64/23.55 | | | | | | | | | | | | | (1130) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | BETA: splitting (15) gives: % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | (1131) all_56_9 = e2 % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | COMBINE_EQS: (104), (1131) imply: % 154.64/23.55 | | | | | | | | | | | | | | (1132) all_52_12 = e2 % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | SIMP: (1132) implies: % 154.64/23.55 | | | | | | | | | | | | | | (1133) all_52_12 = e2 % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | REDUCE: (135), (1133) imply: % 154.64/23.55 | | | | | | | | | | | | | | (1134) ~ (all_10_2 = e2) % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | SIMP: (1134) implies: % 154.64/23.55 | | | | | | | | | | | | | | (1135) ~ (all_10_2 = e2) % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | BETA: splitting (119) gives: % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | (1136) all_56_9 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | COMBINE_EQS: (1131), (1136) imply: % 154.64/23.55 | | | | | | | | | | | | | | | (1137) e3 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | REDUCE: (188), (1137) imply: % 154.64/23.55 | | | | | | | | | | | | | | | (1138) $false % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | CLOSE: (1138) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | (1139) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | (1140) all_58_28 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (1140) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | (1141) all_10_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | REDUCE: (1135), (1141) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | (1142) $false % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | CLOSE: (1142) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | (1143) ~ (all_58_28 = e2) % 154.64/23.55 | | | | | | | | | | | | | | | | (1144) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | BETA: splitting (1144) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | (1145) all_58_29 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (1145) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | (1146) all_8_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | REDUCE: (95), (1146) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | (1147) ~ (all_52_1 = e2) % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | (1148) all_56_0 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (1148) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | (1149) all_10_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | REDUCE: (1135), (1149) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | (1150) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | CLOSE: (1150) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | (1151) all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | BETA: splitting (1151) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | (1152) all_56_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (1152) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | (1153) all_52_1 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | REDUCE: (1147), (1153) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | (1154) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | CLOSE: (1154) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | (1155) all_56_6 = e2 | all_56_12 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | (1156) all_56_6 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (1156) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | (1157) all_52_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | SIMP: (1157) implies: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | (1158) all_52_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (1158) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | (1159) op(e1, e3) = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1139) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1160) all_56_10 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1105), (1160) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1161) e3 = e0 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (1161) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1162) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1162) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1163) all_56_11 = e3 | all_56_15 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1163) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1164) all_56_11 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (915), (1164) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1165) all_4_1 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1165) implies: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1166) all_4_1 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (1166) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1167) all_20_1 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (911), (1166) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1168) op(e1, e3) = all_4_0 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (900) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | (1169) ~ (all_20_0 = e2) % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (1169) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | (1170) ~ (all_4_0 = e2) % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e2, all_4_0, e3, e1, % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1159), (1168) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | (1171) all_4_0 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1170), (1171) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | (1172) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1172) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | (1173) ~ (all_20_1 = e3) % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1167), (1173) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | (1174) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1174) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1175) all_56_15 = e3 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (904), (1175) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1176) e3 = e1 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (1176) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1177) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1177) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | (1178) ~ (all_56_6 = e2) % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (1178) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | (1179) ~ (all_52_2 = e2) % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1180) all_56_6 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (1180) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1181) all_52_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | SIMP: (1181) implies: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1182) all_52_2 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1179), (1182) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1183) $false % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1183) is inconsistent. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1184) all_56_12 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1122), (1184) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1185) e2 = e0 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1145), (1185) imply: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | (1186) all_58_29 = e0 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1144) gives: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (150), (1145), (1186) are inconsistent by % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | sub-proof #706. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | (1187) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (109), (150), (905), (1187) are % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #696. % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | (1188) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (109), (150), (905), (1188) are % 154.64/23.55 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #696. % 154.64/23.55 | | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | (1189) ~ (all_56_9 = e2) % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | REDUCE: (104), (1189) imply: % 154.64/23.55 | | | | | | | | | | | | | | (1190) ~ (all_52_12 = e2) % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | | REF_CLOSE: (4), (30), (31), (104), (105), (107), (109), % 154.64/23.55 | | | | | | | | | | | | | | (119), (126), (135), (140), (148), (150), (168), % 154.64/23.55 | | | | | | | | | | | | | | (169), (905), (908), (1109), (1127), (1130), % 154.64/23.55 | | | | | | | | | | | | | | (1190) are inconsistent by sub-proof #522. % 154.64/23.55 | | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | Case 2: % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | (1191) ~ (all_56_1 = e0) % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | REDUCE: (87), (1191) imply: % 154.64/23.55 | | | | | | | | | | | | (1192) ~ (all_52_4 = e0) % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | | REF_CLOSE: (27), (87), (104), (182), (1109), (1114), (1192) % 154.64/23.55 | | | | | | | | | | | | are inconsistent by sub-proof #519. % 154.64/23.55 | | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | | % 154.64/23.55 | | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | | % 154.64/23.55 | | | | | | | | | End of split % 154.64/23.55 | | | | | | | | | % 154.64/23.55 | | | | | | | | End of split % 154.64/23.55 | | | | | | | | % 154.64/23.55 | | | | | | | End of split % 154.64/23.55 | | | | | | | % 154.64/23.55 | | | | | | End of split % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | End of split % 154.64/23.55 | | | | | % 154.64/23.55 | | | | End of split % 154.64/23.55 | | | | % 154.64/23.55 | | | End of split % 154.64/23.55 | | | % 154.64/23.55 | | End of split % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #519 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_1 = e0 | all_56_4 = e0 | all_56_9 = e0 % 154.64/23.55 (2) all_56_4 = all_52_8 % 154.64/23.55 (3) ~ (all_52_12 = e0) % 154.64/23.55 (4) all_56_1 = all_52_4 % 154.64/23.55 (5) all_56_9 = all_52_12 % 154.64/23.55 (6) ~ (all_52_4 = e0) % 154.64/23.55 (7) ~ (all_52_8 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (1) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (8) all_56_1 = e0 % 154.64/23.55 | | % 154.64/23.55 | | COMBINE_EQS: (4), (8) imply: % 154.64/23.55 | | (9) all_52_4 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REDUCE: (6), (9) imply: % 154.64/23.55 | | (10) $false % 154.64/23.55 | | % 154.64/23.55 | | CLOSE: (10) is inconsistent. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (11) all_56_4 = e0 | all_56_9 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (2), (3), (5), (7), (11) are inconsistent by sub-proof #520. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #520 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_4 = all_52_8 % 154.64/23.55 (2) all_56_4 = e0 | all_56_9 = e0 % 154.64/23.55 (3) ~ (all_52_12 = e0) % 154.64/23.55 (4) all_56_9 = all_52_12 % 154.64/23.55 (5) ~ (all_52_8 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (2) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (6) all_56_4 = e0 % 154.64/23.55 | | % 154.64/23.55 | | COMBINE_EQS: (1), (6) imply: % 154.64/23.55 | | (7) all_52_8 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REDUCE: (5), (7) imply: % 154.64/23.55 | | (8) $false % 154.64/23.55 | | % 154.64/23.55 | | CLOSE: (8) is inconsistent. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (9) all_56_9 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #521. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #521 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_9 = all_52_12 % 154.64/23.55 (2) all_56_9 = e0 % 154.64/23.55 (3) ~ (all_52_12 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | COMBINE_EQS: (1), (2) imply: % 154.64/23.55 | (4) all_52_12 = e0 % 154.64/23.55 | % 154.64/23.55 | SIMP: (4) implies: % 154.64/23.55 | (5) all_52_12 = e0 % 154.64/23.55 | % 154.64/23.55 | REDUCE: (3), (5) imply: % 154.64/23.55 | (6) $false % 154.64/23.55 | % 154.64/23.55 | CLOSE: (6) is inconsistent. % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #522 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.64/23.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.64/23.55 (2) op(e3, e2) = e0 % 154.64/23.55 (3) all_58_31 = e1 % 154.64/23.55 (4) all_54_3 = all_52_12 % 154.64/23.55 (5) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.55 (6) ~ (all_52_12 = e0) % 154.64/23.55 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.64/23.55 (8) all_56_9 = all_52_12 % 154.64/23.55 (9) all_58_29 = all_8_2 % 154.64/23.55 (10) all_58_30 = e0 % 154.64/23.55 (11) ~ (e2 = e1) % 154.64/23.55 (12) all_56_9 = e3 | all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 154.64/23.55 (13) op(e3, all_10_2) = all_58_0 % 154.64/23.55 (14) ~ (all_52_12 = all_10_2) % 154.64/23.55 (15) ~ (all_52_12 = e1) % 154.64/23.55 (16) all_58_28 = all_10_2 % 154.64/23.55 (17) op(all_8_2, e2) = all_8_1 % 154.64/23.55 (18) ~ (e2 = e0) % 154.64/23.55 (19) ~ (all_8_1 = e0) % 154.64/23.55 (20) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.55 (21) ~ (all_52_12 = e2) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (7) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (22) all_54_3 = e1 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (4), (15), (22) are inconsistent by sub-proof #723. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (23) ~ (all_54_3 = e1) % 154.64/23.55 | | (24) all_54_3 = e3 | all_54_3 = e2 % 154.64/23.55 | | % 154.64/23.55 | | BETA: splitting (12) gives: % 154.64/23.55 | | % 154.64/23.55 | | Case 1: % 154.64/23.55 | | | % 154.64/23.55 | | | (25) all_56_9 = e3 % 154.64/23.55 | | | % 154.64/23.55 | | | COMBINE_EQS: (8), (25) imply: % 154.64/23.55 | | | (26) all_52_12 = e3 % 154.64/23.55 | | | % 154.64/23.55 | | | SIMP: (26) implies: % 154.64/23.55 | | | (27) all_52_12 = e3 % 154.64/23.55 | | | % 154.64/23.55 | | | REDUCE: (14), (27) imply: % 154.64/23.55 | | | (28) ~ (all_10_2 = e3) % 154.64/23.55 | | | % 154.64/23.55 | | | SIMP: (28) implies: % 154.64/23.55 | | | (29) ~ (all_10_2 = e3) % 154.64/23.55 | | | % 154.64/23.55 | | | REDUCE: (21), (27) imply: % 154.64/23.55 | | | (30) ~ (e3 = e2) % 154.64/23.55 | | | % 154.64/23.55 | | | REDUCE: (15), (27) imply: % 154.64/23.55 | | | (31) ~ (e3 = e1) % 154.64/23.55 | | | % 154.64/23.55 | | | REDUCE: (6), (27) imply: % 154.64/23.55 | | | (32) ~ (e3 = e0) % 154.64/23.55 | | | % 154.64/23.55 | | | BETA: splitting (20) gives: % 154.64/23.55 | | | % 154.64/23.55 | | | Case 1: % 154.64/23.55 | | | | % 154.64/23.55 | | | | (33) all_58_28 = e3 % 154.64/23.55 | | | | % 154.64/23.55 | | | | REF_CLOSE: (16), (29), (33) are inconsistent by sub-proof #783. % 154.64/23.55 | | | | % 154.64/23.55 | | | Case 2: % 154.64/23.55 | | | | % 154.64/23.55 | | | | (34) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.55 | | | | % 154.64/23.55 | | | | BETA: splitting (34) gives: % 154.64/23.55 | | | | % 154.64/23.55 | | | | Case 1: % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | (35) all_58_29 = e3 % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | COMBINE_EQS: (9), (35) imply: % 154.64/23.55 | | | | | (36) all_8_2 = e3 % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | SIMP: (36) implies: % 154.64/23.55 | | | | | (37) all_8_2 = e3 % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | REDUCE: (17), (37) imply: % 154.64/23.55 | | | | | (38) op(e3, e2) = all_8_1 % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | BETA: splitting (5) gives: % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | Case 1: % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | (39) all_58_28 = e2 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | COMBINE_EQS: (16), (39) imply: % 154.64/23.55 | | | | | | (40) all_10_2 = e2 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | SIMP: (40) implies: % 154.64/23.55 | | | | | | (41) all_10_2 = e2 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | REDUCE: (13), (41) imply: % 154.64/23.55 | | | | | | (42) op(e3, e2) = all_58_0 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | REF_CLOSE: (1), (2), (19), (38), (42) are inconsistent by sub-proof % 154.64/23.55 | | | | | | #823. % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | Case 2: % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | (43) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | | REF_CLOSE: (3), (10), (11), (18), (30), (35), (43) are inconsistent % 154.64/23.55 | | | | | | by sub-proof #683. % 154.64/23.55 | | | | | | % 154.64/23.55 | | | | | End of split % 154.64/23.55 | | | | | % 154.64/23.55 | | | | Case 2: % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | (44) all_58_30 = e3 | all_58_31 = e3 % 154.64/23.55 | | | | | % 154.64/23.55 | | | | | REF_CLOSE: (3), (10), (31), (32), (44) are inconsistent by sub-proof % 154.64/23.55 | | | | | #694. % 154.64/23.55 | | | | | % 154.64/23.55 | | | | End of split % 154.64/23.55 | | | | % 154.64/23.55 | | | End of split % 154.64/23.55 | | | % 154.64/23.55 | | Case 2: % 154.64/23.55 | | | % 154.64/23.55 | | | (45) ~ (all_56_9 = e3) % 154.64/23.55 | | | % 154.64/23.55 | | | REF_CLOSE: (4), (8), (21), (24), (45) are inconsistent by sub-proof #523. % 154.64/23.55 | | | % 154.64/23.55 | | End of split % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #523 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) ~ (all_56_9 = e3) % 154.64/23.55 (2) all_54_3 = all_52_12 % 154.64/23.55 (3) all_56_9 = all_52_12 % 154.64/23.55 (4) all_54_3 = e3 | all_54_3 = e2 % 154.64/23.55 (5) ~ (all_52_12 = e2) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | REDUCE: (1), (3) imply: % 154.64/23.55 | (6) ~ (all_52_12 = e3) % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (4) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (7) all_54_3 = e2 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #614. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (8) all_54_3 = e3 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #721. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #524 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_11 = all_4_1 % 154.64/23.55 (2) all_56_10 = e0 | all_56_11 = e0 % 154.64/23.55 (3) ~ (all_52_13 = e0) % 154.64/23.55 (4) all_56_10 = all_52_13 % 154.64/23.55 (5) ~ (all_4_1 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (2) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (6) all_56_10 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #526. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (7) all_56_11 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #525. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #525 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_11 = all_4_1 % 154.64/23.55 (2) all_56_11 = e0 % 154.64/23.55 (3) ~ (all_4_1 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | COMBINE_EQS: (1), (2) imply: % 154.64/23.55 | (4) all_4_1 = e0 % 154.64/23.55 | % 154.64/23.55 | SIMP: (4) implies: % 154.64/23.55 | (5) all_4_1 = e0 % 154.64/23.55 | % 154.64/23.55 | REDUCE: (3), (5) imply: % 154.64/23.55 | (6) $false % 154.64/23.55 | % 154.64/23.55 | CLOSE: (6) is inconsistent. % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #526 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_10 = all_52_13 % 154.64/23.55 (2) all_56_10 = e0 % 154.64/23.55 (3) ~ (all_52_13 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | COMBINE_EQS: (1), (2) imply: % 154.64/23.55 | (4) all_52_13 = e0 % 154.64/23.55 | % 154.64/23.55 | SIMP: (4) implies: % 154.64/23.55 | (5) all_52_13 = e0 % 154.64/23.55 | % 154.64/23.55 | REDUCE: (3), (5) imply: % 154.64/23.55 | (6) $false % 154.64/23.55 | % 154.64/23.55 | CLOSE: (6) is inconsistent. % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #527 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) ~ (all_6_1 = e1) % 154.64/23.55 (2) all_56_14 = all_6_1 % 154.64/23.55 (3) all_56_8 = e0 % 154.64/23.55 (4) all_56_8 = e1 | all_56_14 = e1 % 154.64/23.55 (5) ~ (e1 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (4) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (6) all_56_8 = e1 % 154.64/23.55 | | % 154.64/23.55 | | COMBINE_EQS: (3), (6) imply: % 154.64/23.55 | | (7) e1 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REDUCE: (5), (7) imply: % 154.64/23.55 | | (8) $false % 154.64/23.55 | | % 154.64/23.55 | | CLOSE: (8) is inconsistent. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (9) all_56_14 = e1 % 154.64/23.55 | | % 154.64/23.55 | | COMBINE_EQS: (2), (9) imply: % 154.64/23.55 | | (10) all_6_1 = e1 % 154.64/23.55 | | % 154.64/23.55 | | SIMP: (10) implies: % 154.64/23.55 | | (11) all_6_1 = e1 % 154.64/23.55 | | % 154.64/23.55 | | REDUCE: (1), (11) imply: % 154.64/23.55 | | (12) $false % 154.64/23.55 | | % 154.64/23.55 | | CLOSE: (12) is inconsistent. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #528 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_7 = all_52_6 % 154.64/23.55 (2) ~ (all_52_6 = e1) % 154.64/23.55 (3) all_56_13 = e0 % 154.64/23.55 (4) all_56_3 = e1 | all_56_7 = e1 | all_56_13 = e1 % 154.64/23.55 (5) all_56_3 = all_8_2 % 154.64/23.55 (6) ~ (e1 = e0) % 154.64/23.55 (7) ~ (all_8_2 = e1) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (4) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (8) all_56_3 = e1 % 154.64/23.55 | | % 154.64/23.55 | | COMBINE_EQS: (5), (8) imply: % 154.64/23.55 | | (9) all_8_2 = e1 % 154.64/23.55 | | % 154.64/23.55 | | REDUCE: (7), (9) imply: % 154.64/23.55 | | (10) $false % 154.64/23.55 | | % 154.64/23.55 | | CLOSE: (10) is inconsistent. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (11) all_56_7 = e1 | all_56_13 = e1 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (1), (2), (3), (6), (11) are inconsistent by sub-proof #529. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #529 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_7 = all_52_6 % 154.64/23.55 (2) ~ (all_52_6 = e1) % 154.64/23.55 (3) all_56_13 = e0 % 154.64/23.55 (4) all_56_7 = e1 | all_56_13 = e1 % 154.64/23.55 (5) ~ (e1 = e0) % 154.64/23.55 % 154.64/23.55 Begin of proof % 154.64/23.55 | % 154.64/23.55 | BETA: splitting (4) gives: % 154.64/23.55 | % 154.64/23.55 | Case 1: % 154.64/23.55 | | % 154.64/23.55 | | (6) all_56_7 = e1 % 154.64/23.55 | | % 154.64/23.55 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #547. % 154.64/23.55 | | % 154.64/23.55 | Case 2: % 154.64/23.55 | | % 154.64/23.55 | | (7) all_56_13 = e1 % 154.64/23.55 | | % 154.64/23.55 | | COMBINE_EQS: (3), (7) imply: % 154.64/23.55 | | (8) e1 = e0 % 154.64/23.55 | | % 154.64/23.55 | | REDUCE: (5), (8) imply: % 154.64/23.55 | | (9) $false % 154.64/23.55 | | % 154.64/23.55 | | CLOSE: (9) is inconsistent. % 154.64/23.55 | | % 154.64/23.55 | End of split % 154.64/23.55 | % 154.64/23.55 End of proof % 154.64/23.55 % 154.64/23.55 Sub-proof #530 shows that the following formulas are inconsistent: % 154.64/23.55 ---------------------------------------------------------------- % 154.64/23.55 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 154.64/23.55 (2) ~ (all_52_3 = e2) % 154.64/23.55 (3) all_56_7 = all_52_6 % 154.64/23.55 (4) all_54_2 = all_52_8 % 154.64/23.55 (5) ~ (all_52_13 = e1) % 154.64/23.55 (6) all_58_31 = e1 % 154.64/23.55 (7) ~ (all_52_8 = all_10_2) % 154.64/23.55 (8) ~ (all_52_6 = all_8_2) % 154.64/23.55 (9) all_58_15 = e1 % 154.64/23.55 (10) all_56_4 = all_52_8 % 154.64/23.55 (11) ~ (all_6_1 = e1) % 154.64/23.55 (12) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.55 (13) all_58_13 = all_52_13 % 154.64/23.55 (14) all_56_11 = all_4_1 % 154.64/23.55 (15) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.64/23.55 (16) ~ (all_52_6 = e1) % 154.64/23.55 (17) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.64/23.55 (18) ~ (all_52_3 = e1) % 154.64/23.55 (19) all_54_5 = all_8_2 % 154.64/23.55 (20) all_58_8 = e0 % 154.64/23.55 (21) all_56_14 = all_6_1 % 154.64/23.55 (22) ~ (all_10_2 = e0) % 154.64/23.55 (23) all_54_9 = all_52_6 % 154.64/23.55 (24) all_56_2 = e2 | all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.64/23.55 (25) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.64/23.55 (26) ~ (all_52_13 = all_8_2) % 154.64/23.55 (27) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.64/23.56 (28) all_56_8 = e0 % 154.64/23.56 (29) all_58_6 = e0 % 154.64/23.56 (30) all_58_11 = e1 % 154.64/23.56 (31) all_56_12 = all_52_3 % 154.64/23.56 (32) ~ (all_52_13 = e0) % 154.64/23.56 (33) all_58_20 = all_4_1 % 154.64/23.56 (34) all_58_24 = e0 % 154.64/23.56 (35) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.64/23.56 (36) ~ (all_10_2 = e1) % 154.64/23.56 (37) all_56_3 = all_8_2 % 154.64/23.56 (38) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 154.64/23.56 (39) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.64/23.56 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.64/23.56 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.64/23.56 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.64/23.56 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.64/23.56 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.64/23.56 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.64/23.56 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.64/23.56 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.64/23.56 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.64/23.56 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.64/23.56 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.64/23.56 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.56 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.56 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.56 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.56 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.56 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.64/23.56 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.56 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.64/23.56 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.56 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.64/23.56 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.64/23.56 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.64/23.56 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.64/23.56 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.64/23.56 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.64/23.56 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.64/23.56 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.56 e0) % 154.64/23.56 (40) all_58_29 = all_8_2 % 154.64/23.56 (41) all_58_30 = e0 % 154.64/23.56 (42) ~ (all_52_8 = all_6_1) % 154.64/23.56 (43) ~ (all_4_1 = e1) % 154.64/23.56 (44) all_56_2 = e0 % 154.64/23.56 (45) all_56_5 = e1 % 154.64/23.56 (46) all_58_26 = all_6_1 % 154.64/23.56 (47) all_56_6 = e1 % 154.64/23.56 (48) all_56_10 = all_52_13 % 154.64/23.56 (49) all_58_28 = all_10_2 % 154.64/23.56 (50) all_56_1 = e1 % 154.64/23.56 (51) all_56_6 = e1 | all_56_12 = e1 % 154.64/23.56 (52) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 154.64/23.56 (53) ~ (all_6_1 = e0) % 154.64/23.56 (54) ~ (all_52_8 = e1) % 154.64/23.56 (55) all_58_17 = all_52_6 % 154.64/23.56 (56) all_58_2 = e1 % 154.64/23.56 (57) all_56_0 = all_10_2 % 154.64/23.56 (58) all_58_22 = all_52_3 % 154.64/23.56 (59) ~ (all_52_3 = all_10_2) % 154.64/23.56 (60) all_58_4 = all_52_8 % 154.64/23.56 (61) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.56 (62) ~ (all_52_13 = all_4_1) % 154.64/23.56 (63) all_54_0 = all_10_2 % 154.64/23.56 (64) ~ (e1 = e0) % 154.64/23.56 (65) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 154.64/23.56 (66) ~ (all_52_8 = e0) % 154.64/23.56 (67) ~ (all_4_1 = e0) % 154.64/23.56 (68) ~ (all_8_2 = e0) % 154.64/23.56 (69) ~ (all_8_2 = e1) % 154.64/23.56 (70) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.64/23.56 (71) all_54_12 = all_52_3 % 154.64/23.56 % 154.64/23.56 Begin of proof % 154.64/23.56 | % 154.64/23.56 | BETA: splitting (70) gives: % 154.64/23.56 | % 154.64/23.56 | Case 1: % 154.64/23.56 | | % 154.64/23.56 | | (72) all_54_12 = e1 % 154.64/23.56 | | % 154.64/23.56 | | REF_CLOSE: (18), (71), (72) are inconsistent by sub-proof #558. % 154.64/23.56 | | % 154.64/23.56 | Case 2: % 154.64/23.56 | | % 154.64/23.56 | | (73) ~ (all_54_12 = e1) % 154.64/23.56 | | (74) all_54_12 = e3 | all_54_12 = e2 % 154.64/23.56 | | % 154.64/23.56 | | BETA: splitting (74) gives: % 154.64/23.56 | | % 154.64/23.56 | | Case 1: % 154.64/23.56 | | | % 154.64/23.56 | | | (75) all_54_12 = e2 % 154.64/23.56 | | | % 154.64/23.56 | | | REF_CLOSE: (2), (71), (75) are inconsistent by sub-proof #749. % 154.64/23.56 | | | % 154.64/23.56 | | Case 2: % 154.64/23.56 | | | % 154.64/23.56 | | | (76) all_54_12 = e3 % 154.64/23.56 | | | % 154.64/23.56 | | | COMBINE_EQS: (71), (76) imply: % 154.64/23.56 | | | (77) all_52_3 = e3 % 154.64/23.56 | | | % 154.64/23.56 | | | SIMP: (77) implies: % 154.64/23.56 | | | (78) all_52_3 = e3 % 154.64/23.56 | | | % 154.64/23.56 | | | COMBINE_EQS: (58), (78) imply: % 154.64/23.56 | | | (79) all_58_22 = e3 % 154.64/23.56 | | | % 154.64/23.56 | | | REDUCE: (59), (78) imply: % 154.64/23.56 | | | (80) ~ (all_10_2 = e3) % 154.64/23.56 | | | % 154.64/23.56 | | | SIMP: (80) implies: % 154.64/23.56 | | | (81) ~ (all_10_2 = e3) % 154.64/23.56 | | | % 154.64/23.56 | | | BETA: splitting (39) gives: % 154.64/23.56 | | | % 154.64/23.56 | | | Case 1: % 154.64/23.56 | | | | % 154.64/23.56 | | | | (82) all_58_31 = e0 % 154.64/23.56 | | | | % 154.64/23.56 | | | | COMBINE_EQS: (6), (82) imply: % 154.64/23.56 | | | | (83) e1 = e0 % 154.64/23.56 | | | | % 154.64/23.56 | | | | COMBINE_EQS: (47), (83) imply: % 154.64/23.56 | | | | (84) all_56_6 = e0 % 154.64/23.56 | | | | % 154.64/23.56 | | | | REF_CLOSE: (18), (31), (51), (64), (84) are inconsistent by sub-proof % 154.64/23.56 | | | | #807. % 154.64/23.56 | | | | % 154.64/23.56 | | | Case 2: % 154.64/23.56 | | | | % 154.64/23.56 | | | | (85) ~ (all_58_31 = e0) % 154.64/23.56 | | | | (86) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = % 154.64/23.56 | | | | e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.64/23.56 | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) % 154.64/23.56 | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = % 154.64/23.56 | | | | e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.56 | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = % 154.64/23.56 | | | | e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 154.64/23.56 | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = % 154.64/23.56 | | | | e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.64/23.56 | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.64/23.56 | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 % 154.64/23.56 | | | | & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 154.64/23.56 | | | | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 % 154.64/23.56 | | | | = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.64/23.56 | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 154.64/23.56 | | | | e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.64/23.56 | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 % 154.64/23.56 | | | | = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 % 154.64/23.56 | | | | = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.56 | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 % 154.64/23.56 | | | | = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.56 | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 % 154.64/23.56 | | | | = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.64/23.56 | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.56 | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.64/23.56 | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.64/23.56 | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 % 154.64/23.56 | | | | = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.64/23.56 | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.64/23.56 | | | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 % 154.64/23.56 | | | | = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.64/23.56 | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.64/23.56 | | | | all_58_26 = e0 & e1 = e0) % 154.64/23.56 | | | | % 154.64/23.56 | | | | BETA: splitting (61) gives: % 154.64/23.56 | | | | % 154.64/23.56 | | | | Case 1: % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | (87) all_58_28 = e3 % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | COMBINE_EQS: (49), (87) imply: % 154.64/23.56 | | | | | (88) all_10_2 = e3 % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | REDUCE: (81), (88) imply: % 154.64/23.56 | | | | | (89) $false % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | CLOSE: (89) is inconsistent. % 154.64/23.56 | | | | | % 154.64/23.56 | | | | Case 2: % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | (90) ~ (all_58_28 = e3) % 154.64/23.56 | | | | | (91) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | BETA: splitting (1) gives: % 154.64/23.56 | | | | | % 154.64/23.56 | | | | | Case 1: % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | (92) all_56_4 = e3 % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | COMBINE_EQS: (10), (92) imply: % 154.64/23.56 | | | | | | (93) all_52_8 = e3 % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | SIMP: (93) implies: % 154.64/23.56 | | | | | | (94) all_52_8 = e3 % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | COMBINE_EQS: (60), (94) imply: % 154.64/23.56 | | | | | | (95) all_58_4 = e3 % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | REDUCE: (42), (94) imply: % 154.64/23.56 | | | | | | (96) ~ (all_6_1 = e3) % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | SIMP: (96) implies: % 154.64/23.56 | | | | | | (97) ~ (all_6_1 = e3) % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | REDUCE: (54), (94) imply: % 154.64/23.56 | | | | | | (98) ~ (e3 = e1) % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | REDUCE: (66), (94) imply: % 154.64/23.56 | | | | | | (99) ~ (e3 = e0) % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | BETA: splitting (52) gives: % 154.64/23.56 | | | | | | % 154.64/23.56 | | | | | | Case 1: % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | (100) all_56_0 = e2 % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | COMBINE_EQS: (57), (100) imply: % 154.64/23.56 | | | | | | | (101) all_10_2 = e2 % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | COMBINE_EQS: (49), (101) imply: % 154.64/23.56 | | | | | | | (102) all_58_28 = e2 % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | REDUCE: (81), (101) imply: % 154.64/23.56 | | | | | | | (103) ~ (e3 = e2) % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | SIMP: (103) implies: % 154.64/23.56 | | | | | | | (104) ~ (e3 = e2) % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | REDUCE: (36), (101) imply: % 154.64/23.56 | | | | | | | (105) ~ (e2 = e1) % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | REDUCE: (22), (101) imply: % 154.64/23.56 | | | | | | | (106) ~ (e2 = e0) % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | BETA: splitting (15) gives: % 154.64/23.56 | | | | | | | % 154.64/23.56 | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | % 154.64/23.56 | | | | | | | | (107) all_56_4 = e2 % 154.64/23.56 | | | | | | | | % 154.64/23.56 | | | | | | | | REF_CLOSE: (92), (104), (107) are inconsistent by sub-proof % 154.64/23.56 | | | | | | | | #543. % 154.64/23.56 | | | | | | | | % 154.64/23.56 | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | % 154.64/23.56 | | | | | | | | (108) ~ (all_56_4 = e2) % 154.64/23.56 | | | | | | | | (109) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 154.64/23.56 | | | | | | | | % 154.64/23.56 | | | | | | | | BETA: splitting (109) gives: % 154.64/23.56 | | | | | | | | % 154.64/23.56 | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | (110) all_56_5 = e2 % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | COMBINE_EQS: (45), (110) imply: % 154.64/23.56 | | | | | | | | | (111) e2 = e1 % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | REDUCE: (105), (111) imply: % 154.64/23.56 | | | | | | | | | (112) $false % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | CLOSE: (112) is inconsistent. % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | (113) ~ (all_56_5 = e2) % 154.64/23.56 | | | | | | | | | (114) all_56_8 = e2 | all_56_14 = e2 % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | REDUCE: (45), (113) imply: % 154.64/23.56 | | | | | | | | | (115) ~ (e2 = e1) % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | BETA: splitting (114) gives: % 154.64/23.56 | | | | | | | | | % 154.64/23.56 | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | (116) all_56_8 = e2 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | COMBINE_EQS: (28), (116) imply: % 154.64/23.56 | | | | | | | | | | (117) e2 = e0 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | COMBINE_EQS: (102), (117) imply: % 154.64/23.56 | | | | | | | | | | (118) all_58_28 = e0 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | REF_CLOSE: (6), (12), (40), (41), (61), (98), (99), (104), % 154.64/23.56 | | | | | | | | | | (105), (106), (118) are inconsistent by sub-proof % 154.64/23.56 | | | | | | | | | | #680. % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | (119) all_56_14 = e2 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | COMBINE_EQS: (21), (119) imply: % 154.64/23.56 | | | | | | | | | | (120) all_6_1 = e2 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | SIMP: (120) implies: % 154.64/23.56 | | | | | | | | | | (121) all_6_1 = e2 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | COMBINE_EQS: (46), (121) imply: % 154.64/23.56 | | | | | | | | | | (122) all_58_26 = e2 % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | BETA: splitting (86) gives: % 154.64/23.56 | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | (123) all_58_30 = e1 % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | COMBINE_EQS: (41), (123) imply: % 154.64/23.56 | | | | | | | | | | | (124) e1 = e0 % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | COMBINE_EQS: (47), (124) imply: % 154.64/23.56 | | | | | | | | | | | (125) all_56_6 = e0 % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | REF_CLOSE: (18), (31), (51), (64), (125) are inconsistent by % 154.64/23.56 | | | | | | | | | | | sub-proof #807. % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | (126) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.64/23.56 | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.64/23.56 | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.64/23.56 | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.64/23.56 | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.64/23.56 | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.64/23.56 | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.64/23.56 | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.64/23.56 | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.64/23.56 | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.64/23.56 | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.64/23.56 | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.56 | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.64/23.56 | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.64/23.56 | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.56 | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.56 | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.64/23.56 | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.56 | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.64/23.56 | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.64/23.56 | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.64/23.56 | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.64/23.56 | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.64/23.56 | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.64/23.56 | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.64/23.56 | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.64/23.56 | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.64/23.56 | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.64/23.56 | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.64/23.56 | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.64/23.56 | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.64/23.56 | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.64/23.56 | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.64/23.56 | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.64/23.56 | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.64/23.56 | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.64/23.56 | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.64/23.56 | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | BETA: splitting (126) gives: % 154.64/23.56 | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | (127) all_58_29 = e2 % 154.64/23.56 | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (104), (127) are % 154.64/23.56 | | | | | | | | | | | | inconsistent by sub-proof #542. % 154.64/23.56 | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | (128) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.64/23.56 | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.64/23.56 | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.64/23.56 | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.64/23.56 | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.64/23.56 | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.64/23.56 | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.64/23.56 | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.64/23.56 | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.64/23.56 | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.64/23.56 | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.64/23.56 | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.64/23.56 | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.64/23.56 | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.64/23.56 | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.64/23.56 | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.64/23.56 | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.64/23.56 | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.64/23.56 | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.64/23.56 | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.64/23.56 | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.64/23.56 | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.56 | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.64/23.56 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.64/23.56 | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.56 | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.64/23.56 | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.64/23.56 | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.64/23.56 | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.64/23.56 | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.64/23.56 | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.64/23.56 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.64/23.56 | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.56 | | | | | | | | | | | | e0) % 154.64/23.56 | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | BETA: splitting (24) gives: % 154.64/23.56 | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | (129) all_56_2 = e2 % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | COMBINE_EQS: (44), (129) imply: % 154.64/23.56 | | | | | | | | | | | | | (130) e2 = e0 % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | COMBINE_EQS: (102), (130) imply: % 154.64/23.56 | | | | | | | | | | | | | (131) all_58_28 = e0 % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | REF_CLOSE: (6), (12), (40), (41), (61), (98), (99), (104), % 154.64/23.56 | | | | | | | | | | | | | (105), (106), (131) are inconsistent by sub-proof % 154.64/23.56 | | | | | | | | | | | | | #680. % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | (132) all_56_3 = e2 | all_56_5 = e2 | all_56_10 = e2 % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | BETA: splitting (132) gives: % 154.64/23.56 | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | (133) all_56_3 = e2 % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | COMBINE_EQS: (37), (133) imply: % 154.64/23.56 | | | | | | | | | | | | | | (134) all_8_2 = e2 % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | SIMP: (134) implies: % 154.64/23.56 | | | | | | | | | | | | | | (135) all_8_2 = e2 % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | COMBINE_EQS: (40), (135) imply: % 154.64/23.56 | | | | | | | | | | | | | | (136) all_58_29 = e2 % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (104), (136) are % 154.64/23.56 | | | | | | | | | | | | | | inconsistent by sub-proof #542. % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | (137) all_56_5 = e2 | all_56_10 = e2 % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | BETA: splitting (137) gives: % 154.64/23.56 | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | (138) all_56_5 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | COMBINE_EQS: (45), (138) imply: % 154.64/23.56 | | | | | | | | | | | | | | | (139) e2 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | REDUCE: (105), (139) imply: % 154.64/23.56 | | | | | | | | | | | | | | | (140) $false % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent. % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | (141) all_56_10 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | COMBINE_EQS: (48), (141) imply: % 154.64/23.56 | | | | | | | | | | | | | | | (142) all_52_13 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | SIMP: (142) implies: % 154.64/23.56 | | | | | | | | | | | | | | | (143) all_52_13 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | COMBINE_EQS: (13), (143) imply: % 154.64/23.56 | | | | | | | | | | | | | | | (144) all_58_13 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | REDUCE: (26), (143) imply: % 154.64/23.56 | | | | | | | | | | | | | | | (145) ~ (all_8_2 = e2) % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | SIMP: (145) implies: % 154.64/23.56 | | | | | | | | | | | | | | | (146) ~ (all_8_2 = e2) % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | REDUCE: (62), (143) imply: % 154.64/23.56 | | | | | | | | | | | | | | | (147) ~ (all_4_1 = e2) % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | SIMP: (147) implies: % 154.64/23.56 | | | | | | | | | | | | | | | (148) ~ (all_4_1 = e2) % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | BETA: splitting (25) gives: % 154.64/23.56 | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | (149) all_54_9 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (149) are inconsistent by sub-proof % 154.64/23.56 | | | | | | | | | | | | | | | | #622. % 154.64/23.56 | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | (150) all_54_9 = e3 | all_54_9 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | (151) all_54_9 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (151) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | (152) all_52_6 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | SIMP: (152) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | (153) all_52_6 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (153) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | (154) all_56_7 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (153) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | (155) all_58_17 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | (156) all_56_6 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (156) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | (157) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | REDUCE: (98), (157) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | (158) $false % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | (159) ~ (all_56_6 = e3) % 154.64/23.56 | | | | | | | | | | | | | | | | | | (160) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | REDUCE: (47), (159) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | (161) ~ (e3 = e1) % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | (162) all_56_1 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (162) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | (163) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | REDUCE: (98), (163) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | (164) $false % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | (165) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | (166) all_56_3 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (166) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | (167) all_8_2 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | SIMP: (167) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | (168) all_8_2 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (168) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | (169) all_58_29 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | (170) all_56_7 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (170) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | (171) e3 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (171) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | (172) all_58_29 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (104), (172) are % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #542. % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | (173) all_56_8 = e3 | all_56_11 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (174) all_56_8 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (174) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (175) e3 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (175) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (176) all_58_29 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (176) are % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693. % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (177) all_56_11 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (177) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (178) all_4_1 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | SIMP: (178) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (179) all_4_1 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (179) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | (180) all_58_20 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_28 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (181) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | (182) e3 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (182) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | (183) all_58_29 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (104), (183) are % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #542. % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | (184) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | e0) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | (185) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | (186) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (187) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_58_8 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_58_4 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (190) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (191) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (189) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) e3 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (169), (192), (193) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #541. % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_58_22 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_58_2 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (197) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (198) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (196) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) e3 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (169), (199), (200) % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #541. % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_11 = e2 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_58_8 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_58_2 = e3 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (204) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) e3 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (203) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) e3 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (202) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) e2 = e1 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (207) imply: % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) e1 = e0 % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (209) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) e1 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (210) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (211) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_28 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (104), (105), (106), (169), (212) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #682. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (213) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (216) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (217) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_28 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (104), (105), (106), (169), (218) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #682. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_2 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (20), (41), (56), (102), (104), (105), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (169), (220), (221) are inconsistent by % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #539. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (224) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (225) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_28 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (104), (105), (106), (169), (226) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #682. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_58_17 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (229) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (228) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (231) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (230), (232) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #540. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (233) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (234) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & e3 = e2) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_58_13 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_2 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (238) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (237) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (240), (242) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #540. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_8 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_2 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (20), (41), (56), (102), (104), (105), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (169), (244), (245) are inconsistent by % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #539. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_22 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_58_15 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (249) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) e3 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (248) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) e3 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (169), (250), (251) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #541. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_15 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (253) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) e3 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (254) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_29 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (61), (98), (99), (102), (104), (255) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #548. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (256) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_58_20 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (61), (98), (99), (102), (104), (169), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (259) are inconsistent by sub-proof #538. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_6 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_4 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (262) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) e3 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (263) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) e3 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (261) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) e3 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (169), (264), (265) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #541. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_4 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (61), (95), (98), (99), (102), (104), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (268) are inconsistent by sub-proof #537. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (169), (270) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #536. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (273) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_58_4 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (61), (95), (98), (99), (102), (104), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (275) are inconsistent by sub-proof #537. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_58_13 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (169), (278) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #535. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (169), (280) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #536. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (284) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (285) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_58_28 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (104), (105), (106), (169), (286) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #682. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_26 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_22 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_20 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (290) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) e3 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (289) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) e3 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (288) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (292) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) e1 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (295) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (296) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_28 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (104), (105), (106), (169), (297) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #682. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_22 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (300) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) e3 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (301) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_29 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (91), (98), (99), (302) are % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_13 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (169), (304) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #535. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (305) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & e1 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (306) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_20 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (41), (61), (98), (99), (102), (104), (169), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180), (309) are inconsistent by sub-proof #538. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (311) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (312) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_58_28 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (104), (105), (106), (169), (313) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #682. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (169), (316) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #536. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_58_17 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (155), (318) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #630. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (319) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (169), (322) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #536. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_58_26 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_58_13 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (325) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (326) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (324) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (328) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) e2 = e1 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (327), (329) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #540. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (331) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_58_13 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (169), (332) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #535. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_58_26 = e0 % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (41), (102), (104), (105), (106), % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (122), (169), (334) are inconsistent by sub-proof % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #536. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | (335) ~ (all_56_3 = e3) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (335) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | (336) ~ (all_8_2 = e3) % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (38), (69), (146), (336) are inconsistent by % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | sub-proof #531. % 154.64/23.57 | | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | Case 2: % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | (337) all_54_9 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (337) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | (338) all_52_6 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | SIMP: (338) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | (339) all_52_6 = e3 % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | REDUCE: (8), (339) imply: % 154.64/23.57 | | | | | | | | | | | | | | | | | (340) ~ (all_8_2 = e3) % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | SIMP: (340) implies: % 154.64/23.57 | | | | | | | | | | | | | | | | | (341) ~ (all_8_2 = e3) % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (38), (69), (146), (341) are inconsistent by % 154.64/23.57 | | | | | | | | | | | | | | | | | sub-proof #531. % 154.64/23.57 | | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | | % 154.64/23.57 | | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | | % 154.64/23.57 | | | | | | | | | End of split % 154.64/23.57 | | | | | | | | | % 154.64/23.57 | | | | | | | | End of split % 154.64/23.57 | | | | | | | | % 154.64/23.57 | | | | | | | End of split % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | Case 2: % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | (342) ~ (all_56_0 = e2) % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | REDUCE: (57), (342) imply: % 154.64/23.57 | | | | | | | (343) ~ (all_10_2 = e2) % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | REF_CLOSE: (17), (36), (63), (81), (343) are inconsistent by % 154.64/23.57 | | | | | | | sub-proof #813. % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | End of split % 154.64/23.57 | | | | | | % 154.64/23.57 | | | | | Case 2: % 154.64/23.57 | | | | | | % 154.64/23.57 | | | | | | (344) ~ (all_56_4 = e3) % 154.64/23.57 | | | | | | % 154.64/23.57 | | | | | | REDUCE: (10), (344) imply: % 154.64/23.57 | | | | | | (345) ~ (all_52_8 = e3) % 154.64/23.57 | | | | | | % 154.64/23.57 | | | | | | BETA: splitting (52) gives: % 154.64/23.57 | | | | | | % 154.64/23.57 | | | | | | Case 1: % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | (346) all_56_0 = e2 % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | COMBINE_EQS: (57), (346) imply: % 154.64/23.57 | | | | | | | (347) all_10_2 = e2 % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | REDUCE: (7), (347) imply: % 154.64/23.57 | | | | | | | (348) ~ (all_52_8 = e2) % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | REF_CLOSE: (4), (35), (54), (345), (348) are inconsistent by % 154.64/23.57 | | | | | | | sub-proof #554. % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | Case 2: % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | (349) ~ (all_56_0 = e2) % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | REDUCE: (57), (349) imply: % 154.64/23.57 | | | | | | | (350) ~ (all_10_2 = e2) % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | | REF_CLOSE: (17), (36), (63), (81), (350) are inconsistent by % 154.64/23.57 | | | | | | | sub-proof #813. % 154.64/23.57 | | | | | | | % 154.64/23.57 | | | | | | End of split % 154.64/23.57 | | | | | | % 154.64/23.57 | | | | | End of split % 154.64/23.57 | | | | | % 154.64/23.57 | | | | End of split % 154.64/23.57 | | | | % 154.64/23.57 | | | End of split % 154.64/23.57 | | | % 154.64/23.57 | | End of split % 154.64/23.57 | | % 154.64/23.57 | End of split % 154.64/23.57 | % 154.64/23.57 End of proof % 154.64/23.57 % 154.64/23.57 Sub-proof #531 shows that the following formulas are inconsistent: % 154.64/23.57 ---------------------------------------------------------------- % 154.64/23.57 (1) ~ (all_8_2 = e3) % 154.64/23.57 (2) all_54_5 = all_8_2 % 154.64/23.57 (3) ~ (all_8_2 = e2) % 154.64/23.57 (4) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 % 154.64/23.57 (5) ~ (all_8_2 = e1) % 154.64/23.57 % 154.64/23.57 Begin of proof % 154.64/23.57 | % 154.64/23.57 | BETA: splitting (4) gives: % 154.64/23.57 | % 154.64/23.57 | Case 1: % 154.64/23.57 | | % 154.64/23.57 | | (6) all_54_5 = e1 % 154.64/23.57 | | % 154.64/23.57 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #534. % 154.64/23.57 | | % 154.64/23.57 | Case 2: % 154.64/23.57 | | % 154.64/23.57 | | (7) all_54_5 = e3 | all_54_5 = e2 % 154.64/23.57 | | % 154.64/23.57 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #532. % 154.64/23.57 | | % 154.64/23.57 | End of split % 154.64/23.57 | % 154.64/23.57 End of proof % 154.64/23.57 % 154.64/23.57 Sub-proof #532 shows that the following formulas are inconsistent: % 154.64/23.57 ---------------------------------------------------------------- % 154.64/23.57 (1) all_54_5 = e3 | all_54_5 = e2 % 154.64/23.57 (2) all_54_5 = all_8_2 % 154.64/23.57 (3) ~ (all_8_2 = e2) % 154.64/23.57 (4) ~ (all_8_2 = e3) % 154.64/23.57 % 154.64/23.57 Begin of proof % 154.64/23.57 | % 154.64/23.57 | BETA: splitting (1) gives: % 154.64/23.57 | % 154.64/23.57 | Case 1: % 154.64/23.57 | | % 154.64/23.57 | | (5) all_54_5 = e2 % 154.64/23.57 | | % 154.64/23.57 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #533. % 154.64/23.57 | | % 154.64/23.57 | Case 2: % 154.64/23.57 | | % 154.64/23.57 | | (6) all_54_5 = e3 % 154.64/23.57 | | % 154.64/23.57 | | COMBINE_EQS: (2), (6) imply: % 154.64/23.57 | | (7) all_8_2 = e3 % 154.64/23.57 | | % 154.64/23.57 | | SIMP: (7) implies: % 154.64/23.57 | | (8) all_8_2 = e3 % 154.64/23.57 | | % 154.64/23.57 | | REDUCE: (4), (8) imply: % 154.64/23.57 | | (9) $false % 154.64/23.57 | | % 154.64/23.57 | | CLOSE: (9) is inconsistent. % 154.64/23.57 | | % 154.64/23.57 | End of split % 154.64/23.57 | % 154.64/23.57 End of proof % 154.64/23.57 % 154.64/23.57 Sub-proof #533 shows that the following formulas are inconsistent: % 154.64/23.57 ---------------------------------------------------------------- % 154.64/23.57 (1) all_54_5 = all_8_2 % 154.64/23.57 (2) all_54_5 = e2 % 154.64/23.57 (3) ~ (all_8_2 = e2) % 154.64/23.57 % 154.64/23.57 Begin of proof % 154.64/23.57 | % 154.64/23.57 | COMBINE_EQS: (1), (2) imply: % 154.64/23.57 | (4) all_8_2 = e2 % 154.64/23.57 | % 154.64/23.57 | SIMP: (4) implies: % 154.64/23.57 | (5) all_8_2 = e2 % 154.64/23.57 | % 154.64/23.57 | REDUCE: (3), (5) imply: % 154.64/23.57 | (6) $false % 154.64/23.57 | % 154.64/23.57 | CLOSE: (6) is inconsistent. % 154.64/23.57 | % 154.64/23.57 End of proof % 154.64/23.57 % 154.64/23.57 Sub-proof #534 shows that the following formulas are inconsistent: % 154.64/23.57 ---------------------------------------------------------------- % 154.64/23.57 (1) all_54_5 = all_8_2 % 154.64/23.57 (2) all_54_5 = e1 % 154.64/23.57 (3) ~ (all_8_2 = e1) % 154.64/23.57 % 154.64/23.57 Begin of proof % 154.64/23.57 | % 154.64/23.57 | COMBINE_EQS: (1), (2) imply: % 154.64/23.57 | (4) all_8_2 = e1 % 154.64/23.57 | % 154.64/23.57 | SIMP: (4) implies: % 154.64/23.57 | (5) all_8_2 = e1 % 154.64/23.57 | % 154.64/23.57 | REDUCE: (3), (5) imply: % 154.64/23.57 | (6) $false % 154.64/23.57 | % 154.64/23.57 | CLOSE: (6) is inconsistent. % 154.64/23.57 | % 154.64/23.57 End of proof % 154.64/23.57 % 154.64/23.57 Sub-proof #535 shows that the following formulas are inconsistent: % 154.64/23.57 ---------------------------------------------------------------- % 154.64/23.57 (1) all_58_31 = e1 % 154.64/23.57 (2) all_58_13 = e0 % 154.64/23.57 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.57 (4) all_58_29 = e3 % 154.64/23.57 (5) all_58_30 = e0 % 154.64/23.57 (6) ~ (e2 = e1) % 154.64/23.57 (7) all_58_13 = e2 % 154.64/23.57 (8) ~ (e2 = e0) % 154.64/23.57 (9) all_58_28 = e2 % 154.64/23.57 (10) ~ (e3 = e2) % 154.64/23.57 % 154.64/23.57 Begin of proof % 154.64/23.57 | % 154.64/23.57 | COMBINE_EQS: (2), (7) imply: % 154.64/23.57 | (11) e2 = e0 % 154.64/23.57 | % 154.64/23.57 | SIMP: (11) implies: % 154.64/23.57 | (12) e2 = e0 % 154.64/23.57 | % 154.64/23.57 | COMBINE_EQS: (9), (12) imply: % 154.64/23.57 | (13) all_58_28 = e0 % 154.64/23.57 | % 154.64/23.57 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (13) are inconsistent by % 154.64/23.57 | sub-proof #682. % 154.64/23.57 | % 154.64/23.57 End of proof % 154.64/23.57 % 154.64/23.57 Sub-proof #536 shows that the following formulas are inconsistent: % 154.64/23.57 ---------------------------------------------------------------- % 154.64/23.57 (1) all_58_31 = e1 % 154.64/23.57 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.57 (3) all_58_29 = e3 % 154.64/23.57 (4) all_58_30 = e0 % 154.64/23.57 (5) ~ (e2 = e1) % 154.64/23.57 (6) all_58_26 = e2 % 154.64/23.57 (7) all_58_26 = e0 % 154.64/23.57 (8) ~ (e2 = e0) % 154.64/23.57 (9) all_58_28 = e2 % 154.64/23.57 (10) ~ (e3 = e2) % 154.64/23.57 % 154.64/23.57 Begin of proof % 154.64/23.57 | % 154.64/23.57 | COMBINE_EQS: (6), (7) imply: % 154.64/23.57 | (11) e2 = e0 % 154.64/23.57 | % 154.64/23.57 | SIMP: (11) implies: % 154.64/23.58 | (12) e2 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (9), (12) imply: % 154.64/23.58 | (13) all_58_28 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (13) are inconsistent by % 154.64/23.58 | sub-proof #682. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #537 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_4 = e3 % 154.64/23.58 (2) all_58_31 = e1 % 154.64/23.58 (3) ~ (e3 = e1) % 154.64/23.58 (4) all_58_4 = e1 % 154.64/23.58 (5) all_58_29 = e3 % 154.64/23.58 (6) all_58_30 = e0 % 154.64/23.58 (7) ~ (e3 = e0) % 154.64/23.58 (8) all_58_28 = e2 % 154.64/23.58 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (10) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (4) imply: % 154.64/23.58 | (11) e3 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (11) implies: % 154.64/23.58 | (12) e3 = e1 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (5), (12) imply: % 154.64/23.58 | (13) all_58_29 = e1 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (13) are inconsistent by % 154.64/23.58 | sub-proof #548. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #538 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = e1 % 154.64/23.58 (2) ~ (e3 = e1) % 154.64/23.58 (3) all_58_29 = e3 % 154.64/23.58 (4) all_58_30 = e0 % 154.64/23.58 (5) ~ (e3 = e0) % 154.64/23.58 (6) all_58_20 = e3 % 154.64/23.58 (7) all_58_28 = e2 % 154.64/23.58 (8) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (9) all_58_20 = e1 % 154.64/23.58 (10) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (6), (9) imply: % 154.64/23.58 | (11) e3 = e1 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (3), (11) imply: % 154.64/23.58 | (12) all_58_29 = e1 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (12) are inconsistent by % 154.64/23.58 | sub-proof #548. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #539 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_2 = e2 % 154.64/23.58 (2) all_58_31 = e1 % 154.64/23.58 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (4) all_58_8 = e0 % 154.64/23.58 (5) all_58_29 = e3 % 154.64/23.58 (6) all_58_30 = e0 % 154.64/23.58 (7) all_58_8 = e2 % 154.64/23.58 (8) ~ (e2 = e1) % 154.64/23.58 (9) ~ (e2 = e0) % 154.64/23.58 (10) all_58_2 = e1 % 154.64/23.58 (11) all_58_28 = e2 % 154.64/23.58 (12) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (10) imply: % 154.64/23.58 | (13) e2 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (13) implies: % 154.64/23.58 | (14) e2 = e1 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (4), (7) imply: % 154.64/23.58 | (15) e2 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (2), (3), (5), (6), (8), (9), (11), (12), (14), (15) are % 154.64/23.58 | inconsistent by sub-proof #540. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #540 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = e1 % 154.64/23.58 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (3) all_58_29 = e3 % 154.64/23.58 (4) all_58_30 = e0 % 154.64/23.58 (5) ~ (e2 = e1) % 154.64/23.58 (6) e2 = e1 % 154.64/23.58 (7) ~ (e2 = e0) % 154.64/23.58 (8) e2 = e0 % 154.64/23.58 (9) all_58_28 = e2 % 154.64/23.58 (10) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (6), (8) imply: % 154.64/23.58 | (11) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (8), (9) imply: % 154.64/23.58 | (12) all_58_28 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (12) are inconsistent by % 154.64/23.58 | sub-proof #682. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #541 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = e1 % 154.64/23.58 (2) ~ (e3 = e1) % 154.64/23.58 (3) e3 = e1 % 154.64/23.58 (4) all_58_29 = e3 % 154.64/23.58 (5) all_58_30 = e0 % 154.64/23.58 (6) ~ (e3 = e0) % 154.64/23.58 (7) e3 = e0 % 154.64/23.58 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (3), (7) imply: % 154.64/23.58 | (9) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (4), (7) imply: % 154.64/23.58 | (10) all_58_29 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (5), (6), (8), (10) are inconsistent by sub-proof #693. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #542 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = e1 % 154.64/23.58 (2) ~ (e3 = e1) % 154.64/23.58 (3) all_58_30 = e0 % 154.64/23.58 (4) ~ (e3 = e0) % 154.64/23.58 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (6) all_58_29 = e2 % 154.64/23.58 (7) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (5) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (8) all_58_29 = e3 % 154.64/23.58 | | % 154.64/23.58 | | COMBINE_EQS: (6), (8) imply: % 154.64/23.58 | | (9) e3 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (7), (9) imply: % 154.64/23.58 | | (10) $false % 154.64/23.58 | | % 154.64/23.58 | | CLOSE: (10) is inconsistent. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (11) all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (1), (2), (3), (4), (11) are inconsistent by sub-proof #694. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #543 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_4 = e3 % 154.64/23.58 (2) all_56_4 = e2 % 154.64/23.58 (3) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) e3 = e2 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) e3 = e2 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #544 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_11 = all_4_1 % 154.64/23.58 (2) all_54_11 = e3 % 154.64/23.58 (3) ~ (all_4_1 = e3) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_4_1 = e3 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_4_1 = e3 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #545 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_11 = all_4_1 % 154.64/23.58 (2) all_54_11 = e1 % 154.64/23.58 (3) ~ (all_4_1 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_4_1 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_4_1 = e1 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #546 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_7 = all_52_6 % 154.64/23.58 (2) ~ (all_52_7 = e1) % 154.64/23.58 (3) ~ (all_52_6 = e1) % 154.64/23.58 (4) all_56_7 = e1 | all_56_13 = e1 % 154.64/23.58 (5) all_56_13 = all_52_7 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (4) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (6) all_56_7 = e1 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #547. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (7) all_56_13 = e1 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #676. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #547 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_7 = all_52_6 % 154.64/23.58 (2) all_56_7 = e1 % 154.64/23.58 (3) ~ (all_52_6 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_52_6 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_52_6 = e1 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #548 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = e1 % 154.64/23.58 (2) ~ (e3 = e1) % 154.64/23.58 (3) all_58_30 = e0 % 154.64/23.58 (4) all_58_29 = e1 % 154.64/23.58 (5) ~ (e3 = e0) % 154.64/23.58 (6) all_58_28 = e2 % 154.64/23.58 (7) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (8) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (7) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (9) all_58_28 = e3 % 154.64/23.58 | | % 154.64/23.58 | | COMBINE_EQS: (6), (9) imply: % 154.64/23.58 | | (10) e3 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (8), (10) imply: % 154.64/23.58 | | (11) $false % 154.64/23.58 | | % 154.64/23.58 | | CLOSE: (11) is inconsistent. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (12) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (1), (2), (3), (4), (5), (12) are inconsistent by sub-proof #640. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #549 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_2 = e1 % 154.64/23.58 (2) all_56_2 = e0 % 154.64/23.58 (3) ~ (e1 = e0) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #550 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_15 = e1 % 154.64/23.58 (2) all_56_15 = e0 % 154.64/23.58 (3) ~ (e1 = e0) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #551 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_11 = all_4_1 % 154.64/23.58 (2) all_54_11 = e0 % 154.64/23.58 (3) ~ (all_4_1 = e0) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_4_1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_4_1 = e0 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #552 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_6 = e3 | all_54_6 = e2 % 154.64/23.58 (2) all_54_6 = all_52_9 % 154.64/23.58 (3) ~ (all_52_9 = e2) % 154.64/23.58 (4) ~ (all_52_9 = e3) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (1) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (5) all_54_6 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #773. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (6) all_54_6 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #772. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #553 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) ~ (all_52_8 = e2) % 154.64/23.58 (2) all_54_2 = all_52_8 % 154.64/23.58 (3) all_54_1 = all_52_4 % 154.64/23.58 (4) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 154.64/23.58 (5) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 154.64/23.58 (6) ~ (all_52_4 = e2) % 154.64/23.58 (7) all_56_1 = all_52_4 % 154.64/23.58 (8) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.64/23.58 (9) ~ (all_52_4 = all_52_8) % 154.64/23.58 (10) ~ (all_52_4 = e1) % 154.64/23.58 (11) ~ (all_52_8 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (5) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (12) all_56_1 = e3 % 154.64/23.58 | | % 154.64/23.58 | | COMBINE_EQS: (7), (12) imply: % 154.64/23.58 | | (13) all_52_4 = e3 % 154.64/23.58 | | % 154.64/23.58 | | SIMP: (13) implies: % 154.64/23.58 | | (14) all_52_4 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (9), (14) imply: % 154.64/23.58 | | (15) ~ (all_52_8 = e3) % 154.64/23.58 | | % 154.64/23.58 | | SIMP: (15) implies: % 154.64/23.58 | | (16) ~ (all_52_8 = e3) % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (1), (2), (8), (11), (16) are inconsistent by sub-proof #554. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (17) ~ (all_56_1 = e3) % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (7), (17) imply: % 154.64/23.58 | | (18) ~ (all_52_4 = e3) % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (3), (4), (6), (10), (18) are inconsistent by sub-proof #738. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #554 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) ~ (all_52_8 = e2) % 154.64/23.58 (2) all_54_2 = all_52_8 % 154.64/23.58 (3) ~ (all_52_8 = e3) % 154.64/23.58 (4) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 154.64/23.58 (5) ~ (all_52_8 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (4) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (6) all_54_2 = e1 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #819. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (7) all_54_2 = e3 | all_54_2 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #555. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #555 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_2 = e3 | all_54_2 = e2 % 154.64/23.58 (2) all_54_2 = all_52_8 % 154.64/23.58 (3) ~ (all_52_8 = e2) % 154.64/23.58 (4) ~ (all_52_8 = e3) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (1) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (5) all_54_2 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #556. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (6) all_54_2 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #816. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #556 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_2 = all_52_8 % 154.64/23.58 (2) all_54_2 = e2 % 154.64/23.58 (3) ~ (all_52_8 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_52_8 = e2 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_52_8 = e2 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #557 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) ~ (all_52_3 = e2) % 154.64/23.58 (2) ~ (all_52_3 = e3) % 154.64/23.58 (3) ~ (all_52_3 = e1) % 154.64/23.58 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 154.64/23.58 (5) all_54_12 = all_52_3 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (4) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (6) all_54_12 = e1 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #558. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (7) all_54_12 = e3 | all_54_12 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #747. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #558 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_12 = all_52_3 % 154.64/23.58 (2) all_54_12 = e1 % 154.64/23.58 (3) ~ (all_52_3 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_52_3 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_52_3 = e1 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #559 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_9 = e3 | all_54_9 = e2 % 154.64/23.58 (2) all_54_9 = all_52_6 % 154.64/23.58 (3) ~ (all_52_6 = e2) % 154.64/23.58 (4) ~ (all_52_6 = e3) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (1) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (5) all_54_9 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #621. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (6) all_54_9 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #620. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #560 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = all_4_2 % 154.64/23.58 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (3) ~ (e3 = e1) % 154.64/23.58 (4) all_58_26 = e1 % 154.64/23.58 (5) all_20_2 = all_4_2 % 154.64/23.58 (6) all_58_28 = e1 % 154.64/23.58 (7) all_58_29 = all_8_2 % 154.64/23.58 (8) all_58_30 = e0 % 154.64/23.58 (9) ~ (e2 = e1) % 154.64/23.58 (10) all_58_26 = e0 % 154.64/23.58 (11) ~ (e3 = e0) % 154.64/23.58 (12) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.64/23.58 (13) ~ (e2 = e0) % 154.64/23.58 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (15) ~ (e1 = e0) % 154.64/23.58 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.64/23.58 (17) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (4), (10) imply: % 154.64/23.58 | (18) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (18) implies: % 154.64/23.58 | (19) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (6), (19) imply: % 154.64/23.58 | (20) all_58_28 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (12), (13), (14), (15), % 154.64/23.58 | (16), (17), (20) are inconsistent by sub-proof #679. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #561 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = all_4_2 % 154.64/23.58 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (3) ~ (e3 = e1) % 154.64/23.58 (4) e3 = e1 % 154.64/23.58 (5) all_20_2 = all_4_2 % 154.64/23.58 (6) all_58_28 = e1 % 154.64/23.58 (7) all_58_29 = all_8_2 % 154.64/23.58 (8) all_58_30 = e0 % 154.64/23.58 (9) ~ (e2 = e1) % 154.64/23.58 (10) ~ (e3 = e0) % 154.64/23.58 (11) e3 = e0 % 154.64/23.58 (12) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.64/23.58 (13) ~ (e2 = e0) % 154.64/23.58 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (15) ~ (e1 = e0) % 154.64/23.58 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.64/23.58 (17) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | SIMP: (11) implies: % 154.64/23.58 | (18) e3 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (4), (18) imply: % 154.64/23.58 | (19) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (19) implies: % 154.64/23.58 | (20) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (6), (20) imply: % 154.64/23.58 | (21) all_58_28 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 154.64/23.58 | (16), (17), (21) are inconsistent by sub-proof #679. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #562 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) ~ (e3 = e1) % 154.64/23.58 (2) all_58_29 = e3 % 154.64/23.58 (3) all_58_30 = e0 % 154.64/23.58 (4) ~ (e3 = e0) % 154.64/23.58 (5) all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (7) ~ (e2 = e0) % 154.64/23.58 (8) e3 = e1 % 154.64/23.58 (9) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | SIMP: (8) implies: % 154.64/23.58 | (10) e3 = e1 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (2), (10) imply: % 154.64/23.58 | (11) all_58_29 = e1 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11) are inconsistent by % 154.64/23.58 | sub-proof #685. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #563 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = all_4_2 % 154.64/23.58 (2) all_58_13 = e0 % 154.64/23.58 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (4) ~ (e3 = e1) % 154.64/23.58 (5) all_20_2 = all_4_2 % 154.64/23.58 (6) all_58_28 = e1 % 154.64/23.58 (7) all_58_29 = all_8_2 % 154.64/23.58 (8) all_58_30 = e0 % 154.64/23.58 (9) ~ (e2 = e1) % 154.64/23.58 (10) ~ (e3 = e0) % 154.64/23.58 (11) all_58_13 = e1 % 154.64/23.58 (12) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.64/23.58 (13) ~ (e2 = e0) % 154.64/23.58 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (15) ~ (e1 = e0) % 154.64/23.58 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.64/23.58 (17) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (2), (11) imply: % 154.64/23.58 | (18) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (18) implies: % 154.64/23.58 | (19) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (6), (19) imply: % 154.64/23.58 | (20) all_58_28 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15), % 154.64/23.58 | (16), (17), (20) are inconsistent by sub-proof #679. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #564 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (2) all_58_28 = e1 % 154.64/23.58 (3) all_58_29 = e3 % 154.64/23.58 (4) all_58_30 = e0 % 154.64/23.58 (5) ~ (e2 = e1) % 154.64/23.58 (6) ~ (e3 = e0) % 154.64/23.58 (7) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (8) ~ (e2 = e0) % 154.64/23.58 (9) e2 = e0 % 154.64/23.58 (10) ~ (e3 = e2) % 154.64/23.58 (11) e3 = e2 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (9), (11) imply: % 154.64/23.58 | (12) e3 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (3), (12) imply: % 154.64/23.58 | (13) all_58_29 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13) are inconsistent by % 154.64/23.58 | sub-proof #702. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #565 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_31 = all_4_2 % 154.64/23.58 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (3) ~ (e3 = e1) % 154.64/23.58 (4) all_20_2 = all_4_2 % 154.64/23.58 (5) all_58_28 = e1 % 154.64/23.58 (6) all_58_29 = all_8_2 % 154.64/23.58 (7) all_58_30 = e0 % 154.64/23.58 (8) ~ (e2 = e1) % 154.64/23.58 (9) e2 = e1 % 154.64/23.58 (10) ~ (e3 = e0) % 154.64/23.58 (11) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.64/23.58 (12) ~ (e2 = e0) % 154.64/23.58 (13) e2 = e0 % 154.64/23.58 (14) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (15) ~ (e1 = e0) % 154.64/23.58 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.64/23.58 (17) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (9), (13) imply: % 154.64/23.58 | (18) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (18) implies: % 154.64/23.58 | (19) e1 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (5), (19) imply: % 154.64/23.58 | (20) all_58_28 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (14), (15), % 154.64/23.58 | (16), (17), (20) are inconsistent by sub-proof #679. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #566 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_58_22 = e0 % 154.64/23.58 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.64/23.58 (3) all_58_28 = e1 % 154.64/23.58 (4) all_58_29 = e3 % 154.64/23.58 (5) all_58_30 = e0 % 154.64/23.58 (6) ~ (e2 = e1) % 154.64/23.58 (7) ~ (e3 = e0) % 154.64/23.58 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.64/23.58 (9) ~ (e2 = e0) % 154.64/23.58 (10) ~ (e3 = e2) % 154.64/23.58 (11) all_58_22 = e3 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (11) imply: % 154.64/23.58 | (12) e3 = e0 % 154.64/23.58 | % 154.64/23.58 | SIMP: (12) implies: % 154.64/23.58 | (13) e3 = e0 % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (4), (13) imply: % 154.64/23.58 | (14) all_58_29 = e0 % 154.64/23.58 | % 154.64/23.58 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (14) are inconsistent by % 154.64/23.58 | sub-proof #702. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #567 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_54_11 = all_52_14 % 154.64/23.58 (2) all_54_11 = e1 % 154.64/23.58 (3) ~ (all_52_14 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) all_52_14 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) all_52_14 = e1 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #568 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_1 = e3 % 154.64/23.58 (2) all_56_1 = e2 % 154.64/23.58 (3) ~ (e3 = e2) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) e3 = e2 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) e3 = e2 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #569 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) all_56_0 = e3 % 154.64/23.58 (2) all_56_0 = e1 % 154.64/23.58 (3) ~ (e3 = e1) % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (1), (2) imply: % 154.64/23.58 | (4) e3 = e1 % 154.64/23.58 | % 154.64/23.58 | SIMP: (4) implies: % 154.64/23.58 | (5) e3 = e1 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (3), (5) imply: % 154.64/23.58 | (6) $false % 154.64/23.58 | % 154.64/23.58 | CLOSE: (6) is inconsistent. % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #570 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.64/23.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.64/23.58 (2) ~ (all_44_0 = e3) | ~ (all_44_2 = e2) % 154.64/23.58 (3) op(e2, e1) = e3 % 154.64/23.58 (4) all_44_2 = all_4_2 % 154.64/23.58 (5) all_4_2 = e2 % 154.64/23.58 (6) op(all_4_2, e1) = all_4_0 % 154.64/23.58 (7) all_44_0 = all_4_0 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | COMBINE_EQS: (4), (5) imply: % 154.64/23.58 | (8) all_44_2 = e2 % 154.64/23.58 | % 154.64/23.58 | REDUCE: (5), (6) imply: % 154.64/23.58 | (9) op(e2, e1) = all_4_0 % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (2) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (10) ~ (all_44_2 = e2) % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (8), (10) imply: % 154.64/23.58 | | (11) $false % 154.64/23.58 | | % 154.64/23.58 | | CLOSE: (11) is inconsistent. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.58 | | (12) ~ (all_44_0 = e3) % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (7), (12) imply: % 154.64/23.58 | | (13) ~ (all_4_0 = e3) % 154.64/23.58 | | % 154.64/23.58 | | GROUND_INST: instantiating (1) with e3, all_4_0, e1, e2, simplifying with % 154.64/23.58 | | (3), (9) gives: % 154.64/23.58 | | (14) all_4_0 = e3 % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (13), (14) imply: % 154.64/23.58 | | (15) $false % 154.64/23.58 | | % 154.64/23.58 | | CLOSE: (15) is inconsistent. % 154.64/23.58 | | % 154.64/23.58 | End of split % 154.64/23.58 | % 154.64/23.58 End of proof % 154.64/23.58 % 154.64/23.58 Sub-proof #571 shows that the following formulas are inconsistent: % 154.64/23.58 ---------------------------------------------------------------- % 154.64/23.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.64/23.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.64/23.58 (2) all_26_0 = all_4_0 % 154.64/23.58 (3) ~ (all_26_0 = e2) | ~ (all_26_2 = e3) % 154.64/23.58 (4) all_26_2 = e3 % 154.64/23.58 (5) op(e3, e1) = all_4_0 % 154.64/23.58 (6) op(e3, e1) = e2 % 154.64/23.58 % 154.64/23.58 Begin of proof % 154.64/23.58 | % 154.64/23.58 | BETA: splitting (3) gives: % 154.64/23.58 | % 154.64/23.58 | Case 1: % 154.64/23.58 | | % 154.64/23.58 | | (7) ~ (all_26_0 = e2) % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (2), (7) imply: % 154.64/23.58 | | (8) ~ (all_4_0 = e2) % 154.64/23.58 | | % 154.64/23.58 | | GROUND_INST: instantiating (1) with e2, all_4_0, e1, e3, simplifying with % 154.64/23.58 | | (5), (6) gives: % 154.64/23.58 | | (9) all_4_0 = e2 % 154.64/23.58 | | % 154.64/23.58 | | REDUCE: (8), (9) imply: % 154.64/23.58 | | (10) $false % 154.64/23.58 | | % 154.64/23.58 | | CLOSE: (10) is inconsistent. % 154.64/23.58 | | % 154.64/23.58 | Case 2: % 154.64/23.58 | | % 154.64/23.59 | | (11) ~ (all_26_2 = e3) % 154.64/23.59 | | % 154.64/23.59 | | REDUCE: (4), (11) imply: % 154.64/23.59 | | (12) $false % 154.64/23.59 | | % 154.64/23.59 | | CLOSE: (12) is inconsistent. % 154.64/23.59 | | % 154.64/23.59 | End of split % 154.64/23.59 | % 154.64/23.59 End of proof % 154.64/23.59 % 154.64/23.59 Sub-proof #572 shows that the following formulas are inconsistent: % 154.64/23.59 ---------------------------------------------------------------- % 154.64/23.59 (1) all_54_9 = all_52_6 % 154.64/23.59 (2) all_54_9 = e0 % 154.64/23.59 (3) ~ (all_52_6 = e0) % 154.64/23.59 % 154.64/23.59 Begin of proof % 154.64/23.59 | % 154.64/23.59 | COMBINE_EQS: (1), (2) imply: % 154.64/23.59 | (4) all_52_6 = e0 % 154.64/23.59 | % 154.64/23.59 | SIMP: (4) implies: % 154.64/23.59 | (5) all_52_6 = e0 % 154.64/23.59 | % 154.64/23.59 | REDUCE: (3), (5) imply: % 154.64/23.59 | (6) $false % 154.64/23.59 | % 154.64/23.59 | CLOSE: (6) is inconsistent. % 154.64/23.59 | % 154.64/23.59 End of proof % 154.64/23.59 % 154.64/23.59 Sub-proof #573 shows that the following formulas are inconsistent: % 154.64/23.59 ---------------------------------------------------------------- % 154.64/23.59 (1) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.64/23.59 (2) all_56_5 = all_52_9 % 154.64/23.59 (3) ~ (all_52_13 = e0) % 154.64/23.59 (4) ~ (all_52_9 = e0) % 154.64/23.59 (5) all_56_3 = all_8_2 % 154.64/23.59 (6) all_56_10 = all_52_13 % 154.64/23.59 (7) ~ (all_8_2 = e0) % 154.64/23.59 % 154.64/23.59 Begin of proof % 154.64/23.59 | % 154.64/23.59 | BETA: splitting (1) gives: % 154.64/23.59 | % 154.64/23.59 | Case 1: % 154.64/23.59 | | % 154.64/23.59 | | (8) all_56_3 = e0 % 154.64/23.59 | | % 154.64/23.59 | | COMBINE_EQS: (5), (8) imply: % 154.64/23.59 | | (9) all_8_2 = e0 % 154.64/23.59 | | % 154.64/23.59 | | REDUCE: (7), (9) imply: % 154.64/23.59 | | (10) $false % 154.64/23.59 | | % 154.64/23.59 | | CLOSE: (10) is inconsistent. % 154.64/23.59 | | % 154.64/23.59 | Case 2: % 154.64/23.59 | | % 154.64/23.59 | | (11) all_56_5 = e0 | all_56_10 = e0 % 154.64/23.59 | | % 154.64/23.59 | | REF_CLOSE: (2), (3), (4), (6), (11) are inconsistent by sub-proof #574. % 154.64/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #574 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_5 = all_52_9 % 154.86/23.59 (2) ~ (all_52_13 = e0) % 154.86/23.59 (3) ~ (all_52_9 = e0) % 154.86/23.59 (4) all_56_10 = all_52_13 % 154.86/23.59 (5) all_56_5 = e0 | all_56_10 = e0 % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (5) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (6) all_56_5 = e0 % 154.86/23.59 | | % 154.86/23.59 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #767. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (7) all_56_10 = e0 % 154.86/23.59 | | % 154.86/23.59 | | COMBINE_EQS: (4), (7) imply: % 154.86/23.59 | | (8) all_52_13 = e0 % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (2), (8) imply: % 154.86/23.59 | | (9) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (9) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #575 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_14 = all_6_1 % 154.86/23.59 (2) all_56_14 = e0 % 154.86/23.59 (3) ~ (all_6_1 = e0) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (2) imply: % 154.86/23.59 | (4) all_6_1 = e0 % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (5) all_6_1 = e0 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (3), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #576 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_58_31 = all_4_2 % 154.86/23.59 (2) all_56_14 = e1 % 154.86/23.59 (3) all_56_15 = all_4_2 % 154.86/23.59 (4) ~ (all_52_3 = e1) % 154.86/23.59 (5) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.86/23.59 (6) ~ (all_52_13 = all_4_2) % 154.86/23.59 (7) ~ (all_52_13 = all_8_2) % 154.86/23.59 (8) all_56_12 = all_52_3 % 154.86/23.59 (9) all_56_11 = all_52_14 % 154.86/23.59 (10) ~ (all_52_13 = e0) % 154.86/23.59 (11) ~ (all_56_0 = e1) % 154.86/23.59 (12) all_56_14 = e1 | all_56_15 = e1 % 154.86/23.59 (13) all_58_29 = all_8_2 % 154.86/23.59 (14) all_58_30 = e0 % 154.86/23.59 (15) all_56_6 = all_52_2 % 154.86/23.59 (16) all_56_2 = e0 % 154.86/23.59 (17) all_56_10 = all_52_13 % 154.86/23.59 (18) all_58_28 = all_10_2 % 154.86/23.59 (19) all_56_0 = all_10_2 % 154.86/23.59 (20) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.86/23.59 (21) ~ (all_52_2 = all_52_14) % 154.86/23.59 (22) ~ (e1 = e0) % 154.86/23.59 (23) ~ (all_4_2 = e1) % 154.86/23.59 (24) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | REDUCE: (11), (19) imply: % 154.86/23.59 | (25) ~ (all_10_2 = e1) % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (24) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (26) all_58_28 = e1 % 154.86/23.59 | | % 154.86/23.59 | | COMBINE_EQS: (18), (26) imply: % 154.86/23.59 | | (27) all_10_2 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (25), (27) imply: % 154.86/23.59 | | (28) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (28) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (29) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.59 | | % 154.86/23.59 | | BETA: splitting (20) gives: % 154.86/23.59 | | % 154.86/23.59 | | Case 1: % 154.86/23.59 | | | % 154.86/23.59 | | | (30) all_56_2 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | COMBINE_EQS: (16), (30) imply: % 154.86/23.59 | | | (31) e1 = e0 % 154.86/23.59 | | | % 154.86/23.59 | | | REF_CLOSE: (2), (3), (12), (22), (23), (31) are inconsistent by sub-proof % 154.86/23.59 | | | #581. % 154.86/23.59 | | | % 154.86/23.59 | | Case 2: % 154.86/23.59 | | | % 154.86/23.59 | | | (32) all_56_6 = e1 | all_56_12 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | BETA: splitting (32) gives: % 154.86/23.59 | | | % 154.86/23.59 | | | Case 1: % 154.86/23.59 | | | | % 154.86/23.59 | | | | (33) all_56_6 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | COMBINE_EQS: (15), (33) imply: % 154.86/23.59 | | | | (34) all_52_2 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | SIMP: (34) implies: % 154.86/23.59 | | | | (35) all_52_2 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | REDUCE: (21), (35) imply: % 154.86/23.59 | | | | (36) ~ (all_52_14 = e1) % 154.86/23.59 | | | | % 154.86/23.59 | | | | SIMP: (36) implies: % 154.86/23.59 | | | | (37) ~ (all_52_14 = e1) % 154.86/23.59 | | | | % 154.86/23.59 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (13), (14), (17), (23), % 154.86/23.59 | | | | (29), (37) are inconsistent by sub-proof #578. % 154.86/23.59 | | | | % 154.86/23.59 | | | Case 2: % 154.86/23.59 | | | | % 154.86/23.59 | | | | (38) all_56_12 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | REF_CLOSE: (4), (8), (38) are inconsistent by sub-proof #577. % 154.86/23.59 | | | | % 154.86/23.59 | | | End of split % 154.86/23.59 | | | % 154.86/23.59 | | End of split % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #577 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_12 = all_52_3 % 154.86/23.59 (2) all_56_12 = e1 % 154.86/23.59 (3) ~ (all_52_3 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (2) imply: % 154.86/23.59 | (4) all_52_3 = e1 % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (5) all_52_3 = e1 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (3), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #578 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_58_31 = all_4_2 % 154.86/23.59 (2) all_56_15 = all_4_2 % 154.86/23.59 (3) ~ (all_52_14 = e1) % 154.86/23.59 (4) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.86/23.59 (5) ~ (all_52_13 = all_4_2) % 154.86/23.59 (6) ~ (all_52_13 = all_8_2) % 154.86/23.59 (7) all_56_11 = all_52_14 % 154.86/23.59 (8) ~ (all_52_13 = e0) % 154.86/23.59 (9) all_58_29 = all_8_2 % 154.86/23.59 (10) all_58_30 = e0 % 154.86/23.59 (11) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.59 (12) all_56_10 = all_52_13 % 154.86/23.59 (13) ~ (all_4_2 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (4) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (14) all_56_10 = e1 % 154.86/23.59 | | % 154.86/23.59 | | COMBINE_EQS: (12), (14) imply: % 154.86/23.59 | | (15) all_52_13 = e1 % 154.86/23.59 | | % 154.86/23.59 | | SIMP: (15) implies: % 154.86/23.59 | | (16) all_52_13 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (6), (16) imply: % 154.86/23.59 | | (17) ~ (all_8_2 = e1) % 154.86/23.59 | | % 154.86/23.59 | | SIMP: (17) implies: % 154.86/23.59 | | (18) ~ (all_8_2 = e1) % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (5), (16) imply: % 154.86/23.59 | | (19) ~ (all_4_2 = e1) % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (8), (16) imply: % 154.86/23.59 | | (20) ~ (e1 = e0) % 154.86/23.59 | | % 154.86/23.59 | | BETA: splitting (11) gives: % 154.86/23.59 | | % 154.86/23.59 | | Case 1: % 154.86/23.59 | | | % 154.86/23.59 | | | (21) all_58_29 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | COMBINE_EQS: (9), (21) imply: % 154.86/23.59 | | | (22) all_8_2 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | REDUCE: (18), (22) imply: % 154.86/23.59 | | | (23) $false % 154.86/23.59 | | | % 154.86/23.59 | | | CLOSE: (23) is inconsistent. % 154.86/23.59 | | | % 154.86/23.59 | | Case 2: % 154.86/23.59 | | | % 154.86/23.59 | | | (24) all_58_30 = e1 | all_58_31 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | REF_CLOSE: (1), (10), (13), (20), (24) are inconsistent by sub-proof #711. % 154.86/23.59 | | | % 154.86/23.59 | | End of split % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (25) all_56_11 = e1 | all_56_15 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REF_CLOSE: (2), (3), (7), (13), (25) are inconsistent by sub-proof #579. % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #579 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_15 = all_4_2 % 154.86/23.59 (2) ~ (all_52_14 = e1) % 154.86/23.59 (3) all_56_11 = all_52_14 % 154.86/23.59 (4) all_56_11 = e1 | all_56_15 = e1 % 154.86/23.59 (5) ~ (all_4_2 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (4) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (6) all_56_11 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #580. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (7) all_56_15 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #671. % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #580 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_11 = all_52_14 % 154.86/23.59 (2) all_56_11 = e1 % 154.86/23.59 (3) ~ (all_52_14 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (2) imply: % 154.86/23.59 | (4) all_52_14 = e1 % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (5) all_52_14 = e1 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (3), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #581 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_14 = e1 % 154.86/23.59 (2) all_56_15 = all_4_2 % 154.86/23.59 (3) all_56_14 = e1 | all_56_15 = e1 % 154.86/23.59 (4) e1 = e0 % 154.86/23.59 (5) ~ (e1 = e0) % 154.86/23.59 (6) ~ (all_4_2 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (7) e1 = e0 % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (7) imply: % 154.86/23.59 | (8) all_56_14 = e0 % 154.86/23.59 | % 154.86/23.59 | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #582. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #582 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_14 = e0 % 154.86/23.59 (2) all_56_15 = all_4_2 % 154.86/23.59 (3) all_56_14 = e1 | all_56_15 = e1 % 154.86/23.59 (4) ~ (e1 = e0) % 154.86/23.59 (5) ~ (all_4_2 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (3) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (6) all_56_14 = e1 % 154.86/23.59 | | % 154.86/23.59 | | COMBINE_EQS: (1), (6) imply: % 154.86/23.59 | | (7) e1 = e0 % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (4), (7) imply: % 154.86/23.59 | | (8) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (8) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (9) all_56_15 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #671. % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #583 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.59 (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.59 (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.86/23.59 (2) all_58_14 = e3 % 154.86/23.59 (3) all_58_25 = e1 % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (1) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (4) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.59 | | (all_58_19 = e0) % 154.86/23.59 | | % 154.86/23.59 | | ALPHA: (4) implies: % 154.86/23.59 | | (5) ~ (all_58_14 = e3) % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (2), (5) imply: % 154.86/23.59 | | (6) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (6) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (7) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.59 | | (all_58_27 = e0) % 154.86/23.59 | | % 154.86/23.59 | | ALPHA: (7) implies: % 154.86/23.59 | | (8) ~ (all_58_25 = e1) % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (3), (8) imply: % 154.86/23.59 | | (9) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (9) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #584 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.59 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.59 (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.86/23.59 (2) all_58_5 = e0 % 154.86/23.59 (3) all_58_9 = e2 % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (1) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (4) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.59 | | (all_58_5 = e0) % 154.86/23.59 | | % 154.86/23.59 | | ALPHA: (4) implies: % 154.86/23.59 | | (5) ~ (all_58_5 = e0) % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (2), (5) imply: % 154.86/23.59 | | (6) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (6) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (7) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 154.86/23.59 | | (all_58_12 = e0) % 154.86/23.59 | | % 154.86/23.59 | | ALPHA: (7) implies: % 154.86/23.59 | | (8) ~ (all_58_9 = e2) % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (3), (8) imply: % 154.86/23.59 | | (9) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (9) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | End of split % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #585 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_58_31 = e3 % 154.86/23.59 (2) all_58_31 = e2 % 154.86/23.59 (3) ~ (e3 = e2) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (2) imply: % 154.86/23.59 | (4) e3 = e2 % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (5) e3 = e2 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (3), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #586 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.86/23.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.86/23.59 (2) op(e2, e0) = all_4_1 % 154.86/23.59 (3) op(e2, e0) = e1 % 154.86/23.59 (4) ~ (all_4_1 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | GROUND_INST: instantiating (1) with e1, all_4_1, e0, e2, simplifying with (2), % 154.86/23.59 | (3) gives: % 154.86/23.59 | (5) all_4_1 = e1 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (4), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #587 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_54_15 = all_4_2 % 154.86/23.59 (2) all_54_15 = e1 % 154.86/23.59 (3) ~ (all_4_2 = e1) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (2) imply: % 154.86/23.59 | (4) all_4_2 = e1 % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (5) all_4_2 = e1 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (3), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #588 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_56_12 = e3 % 154.86/23.59 (2) all_56_12 = e2 % 154.86/23.59 (3) ~ (e3 = e2) % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (1), (2) imply: % 154.86/23.59 | (4) e3 = e2 % 154.86/23.59 | % 154.86/23.59 | SIMP: (4) implies: % 154.86/23.59 | (5) e3 = e2 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (3), (5) imply: % 154.86/23.59 | (6) $false % 154.86/23.59 | % 154.86/23.59 | CLOSE: (6) is inconsistent. % 154.86/23.59 | % 154.86/23.59 End of proof % 154.86/23.59 % 154.86/23.59 Sub-proof #589 shows that the following formulas are inconsistent: % 154.86/23.59 ---------------------------------------------------------------- % 154.86/23.59 (1) all_58_31 = all_4_2 % 154.86/23.59 (2) all_56_15 = all_4_2 % 154.86/23.59 (3) all_58_15 = all_52_2 % 154.86/23.59 (4) all_54_7 = all_52_13 % 154.86/23.59 (5) all_56_4 = all_52_8 % 154.86/23.59 (6) ~ (all_52_4 = all_8_2) % 154.86/23.59 (7) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.59 (8) all_58_13 = all_52_13 % 154.86/23.59 (9) all_58_5 = e0 % 154.86/23.59 (10) all_58_20 = all_52_14 % 154.86/23.59 (11) all_58_8 = e0 % 154.86/23.59 (12) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.86/23.59 (13) ~ (all_52_13 = all_4_2) % 154.86/23.59 (14) ~ (all_52_3 = e0) % 154.86/23.59 (15) all_58_7 = all_52_13 % 154.86/23.59 (16) ~ (all_52_13 = all_8_2) % 154.86/23.59 (17) ~ (e3 = e1) % 154.86/23.59 (18) all_58_6 = e0 % 154.86/23.59 (19) all_56_12 = e1 % 154.86/23.59 (20) all_56_12 = all_52_3 % 154.86/23.59 (21) all_56_11 = all_52_14 % 154.86/23.59 (22) all_56_1 = all_52_4 % 154.86/23.59 (23) ~ (all_52_13 = e0) % 154.86/23.59 (24) ~ (all_52_3 = all_4_2) % 154.86/23.59 (25) all_58_18 = all_52_14 % 154.86/23.59 (26) all_58_24 = e0 % 154.86/23.59 (27) ~ (all_52_13 = all_52_14) % 154.86/23.59 (28) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.86/23.59 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.59 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.86/23.59 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.59 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.59 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.86/23.59 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.59 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.59 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.59 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.59 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.59 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.59 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.59 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.59 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.59 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.59 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.59 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.59 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.59 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.59 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.59 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.59 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.59 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.59 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.59 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.86/23.59 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.59 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.59 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.59 e0) % 154.86/23.59 (29) all_58_29 = all_8_2 % 154.86/23.59 (30) all_58_30 = e0 % 154.86/23.59 (31) ~ (e2 = e1) % 154.86/23.59 (32) ~ (all_52_8 = all_6_1) % 154.86/23.59 (33) all_56_0 = e1 | all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.86/23.59 (34) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.59 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.59 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.86/23.59 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.59 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.59 (all_58_27 = e0)) % 154.86/23.59 (35) ~ (e3 = e0) % 154.86/23.59 (36) all_58_26 = all_6_1 % 154.86/23.59 (37) all_56_10 = all_52_13 % 154.86/23.59 (38) all_58_28 = all_10_2 % 154.86/23.59 (39) all_56_9 = e0 % 154.86/23.59 (40) ~ (e2 = e0) % 154.86/23.59 (41) all_56_0 = all_10_2 % 154.86/23.59 (42) all_58_22 = all_52_3 % 154.86/23.59 (43) all_58_23 = all_4_2 % 154.86/23.59 (44) ~ (all_52_3 = all_10_2) % 154.86/23.59 (45) all_58_4 = all_52_8 % 154.86/23.59 (46) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.59 (47) ~ (all_52_2 = all_52_14) % 154.86/23.59 (48) ~ (all_52_14 = all_4_2) % 154.86/23.59 (49) ~ (all_52_14 = e0) % 154.86/23.59 (50) ~ (all_52_8 = e0) % 154.86/23.59 (51) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.59 (52) ~ (e3 = e2) % 154.86/23.59 (53) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 154.86/23.59 % 154.86/23.59 Begin of proof % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (19), (20) imply: % 154.86/23.59 | (54) all_52_3 = e1 % 154.86/23.59 | % 154.86/23.59 | SIMP: (54) implies: % 154.86/23.59 | (55) all_52_3 = e1 % 154.86/23.59 | % 154.86/23.59 | COMBINE_EQS: (42), (55) imply: % 154.86/23.59 | (56) all_58_22 = e1 % 154.86/23.59 | % 154.86/23.59 | REDUCE: (44), (55) imply: % 154.86/23.59 | (57) ~ (all_10_2 = e1) % 154.86/23.59 | % 154.86/23.59 | SIMP: (57) implies: % 154.86/23.59 | (58) ~ (all_10_2 = e1) % 154.86/23.59 | % 154.86/23.59 | REDUCE: (24), (55) imply: % 154.86/23.59 | (59) ~ (all_4_2 = e1) % 154.86/23.59 | % 154.86/23.59 | SIMP: (59) implies: % 154.86/23.59 | (60) ~ (all_4_2 = e1) % 154.86/23.59 | % 154.86/23.59 | REDUCE: (14), (55) imply: % 154.86/23.59 | (61) ~ (e1 = e0) % 154.86/23.59 | % 154.86/23.59 | BETA: splitting (51) gives: % 154.86/23.59 | % 154.86/23.59 | Case 1: % 154.86/23.59 | | % 154.86/23.59 | | (62) all_58_28 = e1 % 154.86/23.59 | | % 154.86/23.59 | | COMBINE_EQS: (38), (62) imply: % 154.86/23.59 | | (63) all_10_2 = e1 % 154.86/23.59 | | % 154.86/23.59 | | REDUCE: (58), (63) imply: % 154.86/23.59 | | (64) $false % 154.86/23.59 | | % 154.86/23.59 | | CLOSE: (64) is inconsistent. % 154.86/23.59 | | % 154.86/23.59 | Case 2: % 154.86/23.59 | | % 154.86/23.59 | | (65) ~ (all_58_28 = e1) % 154.86/23.59 | | (66) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.59 | | % 154.86/23.59 | | BETA: splitting (66) gives: % 154.86/23.59 | | % 154.86/23.59 | | Case 1: % 154.86/23.59 | | | % 154.86/23.59 | | | (67) all_58_29 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | COMBINE_EQS: (29), (67) imply: % 154.86/23.59 | | | (68) all_8_2 = e1 % 154.86/23.59 | | | % 154.86/23.59 | | | REDUCE: (6), (68) imply: % 154.86/23.59 | | | (69) ~ (all_52_4 = e1) % 154.86/23.59 | | | % 154.86/23.59 | | | REDUCE: (16), (68) imply: % 154.86/23.59 | | | (70) ~ (all_52_13 = e1) % 154.86/23.59 | | | % 154.86/23.59 | | | BETA: splitting (33) gives: % 154.86/23.59 | | | % 154.86/23.59 | | | Case 1: % 154.86/23.59 | | | | % 154.86/23.59 | | | | (71) all_56_0 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | COMBINE_EQS: (41), (71) imply: % 154.86/23.59 | | | | (72) all_10_2 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | REDUCE: (58), (72) imply: % 154.86/23.59 | | | | (73) $false % 154.86/23.59 | | | | % 154.86/23.59 | | | | CLOSE: (73) is inconsistent. % 154.86/23.59 | | | | % 154.86/23.59 | | | Case 2: % 154.86/23.59 | | | | % 154.86/23.59 | | | | (74) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 154.86/23.59 | | | | % 154.86/23.59 | | | | BETA: splitting (74) gives: % 154.86/23.59 | | | | % 154.86/23.59 | | | | Case 1: % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | (75) all_56_1 = e1 % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | COMBINE_EQS: (22), (75) imply: % 154.86/23.59 | | | | | (76) all_52_4 = e1 % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | REDUCE: (69), (76) imply: % 154.86/23.59 | | | | | (77) $false % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | CLOSE: (77) is inconsistent. % 154.86/23.59 | | | | | % 154.86/23.59 | | | | Case 2: % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | (78) all_56_4 = e1 | all_56_9 = e1 % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | BETA: splitting (12) gives: % 154.86/23.59 | | | | | % 154.86/23.59 | | | | | Case 1: % 154.86/23.59 | | | | | | % 154.86/23.59 | | | | | | (79) all_56_10 = e1 % 154.86/23.59 | | | | | | % 154.86/23.59 | | | | | | REF_CLOSE: (37), (70), (79) are inconsistent by sub-proof #606. % 154.86/23.59 | | | | | | % 154.86/23.59 | | | | | Case 2: % 154.86/23.59 | | | | | | % 154.86/23.59 | | | | | | (80) all_56_11 = e1 | all_56_15 = e1 % 154.86/23.59 | | | | | | % 154.86/23.59 | | | | | | BETA: splitting (80) gives: % 154.86/23.59 | | | | | | % 154.86/23.59 | | | | | | Case 1: % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | (81) all_56_11 = e1 % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | COMBINE_EQS: (21), (81) imply: % 154.86/23.59 | | | | | | | (82) all_52_14 = e1 % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | SIMP: (82) implies: % 154.86/23.59 | | | | | | | (83) all_52_14 = e1 % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | COMBINE_EQS: (10), (83) imply: % 154.86/23.59 | | | | | | | (84) all_58_20 = e1 % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | COMBINE_EQS: (25), (83) imply: % 154.86/23.59 | | | | | | | (85) all_58_18 = e1 % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | REDUCE: (47), (83) imply: % 154.86/23.59 | | | | | | | (86) ~ (all_52_2 = e1) % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | BETA: splitting (28) gives: % 154.86/23.59 | | | | | | | % 154.86/23.59 | | | | | | | Case 1: % 154.86/23.59 | | | | | | | | % 154.86/23.59 | | | | | | | | (87) all_58_31 = e0 % 154.86/23.59 | | | | | | | | % 154.86/23.59 | | | | | | | | REF_CLOSE: (7), (17), (30), (31), (35), (40), (46), (52), (67), % 154.86/23.59 | | | | | | | | (87) are inconsistent by sub-proof #713. % 154.86/23.59 | | | | | | | | % 154.86/23.59 | | | | | | | Case 2: % 154.86/23.59 | | | | | | | | % 154.86/23.59 | | | | | | | | (88) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.86/23.59 | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.59 | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.86/23.59 | | | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.86/23.59 | | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.59 | | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.59 | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.59 | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.86/23.59 | | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.59 | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.59 | | | | | | | | all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.59 | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.86/23.59 | | | | | | | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.59 | | | | | | | | e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 154.86/23.59 | | | | | | | | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.86/23.59 | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.59 | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.59 | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.86/23.59 | | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.59 | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.59 | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 % 154.86/23.59 | | | | | | | | = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = % 154.86/23.59 | | | | | | | | e3 & all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.86/23.59 | | | | | | | | & all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & % 154.86/23.59 | | | | | | | | all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.86/23.59 | | | | | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.59 | | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 % 154.86/23.59 | | | | | | | | = e0) | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = % 154.86/23.59 | | | | | | | | e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = % 154.86/23.59 | | | | | | | | e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.86/23.59 | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.86/23.59 | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.59 | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & % 154.86/23.59 | | | | | | | | e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.59 | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.59 | | | | | | | | all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.59 | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 % 154.86/23.59 | | | | | | | | = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.59 | | | | | | | | % 154.86/23.59 | | | | | | | | BETA: splitting (88) gives: % 154.86/23.59 | | | | | | | | % 154.86/23.59 | | | | | | | | Case 1: % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | (89) all_58_30 = e1 % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | COMBINE_EQS: (30), (89) imply: % 154.86/23.59 | | | | | | | | | (90) e1 = e0 % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (90) are % 154.86/23.59 | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | Case 2: % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | (91) ~ (all_58_30 = e1) % 154.86/23.59 | | | | | | | | | (92) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.86/23.59 | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.59 | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.59 | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.59 | | | | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.86/23.59 | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.59 | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.59 | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 154.86/23.59 | | | | | | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.59 | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.59 | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.59 | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.59 | | | | | | | | | e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.59 | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 154.86/23.59 | | | | | | | | | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.86/23.59 | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.59 | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.59 | | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.86/23.59 | | | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.59 | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.59 | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.59 | | | | | | | | | e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.86/23.59 | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & % 154.86/23.59 | | | | | | | | | all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.86/23.59 | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.59 | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.86/23.59 | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.86/23.59 | | | | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & % 154.86/23.59 | | | | | | | | | all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.59 | | | | | | | | | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.59 | | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.59 | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.86/23.59 | | | | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.59 | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.86/23.59 | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.59 | | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.86/23.59 | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.59 | | | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.86/23.59 | | | | | | | | | all_58_26 = e0 & e1 = e0) % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | REDUCE: (30), (91) imply: % 154.86/23.59 | | | | | | | | | (93) ~ (e1 = e0) % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | BETA: splitting (78) gives: % 154.86/23.59 | | | | | | | | | % 154.86/23.59 | | | | | | | | | Case 1: % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | (94) all_56_4 = e1 % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | COMBINE_EQS: (5), (94) imply: % 154.86/23.59 | | | | | | | | | | (95) all_52_8 = e1 % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | COMBINE_EQS: (45), (95) imply: % 154.86/23.59 | | | | | | | | | | (96) all_58_4 = e1 % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | REDUCE: (32), (95) imply: % 154.86/23.59 | | | | | | | | | | (97) ~ (all_6_1 = e1) % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | SIMP: (97) implies: % 154.86/23.59 | | | | | | | | | | (98) ~ (all_6_1 = e1) % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | BETA: splitting (92) gives: % 154.86/23.59 | | | | | | | | | | % 154.86/23.59 | | | | | | | | | | Case 1: % 154.86/23.59 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | (99) all_58_29 = e2 % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | REF_CLOSE: (31), (67), (99) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | #687. % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | (100) ~ (all_58_29 = e2) % 154.86/23.60 | | | | | | | | | | | (101) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.86/23.60 | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.86/23.60 | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.86/23.60 | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.86/23.60 | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.86/23.60 | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.86/23.60 | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.60 | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.86/23.60 | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.60 | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.86/23.60 | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.86/23.60 | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.86/23.60 | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.60 | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.60 | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.86/23.60 | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.60 | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.60 | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.86/23.60 | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.86/23.60 | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.86/23.60 | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.86/23.60 | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.86/23.60 | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.86/23.60 | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.60 | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.86/23.60 | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.86/23.60 | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.86/23.60 | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.60 | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.60 | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.86/23.60 | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.86/23.60 | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.60 | | | | | | | | | | | e0) % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | REDUCE: (67), (100) imply: % 154.86/23.60 | | | | | | | | | | | (102) ~ (e2 = e1) % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | BETA: splitting (101) gives: % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | (103) all_58_28 = e3 % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | COMBINE_EQS: (38), (103) imply: % 154.86/23.60 | | | | | | | | | | | | (104) all_10_2 = e3 % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | BETA: splitting (7) gives: % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | (105) all_58_28 = e2 % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | COMBINE_EQS: (103), (105) imply: % 154.86/23.60 | | | | | | | | | | | | | (106) e3 = e2 % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | REDUCE: (52), (106) imply: % 154.86/23.60 | | | | | | | | | | | | | (107) $false % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | CLOSE: (107) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | (108) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | BETA: splitting (108) gives: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | (109) all_58_29 = e2 % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | COMBINE_EQS: (67), (109) imply: % 154.86/23.60 | | | | | | | | | | | | | | (110) e2 = e1 % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | REDUCE: (31), (110) imply: % 154.86/23.60 | | | | | | | | | | | | | | (111) $false % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | (112) all_58_30 = e2 | all_58_31 = e2 % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | BETA: splitting (112) gives: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (113) all_58_30 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | COMBINE_EQS: (30), (113) imply: % 154.86/23.60 | | | | | | | | | | | | | | | (114) e2 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | REDUCE: (40), (114) imply: % 154.86/23.60 | | | | | | | | | | | | | | | (115) $false % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (116) all_58_31 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | COMBINE_EQS: (1), (116) imply: % 154.86/23.60 | | | | | | | | | | | | | | | (117) all_4_2 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | SIMP: (117) implies: % 154.86/23.60 | | | | | | | | | | | | | | | (118) all_4_2 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | COMBINE_EQS: (43), (118) imply: % 154.86/23.60 | | | | | | | | | | | | | | | (119) all_58_23 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | REDUCE: (13), (118) imply: % 154.86/23.60 | | | | | | | | | | | | | | | (120) ~ (all_52_13 = e2) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (53) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (121) all_54_7 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (121) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | #742. % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (122) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (123) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | BETA: splitting (123) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | (124) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | ALPHA: (124) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | | (125) ~ (all_58_5 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | REDUCE: (9), (125) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | | (126) $false % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | CLOSE: (126) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | (127) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | | (128) ~ (all_58_7 = e3) % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | REDUCE: (15), (128) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | | (129) ~ (all_52_13 = e3) % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (70), (120), (122), (129) are inconsistent by % 154.86/23.60 | | | | | | | | | | | | | | | | | | sub-proof #601. % 154.86/23.60 | | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (130) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.60 | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (119), (130) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #600. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | (131) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.86/23.60 | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.86/23.60 | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.86/23.60 | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.60 | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.60 | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.86/23.60 | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.86/23.60 | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.60 | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.60 | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.86/23.60 | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.60 | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.86/23.60 | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.86/23.60 | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.86/23.60 | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.86/23.60 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.86/23.60 | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.60 | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.86/23.60 | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.86/23.60 | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.60 | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.60 | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.86/23.60 | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.86/23.60 | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.60 | | | | | | | | | | | | e0) % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | BETA: splitting (131) gives: % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | (132) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.86/23.60 | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.86/23.60 | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.86/23.60 | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.60 | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.60 | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.86/23.60 | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.86/23.60 | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.60 | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.60 | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.86/23.60 | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.60 | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | | = e0) % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | BETA: splitting (132) gives: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | (133) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.86/23.60 | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.86/23.60 | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.86/23.60 | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | BETA: splitting (133) gives: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (134) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | | = e2) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (135) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_15 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | ALPHA: (135) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | (136) all_58_8 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (136) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | (137) e3 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | REDUCE: (35), (137) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | (138) $false % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | CLOSE: (138) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (139) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (140) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (140) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (141) all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (141) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (142) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (142) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (143) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (144) all_58_8 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (144) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (145) e3 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | SIMP: (145) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (146) e3 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REDUCE: (35), (146) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (147) $false % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (148) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = % 154.86/23.60 | | | | | | | | | | | | | | | e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.86/23.60 | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.86/23.60 | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (148) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (149) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (150) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (40), (150) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #599. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (151) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_15 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (40), (151) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #598. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (152) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (153) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (154) all_58_22 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | (155) all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (30), (56), (60), (61), (66), (67), % 154.86/23.60 | | | | | | | | | | | | | | | | | (154), (155) are inconsistent by sub-proof #597. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (156) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (157) all_58_8 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (40), (157) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #596. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | (158) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.60 | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.86/23.60 | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.60 | | | | | | | | | | | | | | = e0) % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | BETA: splitting (158) gives: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (159) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | | = e1) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (160) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | & e3 = e2) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (40), (160) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | #595. % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (161) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.60 | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (162) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (162) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (163) all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (163) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (164) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (164) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (165) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_17 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (165) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (166) all_58_4 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (96), (166) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #647. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (167) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.86/23.60 | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (168) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (169) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (169) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (170) all_58_4 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (96), (170) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #647. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (171) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_22 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (171) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (172) all_58_22 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | (173) all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (30), (56), (60), (61), (66), (67), % 154.86/23.60 | | | | | | | | | | | | | | | | | (172), (173) are inconsistent by sub-proof #594. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (174) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.86/23.60 | | | | | | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (175) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_17 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (175) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (176) all_58_15 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (86), (176) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #593. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (177) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (177) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (178) all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (178) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (179) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (179) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | (180) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.60 | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.60 | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.86/23.60 | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 % 154.86/23.60 | | | | | | | | | | | | | & all_58_24 = e2) | (all_58_11 = e1 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.86/23.60 | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.86/23.60 | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.60 | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | BETA: splitting (180) gives: % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | (181) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.86/23.60 | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.86/23.60 | | | | | | | | | | | | | | & all_58_24 = e0) % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | BETA: splitting (181) gives: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (182) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.86/23.60 | | | | | | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (183) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | ALPHA: (183) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | (184) e3 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | REDUCE: (17), (184) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | (185) $false % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (186) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (187) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (187) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (188) all_58_22 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | (189) all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (30), (56), (60), (61), (66), (67), % 154.86/23.60 | | | | | | | | | | | | | | | | | (188), (189) are inconsistent by sub-proof #594. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (190) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (190) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (191) all_58_22 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | (192) all_58_6 = e3 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (30), (56), (60), (61), (66), (67), % 154.86/23.60 | | | | | | | | | | | | | | | | | (191), (192) are inconsistent by sub-proof #597. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (193) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (194) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (195) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (195) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (196) all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (196) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (197) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (197) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (198) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (198) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (199) all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (199) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (200) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (200) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (201) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_24 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (202) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (203) all_58_22 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (203) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (204) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (204) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (205) all_58_29 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (205) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #699. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (206) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_24 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (206) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (207) all_58_13 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (207) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (208) all_52_13 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REDUCE: (23), (208) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (209) $false % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | (210) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.86/23.60 | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.86/23.60 | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.60 | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 = % 154.86/23.60 | | | | | | | | | | | | | | e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.86/23.60 | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 % 154.86/23.60 | | | | | | | | | | | | | | = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.86/23.60 | | | | | | | | | | | | | | e0 & e1 = e0) % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | BETA: splitting (210) gives: % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (211) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.86/23.60 | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.60 | | | | | | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (212) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.86/23.60 | | | | | | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (213) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (213) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (214) all_58_26 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (98), (214) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #592. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (215) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_24 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (40), (215) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #591. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (216) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.86/23.60 | | | | | | | | | | | | | | | | = e1 & e2 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (217) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (218) all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (218) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (219) e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (219) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (220) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (221) e2 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REDUCE: (31), (221) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (222) $false % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | (223) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.86/23.60 | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.60 | | | | | | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (224) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.86/23.60 | | | | | | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.86/23.60 | | | | | | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (225) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (225) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (226) all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (84), (226) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #590. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (227) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.86/23.60 | | | | | | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (228) all_58_26 = e1 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (98), (228) are inconsistent by sub-proof % 154.86/23.60 | | | | | | | | | | | | | | | | | #592. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | (229) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.60 | | | | | | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (230) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (231) e2 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REDUCE: (40), (231) imply: % 154.86/23.60 | | | | | | | | | | | | | | | | | (232) $false % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | (233) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | ALPHA: (233) implies: % 154.86/23.60 | | | | | | | | | | | | | | | | | (234) all_58_20 = e0 % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (67), (84), (234) are % 154.86/23.60 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #590. % 154.86/23.60 | | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | | % 154.86/23.60 | | | | | | | | | Case 2: % 154.86/23.60 | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | (235) all_56_9 = e1 % 154.86/23.60 | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | COMBINE_EQS: (39), (235) imply: % 154.86/23.60 | | | | | | | | | | (236) e1 = e0 % 154.86/23.60 | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | COMBINE_EQS: (67), (236) imply: % 154.86/23.60 | | | | | | | | | | (237) all_58_29 = e0 % 154.86/23.60 | | | | | | | | | | % 154.86/23.60 | | | | | | | | | | REF_CLOSE: (1), (30), (60), (61), (66), (237) are % 154.86/23.60 | | | | | | | | | | inconsistent by sub-proof #699. % 154.86/23.60 | | | | | | | | | | % 154.86/23.60 | | | | | | | | | End of split % 154.86/23.60 | | | | | | | | | % 154.86/23.60 | | | | | | | | End of split % 154.86/23.61 | | | | | | | | % 154.86/23.61 | | | | | | | End of split % 154.86/23.61 | | | | | | | % 154.86/23.61 | | | | | | Case 2: % 154.86/23.61 | | | | | | | % 154.86/23.61 | | | | | | | (238) all_56_15 = e1 % 154.86/23.61 | | | | | | | % 154.86/23.61 | | | | | | | REF_CLOSE: (2), (60), (238) are inconsistent by sub-proof #671. % 154.86/23.61 | | | | | | | % 154.86/23.61 | | | | | | End of split % 154.86/23.61 | | | | | | % 154.86/23.61 | | | | | End of split % 154.86/23.61 | | | | | % 154.86/23.61 | | | | End of split % 154.86/23.61 | | | | % 154.86/23.61 | | | End of split % 154.86/23.61 | | | % 154.86/23.61 | | Case 2: % 154.86/23.61 | | | % 154.86/23.61 | | | (239) all_58_30 = e1 | all_58_31 = e1 % 154.86/23.61 | | | % 154.86/23.61 | | | REF_CLOSE: (1), (30), (60), (61), (239) are inconsistent by sub-proof % 154.86/23.61 | | | #711. % 154.86/23.61 | | | % 154.86/23.61 | | End of split % 154.86/23.61 | | % 154.86/23.61 | End of split % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #590 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_31 = all_4_2 % 154.86/23.61 (2) all_58_20 = e0 % 154.86/23.61 (3) all_58_30 = e0 % 154.86/23.61 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.61 (5) all_58_29 = e1 % 154.86/23.61 (6) ~ (e1 = e0) % 154.86/23.61 (7) all_58_20 = e1 % 154.86/23.61 (8) ~ (all_4_2 = e1) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (2), (7) imply: % 154.86/23.61 | (9) e1 = e0 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (5), (9) imply: % 154.86/23.61 | (10) all_58_29 = e0 % 154.86/23.61 | % 154.86/23.61 | REF_CLOSE: (1), (3), (4), (6), (8), (10) are inconsistent by sub-proof #699. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #591 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2 % 154.86/23.61 (2) all_58_24 = e0 % 154.86/23.61 (3) ~ (e2 = e0) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | ALPHA: (1) implies: % 154.86/23.61 | (4) all_58_24 = e2 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (2), (4) imply: % 154.86/23.61 | (5) e2 = e0 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #592 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_26 = all_6_1 % 154.86/23.61 (2) all_58_26 = e1 % 154.86/23.61 (3) ~ (all_6_1 = e1) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_6_1 = e1 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_6_1 = e1 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #593 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_15 = all_52_2 % 154.86/23.61 (2) all_58_15 = e1 % 154.86/23.61 (3) ~ (all_52_2 = e1) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_52_2 = e1 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_52_2 = e1 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #594 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_31 = all_4_2 % 154.86/23.61 (2) all_58_6 = e0 % 154.86/23.61 (3) all_58_30 = e0 % 154.86/23.61 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.61 (5) all_58_29 = e1 % 154.86/23.61 (6) all_58_6 = e3 % 154.86/23.61 (7) ~ (e1 = e0) % 154.86/23.61 (8) ~ (all_4_2 = e1) % 154.86/23.61 (9) all_58_22 = e1 % 154.86/23.61 (10) all_58_22 = e3 % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (2), (6) imply: % 154.86/23.61 | (11) e3 = e0 % 154.86/23.61 | % 154.86/23.61 | SIMP: (11) implies: % 154.86/23.61 | (12) e3 = e0 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (9), (10) imply: % 154.86/23.61 | (13) e3 = e1 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (12), (13) imply: % 154.86/23.61 | (14) e1 = e0 % 154.86/23.61 | % 154.86/23.61 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (14) are inconsistent by sub-proof % 154.86/23.61 | #677. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #595 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.61 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) % 154.86/23.61 (2) all_58_8 = e0 % 154.86/23.61 (3) ~ (e2 = e0) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | BETA: splitting (1) gives: % 154.86/23.61 | % 154.86/23.61 | Case 1: % 154.86/23.61 | | % 154.86/23.61 | | (4) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0 % 154.86/23.61 | | % 154.86/23.61 | | ALPHA: (4) implies: % 154.86/23.61 | | (5) all_58_8 = e2 % 154.86/23.61 | | % 154.86/23.61 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #596. % 154.86/23.61 | | % 154.86/23.61 | Case 2: % 154.86/23.61 | | % 154.86/23.61 | | (6) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.86/23.61 | | % 154.86/23.61 | | ALPHA: (6) implies: % 154.86/23.61 | | (7) all_58_8 = e2 % 154.86/23.61 | | % 154.86/23.61 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #596. % 154.86/23.61 | | % 154.86/23.61 | End of split % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #596 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_8 = e2 % 154.86/23.61 (2) all_58_8 = e0 % 154.86/23.61 (3) ~ (e2 = e0) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) e2 = e0 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) e2 = e0 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #597 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_31 = all_4_2 % 154.86/23.61 (2) all_58_6 = e0 % 154.86/23.61 (3) all_58_30 = e0 % 154.86/23.61 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.61 (5) all_58_29 = e1 % 154.86/23.61 (6) all_58_6 = e3 % 154.86/23.61 (7) ~ (e1 = e0) % 154.86/23.61 (8) ~ (all_4_2 = e1) % 154.86/23.61 (9) all_58_22 = e1 % 154.86/23.61 (10) all_58_22 = e3 % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (2), (6) imply: % 154.86/23.61 | (11) e3 = e0 % 154.86/23.61 | % 154.86/23.61 | SIMP: (11) implies: % 154.86/23.61 | (12) e3 = e0 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (9), (10) imply: % 154.86/23.61 | (13) e3 = e1 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (12), (13) imply: % 154.86/23.61 | (14) e1 = e0 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (5), (14) imply: % 154.86/23.61 | (15) all_58_29 = e0 % 154.86/23.61 | % 154.86/23.61 | REF_CLOSE: (1), (3), (4), (7), (8), (15) are inconsistent by sub-proof #699. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #598 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3 % 154.86/23.61 (2) all_58_8 = e0 % 154.86/23.61 (3) ~ (e2 = e0) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | ALPHA: (1) implies: % 154.86/23.61 | (4) all_58_8 = e2 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (2), (4) imply: % 154.86/23.61 | (5) e2 = e0 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #599 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2 % 154.86/23.61 (2) all_58_24 = e0 % 154.86/23.61 (3) ~ (e2 = e0) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | ALPHA: (1) implies: % 154.86/23.61 | (4) all_58_24 = e2 % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (2), (4) imply: % 154.86/23.61 | (5) e2 = e0 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #600 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.61 (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.61 (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.86/23.61 (2) all_58_18 = e1 % 154.86/23.61 (3) all_58_23 = e2 % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | BETA: splitting (1) gives: % 154.86/23.61 | % 154.86/23.61 | Case 1: % 154.86/23.61 | | % 154.86/23.61 | | (4) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.61 | | (all_58_19 = e0) % 154.86/23.61 | | % 154.86/23.61 | | ALPHA: (4) implies: % 154.86/23.61 | | (5) ~ (all_58_18 = e1) % 154.86/23.61 | | % 154.86/23.61 | | REDUCE: (2), (5) imply: % 154.86/23.61 | | (6) $false % 154.86/23.61 | | % 154.86/23.61 | | CLOSE: (6) is inconsistent. % 154.86/23.61 | | % 154.86/23.61 | Case 2: % 154.86/23.61 | | % 154.86/23.61 | | (7) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.61 | | (all_58_27 = e0) % 154.86/23.61 | | % 154.86/23.61 | | ALPHA: (7) implies: % 154.86/23.61 | | (8) ~ (all_58_23 = e2) % 154.86/23.61 | | % 154.86/23.61 | | REDUCE: (3), (8) imply: % 154.86/23.61 | | (9) $false % 154.86/23.61 | | % 154.86/23.61 | | CLOSE: (9) is inconsistent. % 154.86/23.61 | | % 154.86/23.61 | End of split % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #601 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) ~ (all_52_13 = e1) % 154.86/23.61 (2) all_54_7 = all_52_13 % 154.86/23.61 (3) ~ (all_52_13 = e2) % 154.86/23.61 (4) ~ (all_52_13 = e3) % 154.86/23.61 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | BETA: splitting (5) gives: % 154.86/23.61 | % 154.86/23.61 | Case 1: % 154.86/23.61 | | % 154.86/23.61 | | (6) all_54_7 = e1 % 154.86/23.61 | | % 154.86/23.61 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #605. % 154.86/23.61 | | % 154.86/23.61 | Case 2: % 154.86/23.61 | | % 154.86/23.61 | | (7) all_54_7 = e3 | all_54_7 = e2 % 154.86/23.61 | | % 154.86/23.61 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #602. % 154.86/23.61 | | % 154.86/23.61 | End of split % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #602 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_54_7 = e3 | all_54_7 = e2 % 154.86/23.61 (2) all_54_7 = all_52_13 % 154.86/23.61 (3) ~ (all_52_13 = e2) % 154.86/23.61 (4) ~ (all_52_13 = e3) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | BETA: splitting (1) gives: % 154.86/23.61 | % 154.86/23.61 | Case 1: % 154.86/23.61 | | % 154.86/23.61 | | (5) all_54_7 = e2 % 154.86/23.61 | | % 154.86/23.61 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #604. % 154.86/23.61 | | % 154.86/23.61 | Case 2: % 154.86/23.61 | | % 154.86/23.61 | | (6) all_54_7 = e3 % 154.86/23.61 | | % 154.86/23.61 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #603. % 154.86/23.61 | | % 154.86/23.61 | End of split % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #603 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_54_7 = all_52_13 % 154.86/23.61 (2) all_54_7 = e3 % 154.86/23.61 (3) ~ (all_52_13 = e3) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_52_13 = e3 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_52_13 = e3 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #604 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_54_7 = all_52_13 % 154.86/23.61 (2) all_54_7 = e2 % 154.86/23.61 (3) ~ (all_52_13 = e2) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_52_13 = e2 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_52_13 = e2 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #605 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_54_7 = all_52_13 % 154.86/23.61 (2) all_54_7 = e1 % 154.86/23.61 (3) ~ (all_52_13 = e1) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_52_13 = e1 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_52_13 = e1 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #606 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_56_10 = all_52_13 % 154.86/23.61 (2) all_56_10 = e1 % 154.86/23.61 (3) ~ (all_52_13 = e1) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_52_13 = e1 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_52_13 = e1 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #607 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_56_12 = all_52_3 % 154.86/23.61 (2) all_56_12 = e0 % 154.86/23.61 (3) ~ (all_52_3 = e0) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | COMBINE_EQS: (1), (2) imply: % 154.86/23.61 | (4) all_52_3 = e0 % 154.86/23.61 | % 154.86/23.61 | SIMP: (4) implies: % 154.86/23.61 | (5) all_52_3 = e0 % 154.86/23.61 | % 154.86/23.61 | REDUCE: (3), (5) imply: % 154.86/23.61 | (6) $false % 154.86/23.61 | % 154.86/23.61 | CLOSE: (6) is inconsistent. % 154.86/23.61 | % 154.86/23.61 End of proof % 154.86/23.61 % 154.86/23.61 Sub-proof #608 shows that the following formulas are inconsistent: % 154.86/23.61 ---------------------------------------------------------------- % 154.86/23.61 (1) all_58_31 = all_4_2 % 154.86/23.61 (2) ~ (all_52_8 = all_52_9) % 154.86/23.61 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 154.86/23.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 154.86/23.61 (4) ~ (all_52_2 = all_52_3) % 154.86/23.61 (5) all_58_11 = all_52_9 % 154.86/23.61 (6) all_56_15 = all_4_2 % 154.86/23.61 (7) all_56_7 = all_52_6 % 154.86/23.61 (8) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 154.86/23.61 (9) all_54_8 = all_52_2 % 154.86/23.61 (10) ~ (all_6_1 = all_4_2) % 154.86/23.61 (11) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.86/23.61 (12) ~ (all_52_8 = all_10_2) % 154.86/23.61 (13) all_58_15 = all_52_2 % 154.86/23.61 (14) op(e1, all_52_14) = all_58_19 % 154.86/23.61 (15) ~ (all_52_11 = all_4_2) % 154.86/23.61 (16) all_58_6 = all_52_12 % 154.86/23.61 (17) ~ (all_52_6 = all_8_2) % 154.86/23.61 (18) all_56_4 = all_52_8 % 154.86/23.61 (19) all_54_3 = all_52_12 % 154.86/23.61 (20) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.61 (21) all_56_2 = e0 | all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.86/23.61 (22) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 154.86/23.61 (23) all_58_13 = all_52_13 % 154.86/23.61 (24) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.86/23.61 (25) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.86/23.61 (26) all_58_20 = all_52_14 % 154.86/23.61 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 % 154.86/23.61 (28) ~ (all_52_12 = all_52_13) % 154.86/23.61 (29) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.86/23.61 (30) op(e0, all_52_3) = all_58_21 % 154.86/23.61 (31) ~ (all_52_6 = all_52_14) % 154.86/23.61 (32) all_54_6 = all_52_9 % 154.86/23.61 (33) all_56_14 = all_6_1 % 154.86/23.61 (34) all_54_15 = all_4_2 % 154.86/23.61 (35) op(e3, e3) = all_10_2 % 154.86/23.61 (36) ~ (all_52_8 = all_52_12) % 154.86/23.61 (37) all_54_9 = all_52_6 % 154.86/23.61 (38) ~ (all_52_13 = all_4_2) % 154.86/23.61 (39) op(e1, e2) = all_52_6 % 154.86/23.61 (40) ~ (all_52_13 = all_8_2) % 154.86/23.61 (41) op(e1, all_52_6) = all_58_16 % 154.86/23.61 (42) ~ (e3 = e1) % 154.86/23.61 (43) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 154.86/23.61 (44) all_56_8 = e0 % 154.86/23.61 (45) ~ (all_52_6 = e0) % 154.86/23.61 (46) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 154.86/23.61 (47) ~ (all_52_1 = all_52_13) % 154.86/23.61 (48) all_56_5 = all_52_9 % 154.86/23.61 (49) all_56_12 = all_52_3 % 154.86/23.61 (50) ~ (all_52_3 = all_52_7) % 154.86/23.61 (51) all_20_2 = all_4_2 % 154.86/23.61 (52) all_56_11 = all_52_14 % 154.86/23.61 (53) all_56_1 = e0 % 154.86/23.61 (54) op(e3, e0) = all_58_1 % 154.86/23.61 (55) all_58_25 = all_6_0 % 154.86/23.61 (56) ~ (all_52_9 = e0) % 154.86/23.61 (57) ~ (all_52_1 = all_8_2) % 154.86/23.61 (58) all_56_3 = all_8_2 % 154.86/23.61 (59) all_58_24 = all_52_7 % 154.86/23.61 (60) ~ (all_52_13 = all_52_14) % 154.86/23.61 (61) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.86/23.61 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.61 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.86/23.61 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.61 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.61 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.86/23.61 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.61 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.61 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.61 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.61 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.61 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.61 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.61 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.61 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.61 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.61 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.61 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.61 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.61 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.61 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.61 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.61 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.61 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.61 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.61 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.86/23.61 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.61 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.61 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.61 e0) % 154.86/23.61 (62) all_56_9 = all_52_12 % 154.86/23.61 (63) all_58_29 = all_8_2 % 154.86/23.61 (64) ~ (all_52_12 = all_52_14) % 154.86/23.61 (65) all_58_30 = e0 % 154.86/23.61 (66) all_58_8 = all_52_1 % 154.86/23.61 (67) ~ (e2 = e1) % 154.86/23.61 (68) op(e3, e0) = all_52_12 % 154.86/23.61 (69) all_56_6 = all_52_2 % 154.86/23.61 (70) ~ (all_52_2 = all_52_6) % 154.86/23.61 (71) all_56_13 = all_52_7 % 154.86/23.61 (72) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.86/23.61 (73) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.61 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.61 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.86/23.61 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.61 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.61 (all_58_27 = e0)) % 154.86/23.61 (74) ~ (all_52_9 = all_52_13) % 154.86/23.61 (75) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.86/23.61 (76) ~ (all_52_11 = all_6_2) % 154.86/23.61 (77) op(e3, all_10_2) = all_58_0 % 154.86/23.61 (78) op(e1, e1) = e0 % 154.86/23.61 (79) ~ (e3 = e0) % 154.86/23.61 (80) all_56_2 = all_52_1 % 154.86/23.61 (81) ~ (all_52_11 = e0) % 154.86/23.61 (82) all_58_26 = all_6_1 % 154.86/23.61 (83) all_56_10 = all_52_13 % 154.86/23.61 (84) ~ (all_52_12 = all_10_2) % 154.86/23.61 (85) ~ (all_52_1 = all_52_3) % 154.86/23.61 (86) op(e0, e1) = all_6_1 % 154.86/23.61 (87) ~ (all_52_9 = all_8_2) % 154.86/23.61 (88) all_56_14 = all_52_11 % 154.86/23.61 (89) all_58_28 = all_10_2 % 154.86/23.61 (90) all_58_17 = all_52_6 % 154.86/23.61 (91) ~ (all_52_1 = all_52_9) % 154.86/23.61 (92) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 154.86/23.61 (93) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 154.86/23.61 (94) op(all_8_2, e2) = all_8_1 % 154.86/23.61 (95) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.86/23.61 (96) ~ (e2 = e0) % 154.86/23.61 (97) ~ (all_52_2 = all_10_2) % 154.86/23.61 (98) all_56_0 = all_10_2 % 154.86/23.61 (99) op(e0, e0) = all_4_2 % 154.86/23.61 (100) all_58_22 = all_52_3 % 154.86/23.61 (101) ~ (all_52_12 = all_4_2) % 154.86/23.61 (102) all_56_1 = e2 | all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.86/23.61 (103) ~ (all_52_1 = all_52_2) % 154.86/23.61 (104) ~ (all_52_7 = all_8_2) % 154.86/23.61 (105) op(e2, e0) = all_52_13 % 154.86/23.61 (106) op(e2, all_52_13) = all_58_12 % 154.86/23.61 (107) all_58_4 = all_52_8 % 154.86/23.61 (108) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.61 (109) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.86/23.61 (110) all_58_2 = e0 % 154.86/23.61 (111) all_54_0 = all_10_2 % 154.86/23.61 (112) ~ (all_52_2 = all_52_14) % 154.86/23.61 (113) ~ (all_52_7 = e0) % 154.86/23.61 (114) ~ (all_52_14 = all_4_2) % 154.86/23.61 (115) ~ (e1 = e0) % 154.86/23.61 (116) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 154.86/23.61 (117) ~ (all_52_7 = all_4_2) % 154.86/23.61 (118) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 154.86/23.61 (119) ~ (all_4_2 = e1) % 154.86/23.61 (120) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 154.86/23.61 (121) ~ (all_52_9 = all_6_1) % 154.86/23.61 (122) all_56_12 = e0 | all_56_13 = e0 | all_56_14 = e0 % 154.86/23.61 (123) all_58_30 = all_6_2 % 154.86/23.61 (124) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.61 (125) ~ (e3 = e2) % 154.86/23.61 (126) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.86/23.61 (127) op(e0, all_6_1) = all_6_0 % 154.86/23.61 (128) all_54_4 = all_52_1 % 154.86/23.61 (129) ~ (all_52_1 = all_10_2) % 154.86/23.61 % 154.86/23.61 Begin of proof % 154.86/23.61 | % 154.86/23.61 | BETA: splitting (122) gives: % 154.86/23.61 | % 154.86/23.61 | Case 1: % 154.86/23.61 | | % 154.86/23.61 | | (130) all_56_12 = e0 % 154.86/23.61 | | % 154.86/23.61 | | COMBINE_EQS: (49), (130) imply: % 154.86/23.61 | | (131) all_52_3 = e0 % 154.86/23.61 | | % 154.86/23.61 | | SIMP: (131) implies: % 154.86/23.61 | | (132) all_52_3 = e0 % 154.86/23.61 | | % 154.86/23.61 | | COMBINE_EQS: (100), (132) imply: % 154.86/23.61 | | (133) all_58_22 = e0 % 154.86/23.61 | | % 154.86/23.61 | | REDUCE: (85), (132) imply: % 154.86/23.61 | | (134) ~ (all_52_1 = e0) % 154.86/23.61 | | % 154.86/23.61 | | REDUCE: (4), (132) imply: % 154.86/23.61 | | (135) ~ (all_52_2 = e0) % 154.86/23.61 | | % 154.86/23.61 | | REDUCE: (50), (132) imply: % 154.86/23.61 | | (136) ~ (all_52_7 = e0) % 154.86/23.61 | | % 154.86/23.61 | | REDUCE: (30), (132) imply: % 154.86/23.61 | | (137) op(e0, e0) = all_58_21 % 154.86/23.61 | | % 154.86/23.61 | | BETA: splitting (21) gives: % 154.86/23.61 | | % 154.86/23.61 | | Case 1: % 154.86/23.61 | | | % 154.86/23.61 | | | (138) all_56_2 = e0 % 154.86/23.61 | | | % 154.86/23.61 | | | COMBINE_EQS: (80), (138) imply: % 154.86/23.61 | | | (139) all_52_1 = e0 % 154.86/23.61 | | | % 154.86/23.61 | | | REDUCE: (134), (139) imply: % 154.86/23.62 | | | (140) $false % 154.86/23.62 | | | % 154.86/23.62 | | | CLOSE: (140) is inconsistent. % 154.86/23.62 | | | % 154.86/23.62 | | Case 2: % 154.86/23.62 | | | % 154.86/23.62 | | | (141) all_56_3 = e0 | all_56_5 = e0 | all_56_10 = e0 % 154.86/23.62 | | | % 154.86/23.62 | | | BETA: splitting (141) gives: % 154.86/23.62 | | | % 154.86/23.62 | | | Case 1: % 154.86/23.62 | | | | % 154.86/23.62 | | | | (142) all_56_3 = e0 % 154.86/23.62 | | | | % 154.86/23.62 | | | | COMBINE_EQS: (58), (142) imply: % 154.86/23.62 | | | | (143) all_8_2 = e0 % 154.86/23.62 | | | | % 154.86/23.62 | | | | COMBINE_EQS: (63), (143) imply: % 154.86/23.62 | | | | (144) all_58_29 = e0 % 154.86/23.62 | | | | % 154.86/23.62 | | | | REF_CLOSE: (1), (20), (42), (51), (65), (67), (79), (89), (92), (96), % 154.86/23.62 | | | | (108), (115), (124), (125), (144) are inconsistent by % 154.86/23.62 | | | | sub-proof #691. % 154.86/23.62 | | | | % 154.86/23.62 | | | Case 2: % 154.86/23.62 | | | | % 154.86/23.62 | | | | (145) all_56_5 = e0 | all_56_10 = e0 % 154.86/23.62 | | | | % 154.86/23.62 | | | | BETA: splitting (145) gives: % 154.86/23.62 | | | | % 154.86/23.62 | | | | Case 1: % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | (146) all_56_5 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | COMBINE_EQS: (48), (146) imply: % 154.86/23.62 | | | | | (147) all_52_9 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (56), (147) imply: % 154.86/23.62 | | | | | (148) $false % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | CLOSE: (148) is inconsistent. % 154.86/23.62 | | | | | % 154.86/23.62 | | | | Case 2: % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | (149) all_56_10 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | COMBINE_EQS: (83), (149) imply: % 154.86/23.62 | | | | | (150) all_52_13 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | SIMP: (150) implies: % 154.86/23.62 | | | | | (151) all_52_13 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | COMBINE_EQS: (23), (151) imply: % 154.86/23.62 | | | | | (152) all_58_13 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (28), (151) imply: % 154.86/23.62 | | | | | (153) ~ (all_52_12 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (60), (151) imply: % 154.86/23.62 | | | | | (154) ~ (all_52_14 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | SIMP: (154) implies: % 154.86/23.62 | | | | | (155) ~ (all_52_14 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (40), (151) imply: % 154.86/23.62 | | | | | (156) ~ (all_8_2 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | SIMP: (156) implies: % 154.86/23.62 | | | | | (157) ~ (all_8_2 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (38), (151) imply: % 154.86/23.62 | | | | | (158) ~ (all_4_2 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | SIMP: (158) implies: % 154.86/23.62 | | | | | (159) ~ (all_4_2 = e0) % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (106), (151) imply: % 154.86/23.62 | | | | | (160) op(e2, e0) = all_58_12 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | REDUCE: (105), (151) imply: % 154.86/23.62 | | | | | (161) op(e2, e0) = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | GROUND_INST: instantiating (3) with all_4_2, all_58_21, e0, e0, % 154.86/23.62 | | | | | simplifying with (99), (137) gives: % 154.86/23.62 | | | | | (162) all_58_21 = all_4_2 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | GROUND_INST: instantiating (3) with e0, all_58_12, e0, e2, simplifying % 154.86/23.62 | | | | | with (160), (161) gives: % 154.86/23.62 | | | | | (163) all_58_12 = e0 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | GROUND_INST: instantiating (3) with all_52_12, all_58_1, e0, e3, % 154.86/23.62 | | | | | simplifying with (54), (68) gives: % 154.86/23.62 | | | | | (164) all_58_1 = all_52_12 % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | BETA: splitting (120) gives: % 154.86/23.62 | | | | | % 154.86/23.62 | | | | | Case 1: % 154.86/23.62 | | | | | | % 154.86/23.62 | | | | | | (165) all_54_6 = e0 % 154.86/23.62 | | | | | | % 154.86/23.62 | | | | | | REF_CLOSE: (32), (56), (165) are inconsistent by sub-proof #797. % 154.86/23.62 | | | | | | % 154.86/23.62 | | | | | Case 2: % 154.86/23.62 | | | | | | % 154.86/23.62 | | | | | | (166) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.86/23.62 | | | | | | % 154.86/23.62 | | | | | | BETA: splitting (8) gives: % 154.86/23.62 | | | | | | % 154.86/23.62 | | | | | | Case 1: % 154.86/23.62 | | | | | | | % 154.86/23.62 | | | | | | | (167) all_54_3 = e0 % 154.86/23.62 | | | | | | | % 154.86/23.62 | | | | | | | REF_CLOSE: (19), (153), (167) are inconsistent by sub-proof #733. % 154.86/23.62 | | | | | | | % 154.86/23.62 | | | | | | Case 2: % 154.86/23.62 | | | | | | | % 154.86/23.62 | | | | | | | (168) ~ (all_54_3 = e0) % 154.86/23.62 | | | | | | | (169) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.86/23.62 | | | | | | | % 154.86/23.62 | | | | | | | BETA: splitting (72) gives: % 154.86/23.62 | | | | | | | % 154.86/23.62 | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | % 154.86/23.62 | | | | | | | | (170) all_54_4 = e0 % 154.86/23.62 | | | | | | | | % 154.86/23.62 | | | | | | | | REF_CLOSE: (128), (134), (170) are inconsistent by sub-proof % 154.86/23.62 | | | | | | | | #859. % 154.86/23.62 | | | | | | | | % 154.86/23.62 | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | % 154.86/23.62 | | | | | | | | (171) ~ (all_54_4 = e0) % 154.86/23.62 | | | | | | | | (172) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.86/23.62 | | | | | | | | % 154.86/23.62 | | | | | | | | BETA: splitting (95) gives: % 154.86/23.62 | | | | | | | | % 154.86/23.62 | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | (173) all_56_12 = e1 % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | COMBINE_EQS: (130), (173) imply: % 154.86/23.62 | | | | | | | | | (174) e1 = e0 % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | REDUCE: (115), (174) imply: % 154.86/23.62 | | | | | | | | | (175) $false % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | CLOSE: (175) is inconsistent. % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | (176) ~ (all_56_12 = e1) % 154.86/23.62 | | | | | | | | | (177) all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | REDUCE: (130), (176) imply: % 154.86/23.62 | | | | | | | | | (178) ~ (e1 = e0) % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | BETA: splitting (46) gives: % 154.86/23.62 | | | | | | | | | % 154.86/23.62 | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | (179) all_54_0 = e0 % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | REF_CLOSE: (1), (20), (42), (51), (63), (65), (67), (79), % 154.86/23.62 | | | | | | | | | | (89), (92), (96), (108), (111), (115), (124), % 154.86/23.62 | | | | | | | | | | (125), (179) are inconsistent by sub-proof #678. % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | (180) ~ (all_54_0 = e0) % 154.86/23.62 | | | | | | | | | | (181) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | REDUCE: (111), (180) imply: % 154.86/23.62 | | | | | | | | | | (182) ~ (all_10_2 = e0) % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | BETA: splitting (75) gives: % 154.86/23.62 | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | (183) all_56_9 = e1 % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | COMBINE_EQS: (62), (183) imply: % 154.86/23.62 | | | | | | | | | | | (184) all_52_12 = e1 % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | SIMP: (184) implies: % 154.86/23.62 | | | | | | | | | | | (185) all_52_12 = e1 % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | COMBINE_EQS: (16), (185) imply: % 154.86/23.62 | | | | | | | | | | | (186) all_58_6 = e1 % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | REDUCE: (36), (185) imply: % 154.86/23.62 | | | | | | | | | | | (187) ~ (all_52_8 = e1) % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | REDUCE: (84), (185) imply: % 154.86/23.62 | | | | | | | | | | | (188) ~ (all_10_2 = e1) % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | SIMP: (188) implies: % 154.86/23.62 | | | | | | | | | | | (189) ~ (all_10_2 = e1) % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | REDUCE: (101), (185) imply: % 154.86/23.62 | | | | | | | | | | | (190) ~ (all_4_2 = e1) % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | BETA: splitting (124) gives: % 154.86/23.62 | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | (191) all_58_28 = e1 % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | COMBINE_EQS: (89), (191) imply: % 154.86/23.62 | | | | | | | | | | | | (192) all_10_2 = e1 % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | REDUCE: (189), (192) imply: % 154.86/23.62 | | | | | | | | | | | | (193) $false % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | CLOSE: (193) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | (194) ~ (all_58_28 = e1) % 154.86/23.62 | | | | | | | | | | | | (195) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | BETA: splitting (195) gives: % 154.86/23.62 | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | (196) all_58_29 = e1 % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | COMBINE_EQS: (63), (196) imply: % 154.86/23.62 | | | | | | | | | | | | | (197) all_8_2 = e1 % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | COMBINE_EQS: (58), (197) imply: % 154.86/23.62 | | | | | | | | | | | | | (198) all_56_3 = e1 % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | REDUCE: (104), (197) imply: % 154.86/23.62 | | | | | | | | | | | | | (199) ~ (all_52_7 = e1) % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | REDUCE: (87), (197) imply: % 154.86/23.62 | | | | | | | | | | | | | (200) ~ (all_52_9 = e1) % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | REDUCE: (94), (197) imply: % 154.86/23.62 | | | | | | | | | | | | | (201) op(e1, e2) = all_8_1 % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | BETA: splitting (93) gives: % 154.86/23.62 | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | (202) all_56_6 = e1 % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | COMBINE_EQS: (69), (202) imply: % 154.86/23.62 | | | | | | | | | | | | | | (203) all_52_2 = e1 % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | SIMP: (203) implies: % 154.86/23.62 | | | | | | | | | | | | | | (204) all_52_2 = e1 % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | COMBINE_EQS: (13), (204) imply: % 154.86/23.62 | | | | | | | | | | | | | | (205) all_58_15 = e1 % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | REDUCE: (103), (204) imply: % 154.86/23.62 | | | | | | | | | | | | | | (206) ~ (all_52_1 = e1) % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | REDUCE: (112), (204) imply: % 154.86/23.62 | | | | | | | | | | | | | | (207) ~ (all_52_14 = e1) % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | SIMP: (207) implies: % 154.86/23.62 | | | | | | | | | | | | | | (208) ~ (all_52_14 = e1) % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | BETA: splitting (29) gives: % 154.86/23.62 | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | (209) all_56_4 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | COMBINE_EQS: (18), (209) imply: % 154.86/23.62 | | | | | | | | | | | | | | | (210) all_52_8 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | REDUCE: (187), (210) imply: % 154.86/23.62 | | | | | | | | | | | | | | | (211) $false % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | (212) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | BETA: splitting (61) gives: % 154.86/23.62 | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | (213) all_58_31 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (42), (65), (67), (79), (96), (108), (125), % 154.86/23.62 | | | | | | | | | | | | | | | | (196), (213) are inconsistent by sub-proof #713. % 154.86/23.62 | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | (214) ~ (all_58_31 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | (215) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | % 154.86/23.62 | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.86/23.62 | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.86/23.62 | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.86/23.62 | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.86/23.62 | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.86/23.62 | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.62 | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.86/23.62 | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.86/23.62 | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.62 | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.86/23.62 | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.86/23.62 | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.86/23.62 | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.86/23.62 | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.86/23.62 | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.86/23.62 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.86/23.62 | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.62 | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.86/23.62 | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.86/23.62 | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.62 | | | | | | | | | | | | | | | | e0) % 154.86/23.62 | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | (216) all_58_30 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (216) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | (217) e1 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (65), (115), (119), (195), (196), (217) are % 154.86/23.62 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #677. % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | (218) ~ (all_58_30 = e1) % 154.86/23.62 | | | | | | | | | | | | | | | | | (219) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) % 154.86/23.62 | | | | | | | | | | | | | | | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.86/23.62 | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 % 154.86/23.62 | | | | | | | | | | | | | | | | | = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.86/23.62 | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.86/23.62 | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.86/23.62 | | | | | | | | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 % 154.86/23.62 | | | | | | | | | | | | | | | | | = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.86/23.62 | | | | | | | | | | | | | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.86/23.62 | | | | | | | | | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | & all_58_26 = e0 & e1 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | (220) all_58_29 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (196), (220) are inconsistent by sub-proof % 154.86/23.62 | | | | | | | | | | | | | | | | | | #687. % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | (221) ~ (all_58_29 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | (222) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e0) | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | & all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.62 | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.62 | | | | | | | | | | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.62 | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.86/23.62 | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.62 | | | | | | | | | | | | | | | | | | e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | REDUCE: (196), (221) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | (223) ~ (e2 = e1) % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (224) all_58_28 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (224) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (225) all_10_2 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | REDUCE: (77), (225) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (226) op(e3, e3) = all_58_0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | REDUCE: (35), (225) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (227) op(e3, e3) = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | (228) all_58_28 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (228) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | (229) e3 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (229) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | (230) $false % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | (231) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | (232) all_58_29 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (196), (232) are inconsistent by sub-proof % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | #687. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | (233) all_58_30 = e2 | all_58_31 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | (234) all_56_5 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (234) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | (235) all_52_9 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (235) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | (236) $false % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | (237) all_56_8 = e1 | all_56_14 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_30 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (96), (238) are inconsistent by sub-proof % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | #718. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_31 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (239) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | (240) all_4_2 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (240) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | (241) ~ (all_52_7 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (240) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | (242) ~ (all_6_1 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | (243) all_56_13 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (199), (243) are inconsistent by sub-proof % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | #676. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | (244) all_56_14 = e1 | all_56_15 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_56_6 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (245) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | (246) e2 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (246) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | (247) e2 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (247) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_31 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (67), (96), (233), (248) are inconsistent by % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_56_1 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (250) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (251) e2 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (251) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (252) e2 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (252) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_31 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (96), (233), (253) are inconsistent by % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #674. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_56_1 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_56_3 = e2 | all_56_7 = e2 | all_56_13 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (254) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (e2 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_56_8 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (257) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e1 = e0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (15), (76), (81), (88), (119), (123), % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (196), (244), (258) are inconsistent by % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #670. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_56_14 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (259) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_6_1 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (260) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_6_1 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (261) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) op(e0, e1) = all_6_0 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (261) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) op(e0, e1) = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_56_7 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (264) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_52_6 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (265) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) op(e1, e2) = all_58_16 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (265) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) op(e1, e2) = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_6_0, e1, e0, % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (262), (263) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_6_0 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_8_1, all_58_16, e2, e1, % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (201), (266) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_16 = all_8_1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_58_16, e2, e1, % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (266), (267) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_16 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_58_0, e3, e3, % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (226), (227) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_0 = e3 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (270) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_8_1 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (268) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_58_25 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (271), (274) are inconsistent by sub-proof % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #669. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) ~ (all_58_16 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (277) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) $false % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) ~ (all_58_25 = e1) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (280) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) $false % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) ~ (all_56_7 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (282) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_52_6 = e2) % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_56_3 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (198), (284) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) e2 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (285) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) e2 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (286) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_58_31 = e1 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (67), (96), (233), (287) are inconsistent by % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_56_7 = e2 | all_56_13 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_56_7 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (289) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_52_6 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (283), (290) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) $false % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_56_13 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (292) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_52_7 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_52_7 = e2 % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (241), (294) imply: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent. % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.62 | | | | | | | | | | | | | | | | | | | % 154.86/23.62 | | | | | | | | | | | | | | | | | | | (296) ~ (all_58_28 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (297) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e2) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_13 = e2 & all_58_24 = e2) | (all_58_2 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | & all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.63 | | | | | | | | | | | | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.63 | | | | | | | | | | | | | | | | | | | e0) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | REDUCE: (89), (296) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (298) ~ (all_10_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (299) all_56_13 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (199), (299) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | #676. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (300) all_56_14 = e1 | all_56_15 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (301) all_58_28 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (301) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (302) all_10_2 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (302) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (303) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (304) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (305) all_56_0 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (305) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (306) all_10_2 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (306) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (307) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (308) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (309) all_56_1 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (79), (309) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | #668. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (310) ~ (all_56_1 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (311) all_56_4 = e3 | all_56_9 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (310) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (312) ~ (e3 = e0) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (313) all_56_14 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (313) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (314) all_6_1 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (315) all_6_1 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (315) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (316) all_58_26 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (18), (20), (25), (26), (42), (59), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (65), (66), (72), (80), (89), (98), (107), (108), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (109), (110), (111), (113), (115), (119), (123), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (124), (128), (129), (133), (134), (152), (181), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (182), (183), (186), (189), (195), (196), (205), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (297), (311), (316) are inconsistent % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #641. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (317) all_56_15 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (317) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (318) all_4_2 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (319) all_4_2 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (319) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_31 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (65), (79), (196), (304), (320) are % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | (321) ~ (all_56_6 = e1) % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | REDUCE: (69), (321) imply: % 154.86/23.63 | | | | | | | | | | | | | | (322) ~ (all_52_2 = e1) % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | REF_CLOSE: (1), (24), (57), (63), (65), (69), (80), (89), % 154.86/23.63 | | | | | | | | | | | | | | (98), (115), (119), (124), (130), (157), (189), % 154.86/23.63 | | | | | | | | | | | | | | (322) are inconsistent by sub-proof #636. % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | (323) all_58_30 = e1 | all_58_31 = e1 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REF_CLOSE: (1), (65), (115), (119), (323) are inconsistent by % 154.86/23.63 | | | | | | | | | | | | | sub-proof #711. % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | (324) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 154.86/23.63 | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | BETA: splitting (324) gives: % 154.86/23.63 | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | (325) all_56_10 = e1 % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | COMBINE_EQS: (149), (325) imply: % 154.86/23.63 | | | | | | | | | | | | (326) e1 = e0 % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | REDUCE: (115), (326) imply: % 154.86/23.63 | | | | | | | | | | | | (327) $false % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | CLOSE: (327) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | (328) all_56_11 = e1 | all_56_15 = e1 % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | BETA: splitting (328) gives: % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | (329) all_56_11 = e1 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | COMBINE_EQS: (52), (329) imply: % 154.86/23.63 | | | | | | | | | | | | | (330) all_52_14 = e1 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | SIMP: (330) implies: % 154.86/23.63 | | | | | | | | | | | | | (331) all_52_14 = e1 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | COMBINE_EQS: (26), (331) imply: % 154.86/23.63 | | | | | | | | | | | | | (332) all_58_20 = e1 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REDUCE: (112), (331) imply: % 154.86/23.63 | | | | | | | | | | | | | (333) ~ (all_52_2 = e1) % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REDUCE: (31), (331) imply: % 154.86/23.63 | | | | | | | | | | | | | (334) ~ (all_52_6 = e1) % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REDUCE: (64), (331) imply: % 154.86/23.63 | | | | | | | | | | | | | (335) ~ (all_52_12 = e1) % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REDUCE: (114), (331) imply: % 154.86/23.63 | | | | | | | | | | | | | (336) ~ (all_4_2 = e1) % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REDUCE: (14), (331) imply: % 154.86/23.63 | | | | | | | | | | | | | (337) op(e1, e1) = all_58_19 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_58_19, e1, e1, % 154.86/23.63 | | | | | | | | | | | | | simplifying with (78), (337) gives: % 154.86/23.63 | | | | | | | | | | | | | (338) all_58_19 = e0 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | BETA: splitting (22) gives: % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | (339) all_54_8 = e0 % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | REF_CLOSE: (9), (135), (339) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | #731. % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | (340) ~ (all_54_8 = e0) % 154.86/23.63 | | | | | | | | | | | | | | (341) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | BETA: splitting (43) gives: % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | (342) all_54_9 = e0 % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | COMBINE_EQS: (37), (342) imply: % 154.86/23.63 | | | | | | | | | | | | | | | (343) all_52_6 = e0 % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | REDUCE: (45), (343) imply: % 154.86/23.63 | | | | | | | | | | | | | | | (344) $false % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | CLOSE: (344) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | (345) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | BETA: splitting (118) gives: % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | (346) all_56_6 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (346) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | (347) all_52_2 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | SIMP: (347) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | (348) all_52_2 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (348) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | (349) all_58_15 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | REDUCE: (103), (348) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | (350) ~ (all_52_1 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | REDUCE: (70), (348) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | (351) ~ (all_52_6 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | SIMP: (351) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | (352) ~ (all_52_6 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | REDUCE: (97), (348) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | (353) ~ (all_10_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | SIMP: (353) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | (354) ~ (all_10_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | (355) all_56_6 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (355) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | (356) e3 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | SIMP: (356) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | (357) e3 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | REDUCE: (125), (357) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | (358) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | CLOSE: (358) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | (359) all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | BETA: splitting (359) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | (360) all_56_7 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (360) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (361) all_52_6 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | SIMP: (361) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (362) all_52_6 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (362) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (363) all_58_17 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (364) all_58_28 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (16), (32), (57), (59), (61), (63), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (65), (66), (79), (82), (89), (91), (107), (110), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (113), (121), (128), (129), (133), (134), (152), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (153), (159), (166), (172), (182), (332), (349), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (350), (354), (363), (364) are inconsistent by % 154.86/23.63 | | | | | | | | | | | | | | | | | | | sub-proof #623. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (365) ~ (all_58_28 = e1) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | REDUCE: (89), (365) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (366) ~ (all_10_2 = e1) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (24), (57), (63), (65), (69), (80), (89), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (98), (115), (119), (124), (130), (157), (333), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (366) are inconsistent by sub-proof #636. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | (367) ~ (all_56_7 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | REDUCE: (7), (367) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (368) ~ (all_52_6 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (334), (345), (352), (368) are inconsistent % 154.86/23.63 | | | | | | | | | | | | | | | | | | by sub-proof #619. % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | (369) ~ (all_56_6 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | REDUCE: (69), (369) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | (370) ~ (all_52_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | (371) all_54_8 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (333), (371) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | | | | #618. % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | (372) all_54_8 = e3 | all_54_8 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | (373) all_54_8 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (373) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (374) all_52_2 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | SIMP: (374) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (375) all_52_2 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | REDUCE: (70), (375) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (376) ~ (all_52_6 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | SIMP: (376) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | (377) ~ (all_52_6 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (378) all_54_9 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (378) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (379) all_52_6 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | REDUCE: (334), (379) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (380) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | CLOSE: (380) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | (381) all_54_9 = e3 | all_54_9 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (382) all_54_9 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (382) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (383) all_52_6 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | REDUCE: (377), (383) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (384) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | CLOSE: (384) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (385) all_54_9 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (385) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (386) all_52_6 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (386) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (387) ~ (all_8_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | SIMP: (387) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | (388) ~ (all_8_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (389) all_56_9 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (389) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (390) all_52_12 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (391) all_52_12 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (391) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (392) all_58_1 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (391) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (393) ~ (all_4_2 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | SIMP: (393) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_4_2 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (395) all_54_15 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (395) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (396) all_4_2 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (396) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (397) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (397) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (398) all_54_15 = e3 | all_54_15 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (399) all_54_15 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (399) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (400) all_4_2 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (400) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (401) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (401) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (402) all_54_15 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (402) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (403) all_4_2 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (403) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (404) all_58_21 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (163), (338), (392), (404) are inconsistent % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #615. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (405) ~ (all_56_9 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (405) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | (406) ~ (all_52_12 = e2) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (407) all_54_3 = e1 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (335), (407) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | #723. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (408) ~ (all_54_3 = e1) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | (409) all_54_3 = e3 | all_54_3 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (410) all_54_3 = e2 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (406), (410) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | #614. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (411) all_54_3 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (411) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (412) all_52_12 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (412) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (413) all_52_12 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (413) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (414) ~ (all_10_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (414) implies: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | (415) ~ (all_10_2 = e3) % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (416) all_58_28 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (416) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (417) all_10_2 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (417) imply: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (418) $false % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (418) is inconsistent. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (419) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (11), (19), (62), (63), (65), (73), (79), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (101), (162), (163), (164), (169), (335), (338), % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | (388), (419) are inconsistent by sub-proof #610. % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | (420) all_54_8 = e3 % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (370), (420) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | | | | | | #786. % 154.86/23.63 | | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | Case 2: % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | (421) all_56_15 = e1 % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | | REF_CLOSE: (6), (119), (421) are inconsistent by sub-proof % 154.86/23.63 | | | | | | | | | | | | | #671. % 154.86/23.63 | | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | | % 154.86/23.63 | | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | | % 154.86/23.63 | | | | | | | | | End of split % 154.86/23.63 | | | | | | | | | % 154.86/23.63 | | | | | | | | End of split % 154.86/23.63 | | | | | | | | % 154.86/23.63 | | | | | | | End of split % 154.86/23.63 | | | | | | | % 154.86/23.63 | | | | | | End of split % 154.86/23.63 | | | | | | % 154.86/23.63 | | | | | End of split % 154.86/23.63 | | | | | % 154.86/23.63 | | | | End of split % 154.86/23.63 | | | | % 154.86/23.63 | | | End of split % 154.86/23.63 | | | % 154.86/23.63 | | End of split % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (422) all_56_13 = e0 | all_56_14 = e0 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (71), (81), (88), (113), (422) are inconsistent by sub-proof % 154.86/23.63 | | #609. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #609 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) all_56_13 = e0 | all_56_14 = e0 % 154.86/23.63 (2) all_56_13 = all_52_7 % 154.86/23.63 (3) ~ (all_52_11 = e0) % 154.86/23.63 (4) all_56_14 = all_52_11 % 154.86/23.63 (5) ~ (all_52_7 = e0) % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (1) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (6) all_56_13 = e0 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #802. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (7) all_56_14 = e0 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #806. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #610 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) all_58_12 = e0 % 154.86/23.63 (2) all_58_31 = all_4_2 % 154.86/23.63 (3) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.86/23.63 (4) all_54_3 = all_52_12 % 154.86/23.63 (5) ~ (all_8_2 = e3) % 154.86/23.63 (6) all_58_19 = e0 % 154.86/23.63 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.86/23.63 (8) all_56_9 = all_52_12 % 154.86/23.63 (9) all_58_29 = all_8_2 % 154.86/23.63 (10) all_58_30 = e0 % 154.86/23.63 (11) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.63 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.63 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.86/23.63 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.63 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.63 (all_58_27 = e0)) % 154.86/23.63 (12) ~ (e3 = e0) % 154.86/23.63 (13) ~ (all_52_12 = e1) % 154.86/23.63 (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.63 (15) all_58_21 = all_4_2 % 154.86/23.63 (16) ~ (all_52_12 = all_4_2) % 154.86/23.63 (17) all_58_1 = all_52_12 % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (14) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (18) all_58_29 = e3 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (5), (9), (18) are inconsistent by sub-proof #756. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (19) all_58_30 = e3 | all_58_31 = e3 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (15), % 154.86/23.63 | | (16), (17), (19) are inconsistent by sub-proof #611. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #611 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) all_58_12 = e0 % 154.86/23.63 (2) all_58_31 = all_4_2 % 154.86/23.63 (3) all_56_9 = e2 | all_56_10 = e2 | all_56_11 = e2 | all_56_15 = e2 % 154.86/23.63 (4) all_54_3 = all_52_12 % 154.86/23.63 (5) all_58_19 = e0 % 154.86/23.63 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.86/23.63 (7) all_56_9 = all_52_12 % 154.86/23.63 (8) all_58_30 = e0 % 154.86/23.63 (9) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.63 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.63 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.86/23.63 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.63 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.63 (all_58_27 = e0)) % 154.86/23.63 (10) ~ (e3 = e0) % 154.86/23.63 (11) ~ (all_52_12 = e1) % 154.86/23.63 (12) all_58_21 = all_4_2 % 154.86/23.63 (13) all_58_30 = e3 | all_58_31 = e3 % 154.86/23.63 (14) ~ (all_52_12 = all_4_2) % 154.86/23.63 (15) all_58_1 = all_52_12 % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (13) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (16) all_58_30 = e3 % 154.86/23.63 | | % 154.86/23.63 | | COMBINE_EQS: (8), (16) imply: % 154.86/23.63 | | (17) e3 = e0 % 154.86/23.63 | | % 154.86/23.63 | | REDUCE: (10), (17) imply: % 154.86/23.63 | | (18) $false % 154.86/23.63 | | % 154.86/23.63 | | CLOSE: (18) is inconsistent. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (19) all_58_31 = e3 % 154.86/23.63 | | % 154.86/23.63 | | COMBINE_EQS: (2), (19) imply: % 154.86/23.63 | | (20) all_4_2 = e3 % 154.86/23.63 | | % 154.86/23.63 | | SIMP: (20) implies: % 154.86/23.63 | | (21) all_4_2 = e3 % 154.86/23.63 | | % 154.86/23.63 | | COMBINE_EQS: (12), (21) imply: % 154.86/23.63 | | (22) all_58_21 = e3 % 154.86/23.63 | | % 154.86/23.63 | | REDUCE: (14), (21) imply: % 154.86/23.63 | | (23) ~ (all_52_12 = e3) % 154.86/23.63 | | % 154.86/23.63 | | BETA: splitting (3) gives: % 154.86/23.63 | | % 154.86/23.63 | | Case 1: % 154.86/23.63 | | | % 154.86/23.63 | | | (24) all_56_9 = e2 % 154.86/23.63 | | | % 154.86/23.63 | | | COMBINE_EQS: (7), (24) imply: % 154.86/23.63 | | | (25) all_52_12 = e2 % 154.86/23.63 | | | % 154.86/23.63 | | | SIMP: (25) implies: % 154.86/23.63 | | | (26) all_52_12 = e2 % 154.86/23.63 | | | % 154.86/23.63 | | | COMBINE_EQS: (15), (26) imply: % 154.86/23.63 | | | (27) all_58_1 = e2 % 154.86/23.63 | | | % 154.86/23.63 | | | REF_CLOSE: (1), (5), (9), (22), (27) are inconsistent by sub-proof #615. % 154.86/23.63 | | | % 154.86/23.63 | | Case 2: % 154.86/23.63 | | | % 154.86/23.63 | | | (28) ~ (all_56_9 = e2) % 154.86/23.63 | | | % 154.86/23.63 | | | REDUCE: (7), (28) imply: % 154.86/23.63 | | | (29) ~ (all_52_12 = e2) % 154.86/23.63 | | | % 154.86/23.63 | | | REF_CLOSE: (4), (6), (11), (23), (29) are inconsistent by sub-proof #612. % 154.86/23.63 | | | % 154.86/23.63 | | End of split % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #612 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) ~ (all_52_12 = e3) % 154.86/23.63 (2) all_54_3 = all_52_12 % 154.86/23.63 (3) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 154.86/23.63 (4) ~ (all_52_12 = e1) % 154.86/23.63 (5) ~ (all_52_12 = e2) % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (3) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (6) all_54_3 = e1 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #723. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (7) all_54_3 = e3 | all_54_3 = e2 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #613. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #613 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) all_54_3 = e3 | all_54_3 = e2 % 154.86/23.63 (2) all_54_3 = all_52_12 % 154.86/23.63 (3) ~ (all_52_12 = e2) % 154.86/23.63 (4) ~ (all_52_12 = e3) % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (1) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (5) all_54_3 = e2 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #614. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (6) all_54_3 = e3 % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #721. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #614 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) all_54_3 = all_52_12 % 154.86/23.63 (2) all_54_3 = e2 % 154.86/23.63 (3) ~ (all_52_12 = e2) % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | COMBINE_EQS: (1), (2) imply: % 154.86/23.63 | (4) all_52_12 = e2 % 154.86/23.63 | % 154.86/23.63 | SIMP: (4) implies: % 154.86/23.63 | (5) all_52_12 = e2 % 154.86/23.63 | % 154.86/23.63 | REDUCE: (3), (5) imply: % 154.86/23.63 | (6) $false % 154.86/23.63 | % 154.86/23.63 | CLOSE: (6) is inconsistent. % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #615 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) all_58_12 = e0 % 154.86/23.63 (2) all_58_19 = e0 % 154.86/23.63 (3) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.63 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.63 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 154.86/23.63 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 154.86/23.63 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.63 (all_58_27 = e0)) % 154.86/23.63 (4) all_58_21 = e3 % 154.86/23.63 (5) all_58_1 = e2 % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (3) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (6) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.63 | | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.63 | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #617. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (7) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.63 | | (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.63 | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.86/23.63 | | % 154.86/23.63 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #616. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #616 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.63 (1) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.63 (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 154.86/23.63 (all_58_25 = e1) & ~ (all_58_27 = e0)) % 154.86/23.63 (2) all_58_19 = e0 % 154.86/23.63 (3) all_58_21 = e3 % 154.86/23.63 % 154.86/23.63 Begin of proof % 154.86/23.63 | % 154.86/23.63 | BETA: splitting (1) gives: % 154.86/23.63 | % 154.86/23.63 | Case 1: % 154.86/23.63 | | % 154.86/23.63 | | (4) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 154.86/23.63 | | (all_58_19 = e0) % 154.86/23.63 | | % 154.86/23.63 | | ALPHA: (4) implies: % 154.86/23.63 | | (5) ~ (all_58_19 = e0) % 154.86/23.63 | | % 154.86/23.63 | | REDUCE: (2), (5) imply: % 154.86/23.63 | | (6) $false % 154.86/23.63 | | % 154.86/23.63 | | CLOSE: (6) is inconsistent. % 154.86/23.63 | | % 154.86/23.63 | Case 2: % 154.86/23.63 | | % 154.86/23.63 | | (7) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 154.86/23.63 | | (all_58_27 = e0) % 154.86/23.63 | | % 154.86/23.63 | | ALPHA: (7) implies: % 154.86/23.63 | | (8) ~ (all_58_21 = e3) % 154.86/23.63 | | % 154.86/23.63 | | REDUCE: (3), (8) imply: % 154.86/23.63 | | (9) $false % 154.86/23.63 | | % 154.86/23.63 | | CLOSE: (9) is inconsistent. % 154.86/23.63 | | % 154.86/23.63 | End of split % 154.86/23.63 | % 154.86/23.63 End of proof % 154.86/23.63 % 154.86/23.63 Sub-proof #617 shows that the following formulas are inconsistent: % 154.86/23.63 ---------------------------------------------------------------- % 154.86/23.64 (1) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.64 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 154.86/23.64 (all_58_10 = e1) & ~ (all_58_12 = e0)) % 154.86/23.64 (2) all_58_1 = e2 % 154.86/23.64 (3) all_58_12 = e0 % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | BETA: splitting (1) gives: % 154.86/23.64 | % 154.86/23.64 | Case 1: % 154.86/23.64 | | % 154.86/23.64 | | (4) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 154.86/23.64 | | (all_58_5 = e0) % 154.86/23.64 | | % 154.86/23.64 | | ALPHA: (4) implies: % 154.86/23.64 | | (5) ~ (all_58_1 = e2) % 154.86/23.64 | | % 154.86/23.64 | | REDUCE: (2), (5) imply: % 154.86/23.64 | | (6) $false % 154.86/23.64 | | % 154.86/23.64 | | CLOSE: (6) is inconsistent. % 154.86/23.64 | | % 154.86/23.64 | Case 2: % 154.86/23.64 | | % 154.86/23.64 | | (7) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 154.86/23.64 | | (all_58_12 = e0) % 154.86/23.64 | | % 154.86/23.64 | | ALPHA: (7) implies: % 154.86/23.64 | | (8) ~ (all_58_12 = e0) % 154.86/23.64 | | % 154.86/23.64 | | REDUCE: (3), (8) imply: % 154.86/23.64 | | (9) $false % 154.86/23.64 | | % 154.86/23.64 | | CLOSE: (9) is inconsistent. % 154.86/23.64 | | % 154.86/23.64 | End of split % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #618 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) all_54_8 = all_52_2 % 154.86/23.64 (2) all_54_8 = e1 % 154.86/23.64 (3) ~ (all_52_2 = e1) % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | COMBINE_EQS: (1), (2) imply: % 154.86/23.64 | (4) all_52_2 = e1 % 154.86/23.64 | % 154.86/23.64 | SIMP: (4) implies: % 154.86/23.64 | (5) all_52_2 = e1 % 154.86/23.64 | % 154.86/23.64 | REDUCE: (3), (5) imply: % 154.86/23.64 | (6) $false % 154.86/23.64 | % 154.86/23.64 | CLOSE: (6) is inconsistent. % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #619 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) ~ (all_52_6 = e2) % 154.86/23.64 (2) ~ (all_52_6 = e3) % 154.86/23.64 (3) ~ (all_52_6 = e1) % 154.86/23.64 (4) all_54_9 = all_52_6 % 154.86/23.64 (5) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | BETA: splitting (5) gives: % 154.86/23.64 | % 154.86/23.64 | Case 1: % 154.86/23.64 | | % 154.86/23.64 | | (6) all_54_9 = e1 % 154.86/23.64 | | % 154.86/23.64 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #622. % 154.86/23.64 | | % 154.86/23.64 | Case 2: % 154.86/23.64 | | % 154.86/23.64 | | (7) all_54_9 = e3 | all_54_9 = e2 % 154.86/23.64 | | % 154.86/23.64 | | BETA: splitting (7) gives: % 154.86/23.64 | | % 154.86/23.64 | | Case 1: % 154.86/23.64 | | | % 154.86/23.64 | | | (8) all_54_9 = e2 % 154.86/23.64 | | | % 154.86/23.64 | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #621. % 154.86/23.64 | | | % 154.86/23.64 | | Case 2: % 154.86/23.64 | | | % 154.86/23.64 | | | (9) all_54_9 = e3 % 154.86/23.64 | | | % 154.86/23.64 | | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #620. % 154.86/23.64 | | | % 154.86/23.64 | | End of split % 154.86/23.64 | | % 154.86/23.64 | End of split % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #620 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) all_54_9 = all_52_6 % 154.86/23.64 (2) all_54_9 = e3 % 154.86/23.64 (3) ~ (all_52_6 = e3) % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | COMBINE_EQS: (1), (2) imply: % 154.86/23.64 | (4) all_52_6 = e3 % 154.86/23.64 | % 154.86/23.64 | SIMP: (4) implies: % 154.86/23.64 | (5) all_52_6 = e3 % 154.86/23.64 | % 154.86/23.64 | REDUCE: (3), (5) imply: % 154.86/23.64 | (6) $false % 154.86/23.64 | % 154.86/23.64 | CLOSE: (6) is inconsistent. % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #621 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) all_54_9 = all_52_6 % 154.86/23.64 (2) all_54_9 = e2 % 154.86/23.64 (3) ~ (all_52_6 = e2) % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | COMBINE_EQS: (1), (2) imply: % 154.86/23.64 | (4) all_52_6 = e2 % 154.86/23.64 | % 154.86/23.64 | SIMP: (4) implies: % 154.86/23.64 | (5) all_52_6 = e2 % 154.86/23.64 | % 154.86/23.64 | REDUCE: (3), (5) imply: % 154.86/23.64 | (6) $false % 154.86/23.64 | % 154.86/23.64 | CLOSE: (6) is inconsistent. % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #622 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) all_54_9 = all_52_6 % 154.86/23.64 (2) all_54_9 = e1 % 154.86/23.64 (3) ~ (all_52_6 = e1) % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | COMBINE_EQS: (1), (2) imply: % 154.86/23.64 | (4) all_52_6 = e1 % 154.86/23.64 | % 154.86/23.64 | SIMP: (4) implies: % 154.86/23.64 | (5) all_52_6 = e1 % 154.86/23.64 | % 154.86/23.64 | REDUCE: (3), (5) imply: % 154.86/23.64 | (6) $false % 154.86/23.64 | % 154.86/23.64 | CLOSE: (6) is inconsistent. % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #623 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) all_58_31 = all_4_2 % 154.86/23.64 (2) ~ (all_52_8 = all_52_9) % 154.86/23.64 (3) all_58_11 = all_52_9 % 154.86/23.64 (4) all_58_22 = e0 % 154.86/23.64 (5) ~ (all_52_1 = e3) % 154.86/23.64 (6) all_58_6 = all_52_12 % 154.86/23.64 (7) all_58_13 = e0 % 154.86/23.64 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.86/23.64 (9) all_54_6 = all_52_9 % 154.86/23.64 (10) ~ (all_10_2 = e0) % 154.86/23.64 (11) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.86/23.64 (12) ~ (all_10_2 = e3) % 154.86/23.64 (13) ~ (all_52_12 = e0) % 154.86/23.64 (14) all_58_28 = e1 % 154.86/23.64 (15) ~ (all_52_1 = all_8_2) % 154.86/23.64 (16) all_58_24 = all_52_7 % 154.86/23.64 (17) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.86/23.64 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.64 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.86/23.64 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.64 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.64 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.86/23.64 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.64 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.64 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.64 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.64 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.64 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.64 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.64 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.64 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.64 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.64 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.64 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.64 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.64 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.64 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.64 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.64 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.64 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.64 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.64 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.86/23.64 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.64 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.64 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.64 e0) % 154.86/23.64 (18) all_58_29 = all_8_2 % 154.86/23.64 (19) all_58_30 = e0 % 154.86/23.64 (20) all_58_8 = all_52_1 % 154.86/23.64 (21) ~ (e3 = e0) % 154.86/23.64 (22) all_58_26 = all_6_1 % 154.86/23.64 (23) all_58_28 = all_10_2 % 154.86/23.64 (24) ~ (all_52_1 = all_52_9) % 154.86/23.64 (25) ~ (all_4_2 = e0) % 154.86/23.64 (26) ~ (all_52_1 = e0) % 154.86/23.64 (27) all_58_17 = e2 % 154.86/23.64 (28) all_58_4 = all_52_8 % 154.86/23.64 (29) all_58_2 = e0 % 154.86/23.64 (30) all_58_15 = e3 % 154.86/23.64 (31) ~ (all_52_7 = e0) % 154.86/23.64 (32) all_58_20 = e1 % 154.86/23.64 (33) ~ (all_52_9 = all_6_1) % 154.86/23.64 (34) all_54_4 = all_52_1 % 154.86/23.64 (35) ~ (all_52_1 = all_10_2) % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | COMBINE_EQS: (14), (23) imply: % 154.86/23.64 | (36) all_10_2 = e1 % 154.86/23.64 | % 154.86/23.64 | REDUCE: (35), (36) imply: % 154.86/23.64 | (37) ~ (all_52_1 = e1) % 154.86/23.64 | % 154.86/23.64 | REDUCE: (12), (36) imply: % 154.86/23.64 | (38) ~ (e3 = e1) % 154.86/23.64 | % 154.86/23.64 | SIMP: (38) implies: % 154.86/23.64 | (39) ~ (e3 = e1) % 154.86/23.64 | % 154.86/23.64 | REDUCE: (10), (36) imply: % 154.86/23.64 | (40) ~ (e1 = e0) % 154.86/23.64 | % 154.86/23.64 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), % 154.86/23.64 | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26), % 154.86/23.64 | (27), (28), (29), (30), (31), (32), (33), (34), (37), (39), (40) % 154.86/23.64 | are inconsistent by sub-proof #624. % 154.86/23.64 | % 154.86/23.64 End of proof % 154.86/23.64 % 154.86/23.64 Sub-proof #624 shows that the following formulas are inconsistent: % 154.86/23.64 ---------------------------------------------------------------- % 154.86/23.64 (1) all_58_31 = all_4_2 % 154.86/23.64 (2) ~ (all_52_8 = all_52_9) % 154.86/23.64 (3) ~ (all_52_1 = e1) % 154.86/23.64 (4) all_58_11 = all_52_9 % 154.86/23.64 (5) all_58_22 = e0 % 154.86/23.64 (6) ~ (all_52_1 = e3) % 154.86/23.64 (7) all_58_6 = all_52_12 % 154.86/23.64 (8) all_58_13 = e0 % 154.86/23.64 (9) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.86/23.64 (10) all_54_6 = all_52_9 % 154.86/23.64 (11) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 154.86/23.64 (12) ~ (e3 = e1) % 154.86/23.64 (13) ~ (all_52_12 = e0) % 154.86/23.64 (14) all_58_28 = e1 % 154.86/23.64 (15) ~ (all_52_1 = all_8_2) % 154.86/23.64 (16) all_58_24 = all_52_7 % 154.86/23.64 (17) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | all_58_31 = e0 | % 154.86/23.64 (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.64 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.86/23.64 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.64 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.64 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.86/23.64 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.64 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.64 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.64 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.64 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.64 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.64 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.64 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.64 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.64 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.64 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.64 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.64 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.64 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.64 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.64 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.64 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.64 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.64 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.64 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.86/23.64 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.64 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.64 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.64 e0) % 154.86/23.64 (18) all_58_29 = all_8_2 % 154.86/23.64 (19) all_58_30 = e0 % 154.86/23.64 (20) all_58_8 = all_52_1 % 154.86/23.64 (21) ~ (e3 = e0) % 154.86/23.64 (22) all_58_26 = all_6_1 % 154.86/23.64 (23) ~ (all_52_1 = all_52_9) % 154.86/23.64 (24) ~ (all_4_2 = e0) % 154.86/23.64 (25) ~ (all_52_1 = e0) % 154.86/23.64 (26) all_58_17 = e2 % 154.86/23.64 (27) all_58_4 = all_52_8 % 154.86/23.64 (28) all_58_2 = e0 % 154.86/23.64 (29) all_58_15 = e3 % 154.86/23.64 (30) ~ (all_52_7 = e0) % 154.86/23.64 (31) ~ (e1 = e0) % 154.86/23.64 (32) all_58_20 = e1 % 154.86/23.64 (33) ~ (all_52_9 = all_6_1) % 154.86/23.64 (34) all_54_4 = all_52_1 % 154.86/23.64 % 154.86/23.64 Begin of proof % 154.86/23.64 | % 154.86/23.64 | BETA: splitting (9) gives: % 154.86/23.64 | % 154.86/23.64 | Case 1: % 154.86/23.64 | | % 154.86/23.64 | | (35) all_54_4 = e1 % 154.86/23.64 | | % 154.86/23.64 | | REF_CLOSE: (3), (34), (35) are inconsistent by sub-proof #832. % 154.86/23.64 | | % 154.86/23.64 | Case 2: % 154.86/23.64 | | % 154.86/23.64 | | (36) ~ (all_54_4 = e1) % 154.86/23.64 | | (37) all_54_4 = e3 | all_54_4 = e2 % 154.86/23.64 | | % 154.86/23.64 | | BETA: splitting (37) gives: % 154.86/23.64 | | % 154.86/23.64 | | Case 1: % 154.86/23.64 | | | % 154.86/23.64 | | | (38) all_54_4 = e2 % 154.86/23.64 | | | % 154.86/23.64 | | | COMBINE_EQS: (34), (38) imply: % 154.86/23.64 | | | (39) all_52_1 = e2 % 154.86/23.64 | | | % 154.86/23.64 | | | SIMP: (39) implies: % 154.86/23.64 | | | (40) all_52_1 = e2 % 154.86/23.64 | | | % 154.86/23.64 | | | COMBINE_EQS: (20), (40) imply: % 154.86/23.64 | | | (41) all_58_8 = e2 % 154.86/23.64 | | | % 154.86/23.64 | | | REDUCE: (23), (40) imply: % 154.86/23.64 | | | (42) ~ (all_52_9 = e2) % 154.86/23.64 | | | % 154.86/23.64 | | | SIMP: (42) implies: % 154.86/23.64 | | | (43) ~ (all_52_9 = e2) % 154.86/23.64 | | | % 154.86/23.64 | | | REDUCE: (15), (40) imply: % 154.86/23.64 | | | (44) ~ (all_8_2 = e2) % 154.86/23.64 | | | % 154.86/23.64 | | | SIMP: (44) implies: % 154.86/23.64 | | | (45) ~ (all_8_2 = e2) % 154.86/23.64 | | | % 154.86/23.64 | | | REDUCE: (3), (40) imply: % 154.86/23.64 | | | (46) ~ (e2 = e1) % 154.86/23.64 | | | % 154.86/23.64 | | | REDUCE: (25), (40) imply: % 154.86/23.64 | | | (47) ~ (e2 = e0) % 154.86/23.64 | | | % 154.86/23.64 | | | BETA: splitting (17) gives: % 154.86/23.64 | | | % 154.86/23.64 | | | Case 1: % 154.86/23.64 | | | | % 154.86/23.64 | | | | (48) all_58_31 = e0 % 154.86/23.64 | | | | % 154.86/23.64 | | | | REF_CLOSE: (1), (24), (48) are inconsistent by sub-proof #635. % 154.86/23.64 | | | | % 154.86/23.64 | | | Case 2: % 154.86/23.64 | | | | % 154.86/23.64 | | | | (49) all_58_28 = e3 | all_58_29 = e2 | all_58_30 = e1 | (all_58_2 = % 154.86/23.64 | | | | e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.64 | | | | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) % 154.86/23.64 | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = % 154.86/23.64 | | | | e2) | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.64 | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = % 154.86/23.64 | | | | e2 & all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 154.86/23.64 | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = % 154.86/23.64 | | | | e2 & all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.86/23.64 | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = % 154.86/23.64 | | | | e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 % 154.86/23.64 | | | | & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 154.86/23.64 | | | | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 % 154.86/23.64 | | | | = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.64 | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & all_58_22 = % 154.86/23.64 | | | | e3) | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.64 | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 % 154.86/23.64 | | | | = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 % 154.86/23.64 | | | | = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.64 | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 % 154.86/23.64 | | | | = e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.64 | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & all_58_20 % 154.86/23.64 | | | | = e1 & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.86/23.64 | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.64 | | | | all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & all_58_17 % 154.86/23.64 | | | | = e2 & all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.86/23.64 | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 % 154.86/23.64 | | | | = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.64 | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.86/23.64 | | | | all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 % 154.86/23.64 | | | | = e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.64 | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.86/23.64 | | | | all_58_26 = e0 & e1 = e0) % 154.86/23.64 | | | | % 154.86/23.64 | | | | BETA: splitting (49) gives: % 154.86/23.64 | | | | % 154.86/23.64 | | | | Case 1: % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | (50) all_58_30 = e1 % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | COMBINE_EQS: (19), (50) imply: % 154.86/23.64 | | | | | (51) e1 = e0 % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | REDUCE: (31), (51) imply: % 154.86/23.64 | | | | | (52) $false % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | CLOSE: (52) is inconsistent. % 154.86/23.64 | | | | | % 154.86/23.64 | | | | Case 2: % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | (53) ~ (all_58_30 = e1) % 154.86/23.64 | | | | | (54) all_58_28 = e3 | all_58_29 = e2 | (all_58_2 = e3 & all_58_4 = % 154.86/23.64 | | | | | e1 & all_58_8 = e3 & all_58_15 = e1) | (all_58_2 = e3 & % 154.86/23.64 | | | | | all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | (all_58_2 % 154.86/23.64 | | | | | = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.64 | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = % 154.86/23.64 | | | | | e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.64 | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 % 154.86/23.64 | | | | | = e2 & all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.64 | | | | | all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & all_58_8 % 154.86/23.64 | | | | | = e2 & all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.86/23.64 | | | | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 154.86/23.64 | | | | | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.86/23.64 | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & all_58_26 = % 154.86/23.64 | | | | | e1) | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.64 | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.64 | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 154.86/23.64 | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.64 | | | | | (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & % 154.86/23.64 | | | | | all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.86/23.64 | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & all_58_26 = % 154.86/23.64 | | | | | e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.64 | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.86/23.64 | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.86/23.64 | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 % 154.86/23.64 | | | | | & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = e2 & % 154.86/23.64 | | | | | all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.64 | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 % 154.86/23.64 | | | | | = e2) | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.64 | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.64 | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.64 | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.86/23.64 | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.64 | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 % 154.86/23.64 | | | | | & e1 = e0) % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | REDUCE: (19), (53) imply: % 154.86/23.64 | | | | | (55) ~ (e1 = e0) % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | BETA: splitting (54) gives: % 154.86/23.64 | | | | | % 154.86/23.64 | | | | | Case 1: % 154.86/23.64 | | | | | | % 154.86/23.64 | | | | | | (56) all_58_29 = e2 % 154.86/23.64 | | | | | | % 154.86/23.64 | | | | | | REF_CLOSE: (18), (45), (56) are inconsistent by sub-proof #634. % 154.86/23.64 | | | | | | % 154.86/23.64 | | | | | Case 2: % 154.86/23.64 | | | | | | % 154.86/23.64 | | | | | | (57) all_58_28 = e3 | (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = % 154.86/23.64 | | | | | | e3 & all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.86/23.64 | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.64 | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 % 154.86/23.64 | | | | | | = e2) | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.64 | | | | | | all_58_15 = e3) | (all_58_2 = e2 & all_58_6 = e3 & % 154.86/23.64 | | | | | | all_58_8 = e2 & all_58_22 = e3) | (all_58_2 = e2 & % 154.86/23.64 | | | | | | all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.64 | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 % 154.86/23.64 | | | | | | = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | % 154.86/23.64 | | | | | | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & all_58_22 % 154.86/23.64 | | | | | | = e0) | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.86/23.64 | | | | | | all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.64 | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & % 154.86/23.64 | | | | | | all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 154.86/23.64 | | | | | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.86/23.64 | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.64 | | | | | | all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & e3 = % 154.86/23.64 | | | | | | e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.64 | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.86/23.64 | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & % 154.86/23.64 | | | | | | all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.86/23.64 | | | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 % 154.86/23.64 | | | | | | = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.64 | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.86/23.64 | | | | | | all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.86/23.64 | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.86/23.64 | | | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.64 | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.64 | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = % 154.86/23.64 | | | | | | e1) | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.64 | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.86/23.64 | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.64 | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = % 154.86/23.64 | | | | | | e0 & e1 = e0) % 154.86/23.64 | | | | | | % 154.86/23.64 | | | | | | BETA: splitting (57) gives: % 154.86/23.64 | | | | | | % 154.86/23.64 | | | | | | Case 1: % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | (58) all_58_28 = e3 % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | COMBINE_EQS: (14), (58) imply: % 154.86/23.64 | | | | | | | (59) e3 = e1 % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | REDUCE: (12), (59) imply: % 154.86/23.64 | | | | | | | (60) $false % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | CLOSE: (60) is inconsistent. % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | Case 2: % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | (61) ~ (all_58_28 = e3) % 154.86/23.64 | | | | | | | (62) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 % 154.86/23.64 | | | | | | | = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.86/23.64 | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.64 | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 % 154.86/23.64 | | | | | | | = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.86/23.64 | | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.64 | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 % 154.86/23.64 | | | | | | | & all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.86/23.64 | | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.86/23.64 | | | | | | | all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = e3 & % 154.86/23.64 | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & % 154.86/23.64 | | | | | | | all_58_6 = e3 & all_58_15 = e1 & all_58_22 = e3) | % 154.86/23.64 | | | | | | | (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.64 | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.64 | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & % 154.86/23.64 | | | | | | | all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 & all_58_13 = % 154.86/23.64 | | | | | | | e0 & all_58_22 = e3 & all_58_24 = e0) | (all_58_6 = e3 & % 154.86/23.64 | | | | | | | all_58_20 = e0 & all_58_22 = e3 & all_58_26 = e0) | % 154.86/23.64 | | | | | | | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.64 | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.86/23.64 | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.86/23.64 | | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & all_58_13 % 154.86/23.64 | | | | | | | = e0 & all_58_17 = e2 & all_58_24 = e0) | (all_58_11 = % 154.86/23.64 | | | | | | | e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.64 | | | | | | | (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.86/23.64 | | | | | | | all_58_24 = e2) | (all_58_11 = e1 & all_58_17 = e1 & % 154.86/23.64 | | | | | | | all_58_20 = e0 & all_58_26 = e0) | (all_58_11 = e1 & % 154.86/23.64 | | | | | | | all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & all_58_20 % 154.86/23.64 | | | | | | | = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = % 154.86/23.64 | | | | | | | e0 & all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.64 | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = % 154.86/23.64 | | | | | | | e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | REDUCE: (14), (61) imply: % 154.86/23.64 | | | | | | | (63) ~ (e3 = e1) % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | BETA: splitting (62) gives: % 154.86/23.64 | | | | | | | % 154.86/23.64 | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | % 154.86/23.64 | | | | | | | | (64) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.86/23.64 | | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.64 | | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.64 | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.64 | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.86/23.64 | | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.64 | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.64 | | | | | | | | all_58_17 = e1) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | | all_58_13 = e0 & all_58_24 = e0) | (all_58_2 = e2 & % 154.86/23.64 | | | | | | | | all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.64 | | | | | | | | e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 154.86/23.64 | | | | | | | | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.86/23.64 | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.64 | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.64 | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.86/23.64 | | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.64 | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.64 | | | | | | | | all_58_26 = e0) % 154.86/23.64 | | | | | | | | % 154.86/23.64 | | | | | | | | BETA: splitting (64) gives: % 154.86/23.64 | | | | | | | | % 154.86/23.64 | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | | (65) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.86/23.64 | | | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.64 | | | | | | | | | (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.64 | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.64 | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.86/23.64 | | | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.64 | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.64 | | | | | | | | | all_58_17 = e1) % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | | BETA: splitting (65) gives: % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | (66) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.86/23.64 | | | | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | BETA: splitting (66) gives: % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | (67) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | | | | | all_58_15 = e1 % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | ALPHA: (67) implies: % 154.86/23.64 | | | | | | | | | | | (68) all_58_15 = e1 % 154.86/23.64 | | | | | | | | | | | (69) all_58_2 = e3 % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | COMBINE_EQS: (28), (69) imply: % 154.86/23.64 | | | | | | | | | | | (70) e3 = e0 % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | COMBINE_EQS: (29), (68) imply: % 154.86/23.64 | | | | | | | | | | | (71) e3 = e1 % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | SIMP: (71) implies: % 154.86/23.64 | | | | | | | | | | | (72) e3 = e1 % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | REF_CLOSE: (31), (70), (72) are inconsistent by sub-proof % 154.86/23.64 | | | | | | | | | | | #633. % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | (73) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 % 154.86/23.64 | | | | | | | | | | | & all_58_11 = e2 & all_58_17 = e2) % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | BETA: splitting (73) gives: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | (74) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.64 | | | | | | | | | | | | all_58_22 = e0 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | ALPHA: (74) implies: % 154.86/23.64 | | | | | | | | | | | | (75) all_58_8 = e3 % 154.86/23.64 | | | | | | | | | | | | (76) all_58_2 = e3 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | REF_CLOSE: (28), (41), (47), (75), (76) are inconsistent by % 154.86/23.64 | | | | | | | | | | | | sub-proof #632. % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | (77) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.86/23.64 | | | | | | | | | | | | all_58_17 = e2 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | ALPHA: (77) implies: % 154.86/23.64 | | | | | | | | | | | | (78) all_58_8 = e3 % 154.86/23.64 | | | | | | | | | | | | (79) all_58_2 = e3 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | REF_CLOSE: (28), (41), (47), (78), (79) are inconsistent by % 154.86/23.64 | | | | | | | | | | | | sub-proof #632. % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | End of split % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | End of split % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | (80) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.64 | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.64 | | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.86/23.64 | | | | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.64 | | | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.64 | | | | | | | | | | all_58_17 = e1) % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | BETA: splitting (80) gives: % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | (81) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.64 | | | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 % 154.86/23.64 | | | | | | | | | | | & all_58_8 = e2 & all_58_15 = e3) % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | BETA: splitting (81) gives: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | (82) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.64 | | | | | | | | | | | | all_58_24 = e2 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | ALPHA: (82) implies: % 154.86/23.64 | | | | | | | | | | | | (83) all_58_8 = e3 % 154.86/23.64 | | | | | | | | | | | | (84) all_58_2 = e3 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | REF_CLOSE: (28), (41), (47), (83), (84) are inconsistent by % 154.86/23.64 | | | | | | | | | | | | sub-proof #632. % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | (85) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | | | | | | all_58_15 = e3 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | ALPHA: (85) implies: % 154.86/23.64 | | | | | | | | | | | | (86) all_58_2 = e2 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | COMBINE_EQS: (28), (86) imply: % 154.86/23.64 | | | | | | | | | | | | (87) e2 = e0 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | REDUCE: (47), (87) imply: % 154.86/23.64 | | | | | | | | | | | | (88) $false % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | CLOSE: (88) is inconsistent. % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | End of split % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | (89) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.64 | | | | | | | | | | | & all_58_11 = e1 & all_58_17 = e1) % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | BETA: splitting (89) gives: % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | (90) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | | | | | | all_58_22 = e3 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | ALPHA: (90) implies: % 154.86/23.64 | | | | | | | | | | | | (91) all_58_2 = e2 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | COMBINE_EQS: (28), (91) imply: % 154.86/23.64 | | | | | | | | | | | | (92) e2 = e0 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | REDUCE: (47), (92) imply: % 154.86/23.64 | | | | | | | | | | | | (93) $false % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | CLOSE: (93) is inconsistent. % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | (94) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.64 | | | | | | | | | | | | all_58_17 = e1 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | ALPHA: (94) implies: % 154.86/23.64 | | | | | | | | | | | | (95) all_58_17 = e1 % 154.86/23.64 | | | | | | | | | | | | (96) all_58_2 = e2 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | COMBINE_EQS: (28), (96) imply: % 154.86/23.64 | | | | | | | | | | | | (97) e2 = e0 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | COMBINE_EQS: (26), (95) imply: % 154.86/23.64 | | | | | | | | | | | | (98) e2 = e1 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | SIMP: (98) implies: % 154.86/23.64 | | | | | | | | | | | | (99) e2 = e1 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | COMBINE_EQS: (97), (99) imply: % 154.86/23.64 | | | | | | | | | | | | (100) e1 = e0 % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | REDUCE: (31), (100) imply: % 154.86/23.64 | | | | | | | | | | | | (101) $false % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | | CLOSE: (101) is inconsistent. % 154.86/23.64 | | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | | End of split % 154.86/23.64 | | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | End of split % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | End of split % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | Case 2: % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | | (102) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.64 | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.64 | | | | | | | | | e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & % 154.86/23.64 | | | | | | | | | all_58_11 = e1 & all_58_15 = e3 & all_58_17 = e1) | % 154.86/23.64 | | | | | | | | | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.64 | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.64 | | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.86/23.64 | | | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.64 | | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.64 | | | | | | | | | all_58_26 = e0) % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | | BETA: splitting (102) gives: % 154.86/23.64 | | | | | | | | | % 154.86/23.64 | | | | | | | | | Case 1: % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | (103) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.64 | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.64 | | | | | | | | | | & e3 = e2) | (all_58_4 = e3 & all_58_6 = e0 & % 154.86/23.64 | | | | | | | | | | all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 % 154.86/23.64 | | | | | | | | | | & all_58_11 = e1 & all_58_15 = e3 & all_58_17 = % 154.86/23.64 | | | | | | | | | | e1) % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | BETA: splitting (103) gives: % 154.86/23.64 | | | | | | | | | | % 154.86/23.64 | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (104) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.65 | | | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 % 154.86/23.65 | | | | | | | | | | | & e3 = e2) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (104) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (105) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.65 | | | | | | | | | | | | all_58_24 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (105) implies: % 154.86/23.65 | | | | | | | | | | | | (106) all_58_2 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (28), (106) imply: % 154.86/23.65 | | | | | | | | | | | | (107) e2 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (47), (107) imply: % 154.86/23.65 | | | | | | | | | | | | (108) $false % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | CLOSE: (108) is inconsistent. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (109) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (109) implies: % 154.86/23.65 | | | | | | | | | | | | (110) all_58_2 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (28), (110) imply: % 154.86/23.65 | | | | | | | | | | | | (111) e2 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (47), (111) imply: % 154.86/23.65 | | | | | | | | | | | | (112) $false % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | CLOSE: (112) is inconsistent. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (113) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.65 | | | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.65 | | | | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (113) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (114) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.65 | | | | | | | | | | | | all_58_22 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (114) implies: % 154.86/23.65 | | | | | | | | | | | | (115) all_58_6 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (7), (13), (115) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #631. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (116) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.86/23.65 | | | | | | | | | | | | all_58_17 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (116) implies: % 154.86/23.65 | | | | | | | | | | | | (117) all_58_17 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (26), (46), (117) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #630. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | (118) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.65 | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.65 | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = % 154.86/23.65 | | | | | | | | | | e1 & all_58_11 = e2 & all_58_15 = e1 & all_58_17 % 154.86/23.65 | | | | | | | | | | = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.65 | | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | BETA: splitting (118) gives: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (119) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.65 | | | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.65 | | | | | | | | | | | & all_58_15 = e1 & all_58_22 = e3) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (119) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (120) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (120) implies: % 154.86/23.65 | | | | | | | | | | | | (121) all_58_26 = e1 % 154.86/23.65 | | | | | | | | | | | | (122) all_58_4 = e3 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (27), (122) imply: % 154.86/23.65 | | | | | | | | | | | | (123) all_52_8 = e3 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (22), (121) imply: % 154.86/23.65 | | | | | | | | | | | | (124) all_6_1 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | SIMP: (124) implies: % 154.86/23.65 | | | | | | | | | | | | (125) all_6_1 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (2), (123) imply: % 154.86/23.65 | | | | | | | | | | | | (126) ~ (all_52_9 = e3) % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | SIMP: (126) implies: % 154.86/23.65 | | | | | | | | | | | | (127) ~ (all_52_9 = e3) % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (33), (125) imply: % 154.86/23.65 | | | | | | | | | | | | (128) ~ (all_52_9 = e1) % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (10), (11), (43), (127), (128) are inconsistent by % 154.86/23.65 | | | | | | | | | | | | sub-proof #771. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (129) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.65 | | | | | | | | | | | | all_58_22 = e3 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (129) implies: % 154.86/23.65 | | | | | | | | | | | | (130) all_58_22 = e3 % 154.86/23.65 | | | | | | | | | | | | (131) all_58_15 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (29), (131) imply: % 154.86/23.65 | | | | | | | | | | | | (132) e3 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | SIMP: (132) implies: % 154.86/23.65 | | | | | | | | | | | | (133) e3 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (5), (130) imply: % 154.86/23.65 | | | | | | | | | | | | (134) e3 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (133), (134) imply: % 154.86/23.65 | | | | | | | | | | | | (135) e1 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (31), (135) imply: % 154.86/23.65 | | | | | | | | | | | | (136) $false % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | CLOSE: (136) is inconsistent. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (137) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.65 | | | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = % 154.86/23.65 | | | | | | | | | | | e1 & all_58_20 = e0 & all_58_26 = e0) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (137) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (138) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.65 | | | | | | | | | | | | all_58_17 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (138) implies: % 154.86/23.65 | | | | | | | | | | | | (139) all_58_15 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (12), (29), (139) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #629. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (140) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (140) implies: % 154.86/23.65 | | | | | | | | | | | | (141) all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (31), (32), (141) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #628. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | End of split % 154.86/23.65 | | | | | | | | % 154.86/23.65 | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | % 154.86/23.65 | | | | | | | | (142) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 % 154.86/23.65 | | | | | | | | = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.86/23.65 | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = % 154.86/23.65 | | | | | | | | e3 & all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = % 154.86/23.65 | | | | | | | | e2 & all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = % 154.86/23.65 | | | | | | | | e0 & all_58_20 = e1 & all_58_22 = e0 & all_58_26 = % 154.86/23.65 | | | | | | | | e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.65 | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.86/23.65 | | | | | | | | all_58_24 = e0) | (all_58_11 = e2 & all_58_17 = e2 & % 154.86/23.65 | | | | | | | | all_58_20 = e1 & all_58_26 = e1) | (all_58_11 = e1 & % 154.86/23.65 | | | | | | | | all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.65 | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.65 | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 & % 154.86/23.65 | | | | | | | | e2 = e1) | (all_58_13 = e2 & all_58_20 = e0 & % 154.86/23.65 | | | | | | | | all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.65 | | | | | | | | all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.65 | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.65 | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.65 | | | | | | | | % 154.86/23.65 | | | | | | | | BETA: splitting (142) gives: % 154.86/23.65 | | | | | | | | % 154.86/23.65 | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | | (143) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.86/23.65 | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.65 | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.86/23.65 | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) | (all_58_6 = e0 & % 154.86/23.65 | | | | | | | | | all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2) | % 154.86/23.65 | | | | | | | | | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.65 | | | | | | | | | all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & % 154.86/23.65 | | | | | | | | | e3 = e0) | (all_58_11 = e2 & all_58_13 = e0 & % 154.86/23.65 | | | | | | | | | all_58_17 = e2 & all_58_24 = e0) % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | | BETA: splitting (143) gives: % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | (144) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | % 154.86/23.65 | | | | | | | | | | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.65 | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | & all_58_22 = e3 & all_58_26 = e0) % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | BETA: splitting (144) gives: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (145) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | ALPHA: (145) implies: % 154.86/23.65 | | | | | | | | | | | (146) all_58_15 = e1 % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | REF_CLOSE: (12), (29), (146) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | #629. % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (147) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.65 | | | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = % 154.86/23.65 | | | | | | | | | | | e0 & all_58_22 = e3 & all_58_26 = e0) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (147) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (148) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.65 | | | | | | | | | | | | all_58_24 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (148) implies: % 154.86/23.65 | | | | | | | | | | | | (149) all_58_22 = e3 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (5), (149) imply: % 154.86/23.65 | | | | | | | | | | | | (150) e3 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (21), (150) imply: % 154.86/23.65 | | | | | | | | | | | | (151) $false % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (152) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (152) implies: % 154.86/23.65 | | | | | | | | | | | | (153) all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (31), (32), (153) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #628. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | (154) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.65 | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 % 154.86/23.65 | | | | | | | | | | & all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = % 154.86/23.65 | | | | | | | | | | e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 % 154.86/23.65 | | | | | | | | | | & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = % 154.86/23.65 | | | | | | | | | | e0) % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | BETA: splitting (154) gives: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (155) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.65 | | | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = % 154.86/23.65 | | | | | | | | | | | e1 & all_58_22 = e0 & all_58_26 = e1) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (155) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (156) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.65 | | | | | | | | | | | | all_58_24 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (8), (47), (156) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #627. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (157) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (157) implies: % 154.86/23.65 | | | | | | | | | | | | (158) all_58_6 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (7), (13), (158) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #631. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (159) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.65 | | | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 % 154.86/23.65 | | | | | | | | | | | & all_58_24 = e0) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (159) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (160) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (160) implies: % 154.86/23.65 | | | | | | | | | | | | (161) e3 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (21), (161) imply: % 154.86/23.65 | | | | | | | | | | | | (162) $false % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (163) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.86/23.65 | | | | | | | | | | | | all_58_24 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (163) implies: % 154.86/23.65 | | | | | | | | | | | | (164) all_58_11 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (4), (43), (164) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #626. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | | (165) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.65 | | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 % 154.86/23.65 | | | | | | | | | & all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = % 154.86/23.65 | | | | | | | | | e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = % 154.86/23.65 | | | | | | | | | e0) | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | % 154.86/23.65 | | | | | | | | | (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.65 | | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 % 154.86/23.65 | | | | | | | | | & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = % 154.86/23.65 | | | | | | | | | e0 & all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.86/23.65 | | | | | | | | | all_58_26 = e0 & e1 = e0) % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | | BETA: splitting (165) gives: % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | (166) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.65 | | | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = % 154.86/23.65 | | | | | | | | | | e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.65 | | | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.65 | | | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = % 154.86/23.65 | | | | | | | | | | e1 & e2 = e1) % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | BETA: splitting (166) gives: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (167) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 % 154.86/23.65 | | | | | | | | | | | & all_58_26 = e1) | (all_58_11 = e1 & all_58_13 % 154.86/23.65 | | | | | | | | | | | = e2 & all_58_17 = e1 & all_58_24 = e2) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (167) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (168) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (168) implies: % 154.86/23.65 | | | | | | | | | | | | (169) all_58_11 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (4), (43), (169) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #626. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (170) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.86/23.65 | | | | | | | | | | | | all_58_24 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (170) implies: % 154.86/23.65 | | | | | | | | | | | | (171) all_58_17 = e1 % 154.86/23.65 | | | | | | | | | | | | (172) all_58_13 = e2 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (8), (172) imply: % 154.86/23.65 | | | | | | | | | | | | (173) e2 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | COMBINE_EQS: (26), (171) imply: % 154.86/23.65 | | | | | | | | | | | | (174) e2 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | SIMP: (174) implies: % 154.86/23.65 | | | | | | | | | | | | (175) e2 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (31), (173), (175) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #625. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (176) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | | & all_58_26 = e0) | (all_58_11 = e1 & all_58_17 % 154.86/23.65 | | | | | | | | | | | = e1 & e2 = e1) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (176) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (177) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (177) implies: % 154.86/23.65 | | | | | | | | | | | | (178) all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (31), (32), (178) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #628. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (179) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (179) implies: % 154.86/23.65 | | | | | | | | | | | | (180) all_58_17 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (26), (46), (180) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #630. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | (181) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.65 | | | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = % 154.86/23.65 | | | | | | | | | | e1 & all_58_24 = e0 & all_58_26 = e1) | % 154.86/23.65 | | | | | | | | | | (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.65 | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | BETA: splitting (181) gives: % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (182) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 % 154.86/23.65 | | | | | | | | | | | & all_58_26 = e0) | (all_58_13 = e0 & all_58_20 % 154.86/23.65 | | | | | | | | | | | = e1 & all_58_24 = e0 & all_58_26 = e1) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (182) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (183) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (183) implies: % 154.86/23.65 | | | | | | | | | | | | (184) all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (31), (32), (184) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #628. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (185) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.86/23.65 | | | | | | | | | | | | all_58_26 = e1 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (185) implies: % 154.86/23.65 | | | | | | | | | | | | (186) all_58_24 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (16), (30), (186) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #643. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | (187) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.65 | | | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | BETA: splitting (187) gives: % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 1: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (188) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (188) implies: % 154.86/23.65 | | | | | | | | | | | | (189) e2 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REDUCE: (47), (189) imply: % 154.86/23.65 | | | | | | | | | | | | (190) $false % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | CLOSE: (190) is inconsistent. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | Case 2: % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | (191) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | ALPHA: (191) implies: % 154.86/23.65 | | | | | | | | | | | | (192) all_58_20 = e0 % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | | REF_CLOSE: (31), (32), (192) are inconsistent by sub-proof % 154.86/23.65 | | | | | | | | | | | | #628. % 154.86/23.65 | | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | | % 154.86/23.65 | | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | | % 154.86/23.65 | | | | | | | | | End of split % 154.86/23.65 | | | | | | | | | % 154.86/23.65 | | | | | | | | End of split % 154.86/23.65 | | | | | | | | % 154.86/23.65 | | | | | | | End of split % 154.86/23.65 | | | | | | | % 154.86/23.65 | | | | | | End of split % 154.86/23.65 | | | | | | % 154.86/23.65 | | | | | End of split % 154.86/23.65 | | | | | % 154.86/23.65 | | | | End of split % 154.86/23.65 | | | | % 154.86/23.65 | | | End of split % 154.86/23.65 | | | % 154.86/23.65 | | Case 2: % 154.86/23.65 | | | % 154.86/23.65 | | | (193) all_54_4 = e3 % 154.86/23.65 | | | % 154.86/23.65 | | | REF_CLOSE: (6), (34), (193) are inconsistent by sub-proof #830. % 154.86/23.65 | | | % 154.86/23.65 | | End of split % 154.86/23.65 | | % 154.86/23.65 | End of split % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #625 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) e2 = e1 % 154.86/23.65 (2) e2 = e0 % 154.86/23.65 (3) ~ (e1 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) e1 = e0 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) e1 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #626 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_11 = all_52_9 % 154.86/23.65 (2) all_58_11 = e2 % 154.86/23.65 (3) ~ (all_52_9 = e2) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) all_52_9 = e2 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) all_52_9 = e2 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #627 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & all_58_24 = e2 % 154.86/23.65 (2) all_58_13 = e0 % 154.86/23.65 (3) ~ (e2 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | ALPHA: (1) implies: % 154.86/23.65 | (4) all_58_13 = e2 % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (2), (4) imply: % 154.86/23.65 | (5) e2 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #628 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_20 = e1 % 154.86/23.65 (2) all_58_20 = e0 % 154.86/23.65 (3) ~ (e1 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) e1 = e0 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) e1 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #629 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_15 = e3 % 154.86/23.65 (2) all_58_15 = e1 % 154.86/23.65 (3) ~ (e3 = e1) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) e3 = e1 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) e3 = e1 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #630 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_17 = e2 % 154.86/23.65 (2) all_58_17 = e1 % 154.86/23.65 (3) ~ (e2 = e1) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) e2 = e1 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) e2 = e1 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #631 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_6 = all_52_12 % 154.86/23.65 (2) all_58_6 = e0 % 154.86/23.65 (3) ~ (all_52_12 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) all_52_12 = e0 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) all_52_12 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #632 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_8 = e3 % 154.86/23.65 (2) all_58_8 = e2 % 154.86/23.65 (3) ~ (e2 = e0) % 154.86/23.65 (4) all_58_2 = e3 % 154.86/23.65 (5) all_58_2 = e0 % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (4), (5) imply: % 154.86/23.65 | (6) e3 = e0 % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (7) e3 = e2 % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (6), (7) imply: % 154.86/23.65 | (8) e2 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (8) imply: % 154.86/23.65 | (9) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (9) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #633 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) e3 = e1 % 154.86/23.65 (2) e3 = e0 % 154.86/23.65 (3) ~ (e1 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) e1 = e0 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) e1 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #634 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_29 = all_8_2 % 154.86/23.65 (2) all_58_29 = e2 % 154.86/23.65 (3) ~ (all_8_2 = e2) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) all_8_2 = e2 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) all_8_2 = e2 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #635 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_31 = all_4_2 % 154.86/23.65 (2) all_58_31 = e0 % 154.86/23.65 (3) ~ (all_4_2 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) all_4_2 = e0 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) all_4_2 = e0 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #636 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_31 = all_4_2 % 154.86/23.65 (2) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.86/23.65 (3) ~ (all_52_2 = e1) % 154.86/23.65 (4) ~ (all_10_2 = e1) % 154.86/23.65 (5) ~ (all_52_1 = all_8_2) % 154.86/23.65 (6) all_58_29 = all_8_2 % 154.86/23.65 (7) all_58_30 = e0 % 154.86/23.65 (8) all_56_6 = all_52_2 % 154.86/23.65 (9) all_56_2 = all_52_1 % 154.86/23.65 (10) all_58_28 = all_10_2 % 154.86/23.65 (11) all_56_12 = e0 % 154.86/23.65 (12) all_56_0 = all_10_2 % 154.86/23.65 (13) ~ (e1 = e0) % 154.86/23.65 (14) ~ (all_4_2 = e1) % 154.86/23.65 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.65 (16) ~ (all_8_2 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | BETA: splitting (2) gives: % 154.86/23.65 | % 154.86/23.65 | Case 1: % 154.86/23.65 | | % 154.86/23.65 | | (17) all_56_0 = e1 % 154.86/23.65 | | % 154.86/23.65 | | COMBINE_EQS: (12), (17) imply: % 154.86/23.65 | | (18) all_10_2 = e1 % 154.86/23.65 | | % 154.86/23.65 | | REDUCE: (4), (18) imply: % 154.86/23.65 | | (19) $false % 154.86/23.65 | | % 154.86/23.65 | | CLOSE: (19) is inconsistent. % 154.86/23.65 | | % 154.86/23.65 | Case 2: % 154.86/23.65 | | % 154.86/23.65 | | (20) ~ (all_56_0 = e1) % 154.86/23.65 | | (21) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.86/23.65 | | % 154.86/23.65 | | BETA: splitting (15) gives: % 154.86/23.65 | | % 154.86/23.65 | | Case 1: % 154.86/23.65 | | | % 154.86/23.65 | | | (22) all_58_28 = e1 % 154.86/23.65 | | | % 154.86/23.65 | | | COMBINE_EQS: (10), (22) imply: % 154.86/23.65 | | | (23) all_10_2 = e1 % 154.86/23.65 | | | % 154.86/23.65 | | | REDUCE: (4), (23) imply: % 154.86/23.65 | | | (24) $false % 154.86/23.65 | | | % 154.86/23.65 | | | CLOSE: (24) is inconsistent. % 154.86/23.65 | | | % 154.86/23.65 | | Case 2: % 154.86/23.65 | | | % 154.86/23.65 | | | (25) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.65 | | | % 154.86/23.65 | | | BETA: splitting (25) gives: % 154.86/23.65 | | | % 154.86/23.65 | | | Case 1: % 154.86/23.65 | | | | % 154.86/23.65 | | | | (26) all_58_29 = e1 % 154.86/23.65 | | | | % 154.86/23.65 | | | | COMBINE_EQS: (6), (26) imply: % 154.86/23.65 | | | | (27) all_8_2 = e1 % 154.86/23.65 | | | | % 154.86/23.65 | | | | REDUCE: (5), (27) imply: % 154.86/23.65 | | | | (28) ~ (all_52_1 = e1) % 154.86/23.65 | | | | % 154.86/23.65 | | | | REF_CLOSE: (3), (8), (9), (11), (13), (21), (28) are inconsistent by % 154.86/23.65 | | | | sub-proof #637. % 154.86/23.65 | | | | % 154.86/23.65 | | | Case 2: % 154.86/23.65 | | | | % 154.86/23.65 | | | | (29) all_58_30 = e1 | all_58_31 = e1 % 154.86/23.65 | | | | % 154.86/23.65 | | | | REF_CLOSE: (1), (7), (13), (14), (29) are inconsistent by sub-proof % 154.86/23.65 | | | | #711. % 154.86/23.65 | | | | % 154.86/23.65 | | | End of split % 154.86/23.65 | | | % 154.86/23.65 | | End of split % 154.86/23.65 | | % 154.86/23.65 | End of split % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #637 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) ~ (all_52_1 = e1) % 154.86/23.65 (2) ~ (all_52_2 = e1) % 154.86/23.65 (3) all_56_6 = all_52_2 % 154.86/23.65 (4) all_56_2 = all_52_1 % 154.86/23.65 (5) all_56_12 = e0 % 154.86/23.65 (6) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 154.86/23.65 (7) ~ (e1 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | BETA: splitting (6) gives: % 154.86/23.65 | % 154.86/23.65 | Case 1: % 154.86/23.65 | | % 154.86/23.65 | | (8) all_56_2 = e1 % 154.86/23.65 | | % 154.86/23.65 | | COMBINE_EQS: (4), (8) imply: % 154.86/23.65 | | (9) all_52_1 = e1 % 154.86/23.65 | | % 154.86/23.65 | | REDUCE: (1), (9) imply: % 154.86/23.65 | | (10) $false % 154.86/23.65 | | % 154.86/23.65 | | CLOSE: (10) is inconsistent. % 154.86/23.65 | | % 154.86/23.65 | Case 2: % 154.86/23.65 | | % 154.86/23.65 | | (11) all_56_6 = e1 | all_56_12 = e1 % 154.86/23.65 | | % 154.86/23.65 | | REF_CLOSE: (2), (3), (5), (7), (11) are inconsistent by sub-proof #638. % 154.86/23.65 | | % 154.86/23.65 | End of split % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #638 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) ~ (all_52_2 = e1) % 154.86/23.65 (2) all_56_6 = all_52_2 % 154.86/23.65 (3) all_56_6 = e1 | all_56_12 = e1 % 154.86/23.65 (4) all_56_12 = e0 % 154.86/23.65 (5) ~ (e1 = e0) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | BETA: splitting (3) gives: % 154.86/23.65 | % 154.86/23.65 | Case 1: % 154.86/23.65 | | % 154.86/23.65 | | (6) all_56_6 = e1 % 154.86/23.65 | | % 154.86/23.65 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #639. % 154.86/23.65 | | % 154.86/23.65 | Case 2: % 154.86/23.65 | | % 154.86/23.65 | | (7) all_56_12 = e1 % 154.86/23.65 | | % 154.86/23.65 | | COMBINE_EQS: (4), (7) imply: % 154.86/23.65 | | (8) e1 = e0 % 154.86/23.65 | | % 154.86/23.65 | | REDUCE: (5), (8) imply: % 154.86/23.65 | | (9) $false % 154.86/23.65 | | % 154.86/23.65 | | CLOSE: (9) is inconsistent. % 154.86/23.65 | | % 154.86/23.65 | End of split % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #639 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_56_6 = all_52_2 % 154.86/23.65 (2) all_56_6 = e1 % 154.86/23.65 (3) ~ (all_52_2 = e1) % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | COMBINE_EQS: (1), (2) imply: % 154.86/23.65 | (4) all_52_2 = e1 % 154.86/23.65 | % 154.86/23.65 | SIMP: (4) implies: % 154.86/23.65 | (5) all_52_2 = e1 % 154.86/23.65 | % 154.86/23.65 | REDUCE: (3), (5) imply: % 154.86/23.65 | (6) $false % 154.86/23.65 | % 154.86/23.65 | CLOSE: (6) is inconsistent. % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #640 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_31 = e1 % 154.86/23.65 (2) ~ (e3 = e1) % 154.86/23.65 (3) all_58_30 = e0 % 154.86/23.65 (4) all_58_29 = e1 % 154.86/23.65 (5) ~ (e3 = e0) % 154.86/23.65 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.65 % 154.86/23.65 Begin of proof % 154.86/23.65 | % 154.86/23.65 | BETA: splitting (6) gives: % 154.86/23.65 | % 154.86/23.65 | Case 1: % 154.86/23.65 | | % 154.86/23.65 | | (7) all_58_29 = e3 % 154.86/23.65 | | % 154.86/23.65 | | COMBINE_EQS: (4), (7) imply: % 154.86/23.65 | | (8) e3 = e1 % 154.86/23.65 | | % 154.86/23.65 | | REDUCE: (2), (8) imply: % 154.86/23.65 | | (9) $false % 154.86/23.65 | | % 154.86/23.65 | | CLOSE: (9) is inconsistent. % 154.86/23.65 | | % 154.86/23.65 | Case 2: % 154.86/23.65 | | % 154.86/23.65 | | (10) ~ (all_58_29 = e3) % 154.86/23.65 | | (11) all_58_30 = e3 | all_58_31 = e3 % 154.86/23.65 | | % 154.86/23.65 | | REDUCE: (4), (10) imply: % 154.86/23.65 | | (12) ~ (e3 = e1) % 154.86/23.65 | | % 154.86/23.65 | | REF_CLOSE: (1), (2), (3), (5), (11) are inconsistent by sub-proof #694. % 154.86/23.65 | | % 154.86/23.65 | End of split % 154.86/23.65 | % 154.86/23.65 End of proof % 154.86/23.65 % 154.86/23.65 Sub-proof #641 shows that the following formulas are inconsistent: % 154.86/23.65 ---------------------------------------------------------------- % 154.86/23.65 (1) all_58_31 = all_4_2 % 154.86/23.65 (2) ~ (all_52_1 = e1) % 154.86/23.65 (3) all_58_22 = e0 % 154.86/23.65 (4) all_56_9 = e1 % 154.86/23.65 (5) ~ (all_52_8 = all_10_2) % 154.86/23.65 (6) all_58_15 = e1 % 154.86/23.65 (7) all_56_4 = all_52_8 % 154.86/23.65 (8) all_58_13 = e0 % 154.86/23.65 (9) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.65 (10) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 154.86/23.65 (11) all_58_20 = all_52_14 % 154.86/23.65 (12) ~ (all_52_14 = e1) % 154.86/23.65 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 154.86/23.65 (14) ~ (all_10_2 = e0) % 154.86/23.65 (15) ~ (e3 = e1) % 154.86/23.65 (16) all_58_26 = e1 % 154.86/23.65 (17) ~ (all_10_2 = e1) % 154.86/23.65 (18) all_58_24 = all_52_7 % 154.86/23.65 (19) all_58_30 = e0 % 154.86/23.65 (20) all_58_6 = e1 % 154.86/23.65 (21) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.65 (22) all_58_8 = all_52_1 % 154.86/23.65 (23) all_58_29 = e1 % 154.86/23.65 (24) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 154.86/23.65 (25) all_56_2 = all_52_1 % 154.86/23.65 (26) all_56_4 = e3 | all_56_9 = e3 % 154.86/23.65 (27) all_58_28 = all_10_2 % 154.86/23.65 (28) all_56_0 = all_10_2 % 154.86/23.65 (29) ~ (all_52_1 = e0) % 154.86/23.65 (30) all_58_4 = all_52_8 % 154.86/23.65 (31) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.65 (32) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 154.86/23.65 (33) all_58_2 = e0 % 154.86/23.65 (34) all_54_0 = all_10_2 % 154.86/23.65 (35) ~ (all_52_7 = e0) % 154.86/23.66 (36) ~ (e1 = e0) % 154.86/23.66 (37) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = e1) | % 154.86/23.66 (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & all_58_22 = e0) | % 154.86/23.66 (all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) | % 154.86/23.66 (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.66 (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = e3) | % 154.86/23.66 (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.66 (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & all_58_17 = e1) | % 154.86/23.66 (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.66 (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & all_58_6 = % 154.86/23.66 e0 & all_58_15 = e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.66 e1 & all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & all_58_15 = % 154.86/23.66 e3 & all_58_20 = e1 & all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 % 154.86/23.66 & all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.66 all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.66 all_58_20 = e0 & all_58_26 = e0) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.66 e3 = e1) | (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.66 all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.66 all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.66 all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.66 all_58_26 = e1) | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.66 (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.66 (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.66 (all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & all_58_24 = e2) | % 154.86/23.66 (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.66 (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = e2 & % 154.86/23.66 all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | (all_58_13 = e0 & % 154.86/23.66 all_58_20 = e1 & all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.66 all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = % 154.86/23.66 e0) % 154.86/23.66 (38) ~ (all_4_2 = e1) % 154.86/23.66 (39) all_58_30 = all_6_2 % 154.86/23.66 (40) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.66 (41) all_54_4 = all_52_1 % 154.86/23.66 (42) ~ (all_52_1 = all_10_2) % 154.86/23.66 % 154.86/23.66 Begin of proof % 154.86/23.66 | % 154.86/23.66 | BETA: splitting (26) gives: % 154.86/23.66 | % 154.86/23.66 | Case 1: % 154.86/23.66 | | % 154.86/23.66 | | (43) all_56_4 = e3 % 154.86/23.66 | | % 154.86/23.66 | | COMBINE_EQS: (7), (43) imply: % 154.86/23.66 | | (44) all_52_8 = e3 % 154.86/23.66 | | % 154.86/23.66 | | SIMP: (44) implies: % 154.86/23.66 | | (45) all_52_8 = e3 % 154.86/23.66 | | % 154.86/23.66 | | COMBINE_EQS: (30), (45) imply: % 154.86/23.66 | | (46) all_58_4 = e3 % 154.86/23.66 | | % 154.86/23.66 | | REDUCE: (5), (45) imply: % 154.86/23.66 | | (47) ~ (all_10_2 = e3) % 154.86/23.66 | | % 154.86/23.66 | | SIMP: (47) implies: % 154.86/23.66 | | (48) ~ (all_10_2 = e3) % 154.86/23.66 | | % 154.86/23.66 | | BETA: splitting (10) gives: % 154.86/23.66 | | % 154.86/23.66 | | Case 1: % 154.86/23.66 | | | % 154.86/23.66 | | | (49) all_56_0 = e2 % 154.86/23.66 | | | % 154.86/23.66 | | | COMBINE_EQS: (28), (49) imply: % 154.86/23.66 | | | (50) all_10_2 = e2 % 154.86/23.66 | | | % 154.86/23.66 | | | SIMP: (50) implies: % 154.86/23.66 | | | (51) all_10_2 = e2 % 154.86/23.66 | | | % 154.86/23.66 | | | COMBINE_EQS: (27), (51) imply: % 154.86/23.66 | | | (52) all_58_28 = e2 % 154.86/23.66 | | | % 154.86/23.66 | | | REDUCE: (42), (51) imply: % 154.86/23.66 | | | (53) ~ (all_52_1 = e2) % 154.86/23.66 | | | % 154.86/23.66 | | | REDUCE: (17), (51) imply: % 154.86/23.66 | | | (54) ~ (e2 = e1) % 154.86/23.66 | | | % 154.86/23.66 | | | REDUCE: (14), (51) imply: % 154.86/23.66 | | | (55) ~ (e2 = e0) % 154.86/23.66 | | | % 154.86/23.66 | | | BETA: splitting (24) gives: % 154.86/23.66 | | | % 154.86/23.66 | | | Case 1: % 154.86/23.66 | | | | % 154.86/23.66 | | | | (56) all_54_4 = e0 % 154.86/23.66 | | | | % 154.86/23.66 | | | | REF_CLOSE: (29), (41), (56) are inconsistent by sub-proof #859. % 154.86/23.66 | | | | % 154.86/23.66 | | | Case 2: % 154.86/23.66 | | | | % 154.86/23.66 | | | | (57) ~ (all_54_4 = e0) % 154.86/23.66 | | | | (58) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 154.86/23.66 | | | | % 154.86/23.66 | | | | BETA: splitting (32) gives: % 154.86/23.66 | | | | % 154.86/23.66 | | | | Case 1: % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | (59) all_56_2 = e3 % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | COMBINE_EQS: (25), (59) imply: % 154.86/23.66 | | | | | (60) all_52_1 = e3 % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | SIMP: (60) implies: % 154.86/23.66 | | | | | (61) all_52_1 = e3 % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | COMBINE_EQS: (22), (61) imply: % 154.86/23.66 | | | | | (62) all_58_8 = e3 % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | REDUCE: (53), (61) imply: % 154.86/23.66 | | | | | (63) ~ (e3 = e2) % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | REDUCE: (29), (61) imply: % 154.86/23.66 | | | | | (64) ~ (e3 = e0) % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | BETA: splitting (37) gives: % 154.86/23.66 | | | | | % 154.86/23.66 | | | | | Case 1: % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | | (65) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 = % 154.86/23.66 | | | | | | e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.66 | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.66 | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.86/23.66 | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.66 | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 = % 154.86/23.66 | | | | | | e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.66 | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.66 | | | | | | all_58_11 = e1 & all_58_17 = e1) | (all_58_2 = e2 & % 154.86/23.66 | | | | | | all_58_8 = e2 & all_58_13 = e0 & all_58_24 = e0) | % 154.86/23.66 | | | | | | (all_58_2 = e2 & all_58_8 = e2 & e3 = e2) | (all_58_4 = e3 & % 154.86/23.66 | | | | | | all_58_6 = e0 & all_58_15 = e3 & all_58_22 = e0) | % 154.86/23.66 | | | | | | (all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & all_58_17 % 154.86/23.66 | | | | | | = e1) | (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.66 | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.66 | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.86/23.66 | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.66 | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & all_58_26 % 154.86/23.66 | | | | | | = e0) % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | | BETA: splitting (65) gives: % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | | Case 1: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | (66) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & all_58_15 % 154.86/23.66 | | | | | | | = e1) | (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | all_58_11 = e2 & all_58_17 = e2) | (all_58_2 = e3 & % 154.86/23.66 | | | | | | | all_58_8 = e3 & all_58_13 = e2 & all_58_24 = e2) | % 154.86/23.66 | | | | | | | (all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & all_58_15 % 154.86/23.66 | | | | | | | = e3) | (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | all_58_11 = e1 & all_58_17 = e1) % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | BETA: splitting (66) gives: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (67) (all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | | all_58_15 = e1) | (all_58_2 = e3 & all_58_6 = e0 & % 154.86/23.66 | | | | | | | | all_58_8 = e3 & all_58_22 = e0) | (all_58_2 = e3 & % 154.86/23.66 | | | | | | | | all_58_8 = e3 & all_58_11 = e2 & all_58_17 = e2) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (67) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (68) all_58_2 = e3 & all_58_4 = e1 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | | | all_58_15 = e1 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | ALPHA: (68) implies: % 154.86/23.66 | | | | | | | | | (69) all_58_4 = e1 % 154.86/23.66 | | | | | | | | | (70) all_58_2 = e3 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | COMBINE_EQS: (33), (70) imply: % 154.86/23.66 | | | | | | | | | (71) e3 = e0 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | SIMP: (71) implies: % 154.86/23.66 | | | | | | | | | (72) e3 = e0 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | COMBINE_EQS: (46), (69) imply: % 154.86/23.66 | | | | | | | | | (73) e3 = e1 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | SIMP: (73) implies: % 154.86/23.66 | | | | | | | | | (74) e3 = e1 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | COMBINE_EQS: (72), (74) imply: % 154.86/23.66 | | | | | | | | | (75) e1 = e0 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (23), (27), (31), (36), (38), % 154.86/23.66 | | | | | | | | | (40), (54), (55), (63), (64), (75) are inconsistent % 154.86/23.66 | | | | | | | | | by sub-proof #667. % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (76) (all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | | | all_58_22 = e0) | (all_58_2 = e3 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | | | all_58_11 = e2 & all_58_17 = e2) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (76) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (77) all_58_2 = e3 & all_58_6 = e0 & all_58_8 = e3 & % 154.86/23.66 | | | | | | | | | | all_58_22 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (77) implies: % 154.86/23.66 | | | | | | | | | | (78) all_58_6 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (20), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (78) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #666. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (79) all_58_2 = e3 & all_58_8 = e3 & all_58_11 = e2 & % 154.86/23.66 | | | | | | | | | | all_58_17 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (79) implies: % 154.86/23.66 | | | | | | | | | | (80) all_58_2 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (33), (80) imply: % 154.86/23.66 | | | | | | | | | | (81) e3 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (81) implies: % 154.86/23.66 | | | | | | | | | | (82) e3 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REDUCE: (64), (82) imply: % 154.86/23.66 | | | | | | | | | | (83) $false % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | CLOSE: (83) is inconsistent. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (84) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.66 | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.66 | | | | | | | | all_58_8 = e2 & all_58_15 = e3) | (all_58_2 = e2 & % 154.86/23.66 | | | | | | | | all_58_6 = e3 & all_58_8 = e2 & all_58_22 = e3) | % 154.86/23.66 | | | | | | | | (all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.66 | | | | | | | | all_58_17 = e1) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (84) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (85) (all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.66 | | | | | | | | | all_58_24 = e2) | (all_58_2 = e2 & all_58_4 = e3 & % 154.86/23.66 | | | | | | | | | all_58_8 = e2 & all_58_15 = e3) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (85) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (86) all_58_2 = e3 & all_58_8 = e3 & all_58_13 = e2 & % 154.86/23.66 | | | | | | | | | | all_58_24 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (86) implies: % 154.86/23.66 | | | | | | | | | | (87) all_58_13 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (8), (55), (87) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #665. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (88) all_58_2 = e2 & all_58_4 = e3 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | | | | all_58_15 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (88) implies: % 154.86/23.66 | | | | | | | | | | (89) all_58_15 = e3 % 154.86/23.66 | | | | | | | | | | (90) all_58_8 = e2 % 154.86/23.66 | | | | | | | | | | (91) all_58_2 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (33), (91) imply: % 154.86/23.66 | | | | | | | | | | (92) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (92) implies: % 154.86/23.66 | | | | | | | | | | (93) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (62), (90) imply: % 154.86/23.66 | | | | | | | | | | (94) e3 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (94) implies: % 154.86/23.66 | | | | | | | | | | (95) e3 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (6), (89) imply: % 154.86/23.66 | | | | | | | | | | (96) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (95), (96) imply: % 154.86/23.66 | | | | | | | | | | (97) e2 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (93), (97) imply: % 154.86/23.66 | | | | | | | | | | (98) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (98) implies: % 154.86/23.66 | | | | | | | | | | (99) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (9), (15), (21), (23), (31), (36), (39), (52), % 154.86/23.66 | | | | | | | | | | (54), (55), (63), (64), (93), (99) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #650. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (100) (all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | | | all_58_22 = e3) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | | | all_58_11 = e1 & all_58_17 = e1) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (100) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (101) all_58_2 = e2 & all_58_6 = e3 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | | | | all_58_22 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (101) implies: % 154.86/23.66 | | | | | | | | | | (102) all_58_8 = e2 % 154.86/23.66 | | | | | | | | | | (103) all_58_6 = e3 % 154.86/23.66 | | | | | | | | | | (104) all_58_2 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (33), (104) imply: % 154.86/23.66 | | | | | | | | | | (105) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (105) implies: % 154.86/23.66 | | | | | | | | | | (106) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (20), (103) imply: % 154.86/23.66 | | | | | | | | | | (107) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (107) implies: % 154.86/23.66 | | | | | | | | | | (108) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (62), (102) imply: % 154.86/23.66 | | | | | | | | | | (109) e3 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (109) implies: % 154.86/23.66 | | | | | | | | | | (110) e3 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (9), (15), (21), (23), (31), (36), (39), (52), % 154.86/23.66 | | | | | | | | | | (54), (55), (63), (64), (106), (108), (110) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #649. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (111) all_58_2 = e2 & all_58_8 = e2 & all_58_11 = e1 & % 154.86/23.66 | | | | | | | | | | all_58_17 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (111) implies: % 154.86/23.66 | | | | | | | | | | (112) all_58_2 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (33), (55), (112) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #648. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | End of split % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | Case 2: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | (113) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.66 | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 = % 154.86/23.66 | | | | | | | e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.66 | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.86/23.66 | | | | | | | all_58_15 = e3 & all_58_17 = e1) | (all_58_4 = e3 & % 154.86/23.66 | | | | | | | all_58_15 = e3 & all_58_20 = e1 & all_58_26 = e1) | % 154.86/23.66 | | | | | | | (all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.66 | | | | | | | all_58_22 = e3) | (all_58_4 = e1 & all_58_11 = e2 & % 154.86/23.66 | | | | | | | all_58_15 = e1 & all_58_17 = e2) | (all_58_4 = e1 & % 154.86/23.66 | | | | | | | all_58_15 = e1 & all_58_20 = e0 & all_58_26 = e0) % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | BETA: splitting (113) gives: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (114) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.66 | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & e3 % 154.86/23.66 | | | | | | | | = e2) | (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = % 154.86/23.66 | | | | | | | | e3 & all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = % 154.86/23.66 | | | | | | | | e1 & all_58_15 = e3 & all_58_17 = e1) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (114) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (115) (all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.66 | | | | | | | | | all_58_24 = e0) | (all_58_2 = e2 & all_58_8 = e2 & % 154.86/23.66 | | | | | | | | | e3 = e2) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (115) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (116) all_58_2 = e2 & all_58_8 = e2 & all_58_13 = e0 & % 154.86/23.66 | | | | | | | | | | all_58_24 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (116) implies: % 154.86/23.66 | | | | | | | | | | (117) all_58_2 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (33), (55), (117) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #648. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (118) all_58_2 = e2 & all_58_8 = e2 & e3 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (118) implies: % 154.86/23.66 | | | | | | | | | | (119) all_58_2 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (33), (55), (119) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #648. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (120) (all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.66 | | | | | | | | | all_58_22 = e0) | (all_58_4 = e3 & all_58_11 = e1 & % 154.86/23.66 | | | | | | | | | all_58_15 = e3 & all_58_17 = e1) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (120) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (121) all_58_4 = e3 & all_58_6 = e0 & all_58_15 = e3 & % 154.86/23.66 | | | | | | | | | | all_58_22 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (121) implies: % 154.86/23.66 | | | | | | | | | | (122) all_58_6 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (20), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (122) % 154.86/23.66 | | | | | | | | | | are inconsistent by sub-proof #666. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (123) all_58_4 = e3 & all_58_11 = e1 & all_58_15 = e3 & % 154.86/23.66 | | | | | | | | | | all_58_17 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (123) implies: % 154.86/23.66 | | | | | | | | | | (124) all_58_15 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (6), (124) imply: % 154.86/23.66 | | | | | | | | | | (125) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REDUCE: (15), (125) imply: % 154.86/23.66 | | | | | | | | | | (126) $false % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | CLOSE: (126) is inconsistent. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (127) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.66 | | | | | | | | all_58_15 = e1 & all_58_22 = e3) | (all_58_4 = e1 & % 154.86/23.66 | | | | | | | | all_58_11 = e2 & all_58_15 = e1 & all_58_17 = e2) | % 154.86/23.66 | | | | | | | | (all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.66 | | | | | | | | all_58_26 = e0) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (127) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (128) (all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | | all_58_26 = e1) | (all_58_4 = e1 & all_58_6 = e3 & % 154.86/23.66 | | | | | | | | | all_58_15 = e1 & all_58_22 = e3) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (128) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (129) all_58_4 = e3 & all_58_15 = e3 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (129) implies: % 154.86/23.66 | | | | | | | | | | (130) all_58_15 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (6), (130) imply: % 154.86/23.66 | | | | | | | | | | (131) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REDUCE: (15), (131) imply: % 154.86/23.66 | | | | | | | | | | (132) $false % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | CLOSE: (132) is inconsistent. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (133) all_58_4 = e1 & all_58_6 = e3 & all_58_15 = e1 & % 154.86/23.66 | | | | | | | | | | all_58_22 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (133) implies: % 154.86/23.66 | | | | | | | | | | (134) all_58_22 = e3 % 154.86/23.66 | | | | | | | | | | (135) all_58_6 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (20), (135) imply: % 154.86/23.66 | | | | | | | | | | (136) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (136) implies: % 154.86/23.66 | | | | | | | | | | (137) e3 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (3), (134) imply: % 154.86/23.66 | | | | | | | | | | (138) e3 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (137), (138) imply: % 154.86/23.66 | | | | | | | | | | (139) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (23), (27), (31), (36), % 154.86/23.66 | | | | | | | | | | (38), (40), (54), (55), (63), (64), (139) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #667. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (140) (all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.66 | | | | | | | | | all_58_17 = e2) | (all_58_4 = e1 & all_58_15 = e1 & % 154.86/23.66 | | | | | | | | | all_58_20 = e0 & all_58_26 = e0) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (140) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (141) all_58_4 = e1 & all_58_11 = e2 & all_58_15 = e1 & % 154.86/23.66 | | | | | | | | | | all_58_17 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (141) implies: % 154.86/23.66 | | | | | | | | | | (142) all_58_4 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (15), (46), (142) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #647. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (143) all_58_4 = e1 & all_58_15 = e1 & all_58_20 = e0 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (143) implies: % 154.86/23.66 | | | | | | | | | | (144) all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (16), (19), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (144) % 154.86/23.66 | | | | | | | | | | are inconsistent by sub-proof #646. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | End of split % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | End of split % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | Case 2: % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | | (145) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = e3 % 154.86/23.66 | | | | | | & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) | % 154.86/23.66 | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.66 | | | | | | all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.66 | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 154.86/23.66 | | | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.86/23.66 | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 154.86/23.66 | | | | | | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) | % 154.86/23.66 | | | | | | (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.66 | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.66 | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.86/23.66 | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.66 | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 = % 154.86/23.66 | | | | | | e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = e0) | % 154.86/23.66 | | | | | | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.86/23.66 | | | | | | all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & e2 = % 154.86/23.66 | | | | | | e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | | BETA: splitting (145) gives: % 154.86/23.66 | | | | | | % 154.86/23.66 | | | | | | Case 1: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | (146) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 = % 154.86/23.66 | | | | | | | e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = e0) % 154.86/23.66 | | | | | | | | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.66 | | | | | | | all_58_26 = e0) | (all_58_6 = e0 & all_58_13 = e2 & % 154.86/23.66 | | | | | | | all_58_22 = e0 & all_58_24 = e2) | (all_58_6 = e0 & % 154.86/23.66 | | | | | | | all_58_20 = e1 & all_58_22 = e0 & all_58_26 = e1) | % 154.86/23.66 | | | | | | | (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | (all_58_11 = % 154.86/23.66 | | | | | | | e2 & all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | BETA: splitting (146) gives: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (147) (all_58_4 = e1 & all_58_15 = e1 & e3 = e1) | (all_58_6 % 154.86/23.66 | | | | | | | | = e3 & all_58_13 = e0 & all_58_22 = e3 & all_58_24 = % 154.86/23.66 | | | | | | | | e0) | (all_58_6 = e3 & all_58_20 = e0 & all_58_22 = % 154.86/23.66 | | | | | | | | e3 & all_58_26 = e0) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (147) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (148) all_58_4 = e1 & all_58_15 = e1 & e3 = e1 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | ALPHA: (148) implies: % 154.86/23.66 | | | | | | | | | (149) all_58_4 = e1 % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | REF_CLOSE: (15), (46), (149) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | #647. % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (150) (all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.66 | | | | | | | | | all_58_24 = e0) | (all_58_6 = e3 & all_58_20 = e0 & % 154.86/23.66 | | | | | | | | | all_58_22 = e3 & all_58_26 = e0) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (150) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (151) all_58_6 = e3 & all_58_13 = e0 & all_58_22 = e3 & % 154.86/23.66 | | | | | | | | | | all_58_24 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (151) implies: % 154.86/23.66 | | | | | | | | | | (152) all_58_22 = e3 % 154.86/23.66 | | | | | | | | | | (153) all_58_6 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (3), (9), (15), (19), (20), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (152), % 154.86/23.66 | | | | | | | | | | (153) are inconsistent by sub-proof #644. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (154) all_58_6 = e3 & all_58_20 = e0 & all_58_22 = e3 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (154) implies: % 154.86/23.66 | | | | | | | | | | (155) all_58_22 = e3 % 154.86/23.66 | | | | | | | | | | (156) all_58_6 = e3 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (3), (9), (15), (19), (20), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (155), % 154.86/23.66 | | | | | | | | | | (156) are inconsistent by sub-proof #644. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (157) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.66 | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | all_58_22 = e0 & all_58_26 = e1) | (all_58_6 = e0 & % 154.86/23.66 | | | | | | | | all_58_22 = e0 & e3 = e0) | (all_58_11 = e2 & % 154.86/23.66 | | | | | | | | all_58_13 = e0 & all_58_17 = e2 & all_58_24 = e0) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (157) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (158) (all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.66 | | | | | | | | | all_58_24 = e2) | (all_58_6 = e0 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | | all_58_22 = e0 & all_58_26 = e1) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (158) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (159) all_58_6 = e0 & all_58_13 = e2 & all_58_22 = e0 & % 154.86/23.66 | | | | | | | | | | all_58_24 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (159) implies: % 154.86/23.66 | | | | | | | | | | (160) all_58_13 = e2 % 154.86/23.66 | | | | | | | | | | (161) all_58_6 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (20), (161) imply: % 154.86/23.66 | | | | | | | | | | (162) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (8), (160) imply: % 154.86/23.66 | | | | | | | | | | (163) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (163) implies: % 154.86/23.66 | | | | | | | | | | (164) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (9), (15), (21), (23), (31), (36), (39), (52), % 154.86/23.66 | | | | | | | | | | (54), (55), (63), (64), (162), (164) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #650. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (165) all_58_6 = e0 & all_58_20 = e1 & all_58_22 = e0 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (165) implies: % 154.86/23.66 | | | | | | | | | | (166) all_58_6 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (20), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (166) % 154.86/23.66 | | | | | | | | | | are inconsistent by sub-proof #666. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (167) (all_58_6 = e0 & all_58_22 = e0 & e3 = e0) | % 154.86/23.66 | | | | | | | | | (all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.86/23.66 | | | | | | | | | all_58_24 = e0) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (167) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (168) all_58_6 = e0 & all_58_22 = e0 & e3 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (168) implies: % 154.86/23.66 | | | | | | | | | | (169) all_58_6 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (20), (23), (27), (31), % 154.86/23.66 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (169) % 154.86/23.66 | | | | | | | | | | are inconsistent by sub-proof #666. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (170) all_58_11 = e2 & all_58_13 = e0 & all_58_17 = e2 & % 154.86/23.66 | | | | | | | | | | all_58_24 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (170) implies: % 154.86/23.66 | | | | | | | | | | (171) all_58_24 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (18), (35), (171) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #643. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | End of split % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | Case 2: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | (172) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.66 | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.86/23.66 | | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.66 | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) | (all_58_13 % 154.86/23.66 | | | | | | | = e2 & all_58_20 = e0 & all_58_24 = e2 & all_58_26 = % 154.86/23.66 | | | | | | | e0) | (all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 % 154.86/23.66 | | | | | | | & all_58_26 = e1) | (all_58_13 = e0 & all_58_24 = e0 & % 154.86/23.66 | | | | | | | e2 = e0) | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | BETA: splitting (172) gives: % 154.86/23.66 | | | | | | | % 154.86/23.66 | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (173) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 & % 154.86/23.66 | | | | | | | | all_58_17 = e1 & all_58_24 = e2) | (all_58_11 = e1 & % 154.86/23.66 | | | | | | | | all_58_17 = e1 & all_58_20 = e0 & all_58_26 = e0) | % 154.86/23.66 | | | | | | | | (all_58_11 = e1 & all_58_17 = e1 & e2 = e1) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (173) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (174) (all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | | all_58_26 = e1) | (all_58_11 = e1 & all_58_13 = e2 % 154.86/23.66 | | | | | | | | | & all_58_17 = e1 & all_58_24 = e2) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (174) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (175) all_58_11 = e2 & all_58_17 = e2 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (175) implies: % 154.86/23.66 | | | | | | | | | | (176) all_58_20 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (11), (12), (176) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #642. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (177) all_58_11 = e1 & all_58_13 = e2 & all_58_17 = e1 & % 154.86/23.66 | | | | | | | | | | all_58_24 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (177) implies: % 154.86/23.66 | | | | | | | | | | (178) all_58_13 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (8), (55), (178) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #665. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (179) (all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.66 | | | | | | | | | all_58_26 = e0) | (all_58_11 = e1 & all_58_17 = e1 % 154.86/23.66 | | | | | | | | | & e2 = e1) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (179) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (180) all_58_11 = e1 & all_58_17 = e1 & all_58_20 = e0 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (180) implies: % 154.86/23.66 | | | | | | | | | | (181) all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (16), (181) imply: % 154.86/23.66 | | | | | | | | | | (182) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (19), (23), (27), (31), (36), % 154.86/23.66 | | | | | | | | | | (38), (40), (54), (55), (63), (64), (182) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #667. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (183) all_58_11 = e1 & all_58_17 = e1 & e2 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (183) implies: % 154.86/23.66 | | | | | | | | | | (184) e2 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REDUCE: (54), (184) imply: % 154.86/23.66 | | | | | | | | | | (185) $false % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | CLOSE: (185) is inconsistent. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | End of split % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | (186) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.66 | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 & % 154.86/23.66 | | | | | | | | all_58_24 = e0 & all_58_26 = e1) | (all_58_13 = e0 & % 154.86/23.66 | | | | | | | | all_58_24 = e0 & e2 = e0) | (all_58_20 = e0 & % 154.86/23.66 | | | | | | | | all_58_26 = e0 & e1 = e0) % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | BETA: splitting (186) gives: % 154.86/23.66 | | | | | | | | % 154.86/23.66 | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (187) (all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.66 | | | | | | | | | all_58_26 = e0) | (all_58_13 = e0 & all_58_20 = e1 % 154.86/23.66 | | | | | | | | | & all_58_24 = e0 & all_58_26 = e1) % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | BETA: splitting (187) gives: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 1: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (188) all_58_13 = e2 & all_58_20 = e0 & all_58_24 = e2 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (188) implies: % 154.86/23.66 | | | | | | | | | | (189) all_58_26 = e0 % 154.86/23.66 | | | | | | | | | | (190) all_58_13 = e2 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (8), (190) imply: % 154.86/23.66 | | | | | | | | | | (191) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (191) implies: % 154.86/23.66 | | | | | | | | | | (192) e2 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | COMBINE_EQS: (16), (189) imply: % 154.86/23.66 | | | | | | | | | | (193) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | SIMP: (193) implies: % 154.86/23.66 | | | | | | | | | | (194) e1 = e0 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (9), (15), (21), (23), (31), (36), (39), (52), % 154.86/23.66 | | | | | | | | | | (54), (55), (63), (64), (192), (194) are % 154.86/23.66 | | | | | | | | | | inconsistent by sub-proof #650. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | (195) all_58_13 = e0 & all_58_20 = e1 & all_58_24 = e0 & % 154.86/23.66 | | | | | | | | | | all_58_26 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | ALPHA: (195) implies: % 154.86/23.66 | | | | | | | | | | (196) all_58_20 = e1 % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | | REF_CLOSE: (11), (12), (196) are inconsistent by sub-proof % 154.86/23.66 | | | | | | | | | | #642. % 154.86/23.66 | | | | | | | | | | % 154.86/23.66 | | | | | | | | | End of split % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | Case 2: % 154.86/23.66 | | | | | | | | | % 154.86/23.66 | | | | | | | | | (197) (all_58_13 = e0 & all_58_24 = e0 & e2 = e0) | % 154.86/23.66 | | | | | | | | | (all_58_20 = e0 & all_58_26 = e0 & e1 = e0) % 154.86/23.67 | | | | | | | | | % 154.86/23.67 | | | | | | | | | BETA: splitting (197) gives: % 154.86/23.67 | | | | | | | | | % 154.86/23.67 | | | | | | | | | Case 1: % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | (198) all_58_13 = e0 & all_58_24 = e0 & e2 = e0 % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | ALPHA: (198) implies: % 154.86/23.67 | | | | | | | | | | (199) e2 = e0 % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | REDUCE: (55), (199) imply: % 154.86/23.67 | | | | | | | | | | (200) $false % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | CLOSE: (200) is inconsistent. % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | Case 2: % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | (201) all_58_20 = e0 & all_58_26 = e0 & e1 = e0 % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | ALPHA: (201) implies: % 154.86/23.67 | | | | | | | | | | (202) all_58_26 = e0 % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | | REF_CLOSE: (1), (9), (15), (16), (19), (23), (27), (31), % 154.86/23.67 | | | | | | | | | | (36), (38), (40), (54), (55), (63), (64), (202) % 154.86/23.67 | | | | | | | | | | are inconsistent by sub-proof #646. % 154.86/23.67 | | | | | | | | | | % 154.86/23.67 | | | | | | | | | End of split % 154.86/23.67 | | | | | | | | | % 154.86/23.67 | | | | | | | | End of split % 154.86/23.67 | | | | | | | | % 154.86/23.67 | | | | | | | End of split % 154.86/23.67 | | | | | | | % 154.86/23.67 | | | | | | End of split % 154.86/23.67 | | | | | | % 154.86/23.67 | | | | | End of split % 154.86/23.67 | | | | | % 154.86/23.67 | | | | Case 2: % 154.86/23.67 | | | | | % 154.86/23.67 | | | | | (203) ~ (all_56_2 = e3) % 154.86/23.67 | | | | | % 154.86/23.67 | | | | | REDUCE: (25), (203) imply: % 154.86/23.67 | | | | | (204) ~ (all_52_1 = e3) % 154.86/23.67 | | | | | % 154.86/23.67 | | | | | REF_CLOSE: (2), (41), (53), (58), (204) are inconsistent by sub-proof % 154.86/23.67 | | | | | #828. % 154.86/23.67 | | | | | % 154.86/23.67 | | | | End of split % 154.86/23.67 | | | | % 154.86/23.67 | | | End of split % 154.86/23.67 | | | % 154.86/23.67 | | Case 2: % 154.86/23.67 | | | % 154.86/23.67 | | | (205) ~ (all_56_0 = e2) % 154.86/23.67 | | | % 154.86/23.67 | | | REDUCE: (28), (205) imply: % 154.86/23.67 | | | (206) ~ (all_10_2 = e2) % 154.86/23.67 | | | % 154.86/23.67 | | | REF_CLOSE: (13), (17), (34), (48), (206) are inconsistent by sub-proof % 154.86/23.67 | | | #813. % 154.86/23.67 | | | % 154.86/23.67 | | End of split % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 154.86/23.67 | | (207) all_56_9 = e3 % 154.86/23.67 | | % 154.86/23.67 | | COMBINE_EQS: (4), (207) imply: % 154.86/23.67 | | (208) e3 = e1 % 154.86/23.67 | | % 154.86/23.67 | | REDUCE: (15), (208) imply: % 154.86/23.67 | | (209) $false % 154.86/23.67 | | % 154.86/23.67 | | CLOSE: (209) is inconsistent. % 154.86/23.67 | | % 154.86/23.67 | End of split % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #642 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_20 = all_52_14 % 154.86/23.67 (2) all_58_20 = e1 % 154.86/23.67 (3) ~ (all_52_14 = e1) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (1), (2) imply: % 154.86/23.67 | (4) all_52_14 = e1 % 154.86/23.67 | % 154.86/23.67 | SIMP: (4) implies: % 154.86/23.67 | (5) all_52_14 = e1 % 154.86/23.67 | % 154.86/23.67 | REDUCE: (3), (5) imply: % 154.86/23.67 | (6) $false % 154.86/23.67 | % 154.86/23.67 | CLOSE: (6) is inconsistent. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #643 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_24 = all_52_7 % 154.86/23.67 (2) all_58_24 = e0 % 154.86/23.67 (3) ~ (all_52_7 = e0) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (1), (2) imply: % 154.86/23.67 | (4) all_52_7 = e0 % 154.86/23.67 | % 154.86/23.67 | SIMP: (4) implies: % 154.86/23.67 | (5) all_52_7 = e0 % 154.86/23.67 | % 154.86/23.67 | REDUCE: (3), (5) imply: % 154.86/23.67 | (6) $false % 154.86/23.67 | % 154.86/23.67 | CLOSE: (6) is inconsistent. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #644 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_31 = all_4_2 % 154.86/23.67 (2) all_58_22 = e0 % 154.86/23.67 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (4) ~ (e3 = e1) % 154.86/23.67 (5) all_58_30 = e0 % 154.86/23.67 (6) all_58_6 = e1 % 154.86/23.67 (7) ~ (e2 = e1) % 154.86/23.67 (8) all_58_29 = e1 % 154.86/23.67 (9) ~ (e3 = e0) % 154.86/23.67 (10) all_58_6 = e3 % 154.86/23.67 (11) all_58_28 = all_10_2 % 154.86/23.67 (12) ~ (e2 = e0) % 154.86/23.67 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (14) ~ (e1 = e0) % 154.86/23.67 (15) ~ (all_4_2 = e1) % 154.86/23.67 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (17) ~ (e3 = e2) % 154.86/23.67 (18) all_58_22 = e3 % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (6), (10) imply: % 154.86/23.67 | (19) e3 = e1 % 154.86/23.67 | % 154.86/23.67 | SIMP: (19) implies: % 154.86/23.67 | (20) e3 = e1 % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (2), (18) imply: % 154.86/23.67 | (21) e3 = e0 % 154.86/23.67 | % 154.86/23.67 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14), (15), % 154.86/23.67 | (16), (17), (20), (21) are inconsistent by sub-proof #645. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #645 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_31 = all_4_2 % 154.86/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (3) ~ (e3 = e1) % 154.86/23.67 (4) e3 = e1 % 154.86/23.67 (5) all_58_30 = e0 % 154.86/23.67 (6) ~ (e2 = e1) % 154.86/23.67 (7) all_58_29 = e1 % 154.86/23.67 (8) ~ (e3 = e0) % 154.86/23.67 (9) e3 = e0 % 154.86/23.67 (10) all_58_28 = all_10_2 % 154.86/23.67 (11) ~ (e2 = e0) % 154.86/23.67 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (13) ~ (e1 = e0) % 154.86/23.67 (14) ~ (all_4_2 = e1) % 154.86/23.67 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (16) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (4), (9) imply: % 154.86/23.67 | (17) e1 = e0 % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (7), (17) imply: % 154.86/23.67 | (18) all_58_29 = e0 % 154.86/23.67 | % 154.86/23.67 | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (13), (14), (15), % 154.86/23.67 | (16), (18) are inconsistent by sub-proof #698. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #646 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_31 = all_4_2 % 154.86/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (3) ~ (e3 = e1) % 154.86/23.67 (4) all_58_26 = e1 % 154.86/23.67 (5) all_58_30 = e0 % 154.86/23.67 (6) ~ (e2 = e1) % 154.86/23.67 (7) all_58_29 = e1 % 154.86/23.67 (8) all_58_26 = e0 % 154.86/23.67 (9) ~ (e3 = e0) % 154.86/23.67 (10) all_58_28 = all_10_2 % 154.86/23.67 (11) ~ (e2 = e0) % 154.86/23.67 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (13) ~ (e1 = e0) % 154.86/23.67 (14) ~ (all_4_2 = e1) % 154.86/23.67 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (16) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (4), (8) imply: % 154.86/23.67 | (17) e1 = e0 % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (7), (17) imply: % 154.86/23.67 | (18) all_58_29 = e0 % 154.86/23.67 | % 154.86/23.67 | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (12), (13), (14), (15), % 154.86/23.67 | (16), (18) are inconsistent by sub-proof #698. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #647 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_4 = e3 % 154.86/23.67 (2) all_58_4 = e1 % 154.86/23.67 (3) ~ (e3 = e1) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (1), (2) imply: % 154.86/23.67 | (4) e3 = e1 % 154.86/23.67 | % 154.86/23.67 | SIMP: (4) implies: % 154.86/23.67 | (5) e3 = e1 % 154.86/23.67 | % 154.86/23.67 | REDUCE: (3), (5) imply: % 154.86/23.67 | (6) $false % 154.86/23.67 | % 154.86/23.67 | CLOSE: (6) is inconsistent. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #648 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_2 = e2 % 154.86/23.67 (2) all_58_2 = e0 % 154.86/23.67 (3) ~ (e2 = e0) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (1), (2) imply: % 154.86/23.67 | (4) e2 = e0 % 154.86/23.67 | % 154.86/23.67 | SIMP: (4) implies: % 154.86/23.67 | (5) e2 = e0 % 154.86/23.67 | % 154.86/23.67 | REDUCE: (3), (5) imply: % 154.86/23.67 | (6) $false % 154.86/23.67 | % 154.86/23.67 | CLOSE: (6) is inconsistent. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #649 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (2) ~ (e3 = e1) % 154.86/23.67 (3) e3 = e1 % 154.86/23.67 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (5) ~ (e2 = e1) % 154.86/23.67 (6) all_58_29 = e1 % 154.86/23.67 (7) ~ (e3 = e0) % 154.86/23.67 (8) ~ (e2 = e0) % 154.86/23.67 (9) e2 = e0 % 154.86/23.67 (10) all_58_28 = e2 % 154.86/23.67 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (12) ~ (e1 = e0) % 154.86/23.67 (13) all_58_30 = all_6_2 % 154.86/23.67 (14) ~ (e3 = e2) % 154.86/23.67 (15) e3 = e2 % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (3), (15) imply: % 154.86/23.67 | (16) e2 = e1 % 154.86/23.67 | % 154.86/23.67 | SIMP: (16) implies: % 154.86/23.67 | (17) e2 = e1 % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (9), (17) imply: % 154.86/23.67 | (18) e1 = e0 % 154.86/23.67 | % 154.86/23.67 | SIMP: (18) implies: % 154.86/23.67 | (19) e1 = e0 % 154.86/23.67 | % 154.86/23.67 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 154.86/23.67 | (14), (19) are inconsistent by sub-proof #650. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #650 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (2) ~ (e3 = e1) % 154.86/23.67 (3) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (4) ~ (e2 = e1) % 154.86/23.67 (5) all_58_29 = e1 % 154.86/23.67 (6) ~ (e3 = e0) % 154.86/23.67 (7) ~ (e2 = e0) % 154.86/23.67 (8) e2 = e0 % 154.86/23.67 (9) all_58_28 = e2 % 154.86/23.67 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (11) ~ (e1 = e0) % 154.86/23.67 (12) e1 = e0 % 154.86/23.67 (13) all_58_30 = all_6_2 % 154.86/23.67 (14) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (5), (12) imply: % 154.86/23.67 | (15) all_58_29 = e0 % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (8), (9) imply: % 154.86/23.67 | (16) all_58_28 = e0 % 154.86/23.67 | % 154.86/23.67 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (10), (11), (13), (14), (15), (16) % 154.86/23.67 | are inconsistent by sub-proof #651. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #651 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_28 = e0 % 154.86/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (3) ~ (e3 = e1) % 154.86/23.67 (4) all_58_29 = e0 % 154.86/23.67 (5) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (6) ~ (e2 = e1) % 154.86/23.67 (7) ~ (e3 = e0) % 154.86/23.67 (8) ~ (e2 = e0) % 154.86/23.67 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (10) ~ (e1 = e0) % 154.86/23.67 (11) all_58_30 = all_6_2 % 154.86/23.67 (12) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | BETA: splitting (5) gives: % 154.86/23.67 | % 154.86/23.67 | Case 1: % 154.86/23.67 | | % 154.86/23.67 | | (13) all_58_29 = e1 % 154.86/23.67 | | % 154.86/23.67 | | COMBINE_EQS: (4), (13) imply: % 154.86/23.67 | | (14) e1 = e0 % 154.86/23.67 | | % 154.86/23.67 | | REDUCE: (10), (14) imply: % 154.86/23.67 | | (15) $false % 154.86/23.67 | | % 154.86/23.67 | | CLOSE: (15) is inconsistent. % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 154.86/23.67 | | (16) all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (16) are % 154.86/23.67 | | inconsistent by sub-proof #652. % 154.86/23.67 | | % 154.86/23.67 | End of split % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #652 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_28 = e0 % 154.86/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (3) ~ (e3 = e1) % 154.86/23.67 (4) all_58_29 = e0 % 154.86/23.67 (5) ~ (e2 = e1) % 154.86/23.67 (6) ~ (e3 = e0) % 154.86/23.67 (7) ~ (e2 = e0) % 154.86/23.67 (8) all_58_30 = e1 | all_58_31 = e1 % 154.86/23.67 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (10) all_58_30 = all_6_2 % 154.86/23.67 (11) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | BETA: splitting (8) gives: % 154.86/23.67 | % 154.86/23.67 | Case 1: % 154.86/23.67 | | % 154.86/23.67 | | (12) all_58_30 = e1 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12) are % 154.86/23.67 | | inconsistent by sub-proof #660. % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 154.86/23.67 | | (13) all_58_31 = e1 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13) are % 154.86/23.67 | | inconsistent by sub-proof #653. % 154.86/23.67 | | % 154.86/23.67 | End of split % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #653 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_28 = e0 % 154.86/23.67 (2) all_58_31 = e1 % 154.86/23.67 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (4) ~ (e3 = e1) % 154.86/23.67 (5) all_58_29 = e0 % 154.86/23.67 (6) ~ (e2 = e1) % 154.86/23.67 (7) ~ (e3 = e0) % 154.86/23.67 (8) ~ (e2 = e0) % 154.86/23.67 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (10) all_58_30 = all_6_2 % 154.86/23.67 (11) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | BETA: splitting (9) gives: % 154.86/23.67 | % 154.86/23.67 | Case 1: % 154.86/23.67 | | % 154.86/23.67 | | (12) all_58_28 = e3 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #689. % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 154.86/23.67 | | (13) ~ (all_58_28 = e3) % 154.86/23.67 | | (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 | | % 154.86/23.67 | | REDUCE: (1), (13) imply: % 154.86/23.67 | | (15) ~ (e3 = e0) % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14) are % 154.86/23.67 | | inconsistent by sub-proof #654. % 154.86/23.67 | | % 154.86/23.67 | End of split % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #654 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_28 = e0 % 154.86/23.67 (2) all_58_31 = e1 % 154.86/23.67 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (4) ~ (e3 = e1) % 154.86/23.67 (5) all_58_29 = e0 % 154.86/23.67 (6) ~ (e2 = e1) % 154.86/23.67 (7) ~ (e3 = e0) % 154.86/23.67 (8) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (9) ~ (e2 = e0) % 154.86/23.67 (10) all_58_30 = all_6_2 % 154.86/23.67 (11) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | BETA: splitting (3) gives: % 154.86/23.67 | % 154.86/23.67 | Case 1: % 154.86/23.67 | | % 154.86/23.67 | | (12) all_58_28 = e2 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (9), (12) are inconsistent by sub-proof #688. % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 154.86/23.67 | | (13) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 | | % 154.86/23.67 | | BETA: splitting (8) gives: % 154.86/23.67 | | % 154.86/23.67 | | Case 1: % 154.86/23.67 | | | % 154.86/23.67 | | | (14) all_58_29 = e3 % 154.86/23.67 | | | % 154.86/23.67 | | | REF_CLOSE: (5), (7), (14) are inconsistent by sub-proof #707. % 154.86/23.67 | | | % 154.86/23.67 | | Case 2: % 154.86/23.67 | | | % 154.86/23.67 | | | (15) all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 | | | % 154.86/23.67 | | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (11), (13), (15) are % 154.86/23.67 | | | inconsistent by sub-proof #655. % 154.86/23.67 | | | % 154.86/23.67 | | End of split % 154.86/23.67 | | % 154.86/23.67 | End of split % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #655 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_31 = e1 % 154.86/23.67 (2) ~ (e3 = e1) % 154.86/23.67 (3) all_58_29 = e0 % 154.86/23.67 (4) ~ (e2 = e1) % 154.86/23.67 (5) all_58_30 = e3 | all_58_31 = e3 % 154.86/23.67 (6) ~ (e2 = e0) % 154.86/23.67 (7) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (8) all_58_30 = all_6_2 % 154.86/23.67 (9) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | BETA: splitting (5) gives: % 154.86/23.67 | % 154.86/23.67 | Case 1: % 154.86/23.67 | | % 154.86/23.67 | | (10) all_58_30 = e3 % 154.86/23.67 | | % 154.86/23.67 | | COMBINE_EQS: (8), (10) imply: % 154.86/23.67 | | (11) all_6_2 = e3 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10) are inconsistent by sub-proof % 154.86/23.67 | | #657. % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 154.86/23.67 | | (12) all_58_31 = e3 % 154.86/23.67 | | % 154.86/23.67 | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #656. % 154.86/23.67 | | % 154.86/23.67 | End of split % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #656 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_31 = e3 % 154.86/23.67 (2) all_58_31 = e1 % 154.86/23.67 (3) ~ (e3 = e1) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | COMBINE_EQS: (1), (2) imply: % 154.86/23.67 | (4) e3 = e1 % 154.86/23.67 | % 154.86/23.67 | SIMP: (4) implies: % 154.86/23.67 | (5) e3 = e1 % 154.86/23.67 | % 154.86/23.67 | REDUCE: (3), (5) imply: % 154.86/23.67 | (6) $false % 154.86/23.67 | % 154.86/23.67 | CLOSE: (6) is inconsistent. % 154.86/23.67 | % 154.86/23.67 End of proof % 154.86/23.67 % 154.86/23.67 Sub-proof #657 shows that the following formulas are inconsistent: % 154.86/23.67 ---------------------------------------------------------------- % 154.86/23.67 (1) all_58_31 = e1 % 154.86/23.67 (2) all_58_30 = e3 % 154.86/23.67 (3) all_58_29 = e0 % 154.86/23.67 (4) ~ (e2 = e1) % 154.86/23.67 (5) ~ (e2 = e0) % 154.86/23.67 (6) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 154.86/23.67 (7) ~ (e3 = e2) % 154.86/23.67 % 154.86/23.67 Begin of proof % 154.86/23.67 | % 154.86/23.67 | BETA: splitting (6) gives: % 154.86/23.67 | % 154.86/23.67 | Case 1: % 154.86/23.67 | | % 154.86/23.67 | | (8) all_58_29 = e2 % 154.86/23.67 | | % 154.86/23.67 | | COMBINE_EQS: (3), (8) imply: % 154.86/23.67 | | (9) e2 = e0 % 154.86/23.67 | | % 154.86/23.67 | | REDUCE: (5), (9) imply: % 154.86/23.67 | | (10) $false % 154.86/23.67 | | % 154.86/23.67 | | CLOSE: (10) is inconsistent. % 154.86/23.67 | | % 154.86/23.67 | Case 2: % 154.86/23.67 | | % 155.03/23.67 | | (11) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 | | % 155.03/23.67 | | REF_CLOSE: (1), (2), (4), (7), (11) are inconsistent by sub-proof #658. % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #658 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_31 = e1 % 155.03/23.67 (2) all_58_30 = e3 % 155.03/23.67 (3) ~ (e2 = e1) % 155.03/23.67 (4) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 (5) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | BETA: splitting (4) gives: % 155.03/23.67 | % 155.03/23.67 | Case 1: % 155.03/23.67 | | % 155.03/23.67 | | (6) all_58_30 = e2 % 155.03/23.67 | | % 155.03/23.67 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #659. % 155.03/23.67 | | % 155.03/23.67 | Case 2: % 155.03/23.67 | | % 155.03/23.67 | | (7) all_58_31 = e2 % 155.03/23.67 | | % 155.03/23.67 | | COMBINE_EQS: (1), (7) imply: % 155.03/23.67 | | (8) e2 = e1 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (3), (8) imply: % 155.03/23.67 | | (9) $false % 155.03/23.67 | | % 155.03/23.67 | | CLOSE: (9) is inconsistent. % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #659 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_30 = e3 % 155.03/23.67 (2) all_58_30 = e2 % 155.03/23.67 (3) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | COMBINE_EQS: (1), (2) imply: % 155.03/23.67 | (4) e3 = e2 % 155.03/23.67 | % 155.03/23.67 | SIMP: (4) implies: % 155.03/23.67 | (5) e3 = e2 % 155.03/23.67 | % 155.03/23.67 | REDUCE: (3), (5) imply: % 155.03/23.67 | (6) $false % 155.03/23.67 | % 155.03/23.67 | CLOSE: (6) is inconsistent. % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #660 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_28 = e0 % 155.03/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 (3) ~ (e3 = e1) % 155.03/23.67 (4) all_58_29 = e0 % 155.03/23.67 (5) ~ (e2 = e1) % 155.03/23.67 (6) ~ (e3 = e0) % 155.03/23.67 (7) all_58_30 = e1 % 155.03/23.67 (8) ~ (e2 = e0) % 155.03/23.67 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (10) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | BETA: splitting (9) gives: % 155.03/23.67 | % 155.03/23.67 | Case 1: % 155.03/23.67 | | % 155.03/23.67 | | (11) all_58_28 = e3 % 155.03/23.67 | | % 155.03/23.67 | | REF_CLOSE: (1), (6), (11) are inconsistent by sub-proof #689. % 155.03/23.67 | | % 155.03/23.67 | Case 2: % 155.03/23.67 | | % 155.03/23.67 | | (12) ~ (all_58_28 = e3) % 155.03/23.67 | | (13) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (1), (12) imply: % 155.03/23.67 | | (14) ~ (e3 = e0) % 155.03/23.67 | | % 155.03/23.67 | | BETA: splitting (2) gives: % 155.03/23.67 | | % 155.03/23.67 | | Case 1: % 155.03/23.67 | | | % 155.03/23.67 | | | (15) all_58_28 = e2 % 155.03/23.67 | | | % 155.03/23.67 | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #688. % 155.03/23.67 | | | % 155.03/23.67 | | Case 2: % 155.03/23.67 | | | % 155.03/23.67 | | | (16) ~ (all_58_28 = e2) % 155.03/23.67 | | | (17) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 | | | % 155.03/23.67 | | | REDUCE: (1), (16) imply: % 155.03/23.67 | | | (18) ~ (e2 = e0) % 155.03/23.67 | | | % 155.03/23.67 | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (13), (17) are inconsistent % 155.03/23.67 | | | by sub-proof #661. % 155.03/23.67 | | | % 155.03/23.67 | | End of split % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #661 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) ~ (e3 = e1) % 155.03/23.67 (2) all_58_29 = e0 % 155.03/23.67 (3) ~ (e2 = e1) % 155.03/23.67 (4) ~ (e3 = e0) % 155.03/23.67 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (6) all_58_30 = e1 % 155.03/23.67 (7) ~ (e2 = e0) % 155.03/23.67 (8) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 (9) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | BETA: splitting (8) gives: % 155.03/23.67 | % 155.03/23.67 | Case 1: % 155.03/23.67 | | % 155.03/23.67 | | (10) all_58_29 = e2 % 155.03/23.67 | | % 155.03/23.67 | | COMBINE_EQS: (2), (10) imply: % 155.03/23.67 | | (11) e2 = e0 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (7), (11) imply: % 155.03/23.67 | | (12) $false % 155.03/23.67 | | % 155.03/23.67 | | CLOSE: (12) is inconsistent. % 155.03/23.67 | | % 155.03/23.67 | Case 2: % 155.03/23.67 | | % 155.03/23.67 | | (13) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 | | % 155.03/23.67 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (13) are inconsistent by % 155.03/23.67 | | sub-proof #662. % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #662 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) ~ (e3 = e1) % 155.03/23.67 (2) all_58_29 = e0 % 155.03/23.67 (3) ~ (e2 = e1) % 155.03/23.67 (4) ~ (e3 = e0) % 155.03/23.67 (5) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (7) all_58_30 = e1 % 155.03/23.67 (8) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | BETA: splitting (5) gives: % 155.03/23.67 | % 155.03/23.67 | Case 1: % 155.03/23.67 | | % 155.03/23.67 | | (9) all_58_30 = e2 % 155.03/23.67 | | % 155.03/23.67 | | COMBINE_EQS: (7), (9) imply: % 155.03/23.67 | | (10) e2 = e1 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (3), (10) imply: % 155.03/23.67 | | (11) $false % 155.03/23.67 | | % 155.03/23.67 | | CLOSE: (11) is inconsistent. % 155.03/23.67 | | % 155.03/23.67 | Case 2: % 155.03/23.67 | | % 155.03/23.67 | | (12) all_58_31 = e2 % 155.03/23.67 | | % 155.03/23.67 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (12) are inconsistent by sub-proof % 155.03/23.67 | | #663. % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #663 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_31 = e2 % 155.03/23.67 (2) ~ (e3 = e1) % 155.03/23.67 (3) all_58_29 = e0 % 155.03/23.67 (4) ~ (e3 = e0) % 155.03/23.67 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (6) all_58_30 = e1 % 155.03/23.67 (7) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | BETA: splitting (5) gives: % 155.03/23.67 | % 155.03/23.67 | Case 1: % 155.03/23.67 | | % 155.03/23.67 | | (8) all_58_29 = e3 % 155.03/23.67 | | % 155.03/23.67 | | COMBINE_EQS: (3), (8) imply: % 155.03/23.67 | | (9) e3 = e0 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (4), (9) imply: % 155.03/23.67 | | (10) $false % 155.03/23.67 | | % 155.03/23.67 | | CLOSE: (10) is inconsistent. % 155.03/23.67 | | % 155.03/23.67 | Case 2: % 155.03/23.67 | | % 155.03/23.67 | | (11) all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 | | % 155.03/23.67 | | REF_CLOSE: (1), (2), (6), (7), (11) are inconsistent by sub-proof #664. % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #664 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_31 = e2 % 155.03/23.67 (2) ~ (e3 = e1) % 155.03/23.67 (3) all_58_30 = e1 % 155.03/23.67 (4) all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (5) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | BETA: splitting (4) gives: % 155.03/23.67 | % 155.03/23.67 | Case 1: % 155.03/23.67 | | % 155.03/23.67 | | (6) all_58_30 = e3 % 155.03/23.67 | | % 155.03/23.67 | | COMBINE_EQS: (3), (6) imply: % 155.03/23.67 | | (7) e3 = e1 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (2), (7) imply: % 155.03/23.67 | | (8) $false % 155.03/23.67 | | % 155.03/23.67 | | CLOSE: (8) is inconsistent. % 155.03/23.67 | | % 155.03/23.67 | Case 2: % 155.03/23.67 | | % 155.03/23.67 | | (9) all_58_31 = e3 % 155.03/23.67 | | % 155.03/23.67 | | COMBINE_EQS: (1), (9) imply: % 155.03/23.67 | | (10) e3 = e2 % 155.03/23.67 | | % 155.03/23.67 | | REDUCE: (5), (10) imply: % 155.03/23.67 | | (11) $false % 155.03/23.67 | | % 155.03/23.67 | | CLOSE: (11) is inconsistent. % 155.03/23.67 | | % 155.03/23.67 | End of split % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #665 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_13 = e2 % 155.03/23.67 (2) all_58_13 = e0 % 155.03/23.67 (3) ~ (e2 = e0) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | COMBINE_EQS: (1), (2) imply: % 155.03/23.67 | (4) e2 = e0 % 155.03/23.67 | % 155.03/23.67 | SIMP: (4) implies: % 155.03/23.67 | (5) e2 = e0 % 155.03/23.67 | % 155.03/23.67 | REDUCE: (3), (5) imply: % 155.03/23.67 | (6) $false % 155.03/23.67 | % 155.03/23.67 | CLOSE: (6) is inconsistent. % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #666 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_31 = all_4_2 % 155.03/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 (3) ~ (e3 = e1) % 155.03/23.67 (4) all_58_6 = e0 % 155.03/23.67 (5) all_58_30 = e0 % 155.03/23.67 (6) all_58_6 = e1 % 155.03/23.67 (7) ~ (e2 = e1) % 155.03/23.67 (8) all_58_29 = e1 % 155.03/23.67 (9) ~ (e3 = e0) % 155.03/23.67 (10) all_58_28 = all_10_2 % 155.03/23.67 (11) ~ (e2 = e0) % 155.03/23.67 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (13) ~ (e1 = e0) % 155.03/23.67 (14) ~ (all_4_2 = e1) % 155.03/23.67 (15) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.67 (16) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | COMBINE_EQS: (4), (6) imply: % 155.03/23.67 | (17) e1 = e0 % 155.03/23.67 | % 155.03/23.67 | COMBINE_EQS: (8), (17) imply: % 155.03/23.67 | (18) all_58_29 = e0 % 155.03/23.67 | % 155.03/23.67 | REF_CLOSE: (1), (2), (3), (5), (7), (9), (10), (11), (12), (13), (14), (15), % 155.03/23.67 | (16), (18) are inconsistent by sub-proof #698. % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #667 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_58_31 = all_4_2 % 155.03/23.67 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.67 (3) ~ (e3 = e1) % 155.03/23.67 (4) all_58_30 = e0 % 155.03/23.67 (5) ~ (e2 = e1) % 155.03/23.67 (6) all_58_29 = e1 % 155.03/23.67 (7) ~ (e3 = e0) % 155.03/23.67 (8) all_58_28 = all_10_2 % 155.03/23.67 (9) ~ (e2 = e0) % 155.03/23.67 (10) e1 = e0 % 155.03/23.67 (11) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.67 (12) ~ (e1 = e0) % 155.03/23.67 (13) ~ (all_4_2 = e1) % 155.03/23.67 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.67 (15) ~ (e3 = e2) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | SIMP: (10) implies: % 155.03/23.67 | (16) e1 = e0 % 155.03/23.67 | % 155.03/23.67 | COMBINE_EQS: (6), (16) imply: % 155.03/23.67 | (17) all_58_29 = e0 % 155.03/23.67 | % 155.03/23.67 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14), % 155.03/23.67 | (15), (17) are inconsistent by sub-proof #698. % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #668 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.67 (1) all_56_1 = e3 % 155.03/23.67 (2) all_56_1 = e0 % 155.03/23.67 (3) ~ (e3 = e0) % 155.03/23.67 % 155.03/23.67 Begin of proof % 155.03/23.67 | % 155.03/23.67 | COMBINE_EQS: (1), (2) imply: % 155.03/23.67 | (4) e3 = e0 % 155.03/23.67 | % 155.03/23.67 | SIMP: (4) implies: % 155.03/23.67 | (5) e3 = e0 % 155.03/23.67 | % 155.03/23.67 | REDUCE: (3), (5) imply: % 155.03/23.67 | (6) $false % 155.03/23.67 | % 155.03/23.67 | CLOSE: (6) is inconsistent. % 155.03/23.67 | % 155.03/23.67 End of proof % 155.03/23.67 % 155.03/23.67 Sub-proof #669 shows that the following formulas are inconsistent: % 155.03/23.67 ---------------------------------------------------------------- % 155.03/23.68 (1) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.03/23.68 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.03/23.68 (all_58_10 = e1) & ~ (all_58_12 = e0)) % 155.03/23.68 (2) all_58_0 = e3 % 155.03/23.68 (3) all_58_12 = e0 % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (1) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (4) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.03/23.68 | | (all_58_5 = e0) % 155.03/23.68 | | % 155.03/23.68 | | ALPHA: (4) implies: % 155.03/23.68 | | (5) ~ (all_58_0 = e3) % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (2), (5) imply: % 155.03/23.68 | | (6) $false % 155.03/23.68 | | % 155.03/23.68 | | CLOSE: (6) is inconsistent. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (7) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 155.03/23.68 | | (all_58_12 = e0) % 155.03/23.68 | | % 155.03/23.68 | | ALPHA: (7) implies: % 155.03/23.68 | | (8) ~ (all_58_12 = e0) % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (3), (8) imply: % 155.03/23.68 | | (9) $false % 155.03/23.68 | | % 155.03/23.68 | | CLOSE: (9) is inconsistent. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #670 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_56_15 = all_4_2 % 155.03/23.68 (3) ~ (all_52_11 = all_4_2) % 155.03/23.68 (4) all_56_14 = e1 | all_56_15 = e1 % 155.03/23.68 (5) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (6) all_58_29 = e1 % 155.03/23.68 (7) ~ (all_52_11 = all_6_2) % 155.03/23.68 (8) ~ (all_52_11 = e0) % 155.03/23.68 (9) all_56_14 = all_52_11 % 155.03/23.68 (10) e1 = e0 % 155.03/23.68 (11) ~ (all_4_2 = e1) % 155.03/23.68 (12) all_58_30 = all_6_2 % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | SIMP: (10) implies: % 155.03/23.68 | (13) e1 = e0 % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (6), (13) imply: % 155.03/23.68 | (14) all_58_29 = e0 % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (4) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (15) all_56_14 = e1 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (9), (15) imply: % 155.03/23.68 | | (16) all_52_11 = e1 % 155.03/23.68 | | % 155.03/23.68 | | SIMP: (16) implies: % 155.03/23.68 | | (17) all_52_11 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (7), (17) imply: % 155.03/23.68 | | (18) ~ (all_6_2 = e1) % 155.03/23.68 | | % 155.03/23.68 | | SIMP: (18) implies: % 155.03/23.68 | | (19) ~ (all_6_2 = e1) % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (3), (17) imply: % 155.03/23.68 | | (20) ~ (all_4_2 = e1) % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (8), (17) imply: % 155.03/23.68 | | (21) ~ (e1 = e0) % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (5), (11), (12), (14), (19), (21) are inconsistent by % 155.03/23.68 | | sub-proof #672. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (22) all_56_15 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (11), (22) are inconsistent by sub-proof #671. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #671 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_56_15 = all_4_2 % 155.03/23.68 (2) all_56_15 = e1 % 155.03/23.68 (3) ~ (all_4_2 = e1) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (1), (2) imply: % 155.03/23.68 | (4) all_4_2 = e1 % 155.03/23.68 | % 155.03/23.68 | SIMP: (4) implies: % 155.03/23.68 | (5) all_4_2 = e1 % 155.03/23.68 | % 155.03/23.68 | REDUCE: (3), (5) imply: % 155.03/23.68 | (6) $false % 155.03/23.68 | % 155.03/23.68 | CLOSE: (6) is inconsistent. % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #672 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_58_29 = e0 % 155.03/23.68 (3) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (4) ~ (e1 = e0) % 155.03/23.68 (5) ~ (all_6_2 = e1) % 155.03/23.68 (6) ~ (all_4_2 = e1) % 155.03/23.68 (7) all_58_30 = all_6_2 % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (3) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (8) all_58_29 = e1 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (2), (8) imply: % 155.03/23.68 | | (9) e1 = e0 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (4), (9) imply: % 155.03/23.68 | | (10) $false % 155.03/23.68 | | % 155.03/23.68 | | CLOSE: (10) is inconsistent. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (11) all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (5), (6), (7), (11) are inconsistent by sub-proof #673. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #673 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (3) ~ (all_6_2 = e1) % 155.03/23.68 (4) ~ (all_4_2 = e1) % 155.03/23.68 (5) all_58_30 = all_6_2 % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (2) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (6) all_58_30 = e1 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (5), (6) imply: % 155.03/23.68 | | (7) all_6_2 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (3), (7) imply: % 155.03/23.68 | | (8) $false % 155.03/23.68 | | % 155.03/23.68 | | CLOSE: (8) is inconsistent. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (9) all_58_31 = e1 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (1), (9) imply: % 155.03/23.68 | | (10) all_4_2 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (4), (10) imply: % 155.03/23.68 | | (11) $false % 155.03/23.68 | | % 155.03/23.68 | | CLOSE: (11) is inconsistent. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #674 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (2) all_58_30 = e0 % 155.03/23.68 (3) ~ (e2 = e0) % 155.03/23.68 (4) all_58_31 = e0 % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (1) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (5) all_58_30 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #718. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (6) all_58_31 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #855. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #675 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = e1 % 155.03/23.68 (2) all_58_30 = e0 % 155.03/23.68 (3) ~ (e2 = e1) % 155.03/23.68 (4) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (5) ~ (e2 = e0) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (4) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (6) all_58_30 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #718. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (7) all_58_31 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #697. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #676 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_56_13 = all_52_7 % 155.03/23.68 (2) all_56_13 = e1 % 155.03/23.68 (3) ~ (all_52_7 = e1) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (1), (2) imply: % 155.03/23.68 | (4) all_52_7 = e1 % 155.03/23.68 | % 155.03/23.68 | SIMP: (4) implies: % 155.03/23.68 | (5) all_52_7 = e1 % 155.03/23.68 | % 155.03/23.68 | REDUCE: (3), (5) imply: % 155.03/23.68 | (6) $false % 155.03/23.68 | % 155.03/23.68 | CLOSE: (6) is inconsistent. % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #677 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_58_30 = e0 % 155.03/23.68 (3) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (4) all_58_29 = e1 % 155.03/23.68 (5) e1 = e0 % 155.03/23.68 (6) ~ (e1 = e0) % 155.03/23.68 (7) ~ (all_4_2 = e1) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | SIMP: (5) implies: % 155.03/23.68 | (8) e1 = e0 % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (4), (8) imply: % 155.03/23.68 | (9) all_58_29 = e0 % 155.03/23.68 | % 155.03/23.68 | REF_CLOSE: (1), (2), (3), (6), (7), (9) are inconsistent by sub-proof #699. % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #678 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (3) ~ (e3 = e1) % 155.03/23.68 (4) all_20_2 = all_4_2 % 155.03/23.68 (5) all_58_29 = all_8_2 % 155.03/23.68 (6) all_58_30 = e0 % 155.03/23.68 (7) ~ (e2 = e1) % 155.03/23.68 (8) all_54_0 = e0 % 155.03/23.68 (9) ~ (e3 = e0) % 155.03/23.68 (10) all_58_28 = all_10_2 % 155.03/23.68 (11) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 155.03/23.68 (12) ~ (e2 = e0) % 155.03/23.68 (13) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 (14) all_54_0 = all_10_2 % 155.03/23.68 (15) ~ (e1 = e0) % 155.03/23.68 (16) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (17) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (8), (14) imply: % 155.03/23.68 | (18) all_10_2 = e0 % 155.03/23.68 | % 155.03/23.68 | SIMP: (18) implies: % 155.03/23.68 | (19) all_10_2 = e0 % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (10), (19) imply: % 155.03/23.68 | (20) all_58_28 = e0 % 155.03/23.68 | % 155.03/23.68 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13), (15), % 155.03/23.68 | (16), (17), (20) are inconsistent by sub-proof #679. % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #679 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_58_28 = e0 % 155.03/23.68 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (4) ~ (e3 = e1) % 155.03/23.68 (5) all_20_2 = all_4_2 % 155.03/23.68 (6) all_58_29 = all_8_2 % 155.03/23.68 (7) all_58_30 = e0 % 155.03/23.68 (8) ~ (e2 = e1) % 155.03/23.68 (9) ~ (e3 = e0) % 155.03/23.68 (10) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 155.03/23.68 (11) ~ (e2 = e0) % 155.03/23.68 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 (13) ~ (e1 = e0) % 155.03/23.68 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (15) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (10) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (16) ~ (all_20_2 = e1) % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (5), (16) imply: % 155.03/23.68 | | (17) ~ (all_4_2 = e1) % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14), % 155.03/23.68 | | (15), (17) are inconsistent by sub-proof #684. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (18) all_20_2 = e1 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (5), (18) imply: % 155.03/23.68 | | (19) all_4_2 = e1 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (1), (19) imply: % 155.03/23.68 | | (20) all_58_31 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), (15), (20) are % 155.03/23.68 | | inconsistent by sub-proof #680. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #680 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_28 = e0 % 155.03/23.68 (2) all_58_31 = e1 % 155.03/23.68 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (4) ~ (e3 = e1) % 155.03/23.68 (5) all_58_29 = all_8_2 % 155.03/23.68 (6) all_58_30 = e0 % 155.03/23.68 (7) ~ (e2 = e1) % 155.03/23.68 (8) ~ (e3 = e0) % 155.03/23.68 (9) ~ (e2 = e0) % 155.03/23.68 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 (11) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (10) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (12) all_58_28 = e3 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #689. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (13) ~ (all_58_28 = e3) % 155.03/23.68 | | (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (1), (13) imply: % 155.03/23.68 | | (15) ~ (e3 = e0) % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (14) are % 155.03/23.68 | | inconsistent by sub-proof #681. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #681 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_28 = e0 % 155.03/23.68 (2) all_58_31 = e1 % 155.03/23.68 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (4) ~ (e3 = e1) % 155.03/23.68 (5) all_58_29 = all_8_2 % 155.03/23.68 (6) all_58_30 = e0 % 155.03/23.68 (7) ~ (e2 = e1) % 155.03/23.68 (8) ~ (e3 = e0) % 155.03/23.68 (9) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 (10) ~ (e2 = e0) % 155.03/23.68 (11) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (9) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (12) all_58_29 = e3 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (5), (12) imply: % 155.03/23.68 | | (13) all_8_2 = e3 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (2), (3), (6), (7), (10), (11), (12) are inconsistent by % 155.03/23.68 | | sub-proof #682. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (14) all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (4), (6), (8), (14) are inconsistent by sub-proof #694. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #682 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_28 = e0 % 155.03/23.68 (2) all_58_31 = e1 % 155.03/23.68 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (4) all_58_29 = e3 % 155.03/23.68 (5) all_58_30 = e0 % 155.03/23.68 (6) ~ (e2 = e1) % 155.03/23.68 (7) ~ (e2 = e0) % 155.03/23.68 (8) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (3) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (9) all_58_28 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (7), (9) are inconsistent by sub-proof #688. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (10) ~ (all_58_28 = e2) % 155.03/23.68 | | (11) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (1), (10) imply: % 155.03/23.68 | | (12) ~ (e2 = e0) % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (11) are inconsistent by sub-proof % 155.03/23.68 | | #683. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #683 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = e1 % 155.03/23.68 (2) all_58_29 = e3 % 155.03/23.68 (3) all_58_30 = e0 % 155.03/23.68 (4) ~ (e2 = e1) % 155.03/23.68 (5) ~ (e2 = e0) % 155.03/23.68 (6) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (7) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (6) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (8) all_58_29 = e2 % 155.03/23.68 | | % 155.03/23.68 | | COMBINE_EQS: (2), (8) imply: % 155.03/23.68 | | (9) e3 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (7), (9) imply: % 155.03/23.68 | | (10) $false % 155.03/23.68 | | % 155.03/23.68 | | CLOSE: (10) is inconsistent. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (11) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (3), (4), (5), (11) are inconsistent by sub-proof #696. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #684 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_31 = all_4_2 % 155.03/23.68 (2) all_58_28 = e0 % 155.03/23.68 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (4) ~ (e3 = e1) % 155.03/23.68 (5) all_58_29 = all_8_2 % 155.03/23.68 (6) all_58_30 = e0 % 155.03/23.68 (7) ~ (e2 = e1) % 155.03/23.68 (8) ~ (e3 = e0) % 155.03/23.68 (9) ~ (e2 = e0) % 155.03/23.68 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 (11) ~ (e1 = e0) % 155.03/23.68 (12) ~ (all_4_2 = e1) % 155.03/23.68 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 (14) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (13) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (15) all_58_28 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (11), (15) are inconsistent by sub-proof #690. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (16) ~ (all_58_28 = e1) % 155.03/23.68 | | (17) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 | | % 155.03/23.68 | | REDUCE: (2), (16) imply: % 155.03/23.68 | | (18) ~ (e1 = e0) % 155.03/23.68 | | % 155.03/23.68 | | BETA: splitting (17) gives: % 155.03/23.68 | | % 155.03/23.68 | | Case 1: % 155.03/23.68 | | | % 155.03/23.68 | | | (19) all_58_29 = e1 % 155.03/23.68 | | | % 155.03/23.68 | | | COMBINE_EQS: (5), (19) imply: % 155.03/23.68 | | | (20) all_8_2 = e1 % 155.03/23.68 | | | % 155.03/23.68 | | | BETA: splitting (10) gives: % 155.03/23.68 | | | % 155.03/23.68 | | | Case 1: % 155.03/23.68 | | | | % 155.03/23.68 | | | | (21) all_58_28 = e3 % 155.03/23.68 | | | | % 155.03/23.68 | | | | REF_CLOSE: (2), (8), (21) are inconsistent by sub-proof #689. % 155.03/23.68 | | | | % 155.03/23.68 | | | Case 2: % 155.03/23.68 | | | | % 155.03/23.68 | | | | (22) ~ (all_58_28 = e3) % 155.03/23.68 | | | | (23) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 | | | | % 155.03/23.68 | | | | REDUCE: (2), (22) imply: % 155.03/23.68 | | | | (24) ~ (e3 = e0) % 155.03/23.68 | | | | % 155.03/23.68 | | | | BETA: splitting (3) gives: % 155.03/23.68 | | | | % 155.03/23.68 | | | | Case 1: % 155.03/23.68 | | | | | % 155.03/23.68 | | | | | (25) all_58_28 = e2 % 155.03/23.68 | | | | | % 155.03/23.68 | | | | | REF_CLOSE: (2), (9), (25) are inconsistent by sub-proof #688. % 155.03/23.68 | | | | | % 155.03/23.68 | | | | Case 2: % 155.03/23.68 | | | | | % 155.03/23.68 | | | | | (26) ~ (all_58_28 = e2) % 155.03/23.68 | | | | | (27) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 | | | | | % 155.03/23.68 | | | | | REDUCE: (2), (26) imply: % 155.03/23.68 | | | | | (28) ~ (e2 = e0) % 155.03/23.68 | | | | | % 155.03/23.68 | | | | | BETA: splitting (27) gives: % 155.03/23.68 | | | | | % 155.03/23.68 | | | | | Case 1: % 155.03/23.68 | | | | | | % 155.03/23.68 | | | | | | (29) all_58_29 = e2 % 155.03/23.68 | | | | | | % 155.03/23.68 | | | | | | REF_CLOSE: (7), (19), (29) are inconsistent by sub-proof #687. % 155.03/23.68 | | | | | | % 155.03/23.68 | | | | | Case 2: % 155.03/23.68 | | | | | | % 155.03/23.68 | | | | | | (30) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 | | | | | | % 155.03/23.68 | | | | | | REF_CLOSE: (4), (6), (8), (9), (14), (19), (23), (30) are % 155.03/23.68 | | | | | | inconsistent by sub-proof #685. % 155.03/23.68 | | | | | | % 155.03/23.68 | | | | | End of split % 155.03/23.68 | | | | | % 155.03/23.68 | | | | End of split % 155.03/23.68 | | | | % 155.03/23.68 | | | End of split % 155.03/23.68 | | | % 155.03/23.68 | | Case 2: % 155.03/23.68 | | | % 155.03/23.68 | | | (31) all_58_30 = e1 | all_58_31 = e1 % 155.03/23.68 | | | % 155.03/23.68 | | | REF_CLOSE: (1), (6), (11), (12), (31) are inconsistent by sub-proof #711. % 155.03/23.68 | | | % 155.03/23.68 | | End of split % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #685 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) ~ (e3 = e1) % 155.03/23.68 (2) all_58_30 = e0 % 155.03/23.68 (3) all_58_29 = e1 % 155.03/23.68 (4) ~ (e3 = e0) % 155.03/23.68 (5) all_58_30 = e2 | all_58_31 = e2 % 155.03/23.68 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 (7) ~ (e2 = e0) % 155.03/23.68 (8) ~ (e3 = e2) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | BETA: splitting (6) gives: % 155.03/23.68 | % 155.03/23.68 | Case 1: % 155.03/23.68 | | % 155.03/23.68 | | (9) all_58_29 = e3 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #686. % 155.03/23.68 | | % 155.03/23.68 | Case 2: % 155.03/23.68 | | % 155.03/23.68 | | (10) all_58_30 = e3 | all_58_31 = e3 % 155.03/23.68 | | % 155.03/23.68 | | REF_CLOSE: (2), (4), (5), (7), (8), (10) are inconsistent by sub-proof #704. % 155.03/23.68 | | % 155.03/23.68 | End of split % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #686 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_29 = e3 % 155.03/23.68 (2) all_58_29 = e1 % 155.03/23.68 (3) ~ (e3 = e1) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (1), (2) imply: % 155.03/23.68 | (4) e3 = e1 % 155.03/23.68 | % 155.03/23.68 | SIMP: (4) implies: % 155.03/23.68 | (5) e3 = e1 % 155.03/23.68 | % 155.03/23.68 | REDUCE: (3), (5) imply: % 155.03/23.68 | (6) $false % 155.03/23.68 | % 155.03/23.68 | CLOSE: (6) is inconsistent. % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #687 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_29 = e2 % 155.03/23.68 (2) all_58_29 = e1 % 155.03/23.68 (3) ~ (e2 = e1) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (1), (2) imply: % 155.03/23.68 | (4) e2 = e1 % 155.03/23.68 | % 155.03/23.68 | SIMP: (4) implies: % 155.03/23.68 | (5) e2 = e1 % 155.03/23.68 | % 155.03/23.68 | REDUCE: (3), (5) imply: % 155.03/23.68 | (6) $false % 155.03/23.68 | % 155.03/23.68 | CLOSE: (6) is inconsistent. % 155.03/23.68 | % 155.03/23.68 End of proof % 155.03/23.68 % 155.03/23.68 Sub-proof #688 shows that the following formulas are inconsistent: % 155.03/23.68 ---------------------------------------------------------------- % 155.03/23.68 (1) all_58_28 = e2 % 155.03/23.68 (2) all_58_28 = e0 % 155.03/23.68 (3) ~ (e2 = e0) % 155.03/23.68 % 155.03/23.68 Begin of proof % 155.03/23.68 | % 155.03/23.68 | COMBINE_EQS: (1), (2) imply: % 155.05/23.68 | (4) e2 = e0 % 155.05/23.68 | % 155.05/23.68 | SIMP: (4) implies: % 155.05/23.68 | (5) e2 = e0 % 155.05/23.68 | % 155.05/23.68 | REDUCE: (3), (5) imply: % 155.05/23.68 | (6) $false % 155.05/23.68 | % 155.05/23.68 | CLOSE: (6) is inconsistent. % 155.05/23.68 | % 155.05/23.68 End of proof % 155.05/23.68 % 155.05/23.68 Sub-proof #689 shows that the following formulas are inconsistent: % 155.05/23.68 ---------------------------------------------------------------- % 155.05/23.68 (1) all_58_28 = e3 % 155.05/23.68 (2) all_58_28 = e0 % 155.05/23.68 (3) ~ (e3 = e0) % 155.05/23.68 % 155.05/23.68 Begin of proof % 155.05/23.68 | % 155.05/23.68 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) e3 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) e3 = e0 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #690 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_28 = e1 % 155.05/23.69 (2) all_58_28 = e0 % 155.05/23.69 (3) ~ (e1 = e0) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) e1 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) e1 = e0 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #691 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) ~ (e3 = e1) % 155.05/23.69 (4) all_20_2 = all_4_2 % 155.05/23.69 (5) all_58_29 = e0 % 155.05/23.69 (6) all_58_30 = e0 % 155.05/23.69 (7) ~ (e2 = e1) % 155.05/23.69 (8) ~ (e3 = e0) % 155.05/23.69 (9) all_58_28 = all_10_2 % 155.05/23.69 (10) ~ (all_20_0 = e2) | ~ (all_20_1 = e3) | ~ (all_20_2 = e1) % 155.05/23.69 (11) ~ (e2 = e0) % 155.05/23.69 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (13) ~ (e1 = e0) % 155.05/23.69 (14) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (15) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (10) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (16) ~ (all_20_2 = e1) % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (4), (16) imply: % 155.05/23.69 | | (17) ~ (all_4_2 = e1) % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 155.05/23.69 | | (15), (17) are inconsistent by sub-proof #698. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (18) all_20_2 = e1 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (4), (18) imply: % 155.05/23.69 | | (19) all_4_2 = e1 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (1), (19) imply: % 155.05/23.69 | | (20) all_58_31 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (15), (20) are % 155.05/23.69 | | inconsistent by sub-proof #692. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #692 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = e1 % 155.05/23.69 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) ~ (e3 = e1) % 155.05/23.69 (4) all_58_29 = e0 % 155.05/23.69 (5) all_58_30 = e0 % 155.05/23.69 (6) ~ (e2 = e1) % 155.05/23.69 (7) ~ (e3 = e0) % 155.05/23.69 (8) all_58_28 = all_10_2 % 155.05/23.69 (9) ~ (e2 = e0) % 155.05/23.69 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (11) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (10) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (12) all_58_28 = e3 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (8), (12) imply: % 155.05/23.69 | | (13) all_10_2 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (11), (12) are inconsistent by % 155.05/23.69 | | sub-proof #695. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (3), (4), (5), (7), (14) are inconsistent by sub-proof #693. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #693 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = e1 % 155.05/23.69 (2) ~ (e3 = e1) % 155.05/23.69 (3) all_58_29 = e0 % 155.05/23.69 (4) all_58_30 = e0 % 155.05/23.69 (5) ~ (e3 = e0) % 155.05/23.69 (6) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (6) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (7) all_58_29 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #707. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (8) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (2), (4), (5), (8) are inconsistent by sub-proof #694. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #694 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = e1 % 155.05/23.69 (2) ~ (e3 = e1) % 155.05/23.69 (3) all_58_30 = e0 % 155.05/23.69 (4) ~ (e3 = e0) % 155.05/23.69 (5) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (5) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (6) all_58_30 = e3 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (3), (6) imply: % 155.05/23.69 | | (7) e3 = e0 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (4), (7) imply: % 155.05/23.69 | | (8) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (8) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (9) all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (1), (9) imply: % 155.05/23.69 | | (10) e3 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (2), (10) imply: % 155.05/23.69 | | (11) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (11) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #695 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = e1 % 155.05/23.69 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) all_58_29 = e0 % 155.05/23.69 (4) all_58_30 = e0 % 155.05/23.69 (5) ~ (e2 = e1) % 155.05/23.69 (6) ~ (e2 = e0) % 155.05/23.69 (7) all_58_28 = e3 % 155.05/23.69 (8) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (2) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (9) all_58_28 = e2 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (7), (9) imply: % 155.05/23.69 | | (10) e3 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (8), (10) imply: % 155.05/23.69 | | (11) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (11) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (12) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | % 155.05/23.69 | | BETA: splitting (12) gives: % 155.05/23.69 | | % 155.05/23.69 | | Case 1: % 155.05/23.69 | | | % 155.05/23.69 | | | (13) all_58_29 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #706. % 155.05/23.69 | | | % 155.05/23.69 | | Case 2: % 155.05/23.69 | | | % 155.05/23.69 | | | (14) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | REF_CLOSE: (1), (4), (5), (6), (14) are inconsistent by sub-proof #696. % 155.05/23.69 | | | % 155.05/23.69 | | End of split % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #696 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = e1 % 155.05/23.69 (2) all_58_30 = e0 % 155.05/23.69 (3) ~ (e2 = e1) % 155.05/23.69 (4) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (5) ~ (e2 = e0) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (4) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (6) all_58_30 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #718. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (7) all_58_31 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #697. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #697 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = e2 % 155.05/23.69 (2) all_58_31 = e1 % 155.05/23.69 (3) ~ (e2 = e1) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) e2 = e1 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) e2 = e1 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #698 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) ~ (e3 = e1) % 155.05/23.69 (4) all_58_29 = e0 % 155.05/23.69 (5) all_58_30 = e0 % 155.05/23.69 (6) ~ (e2 = e1) % 155.05/23.69 (7) ~ (e3 = e0) % 155.05/23.69 (8) all_58_28 = all_10_2 % 155.05/23.69 (9) ~ (e2 = e0) % 155.05/23.69 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (11) ~ (e1 = e0) % 155.05/23.69 (12) ~ (all_4_2 = e1) % 155.05/23.69 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (14) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (13) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (15) all_58_28 = e1 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (8), (15) imply: % 155.05/23.69 | | (16) all_10_2 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (14), (15) are % 155.05/23.69 | | inconsistent by sub-proof #701. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (17) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (4), (5), (11), (12), (17) are inconsistent by sub-proof % 155.05/23.69 | | #699. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #699 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_29 = e0 % 155.05/23.69 (3) all_58_30 = e0 % 155.05/23.69 (4) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (5) ~ (e1 = e0) % 155.05/23.69 (6) ~ (all_4_2 = e1) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (4) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (7) all_58_29 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #700. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (8) all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (3), (5), (6), (8) are inconsistent by sub-proof #711. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #700 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_29 = e1 % 155.05/23.69 (2) all_58_29 = e0 % 155.05/23.69 (3) ~ (e1 = e0) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) e1 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) e1 = e0 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #701 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (2) ~ (e3 = e1) % 155.05/23.69 (3) all_58_28 = e1 % 155.05/23.69 (4) all_58_29 = e0 % 155.05/23.69 (5) all_58_30 = e0 % 155.05/23.69 (6) ~ (e2 = e1) % 155.05/23.69 (7) ~ (e3 = e0) % 155.05/23.69 (8) ~ (e2 = e0) % 155.05/23.69 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (10) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (9) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (11) all_58_28 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #857. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (12) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (12) are inconsistent by % 155.05/23.69 | | sub-proof #702. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #702 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (2) all_58_28 = e1 % 155.05/23.69 (3) all_58_29 = e0 % 155.05/23.69 (4) all_58_30 = e0 % 155.05/23.69 (5) ~ (e2 = e1) % 155.05/23.69 (6) ~ (e3 = e0) % 155.05/23.69 (7) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (8) ~ (e2 = e0) % 155.05/23.69 (9) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (7) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (10) all_58_29 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #707. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (11) ~ (all_58_29 = e3) % 155.05/23.69 | | (12) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (3), (11) imply: % 155.05/23.69 | | (13) ~ (e3 = e0) % 155.05/23.69 | | % 155.05/23.69 | | BETA: splitting (1) gives: % 155.05/23.69 | | % 155.05/23.69 | | Case 1: % 155.05/23.69 | | | % 155.05/23.69 | | | (14) all_58_28 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #856. % 155.05/23.69 | | | % 155.05/23.69 | | Case 2: % 155.05/23.69 | | | % 155.05/23.69 | | | (15) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | REF_CLOSE: (3), (4), (6), (8), (9), (12), (15) are inconsistent by % 155.05/23.69 | | | sub-proof #703. % 155.05/23.69 | | | % 155.05/23.69 | | End of split % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #703 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_29 = e0 % 155.05/23.69 (2) all_58_30 = e0 % 155.05/23.69 (3) ~ (e3 = e0) % 155.05/23.69 (4) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (5) ~ (e2 = e0) % 155.05/23.69 (6) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (7) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (6) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (8) all_58_29 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #706. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (9) ~ (all_58_29 = e2) % 155.05/23.69 | | (10) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (1), (9) imply: % 155.05/23.69 | | (11) ~ (e2 = e0) % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (3), (4), (5), (7), (10) are inconsistent by sub-proof #704. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #704 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_30 = e0 % 155.05/23.69 (2) ~ (e3 = e0) % 155.05/23.69 (3) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (4) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (5) ~ (e2 = e0) % 155.05/23.69 (6) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (4) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (7) all_58_30 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #755. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (8) all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (3), (5), (6), (8) are inconsistent by sub-proof #705. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #705 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_30 = e0 % 155.05/23.69 (2) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) all_58_31 = e3 % 155.05/23.69 (4) ~ (e2 = e0) % 155.05/23.69 (5) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (2) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (6) all_58_30 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #718. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (7) all_58_31 = e2 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (3), (7) imply: % 155.05/23.69 | | (8) e3 = e2 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (5), (8) imply: % 155.05/23.69 | | (9) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (9) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #706 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_29 = e2 % 155.05/23.69 (2) all_58_29 = e0 % 155.05/23.69 (3) ~ (e2 = e0) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) e2 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) e2 = e0 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #707 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_29 = e3 % 155.05/23.69 (2) all_58_29 = e0 % 155.05/23.69 (3) ~ (e3 = e0) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) e3 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) e3 = e0 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #708 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) all_54_15 = all_4_2 % 155.05/23.69 (4) ~ (e3 = e1) % 155.05/23.69 (5) all_54_15 = e0 % 155.05/23.69 (6) all_58_30 = e0 % 155.05/23.69 (7) ~ (e2 = e1) % 155.05/23.69 (8) ~ (e3 = e0) % 155.05/23.69 (9) ~ (e2 = e0) % 155.05/23.69 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (11) ~ (e1 = e0) % 155.05/23.69 (12) ~ (all_4_2 = e1) % 155.05/23.69 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (14) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (3), (5) imply: % 155.05/23.69 | (15) all_4_2 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (15) implies: % 155.05/23.69 | (16) all_4_2 = e0 % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (16) imply: % 155.05/23.69 | (17) all_58_31 = e0 % 155.05/23.69 | % 155.05/23.69 | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 155.05/23.69 | (17) are inconsistent by sub-proof #710. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #709 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_56_15 = all_4_2 % 155.05/23.69 (3) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (4) ~ (e3 = e1) % 155.05/23.69 (5) all_58_30 = e0 % 155.05/23.69 (6) ~ (e2 = e1) % 155.05/23.69 (7) ~ (e3 = e0) % 155.05/23.69 (8) all_56_15 = e0 % 155.05/23.69 (9) ~ (e2 = e0) % 155.05/23.69 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (11) ~ (e1 = e0) % 155.05/23.69 (12) ~ (all_4_2 = e1) % 155.05/23.69 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (14) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (2), (8) imply: % 155.05/23.69 | (15) all_4_2 = e0 % 155.05/23.69 | % 155.05/23.69 | SIMP: (15) implies: % 155.05/23.69 | (16) all_4_2 = e0 % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (16) imply: % 155.05/23.69 | (17) all_58_31 = e0 % 155.05/23.69 | % 155.05/23.69 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), % 155.05/23.69 | (17) are inconsistent by sub-proof #710. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #710 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (3) ~ (e3 = e1) % 155.05/23.69 (4) all_58_30 = e0 % 155.05/23.69 (5) ~ (e2 = e1) % 155.05/23.69 (6) ~ (e3 = e0) % 155.05/23.69 (7) ~ (e2 = e0) % 155.05/23.69 (8) all_58_31 = e0 % 155.05/23.69 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (10) ~ (e1 = e0) % 155.05/23.69 (11) ~ (all_4_2 = e1) % 155.05/23.69 (12) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (13) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (12) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (14) all_58_28 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (13), (14) are % 155.05/23.69 | | inconsistent by sub-proof #715. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (15) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 | | % 155.05/23.69 | | BETA: splitting (15) gives: % 155.05/23.69 | | % 155.05/23.69 | | Case 1: % 155.05/23.69 | | | % 155.05/23.69 | | | (16) all_58_29 = e1 % 155.05/23.69 | | | % 155.05/23.69 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (13), (16) are % 155.05/23.69 | | | inconsistent by sub-proof #713. % 155.05/23.69 | | | % 155.05/23.69 | | Case 2: % 155.05/23.69 | | | % 155.05/23.69 | | | (17) all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 | | | % 155.05/23.69 | | | REF_CLOSE: (1), (4), (10), (11), (17) are inconsistent by sub-proof #711. % 155.05/23.69 | | | % 155.05/23.69 | | End of split % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #711 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_30 = e0 % 155.05/23.69 (3) all_58_30 = e1 | all_58_31 = e1 % 155.05/23.69 (4) ~ (e1 = e0) % 155.05/23.69 (5) ~ (all_4_2 = e1) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (3) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (6) all_58_30 = e1 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (2), (6) imply: % 155.05/23.69 | | (7) e1 = e0 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (4), (7) imply: % 155.05/23.69 | | (8) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (8) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (9) all_58_31 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #712. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #712 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_31 = all_4_2 % 155.05/23.69 (2) all_58_31 = e1 % 155.05/23.69 (3) ~ (all_4_2 = e1) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | COMBINE_EQS: (1), (2) imply: % 155.05/23.69 | (4) all_4_2 = e1 % 155.05/23.69 | % 155.05/23.69 | SIMP: (4) implies: % 155.05/23.69 | (5) all_4_2 = e1 % 155.05/23.69 | % 155.05/23.69 | REDUCE: (3), (5) imply: % 155.05/23.69 | (6) $false % 155.05/23.69 | % 155.05/23.69 | CLOSE: (6) is inconsistent. % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #713 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (2) ~ (e3 = e1) % 155.05/23.69 (3) all_58_30 = e0 % 155.05/23.69 (4) ~ (e2 = e1) % 155.05/23.69 (5) all_58_29 = e1 % 155.05/23.69 (6) ~ (e3 = e0) % 155.05/23.69 (7) ~ (e2 = e0) % 155.05/23.69 (8) all_58_31 = e0 % 155.05/23.69 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (10) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (9) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (11) all_58_28 = e3 % 155.05/23.69 | | % 155.05/23.69 | | BETA: splitting (1) gives: % 155.05/23.69 | | % 155.05/23.69 | | Case 1: % 155.05/23.69 | | | % 155.05/23.69 | | | (12) all_58_28 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | COMBINE_EQS: (11), (12) imply: % 155.05/23.69 | | | (13) e3 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | REDUCE: (10), (13) imply: % 155.05/23.69 | | | (14) $false % 155.05/23.69 | | | % 155.05/23.69 | | | CLOSE: (14) is inconsistent. % 155.05/23.69 | | | % 155.05/23.69 | | Case 2: % 155.05/23.69 | | | % 155.05/23.69 | | | (15) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | BETA: splitting (15) gives: % 155.05/23.69 | | | % 155.05/23.69 | | | Case 1: % 155.05/23.69 | | | | % 155.05/23.69 | | | | (16) all_58_29 = e2 % 155.05/23.69 | | | | % 155.05/23.69 | | | | COMBINE_EQS: (5), (16) imply: % 155.05/23.69 | | | | (17) e2 = e1 % 155.05/23.69 | | | | % 155.05/23.69 | | | | REDUCE: (4), (17) imply: % 155.05/23.69 | | | | (18) $false % 155.05/23.69 | | | | % 155.05/23.69 | | | | CLOSE: (18) is inconsistent. % 155.05/23.69 | | | | % 155.05/23.69 | | | Case 2: % 155.05/23.69 | | | | % 155.05/23.69 | | | | (19) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | | | % 155.05/23.69 | | | | REF_CLOSE: (3), (7), (8), (19) are inconsistent by sub-proof #717. % 155.05/23.69 | | | | % 155.05/23.69 | | | End of split % 155.05/23.69 | | | % 155.05/23.69 | | End of split % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (20) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (3), (5), (6), (8), (20) are inconsistent by sub-proof #714. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #714 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) ~ (e3 = e1) % 155.05/23.69 (2) all_58_30 = e0 % 155.05/23.69 (3) all_58_29 = e1 % 155.05/23.69 (4) ~ (e3 = e0) % 155.05/23.69 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (6) all_58_31 = e0 % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (5) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (7) all_58_29 = e3 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (3), (7) imply: % 155.05/23.69 | | (8) e3 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (1), (8) imply: % 155.05/23.69 | | (9) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (9) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (10) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #716. % 155.05/23.69 | | % 155.05/23.69 | End of split % 155.05/23.69 | % 155.05/23.69 End of proof % 155.05/23.69 % 155.05/23.69 Sub-proof #715 shows that the following formulas are inconsistent: % 155.05/23.69 ---------------------------------------------------------------- % 155.05/23.69 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 (2) ~ (e3 = e1) % 155.05/23.69 (3) all_58_28 = e1 % 155.05/23.69 (4) all_58_30 = e0 % 155.05/23.69 (5) ~ (e2 = e1) % 155.05/23.69 (6) ~ (e3 = e0) % 155.05/23.69 (7) ~ (e2 = e0) % 155.05/23.69 (8) all_58_31 = e0 % 155.05/23.69 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 (10) ~ (e3 = e2) % 155.05/23.69 % 155.05/23.69 Begin of proof % 155.05/23.69 | % 155.05/23.69 | BETA: splitting (9) gives: % 155.05/23.69 | % 155.05/23.69 | Case 1: % 155.05/23.69 | | % 155.05/23.69 | | (11) all_58_28 = e3 % 155.05/23.69 | | % 155.05/23.69 | | COMBINE_EQS: (3), (11) imply: % 155.05/23.69 | | (12) e3 = e1 % 155.05/23.69 | | % 155.05/23.69 | | REDUCE: (2), (12) imply: % 155.05/23.69 | | (13) $false % 155.05/23.69 | | % 155.05/23.69 | | CLOSE: (13) is inconsistent. % 155.05/23.69 | | % 155.05/23.69 | Case 2: % 155.05/23.69 | | % 155.05/23.69 | | (14) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.69 | | % 155.05/23.69 | | BETA: splitting (1) gives: % 155.05/23.69 | | % 155.05/23.69 | | Case 1: % 155.05/23.69 | | | % 155.05/23.69 | | | (15) all_58_28 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | COMBINE_EQS: (3), (15) imply: % 155.05/23.69 | | | (16) e2 = e1 % 155.05/23.69 | | | % 155.05/23.69 | | | REDUCE: (5), (16) imply: % 155.05/23.69 | | | (17) $false % 155.05/23.69 | | | % 155.05/23.69 | | | CLOSE: (17) is inconsistent. % 155.05/23.69 | | | % 155.05/23.69 | | Case 2: % 155.05/23.69 | | | % 155.05/23.69 | | | (18) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | | % 155.05/23.69 | | | BETA: splitting (14) gives: % 155.05/23.69 | | | % 155.05/23.69 | | | Case 1: % 155.05/23.69 | | | | % 155.05/23.69 | | | | (19) all_58_29 = e3 % 155.05/23.69 | | | | % 155.05/23.69 | | | | BETA: splitting (18) gives: % 155.05/23.69 | | | | % 155.05/23.69 | | | | Case 1: % 155.05/23.69 | | | | | % 155.05/23.69 | | | | | (20) all_58_29 = e2 % 155.05/23.69 | | | | | % 155.05/23.69 | | | | | REF_CLOSE: (10), (19), (20) are inconsistent by sub-proof #780. % 155.05/23.69 | | | | | % 155.05/23.69 | | | | Case 2: % 155.05/23.69 | | | | | % 155.05/23.69 | | | | | (21) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.69 | | | | | % 155.05/23.70 | | | | | REF_CLOSE: (4), (7), (8), (21) are inconsistent by sub-proof #717. % 155.05/23.70 | | | | | % 155.05/23.70 | | | | End of split % 155.05/23.70 | | | | % 155.05/23.70 | | | Case 2: % 155.05/23.70 | | | | % 155.05/23.70 | | | | (22) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 | | | | % 155.05/23.70 | | | | REF_CLOSE: (4), (6), (8), (22) are inconsistent by sub-proof #716. % 155.05/23.70 | | | | % 155.05/23.70 | | | End of split % 155.05/23.70 | | | % 155.05/23.70 | | End of split % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #716 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 (2) all_58_30 = e0 % 155.05/23.70 (3) ~ (e3 = e0) % 155.05/23.70 (4) all_58_31 = e0 % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (1) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (5) all_58_30 = e3 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #755. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (6) all_58_31 = e3 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #853. % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #717 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.70 (2) all_58_30 = e0 % 155.05/23.70 (3) ~ (e2 = e0) % 155.05/23.70 (4) all_58_31 = e0 % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (1) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (5) all_58_30 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #718. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (6) all_58_31 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #855. % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #718 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_58_30 = e2 % 155.05/23.70 (2) all_58_30 = e0 % 155.05/23.70 (3) ~ (e2 = e0) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) e2 = e0 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) e2 = e0 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #719 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_56_0 = e3 % 155.05/23.70 (2) all_56_0 = e2 % 155.05/23.70 (3) ~ (e3 = e2) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) e3 = e2 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) e3 = e2 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #720 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.05/23.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.05/23.70 (2) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.05/23.70 (3) ~ (all_52_4 = all_8_2) % 155.05/23.70 (4) ~ (all_52_12 = e3) % 155.05/23.70 (5) all_54_3 = all_52_12 % 155.05/23.70 (6) all_54_1 = all_52_4 % 155.05/23.70 (7) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 155.05/23.70 (8) all_56_1 = all_52_4 % 155.05/23.70 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 % 155.05/23.70 (10) all_58_29 = all_8_2 % 155.05/23.70 (11) ~ (all_52_4 = e1) % 155.05/23.70 (12) op(all_6_2, e1) = all_6_1 % 155.05/23.70 (13) ~ (all_52_4 = e0) % 155.05/23.70 (14) op(e3, e1) = all_58_0 % 155.05/23.70 (15) ~ (all_52_12 = e1) % 155.05/23.70 (16) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 (17) ~ (all_6_1 = e0) % 155.05/23.70 (18) all_58_31 = e0 % 155.05/23.70 (19) all_58_30 = all_6_2 % 155.05/23.70 (20) ~ (all_52_4 = all_52_12) % 155.05/23.70 (21) op(e3, e1) = e0 % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (9) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (22) all_54_3 = e1 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (5), (15), (22) are inconsistent by sub-proof #723. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (23) all_54_3 = e3 | all_54_3 = e2 % 155.05/23.70 | | % 155.05/23.70 | | BETA: splitting (23) gives: % 155.05/23.70 | | % 155.05/23.70 | | Case 1: % 155.05/23.70 | | | % 155.05/23.70 | | | (24) all_54_3 = e2 % 155.05/23.70 | | | % 155.05/23.70 | | | COMBINE_EQS: (5), (24) imply: % 155.05/23.70 | | | (25) all_52_12 = e2 % 155.05/23.70 | | | % 155.05/23.70 | | | SIMP: (25) implies: % 155.05/23.70 | | | (26) all_52_12 = e2 % 155.05/23.70 | | | % 155.05/23.70 | | | REDUCE: (20), (26) imply: % 155.05/23.70 | | | (27) ~ (all_52_4 = e2) % 155.05/23.70 | | | % 155.05/23.70 | | | BETA: splitting (7) gives: % 155.05/23.70 | | | % 155.05/23.70 | | | Case 1: % 155.05/23.70 | | | | % 155.05/23.70 | | | | (28) all_54_1 = e1 % 155.05/23.70 | | | | % 155.05/23.70 | | | | REF_CLOSE: (6), (11), (28) are inconsistent by sub-proof #741. % 155.05/23.70 | | | | % 155.05/23.70 | | | Case 2: % 155.05/23.70 | | | | % 155.05/23.70 | | | | (29) all_54_1 = e3 | all_54_1 = e2 % 155.05/23.70 | | | | % 155.05/23.70 | | | | BETA: splitting (2) gives: % 155.05/23.70 | | | | % 155.05/23.70 | | | | Case 1: % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | (30) all_56_1 = e3 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | COMBINE_EQS: (8), (30) imply: % 155.05/23.70 | | | | | (31) all_52_4 = e3 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REDUCE: (3), (31) imply: % 155.05/23.70 | | | | | (32) ~ (all_8_2 = e3) % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | SIMP: (32) implies: % 155.05/23.70 | | | | | (33) ~ (all_8_2 = e3) % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REDUCE: (13), (31) imply: % 155.05/23.70 | | | | | (34) ~ (e3 = e0) % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | BETA: splitting (16) gives: % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | Case 1: % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | (35) all_58_29 = e3 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | REF_CLOSE: (10), (33), (35) are inconsistent by sub-proof #756. % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | Case 2: % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | (36) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | REF_CLOSE: (1), (12), (14), (17), (18), (19), (21), (34), (36) are % 155.05/23.70 | | | | | | inconsistent by sub-proof #790. % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | End of split % 155.05/23.70 | | | | | % 155.05/23.70 | | | | Case 2: % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | (37) ~ (all_56_1 = e3) % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REDUCE: (8), (37) imply: % 155.05/23.70 | | | | | (38) ~ (all_52_4 = e3) % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REF_CLOSE: (6), (27), (29), (38) are inconsistent by sub-proof #722. % 155.05/23.70 | | | | | % 155.05/23.70 | | | | End of split % 155.05/23.70 | | | | % 155.05/23.70 | | | End of split % 155.05/23.70 | | | % 155.05/23.70 | | Case 2: % 155.05/23.70 | | | % 155.05/23.70 | | | (39) all_54_3 = e3 % 155.05/23.70 | | | % 155.05/23.70 | | | REF_CLOSE: (4), (5), (39) are inconsistent by sub-proof #721. % 155.05/23.70 | | | % 155.05/23.70 | | End of split % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #721 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_3 = all_52_12 % 155.05/23.70 (2) all_54_3 = e3 % 155.05/23.70 (3) ~ (all_52_12 = e3) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_52_12 = e3 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_52_12 = e3 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #722 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_1 = e3 | all_54_1 = e2 % 155.05/23.70 (2) all_54_1 = all_52_4 % 155.05/23.70 (3) ~ (all_52_4 = e2) % 155.05/23.70 (4) ~ (all_52_4 = e3) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (1) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (5) all_54_1 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #740. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (6) all_54_1 = e3 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #739. % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #723 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_3 = all_52_12 % 155.05/23.70 (2) all_54_3 = e1 % 155.05/23.70 (3) ~ (all_52_12 = e1) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_52_12 = e1 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_52_12 = e1 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #724 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.05/23.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.05/23.70 (2) all_54_13 = all_52_7 % 155.05/23.70 (3) ~ (all_10_1 = e0) % 155.05/23.70 (4) ~ (all_6_2 = e0) % 155.05/23.70 (5) all_54_6 = all_52_9 % 155.05/23.70 (6) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 155.05/23.70 (7) ~ (all_52_7 = e2) % 155.05/23.70 (8) op(e1, all_10_1) = all_10_0 % 155.05/23.70 (9) op(e2, e1) = all_52_9 % 155.05/23.70 (10) all_58_29 = all_8_2 % 155.05/23.70 (11) all_56_6 = all_10_1 % 155.05/23.70 (12) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.05/23.70 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.05/23.70 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.05/23.70 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.05/23.70 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.05/23.70 (all_58_27 = e0)) % 155.05/23.70 (13) op(all_6_2, e1) = all_6_1 % 155.05/23.70 (14) op(e2, all_52_9) = all_58_10 % 155.05/23.70 (15) op(e3, e2) = e2 % 155.05/23.70 (16) op(e3, e2) = all_58_1 % 155.05/23.70 (17) all_58_30 = e2 | all_58_31 = e2 % 155.05/23.70 (18) all_58_14 = all_10_0 % 155.05/23.70 (19) ~ (all_52_9 = all_8_2) % 155.05/23.70 (20) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 (21) ~ (e2 = e0) % 155.05/23.70 (22) ~ (all_52_9 = all_6_2) % 155.05/23.70 (23) all_58_31 = e0 % 155.05/23.70 (24) ~ (all_10_1 = e1) % 155.05/23.70 (25) op(e1, e3) = all_10_1 % 155.05/23.70 (26) all_58_27 = e0 % 155.05/23.70 (27) ~ (all_52_7 = all_8_2) % 155.05/23.70 (28) ~ (all_10_1 = all_6_2) % 155.05/23.70 (29) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 155.05/23.70 (30) all_54_8 = all_10_1 % 155.05/23.70 (31) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 155.05/23.70 (32) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 % 155.05/23.70 (33) all_58_30 = all_6_2 % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (17) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (34) all_58_30 = e2 % 155.05/23.70 | | % 155.05/23.70 | | COMBINE_EQS: (33), (34) imply: % 155.05/23.70 | | (35) all_6_2 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REDUCE: (22), (35) imply: % 155.05/23.70 | | (36) ~ (all_52_9 = e2) % 155.05/23.70 | | % 155.05/23.70 | | REDUCE: (28), (35) imply: % 155.05/23.70 | | (37) ~ (all_10_1 = e2) % 155.05/23.70 | | % 155.05/23.70 | | REDUCE: (13), (35) imply: % 155.05/23.70 | | (38) op(e2, e1) = all_6_1 % 155.05/23.70 | | % 155.05/23.70 | | BETA: splitting (31) gives: % 155.05/23.70 | | % 155.05/23.70 | | Case 1: % 155.05/23.70 | | | % 155.05/23.70 | | | (39) all_56_6 = e3 % 155.05/23.70 | | | % 155.05/23.70 | | | COMBINE_EQS: (11), (39) imply: % 155.05/23.70 | | | (40) all_10_1 = e3 % 155.05/23.70 | | | % 155.05/23.70 | | | SIMP: (40) implies: % 155.05/23.70 | | | (41) all_10_1 = e3 % 155.05/23.70 | | | % 155.05/23.70 | | | REDUCE: (37), (41) imply: % 155.05/23.70 | | | (42) ~ (e3 = e2) % 155.05/23.70 | | | % 155.05/23.70 | | | REDUCE: (3), (41) imply: % 155.05/23.70 | | | (43) ~ (e3 = e0) % 155.05/23.70 | | | % 155.05/23.70 | | | REDUCE: (8), (41) imply: % 155.05/23.70 | | | (44) op(e1, e3) = all_10_0 % 155.05/23.70 | | | % 155.05/23.70 | | | REDUCE: (25), (41) imply: % 155.05/23.70 | | | (45) op(e1, e3) = e3 % 155.05/23.70 | | | % 155.05/23.70 | | | BETA: splitting (20) gives: % 155.05/23.70 | | | % 155.05/23.70 | | | Case 1: % 155.05/23.70 | | | | % 155.05/23.70 | | | | (46) all_58_29 = e3 % 155.05/23.70 | | | | % 155.05/23.70 | | | | COMBINE_EQS: (10), (46) imply: % 155.05/23.70 | | | | (47) all_8_2 = e3 % 155.05/23.70 | | | | % 155.05/23.70 | | | | SIMP: (47) implies: % 155.05/23.70 | | | | (48) all_8_2 = e3 % 155.05/23.70 | | | | % 155.05/23.70 | | | | REDUCE: (27), (48) imply: % 155.05/23.70 | | | | (49) ~ (all_52_7 = e3) % 155.05/23.70 | | | | % 155.05/23.70 | | | | REDUCE: (19), (48) imply: % 155.05/23.70 | | | | (50) ~ (all_52_9 = e3) % 155.05/23.70 | | | | % 155.05/23.70 | | | | BETA: splitting (6) gives: % 155.05/23.70 | | | | % 155.05/23.70 | | | | Case 1: % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | (51) all_54_6 = e1 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | COMBINE_EQS: (5), (51) imply: % 155.05/23.70 | | | | | (52) all_52_9 = e1 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | SIMP: (52) implies: % 155.05/23.70 | | | | | (53) all_52_9 = e1 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REDUCE: (14), (53) imply: % 155.05/23.70 | | | | | (54) op(e2, e1) = all_58_10 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REDUCE: (9), (53) imply: % 155.05/23.70 | | | | | (55) op(e2, e1) = e1 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | BETA: splitting (32) gives: % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | Case 1: % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | GROUND_INST: instantiating (1) with e3, all_10_0, e3, e1, % 155.05/23.70 | | | | | | simplifying with (44), (45) gives: % 155.05/23.70 | | | | | | (56) all_10_0 = e3 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | GROUND_INST: instantiating (1) with all_6_1, all_58_10, e1, e2, % 155.05/23.70 | | | | | | simplifying with (38), (54) gives: % 155.05/23.70 | | | | | | (57) all_58_10 = all_6_1 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | GROUND_INST: instantiating (1) with e1, all_58_10, e1, e2, % 155.05/23.70 | | | | | | simplifying with (54), (55) gives: % 155.05/23.70 | | | | | | (58) all_58_10 = e1 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | GROUND_INST: instantiating (1) with e2, all_58_1, e2, e3, % 155.05/23.70 | | | | | | simplifying with (15), (16) gives: % 155.05/23.70 | | | | | | (59) all_58_1 = e2 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | COMBINE_EQS: (57), (58) imply: % 155.05/23.70 | | | | | | (60) all_6_1 = e1 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | COMBINE_EQS: (18), (56) imply: % 155.05/23.70 | | | | | | (61) all_58_14 = e3 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | REF_CLOSE: (12), (26), (58), (59), (61) are inconsistent by % 155.05/23.70 | | | | | | sub-proof #778. % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | Case 2: % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | (62) all_54_13 = e3 | all_54_13 = e2 % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | | REF_CLOSE: (2), (7), (49), (62) are inconsistent by sub-proof #730. % 155.05/23.70 | | | | | | % 155.05/23.70 | | | | | End of split % 155.05/23.70 | | | | | % 155.05/23.70 | | | | Case 2: % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | (63) all_54_6 = e3 | all_54_6 = e2 % 155.05/23.70 | | | | | % 155.05/23.70 | | | | | REF_CLOSE: (5), (36), (50), (63) are inconsistent by sub-proof #729. % 155.05/23.70 | | | | | % 155.05/23.70 | | | | End of split % 155.05/23.70 | | | | % 155.05/23.70 | | | Case 2: % 155.05/23.70 | | | | % 155.05/23.70 | | | | (64) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 | | | | % 155.05/23.70 | | | | REF_CLOSE: (17), (21), (23), (42), (43), (64) are inconsistent by % 155.05/23.70 | | | | sub-proof #852. % 155.05/23.70 | | | | % 155.05/23.70 | | | End of split % 155.05/23.70 | | | % 155.05/23.70 | | Case 2: % 155.05/23.70 | | | % 155.05/23.70 | | | (65) ~ (all_56_6 = e3) % 155.05/23.70 | | | % 155.05/23.70 | | | REDUCE: (11), (65) imply: % 155.05/23.70 | | | (66) ~ (all_10_1 = e3) % 155.05/23.70 | | | % 155.05/23.70 | | | REF_CLOSE: (24), (29), (30), (37), (66) are inconsistent by sub-proof % 155.05/23.70 | | | #725. % 155.05/23.70 | | | % 155.05/23.70 | | End of split % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (67) all_58_31 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (21), (23), (67) are inconsistent by sub-proof #855. % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #725 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) ~ (all_10_1 = e2) % 155.05/23.70 (2) ~ (all_10_1 = e3) % 155.05/23.70 (3) ~ (all_10_1 = e1) % 155.05/23.70 (4) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 155.05/23.70 (5) all_54_8 = all_10_1 % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (4) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (6) all_54_8 = e1 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #728. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (7) all_54_8 = e3 | all_54_8 = e2 % 155.05/23.70 | | % 155.05/23.70 | | BETA: splitting (7) gives: % 155.05/23.70 | | % 155.05/23.70 | | Case 1: % 155.05/23.70 | | | % 155.05/23.70 | | | (8) all_54_8 = e2 % 155.05/23.70 | | | % 155.05/23.70 | | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #727. % 155.05/23.70 | | | % 155.05/23.70 | | Case 2: % 155.05/23.70 | | | % 155.05/23.70 | | | (9) all_54_8 = e3 % 155.05/23.70 | | | % 155.05/23.70 | | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #726. % 155.05/23.70 | | | % 155.05/23.70 | | End of split % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #726 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_8 = all_10_1 % 155.05/23.70 (2) all_54_8 = e3 % 155.05/23.70 (3) ~ (all_10_1 = e3) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_10_1 = e3 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_10_1 = e3 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #727 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_8 = all_10_1 % 155.05/23.70 (2) all_54_8 = e2 % 155.05/23.70 (3) ~ (all_10_1 = e2) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_10_1 = e2 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_10_1 = e2 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #728 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_8 = all_10_1 % 155.05/23.70 (2) all_54_8 = e1 % 155.05/23.70 (3) ~ (all_10_1 = e1) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_10_1 = e1 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_10_1 = e1 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #729 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_6 = e3 | all_54_6 = e2 % 155.05/23.70 (2) all_54_6 = all_52_9 % 155.05/23.70 (3) ~ (all_52_9 = e2) % 155.05/23.70 (4) ~ (all_52_9 = e3) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (1) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (5) all_54_6 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #773. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (6) all_54_6 = e3 % 155.05/23.70 | | % 155.05/23.70 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #772. % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #730 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_13 = e3 | all_54_13 = e2 % 155.05/23.70 (2) all_54_13 = all_52_7 % 155.05/23.70 (3) ~ (all_52_7 = e2) % 155.05/23.70 (4) ~ (all_52_7 = e3) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | BETA: splitting (1) gives: % 155.05/23.70 | % 155.05/23.70 | Case 1: % 155.05/23.70 | | % 155.05/23.70 | | (5) all_54_13 = e2 % 155.05/23.70 | | % 155.05/23.70 | | COMBINE_EQS: (2), (5) imply: % 155.05/23.70 | | (6) all_52_7 = e2 % 155.05/23.70 | | % 155.05/23.70 | | SIMP: (6) implies: % 155.05/23.70 | | (7) all_52_7 = e2 % 155.05/23.70 | | % 155.05/23.70 | | REDUCE: (3), (7) imply: % 155.05/23.70 | | (8) $false % 155.05/23.70 | | % 155.05/23.70 | | CLOSE: (8) is inconsistent. % 155.05/23.70 | | % 155.05/23.70 | Case 2: % 155.05/23.70 | | % 155.05/23.70 | | (9) all_54_13 = e3 % 155.05/23.70 | | % 155.05/23.70 | | COMBINE_EQS: (2), (9) imply: % 155.05/23.70 | | (10) all_52_7 = e3 % 155.05/23.70 | | % 155.05/23.70 | | SIMP: (10) implies: % 155.05/23.70 | | (11) all_52_7 = e3 % 155.05/23.70 | | % 155.05/23.70 | | REDUCE: (4), (11) imply: % 155.05/23.70 | | (12) $false % 155.05/23.70 | | % 155.05/23.70 | | CLOSE: (12) is inconsistent. % 155.05/23.70 | | % 155.05/23.70 | End of split % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #731 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_8 = all_52_2 % 155.05/23.70 (2) all_54_8 = e0 % 155.05/23.70 (3) ~ (all_52_2 = e0) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_52_2 = e0 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_52_2 = e0 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #732 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_13 = all_52_7 % 155.05/23.70 (2) all_54_13 = e0 % 155.05/23.70 (3) ~ (all_52_7 = e0) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_52_7 = e0 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_52_7 = e0 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #733 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_54_3 = all_52_12 % 155.05/23.70 (2) all_54_3 = e0 % 155.05/23.70 (3) ~ (all_52_12 = e0) % 155.05/23.70 % 155.05/23.70 Begin of proof % 155.05/23.70 | % 155.05/23.70 | COMBINE_EQS: (1), (2) imply: % 155.05/23.70 | (4) all_52_12 = e0 % 155.05/23.70 | % 155.05/23.70 | SIMP: (4) implies: % 155.05/23.70 | (5) all_52_12 = e0 % 155.05/23.70 | % 155.05/23.70 | REDUCE: (3), (5) imply: % 155.05/23.70 | (6) $false % 155.05/23.70 | % 155.05/23.70 | CLOSE: (6) is inconsistent. % 155.05/23.70 | % 155.05/23.70 End of proof % 155.05/23.70 % 155.05/23.70 Sub-proof #734 shows that the following formulas are inconsistent: % 155.05/23.70 ---------------------------------------------------------------- % 155.05/23.70 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 155.05/23.70 (2) ~ (all_52_8 = all_52_9) % 155.05/23.70 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.05/23.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.05/23.70 (4) all_46_2 = all_6_2 % 155.05/23.70 (5) ~ (all_52_2 = all_52_3) % 155.05/23.70 (6) all_32_0 = all_10_0 % 155.05/23.70 (7) all_56_7 = all_52_6 % 155.05/23.70 (8) ~ (all_52_6 = all_6_2) % 155.05/23.70 (9) all_54_2 = all_52_8 % 155.05/23.70 (10) all_46_1 = all_6_1 % 155.05/23.70 (11) all_46_0 = all_6_0 % 155.05/23.70 (12) ~ (all_52_8 = all_10_2) % 155.05/23.70 (13) all_54_7 = all_52_13 % 155.05/23.70 (14) all_56_4 = all_52_8 % 155.05/23.70 (15) ~ (all_52_4 = all_8_2) % 155.05/23.70 (16) all_32_2 = all_10_2 % 155.05/23.70 (17) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.05/23.70 (18) all_54_1 = all_52_4 % 155.05/23.70 (19) ~ (all_6_2 = e0) % 155.05/23.70 (20) ~ (all_52_4 = all_52_6) % 155.05/23.70 (21) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 155.05/23.70 (22) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 155.05/23.70 (23) all_54_11 = all_52_14 % 155.05/23.70 (24) op(e3, e2) = all_52_4 % 155.05/23.70 (25) all_56_0 = e2 | all_56_1 = e2 | all_56_4 = e2 | all_56_9 = e2 % 155.05/23.70 (26) ~ (all_52_8 = all_6_2) % 155.05/23.70 (27) op(e2, e3) = all_52_1 % 155.05/23.70 (28) ~ (all_52_12 = all_52_13) % 155.05/23.70 (29) ~ (all_52_6 = all_52_14) % 155.05/23.70 (30) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 155.05/23.70 (31) ~ (all_10_2 = e0) % 155.05/23.70 (32) ~ (all_52_2 = all_6_2) % 155.05/23.70 (33) ~ (all_32_0 = e1) | ~ (all_32_2 = e2) % 155.05/23.70 (34) op(e3, e3) = all_10_2 % 155.05/23.70 (35) op(e3, all_52_8) = all_58_3 % 155.05/23.70 (36) ~ (all_52_8 = all_52_12) % 155.05/23.70 (37) op(e1, e2) = all_52_6 % 155.05/23.70 (38) op(all_10_2, e0) = all_10_0 % 155.05/23.70 (39) ~ (all_52_3 = e0) % 155.05/23.70 (40) op(e1, all_52_6) = all_58_16 % 155.05/23.70 (41) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 155.05/23.70 (42) ~ (e3 = e1) % 155.05/23.70 (43) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 155.05/23.70 (44) ~ (all_52_1 = all_52_13) % 155.05/23.70 (45) all_56_5 = all_52_9 % 155.05/23.70 (46) all_56_12 = all_52_3 % 155.05/23.70 (47) ~ (all_52_3 = all_52_7) % 155.05/23.70 (48) all_56_11 = all_52_14 % 155.05/23.70 (49) all_56_1 = all_52_4 % 155.05/23.70 (50) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.05/23.70 (51) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.05/23.70 (52) op(e1, e3) = all_52_2 % 155.05/23.70 (53) op(e1, e0) = all_52_14 % 155.05/23.70 (54) ~ (all_52_1 = all_8_2) % 155.05/23.70 (55) all_56_3 = all_8_2 % 155.05/23.70 (56) ~ (all_52_13 = all_52_14) % 155.05/23.70 (57) all_56_12 = e3 | all_56_13 = e3 | all_56_14 = e3 | all_56_15 = e3 % 155.05/23.70 (58) ~ (all_52_4 = all_52_8) % 155.05/23.70 (59) all_56_9 = all_52_12 % 155.05/23.70 (60) all_58_29 = all_8_2 % 155.05/23.70 (61) ~ (all_52_12 = all_52_14) % 155.05/23.70 (62) ~ (e2 = e1) % 155.05/23.70 (63) op(e3, e0) = all_52_12 % 155.05/23.70 (64) all_56_6 = all_52_2 % 155.05/23.70 (65) ~ (all_52_2 = all_52_6) % 155.05/23.70 (66) all_56_13 = all_52_7 % 155.05/23.70 (67) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 155.05/23.70 (68) op(all_6_2, all_6_1) = all_6_0 % 155.05/23.70 (69) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.05/23.70 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.05/23.70 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.05/23.70 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.05/23.70 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.05/23.70 (all_58_27 = e0)) % 155.05/23.70 (70) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 155.05/23.70 (71) op(all_6_2, e1) = all_6_1 % 155.05/23.70 (72) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 155.05/23.70 (73) op(all_10_2, e3) = e0 % 155.05/23.70 (74) op(e3, all_10_2) = all_58_0 % 155.05/23.70 (75) ~ (e3 = e0) % 155.05/23.70 (76) ~ (all_40_0 = e0) | ~ (all_40_1 = e3) | ~ (all_40_2 = e2) % 155.05/23.70 (77) all_56_2 = all_52_1 % 155.05/23.70 (78) ~ (all_52_11 = e0) % 155.05/23.70 (79) ~ (all_46_0 = e0) | ~ (all_46_1 = e2) | ~ (all_46_2 = e3) % 155.05/23.70 (80) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 155.05/23.70 (81) all_56_10 = all_52_13 % 155.05/23.70 (82) ~ (all_52_12 = all_10_2) % 155.05/23.70 (83) ~ (all_52_1 = all_52_3) % 155.05/23.70 (84) all_56_14 = all_52_11 % 155.05/23.70 (85) all_58_28 = all_10_2 % 155.05/23.70 (86) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 155.05/23.70 (87) ~ (all_52_1 = all_52_9) % 155.05/23.70 (88) all_40_0 = all_6_0 % 155.05/23.70 (89) op(e3, e1) = all_52_8 % 155.05/23.70 (90) op(all_8_2, e2) = all_8_1 % 155.05/23.70 (91) all_56_15 = e0 % 155.05/23.70 (92) ~ (e2 = e0) % 155.05/23.70 (93) ~ (all_52_9 = all_6_2) % 155.05/23.70 (94) all_56_0 = all_10_2 % 155.05/23.70 (95) all_58_31 = e0 % 155.05/23.70 (96) ~ (all_52_3 = all_52_11) % 155.05/23.70 (97) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 155.05/23.70 (98) ~ (all_52_3 = all_10_2) % 155.05/23.70 (99) all_56_8 = all_6_2 % 155.05/23.70 (100) all_58_27 = e0 % 155.05/23.70 (101) op(e2, e0) = all_52_13 % 155.05/23.70 (102) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 155.05/23.70 (103) ~ (all_8_1 = e0) % 155.05/23.70 (104) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.70 (105) all_54_0 = all_10_2 % 155.05/23.70 (106) all_56_6 = e0 | all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 155.05/23.70 (107) ~ (all_52_7 = e0) % 155.05/23.70 (108) ~ (e1 = e0) % 155.05/23.70 (109) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.05/23.70 (110) ~ (all_52_14 = e0) % 155.05/23.70 (111) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 155.05/23.70 (112) ~ (all_52_4 = all_10_2) % 155.05/23.70 (113) all_58_30 = all_6_2 % 155.05/23.70 (114) op(e2, all_52_1) = all_58_7 % 155.05/23.70 (115) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.05/23.70 (116) ~ (e3 = e2) % 155.05/23.70 (117) ~ (all_52_14 = all_6_2) % 155.05/23.70 (118) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 155.05/23.70 (119) ~ (all_52_4 = all_52_12) % 155.05/23.70 (120) all_54_12 = all_52_3 % 155.05/23.70 (121) all_54_4 = all_52_1 % 155.05/23.71 (122) ~ (all_52_1 = all_10_2) % 155.05/23.71 % 155.05/23.71 Begin of proof % 155.05/23.71 | % 155.05/23.71 | BETA: splitting (76) gives: % 155.05/23.71 | % 155.05/23.71 | Case 1: % 155.05/23.71 | | % 155.05/23.71 | | (123) ~ (all_40_0 = e0) % 155.05/23.71 | | % 155.05/23.71 | | REDUCE: (88), (123) imply: % 155.05/23.71 | | (124) ~ (all_6_0 = e0) % 155.05/23.71 | | % 155.05/23.71 | | BETA: splitting (106) gives: % 155.05/23.71 | | % 155.05/23.71 | | Case 1: % 155.05/23.71 | | | % 155.05/23.71 | | | (125) all_56_6 = e0 % 155.05/23.71 | | | % 155.05/23.71 | | | COMBINE_EQS: (64), (125) imply: % 155.05/23.71 | | | (126) all_52_2 = e0 % 155.05/23.71 | | | % 155.05/23.71 | | | SIMP: (126) implies: % 155.05/23.71 | | | (127) all_52_2 = e0 % 155.05/23.71 | | | % 155.05/23.71 | | | REDUCE: (5), (127) imply: % 155.05/23.71 | | | (128) ~ (all_52_3 = e0) % 155.05/23.71 | | | % 155.05/23.71 | | | REDUCE: (65), (127) imply: % 155.05/23.71 | | | (129) ~ (all_52_6 = e0) % 155.05/23.71 | | | % 155.05/23.71 | | | SIMP: (129) implies: % 155.05/23.71 | | | (130) ~ (all_52_6 = e0) % 155.05/23.71 | | | % 155.05/23.71 | | | REDUCE: (32), (127) imply: % 155.05/23.71 | | | (131) ~ (all_6_2 = e0) % 155.05/23.71 | | | % 155.05/23.71 | | | BETA: splitting (70) gives: % 155.05/23.71 | | | % 155.05/23.71 | | | Case 1: % 155.05/23.71 | | | | % 155.05/23.71 | | | | (132) all_56_1 = e0 % 155.05/23.71 | | | | % 155.05/23.71 | | | | COMBINE_EQS: (49), (132) imply: % 155.05/23.71 | | | | (133) all_52_4 = e0 % 155.05/23.71 | | | | % 155.05/23.71 | | | | SIMP: (133) implies: % 155.05/23.71 | | | | (134) all_52_4 = e0 % 155.05/23.71 | | | | % 155.05/23.71 | | | | REDUCE: (58), (134) imply: % 155.05/23.71 | | | | (135) ~ (all_52_8 = e0) % 155.05/23.71 | | | | % 155.05/23.71 | | | | SIMP: (135) implies: % 155.05/23.71 | | | | (136) ~ (all_52_8 = e0) % 155.05/23.71 | | | | % 155.05/23.71 | | | | REDUCE: (119), (134) imply: % 155.05/23.71 | | | | (137) ~ (all_52_12 = e0) % 155.05/23.71 | | | | % 155.05/23.71 | | | | SIMP: (137) implies: % 155.05/23.71 | | | | (138) ~ (all_52_12 = e0) % 155.05/23.71 | | | | % 155.05/23.71 | | | | REDUCE: (112), (134) imply: % 155.05/23.71 | | | | (139) ~ (all_10_2 = e0) % 155.05/23.71 | | | | % 155.05/23.71 | | | | REDUCE: (24), (134) imply: % 155.05/23.71 | | | | (140) op(e3, e2) = e0 % 155.05/23.71 | | | | % 155.05/23.71 | | | | BETA: splitting (50) gives: % 155.05/23.71 | | | | % 155.05/23.71 | | | | Case 1: % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | (141) all_56_4 = e0 % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | COMBINE_EQS: (14), (141) imply: % 155.05/23.71 | | | | | (142) all_52_8 = e0 % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | REDUCE: (136), (142) imply: % 155.05/23.71 | | | | | (143) $false % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | CLOSE: (143) is inconsistent. % 155.05/23.71 | | | | | % 155.05/23.71 | | | | Case 2: % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | (144) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | BETA: splitting (144) gives: % 155.05/23.71 | | | | | % 155.05/23.71 | | | | | Case 1: % 155.05/23.71 | | | | | | % 155.05/23.71 | | | | | | (145) all_56_5 = e0 % 155.05/23.71 | | | | | | % 155.05/23.71 | | | | | | COMBINE_EQS: (45), (145) imply: % 155.05/23.71 | | | | | | (146) all_52_9 = e0 % 155.05/23.71 | | | | | | % 155.05/23.71 | | | | | | SIMP: (146) implies: % 155.05/23.71 | | | | | | (147) all_52_9 = e0 % 155.05/23.71 | | | | | | % 155.05/23.71 | | | | | | REDUCE: (87), (147) imply: % 155.05/23.71 | | | | | | (148) ~ (all_52_1 = e0) % 155.05/23.71 | | | | | | % 155.05/23.71 | | | | | | BETA: splitting (43) gives: % 155.05/23.71 | | | | | | % 155.05/23.71 | | | | | | Case 1: % 155.05/23.71 | | | | | | | % 155.05/23.71 | | | | | | | (149) all_54_0 = e0 % 155.05/23.71 | | | | | | | % 155.05/23.71 | | | | | | | REF_CLOSE: (31), (105), (149) are inconsistent by sub-proof #861. % 155.05/23.71 | | | | | | | % 155.05/23.71 | | | | | | Case 2: % 155.05/23.71 | | | | | | | % 155.05/23.71 | | | | | | | (150) ~ (all_54_0 = e0) % 155.05/23.71 | | | | | | | (151) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.05/23.71 | | | | | | | % 155.05/23.71 | | | | | | | BETA: splitting (80) gives: % 155.05/23.71 | | | | | | | % 155.05/23.71 | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | % 155.05/23.71 | | | | | | | | (152) all_54_12 = e0 % 155.05/23.71 | | | | | | | | % 155.05/23.71 | | | | | | | | REF_CLOSE: (39), (120), (152) are inconsistent by sub-proof % 155.05/23.71 | | | | | | | | #762. % 155.05/23.71 | | | | | | | | % 155.05/23.71 | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | % 155.05/23.71 | | | | | | | | (153) ~ (all_54_12 = e0) % 155.05/23.71 | | | | | | | | (154) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 155.05/23.71 | | | | | | | | % 155.05/23.71 | | | | | | | | BETA: splitting (111) gives: % 155.05/23.71 | | | | | | | | % 155.05/23.71 | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | % 155.05/23.71 | | | | | | | | | (155) all_54_2 = e0 % 155.05/23.71 | | | | | | | | | % 155.05/23.71 | | | | | | | | | REF_CLOSE: (9), (136), (155) are inconsistent by sub-proof % 155.05/23.71 | | | | | | | | | #860. % 155.05/23.71 | | | | | | | | | % 155.05/23.71 | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | % 155.05/23.71 | | | | | | | | | (156) ~ (all_54_2 = e0) % 155.05/23.71 | | | | | | | | | (157) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 155.05/23.71 | | | | | | | | | % 155.05/23.71 | | | | | | | | | BETA: splitting (67) gives: % 155.05/23.71 | | | | | | | | | % 155.05/23.71 | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | (158) all_54_4 = e0 % 155.05/23.71 | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | REF_CLOSE: (121), (148), (158) are inconsistent by sub-proof % 155.05/23.71 | | | | | | | | | | #859. % 155.05/23.71 | | | | | | | | | | % 155.05/23.71 | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | (159) ~ (all_54_4 = e0) % 155.05/23.71 | | | | | | | | | | (160) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.05/23.71 | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | BETA: splitting (57) gives: % 155.05/23.71 | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | (161) all_56_12 = e3 % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | COMBINE_EQS: (46), (161) imply: % 155.05/23.71 | | | | | | | | | | | (162) all_52_3 = e3 % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | SIMP: (162) implies: % 155.05/23.71 | | | | | | | | | | | (163) all_52_3 = e3 % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | REDUCE: (47), (163) imply: % 155.05/23.71 | | | | | | | | | | | (164) ~ (all_52_7 = e3) % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | SIMP: (164) implies: % 155.05/23.71 | | | | | | | | | | | (165) ~ (all_52_7 = e3) % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | REDUCE: (96), (163) imply: % 155.05/23.71 | | | | | | | | | | | (166) ~ (all_52_11 = e3) % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | SIMP: (166) implies: % 155.05/23.71 | | | | | | | | | | | (167) ~ (all_52_11 = e3) % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (8), (12), (14), (26), (41), (55), % 155.05/23.71 | | | | | | | | | | | (60), (66), (75), (84), (85), (90), (95), (99), % 155.05/23.71 | | | | | | | | | | | (103), (104), (113), (132), (136), (140), (145), % 155.05/23.71 | | | | | | | | | | | (165), (167) are inconsistent by sub-proof #758. % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | (168) ~ (all_56_12 = e3) % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | REDUCE: (46), (168) imply: % 155.05/23.71 | | | | | | | | | | | (169) ~ (all_52_3 = e3) % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | BETA: splitting (51) gives: % 155.05/23.71 | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | (170) all_56_0 = e3 % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | COMBINE_EQS: (94), (170) imply: % 155.05/23.71 | | | | | | | | | | | | (171) all_10_2 = e3 % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | REDUCE: (73), (171) imply: % 155.05/23.71 | | | | | | | | | | | | (172) op(e3, e3) = e0 % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | REDUCE: (74), (171) imply: % 155.05/23.71 | | | | | | | | | | | | (173) op(e3, e3) = all_58_0 % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | REDUCE: (34), (171) imply: % 155.05/23.71 | | | | | | | | | | | | (174) op(e3, e3) = e3 % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | REF_CLOSE: (3), (75), (172), (173), (174) are inconsistent by % 155.05/23.71 | | | | | | | | | | | | sub-proof #757. % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | (175) ~ (all_56_0 = e3) % 155.05/23.71 | | | | | | | | | | | | (176) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | REDUCE: (94), (175) imply: % 155.05/23.71 | | | | | | | | | | | | (177) ~ (all_10_2 = e3) % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | BETA: splitting (176) gives: % 155.05/23.71 | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | (178) all_56_2 = e3 % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | COMBINE_EQS: (77), (178) imply: % 155.05/23.71 | | | | | | | | | | | | | (179) all_52_1 = e3 % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | SIMP: (179) implies: % 155.05/23.71 | | | | | | | | | | | | | (180) all_52_1 = e3 % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | REDUCE: (83), (180) imply: % 155.05/23.71 | | | | | | | | | | | | | (181) ~ (all_52_3 = e3) % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | REDUCE: (122), (180) imply: % 155.05/23.71 | | | | | | | | | | | | | (182) ~ (all_10_2 = e3) % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | REDUCE: (54), (180) imply: % 155.05/23.71 | | | | | | | | | | | | | (183) ~ (all_8_2 = e3) % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | SIMP: (183) implies: % 155.05/23.71 | | | | | | | | | | | | | (184) ~ (all_8_2 = e3) % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | REDUCE: (114), (180) imply: % 155.05/23.71 | | | | | | | | | | | | | (185) op(e2, e3) = all_58_7 % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | REDUCE: (27), (180) imply: % 155.05/23.71 | | | | | | | | | | | | | (186) op(e2, e3) = e3 % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | BETA: splitting (104) gives: % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | (187) all_58_28 = e3 % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | COMBINE_EQS: (85), (187) imply: % 155.05/23.71 | | | | | | | | | | | | | | (188) all_10_2 = e3 % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | REDUCE: (177), (188) imply: % 155.05/23.71 | | | | | | | | | | | | | | (189) $false % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | CLOSE: (189) is inconsistent. % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | (190) ~ (all_58_28 = e3) % 155.05/23.71 | | | | | | | | | | | | | | (191) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | BETA: splitting (191) gives: % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | (192) all_58_29 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | REF_CLOSE: (60), (184), (192) are inconsistent by sub-proof % 155.05/23.71 | | | | | | | | | | | | | | | #756. % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | (193) all_58_30 = e3 | all_58_31 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | (194) all_58_30 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (194) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | (195) all_6_2 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | SIMP: (195) implies: % 155.05/23.71 | | | | | | | | | | | | | | | | (196) all_6_2 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (196) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | (197) all_56_8 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | REDUCE: (26), (196) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | (198) ~ (all_52_8 = e3) % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | REDUCE: (68), (196) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | (199) op(e3, all_6_1) = all_6_0 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | REDUCE: (71), (196) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | (200) op(e3, e1) = all_6_1 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | (201) all_56_0 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (201) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | (202) all_10_2 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | REDUCE: (177), (202) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | (203) $false % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | (204) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | (205) all_56_1 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (95), (132), (193), (194), (205) are % 155.05/23.71 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #754. % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | (206) all_56_4 = e3 | all_56_9 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (207) all_56_4 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (198), (207) are inconsistent by sub-proof % 155.05/23.71 | | | | | | | | | | | | | | | | | | | #753. % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (208) all_56_9 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (208) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (209) all_52_12 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_58_7, e3, e2, % 155.05/23.71 | | | | | | | | | | | | | | | | | | | simplifying with (185), (186) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (210) all_58_7 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_8, all_6_1, e1, e3, % 155.05/23.71 | | | | | | | | | | | | | | | | | | | simplifying with (89), (200) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (211) all_52_8 = all_6_1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (211) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (212) all_54_2 = all_6_1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (211) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (213) all_56_4 = all_6_1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | REDUCE: (12), (211) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (214) ~ (all_10_2 = all_6_1) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | SIMP: (214) implies: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (215) ~ (all_10_2 = all_6_1) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | REDUCE: (198), (211) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (216) ~ (all_6_1 = e3) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | REDUCE: (35), (211) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (217) op(e3, all_6_1) = all_58_3 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_6_0, all_58_3, all_6_1, % 155.05/23.71 | | | | | | | | | | | | | | | | | | | e3, simplifying with (199), (217) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | (218) all_58_3 = all_6_0 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (219) all_56_0 = e1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (219) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (220) all_10_2 = e1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | SIMP: (220) implies: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (221) all_10_2 = e1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (221) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (222) ~ (all_6_1 = e1) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (223) ~ (all_6_1 = e1) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (224) all_56_4 = e2 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (224) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (225) all_6_1 = e2 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (225) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (226) op(e3, e2) = all_6_0 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_6_0, e2, e3, % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | simplifying with (140), (226) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (227) all_6_0 = e0 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (227) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (228) $false % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_56_4 = e2) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (229) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_6_1 = e2) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | (231) all_54_2 = e1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (231) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | (232) all_6_1 = e1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | (233) all_6_1 = e1 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (233) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | (234) $false % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent. % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | (235) all_54_2 = e3 | all_54_2 = e2 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (212), (216), (230), (235) are inconsistent by % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | sub-proof #752. % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (236) ~ (all_56_0 = e1) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (236) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | (237) ~ (all_10_2 = e1) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | Case 1: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (238) all_58_28 = e2 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (238) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (239) all_10_2 = e2 % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (14), (21), (31), (42), (46), (73), (75), % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (98), (120), (125), (145), (154), (169), (176), % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (177), (178), (185), (186), (197), (198), (206), % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (208), (213), (215), (239) are inconsistent by % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | sub-proof #746. % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (240) ~ (all_58_28 = e2) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (240) imply: % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | (241) ~ (all_10_2 = e2) % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (151), (177), (237), (241) are inconsistent % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | by sub-proof #813. % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | (242) all_58_31 = e3 % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | | REF_CLOSE: (75), (95), (242) are inconsistent by sub-proof % 155.05/23.71 | | | | | | | | | | | | | | | | #853. % 155.05/23.71 | | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | End of split % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | Case 2: % 155.05/23.71 | | | | | | | | | | | | | % 155.05/23.71 | | | | | | | | | | | | | (243) ~ (all_56_2 = e3) % 155.12/23.71 | | | | | | | | | | | | | (244) all_56_6 = e3 | all_56_12 = e3 % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | REF_CLOSE: (42), (46), (75), (77), (83), (98), (105), (120), % 155.12/23.71 | | | | | | | | | | | | | (121), (122), (125), (151), (154), (160), (169), % 155.12/23.71 | | | | | | | | | | | | | (177), (243), (244) are inconsistent by sub-proof % 155.12/23.71 | | | | | | | | | | | | | #744. % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | End of split % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | End of split % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | End of split % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | End of split % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | End of split % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | End of split % 155.12/23.71 | | | | | | | % 155.12/23.71 | | | | | | End of split % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | Case 2: % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | (245) all_56_8 = e0 | all_56_14 = e0 % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | REF_CLOSE: (19), (78), (84), (99), (245) are inconsistent by % 155.12/23.71 | | | | | | sub-proof #805. % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | End of split % 155.12/23.71 | | | | | % 155.12/23.71 | | | | End of split % 155.12/23.71 | | | | % 155.12/23.71 | | | Case 2: % 155.12/23.71 | | | | % 155.12/23.71 | | | | (246) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 155.12/23.71 | | | | % 155.12/23.71 | | | | REF_CLOSE: (7), (17), (42), (55), (60), (62), (66), (75), (92), (95), % 155.12/23.71 | | | | (104), (107), (108), (113), (115), (116), (130), (246) are % 155.12/23.71 | | | | inconsistent by sub-proof #801. % 155.12/23.71 | | | | % 155.12/23.71 | | | End of split % 155.12/23.71 | | | % 155.12/23.71 | | Case 2: % 155.12/23.71 | | | % 155.12/23.71 | | | (247) ~ (all_56_6 = e0) % 155.12/23.71 | | | (248) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 155.12/23.71 | | | % 155.12/23.71 | | | REDUCE: (64), (247) imply: % 155.12/23.71 | | | (249) ~ (all_52_2 = e0) % 155.12/23.71 | | | % 155.12/23.71 | | | REF_CLOSE: (3), (6), (7), (12), (13), (14), (15), (16), (18), (19), (20), % 155.12/23.71 | | | (22), (23), (26), (28), (29), (30), (31), (33), (34), (35), % 155.12/23.71 | | | (37), (38), (39), (40), (43), (44), (45), (46), (48), (49), % 155.12/23.71 | | | (50), (52), (53), (56), (59), (60), (61), (62), (63), (64), % 155.12/23.71 | | | (65), (69), (72), (73), (74), (77), (78), (81), (84), (85), % 155.12/23.71 | | | (86), (87), (90), (91), (94), (95), (97), (99), (100), (101), % 155.12/23.71 | | | (102), (103), (104), (105), (108), (109), (110), (112), (113), % 155.12/23.71 | | | (114), (115), (116), (117), (118), (119), (248), (249) are % 155.12/23.71 | | | inconsistent by sub-proof #735. % 155.12/23.71 | | | % 155.12/23.71 | | End of split % 155.12/23.71 | | % 155.12/23.71 | Case 2: % 155.12/23.71 | | % 155.12/23.71 | | (250) all_40_0 = e0 % 155.12/23.71 | | % 155.12/23.71 | | COMBINE_EQS: (88), (250) imply: % 155.12/23.71 | | (251) all_6_0 = e0 % 155.12/23.71 | | % 155.12/23.71 | | SIMP: (251) implies: % 155.12/23.71 | | (252) all_6_0 = e0 % 155.12/23.71 | | % 155.12/23.71 | | COMBINE_EQS: (11), (252) imply: % 155.12/23.71 | | (253) all_46_0 = e0 % 155.12/23.71 | | % 155.12/23.71 | | BETA: splitting (79) gives: % 155.12/23.71 | | % 155.12/23.71 | | Case 1: % 155.12/23.71 | | | % 155.12/23.71 | | | (254) ~ (all_46_0 = e0) % 155.12/23.71 | | | % 155.12/23.71 | | | REDUCE: (253), (254) imply: % 155.12/23.71 | | | (255) $false % 155.12/23.71 | | | % 155.12/23.71 | | | CLOSE: (255) is inconsistent. % 155.12/23.71 | | | % 155.12/23.71 | | Case 2: % 155.12/23.71 | | | % 155.12/23.71 | | | (256) ~ (all_46_1 = e2) | ~ (all_46_2 = e3) % 155.12/23.71 | | | % 155.12/23.71 | | | BETA: splitting (106) gives: % 155.12/23.71 | | | % 155.12/23.71 | | | Case 1: % 155.12/23.71 | | | | % 155.12/23.71 | | | | (257) all_56_6 = e0 % 155.12/23.71 | | | | % 155.12/23.71 | | | | COMBINE_EQS: (64), (257) imply: % 155.12/23.71 | | | | (258) all_52_2 = e0 % 155.12/23.71 | | | | % 155.12/23.71 | | | | SIMP: (258) implies: % 155.12/23.71 | | | | (259) all_52_2 = e0 % 155.12/23.71 | | | | % 155.12/23.71 | | | | REDUCE: (5), (259) imply: % 155.12/23.71 | | | | (260) ~ (all_52_3 = e0) % 155.12/23.71 | | | | % 155.12/23.71 | | | | REDUCE: (65), (259) imply: % 155.12/23.71 | | | | (261) ~ (all_52_6 = e0) % 155.12/23.71 | | | | % 155.12/23.71 | | | | SIMP: (261) implies: % 155.12/23.71 | | | | (262) ~ (all_52_6 = e0) % 155.12/23.71 | | | | % 155.12/23.71 | | | | REDUCE: (32), (259) imply: % 155.12/23.71 | | | | (263) ~ (all_6_2 = e0) % 155.12/23.71 | | | | % 155.12/23.71 | | | | BETA: splitting (70) gives: % 155.12/23.71 | | | | % 155.12/23.71 | | | | Case 1: % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | (264) all_56_1 = e0 % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | COMBINE_EQS: (49), (264) imply: % 155.12/23.71 | | | | | (265) all_52_4 = e0 % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | SIMP: (265) implies: % 155.12/23.71 | | | | | (266) all_52_4 = e0 % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | REDUCE: (58), (266) imply: % 155.12/23.71 | | | | | (267) ~ (all_52_8 = e0) % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | SIMP: (267) implies: % 155.12/23.71 | | | | | (268) ~ (all_52_8 = e0) % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | REDUCE: (119), (266) imply: % 155.12/23.71 | | | | | (269) ~ (all_52_12 = e0) % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | SIMP: (269) implies: % 155.12/23.71 | | | | | (270) ~ (all_52_12 = e0) % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | REDUCE: (112), (266) imply: % 155.12/23.71 | | | | | (271) ~ (all_10_2 = e0) % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | REDUCE: (24), (266) imply: % 155.12/23.71 | | | | | (272) op(e3, e2) = e0 % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | BETA: splitting (50) gives: % 155.12/23.71 | | | | | % 155.12/23.71 | | | | | Case 1: % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | (273) all_56_4 = e0 % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | COMBINE_EQS: (14), (273) imply: % 155.12/23.71 | | | | | | (274) all_52_8 = e0 % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | REDUCE: (268), (274) imply: % 155.12/23.71 | | | | | | (275) $false % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | CLOSE: (275) is inconsistent. % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | Case 2: % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | (276) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | BETA: splitting (276) gives: % 155.12/23.71 | | | | | | % 155.12/23.71 | | | | | | Case 1: % 155.12/23.71 | | | | | | | % 155.12/23.71 | | | | | | | (277) all_56_5 = e0 % 155.12/23.71 | | | | | | | % 155.12/23.71 | | | | | | | COMBINE_EQS: (45), (277) imply: % 155.12/23.71 | | | | | | | (278) all_52_9 = e0 % 155.12/23.71 | | | | | | | % 155.12/23.71 | | | | | | | REDUCE: (87), (278) imply: % 155.12/23.71 | | | | | | | (279) ~ (all_52_1 = e0) % 155.12/23.71 | | | | | | | % 155.12/23.71 | | | | | | | BETA: splitting (43) gives: % 155.12/23.71 | | | | | | | % 155.12/23.71 | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | | (280) all_54_0 = e0 % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | | REF_CLOSE: (31), (105), (280) are inconsistent by sub-proof % 155.12/23.71 | | | | | | | | #861. % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | | (281) ~ (all_54_0 = e0) % 155.12/23.71 | | | | | | | | (282) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | | BETA: splitting (80) gives: % 155.12/23.71 | | | | | | | | % 155.12/23.71 | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | (283) all_54_12 = e0 % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | COMBINE_EQS: (120), (283) imply: % 155.12/23.71 | | | | | | | | | (284) all_52_3 = e0 % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | REDUCE: (39), (284) imply: % 155.12/23.71 | | | | | | | | | (285) $false % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | CLOSE: (285) is inconsistent. % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | (286) ~ (all_54_12 = e0) % 155.12/23.71 | | | | | | | | | (287) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | BETA: splitting (111) gives: % 155.12/23.71 | | | | | | | | | % 155.12/23.71 | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | (288) all_54_2 = e0 % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | REF_CLOSE: (9), (268), (288) are inconsistent by sub-proof % 155.12/23.71 | | | | | | | | | | #860. % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | (289) ~ (all_54_2 = e0) % 155.12/23.71 | | | | | | | | | | (290) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | BETA: splitting (67) gives: % 155.12/23.71 | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | (291) all_54_4 = e0 % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | REF_CLOSE: (121), (279), (291) are inconsistent by sub-proof % 155.12/23.71 | | | | | | | | | | | #859. % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | (292) ~ (all_54_4 = e0) % 155.12/23.71 | | | | | | | | | | | (293) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | BETA: splitting (57) gives: % 155.12/23.71 | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | (294) all_56_12 = e3 % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | COMBINE_EQS: (46), (294) imply: % 155.12/23.71 | | | | | | | | | | | | (295) all_52_3 = e3 % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | REDUCE: (47), (295) imply: % 155.12/23.71 | | | | | | | | | | | | (296) ~ (all_52_7 = e3) % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | SIMP: (296) implies: % 155.12/23.71 | | | | | | | | | | | | (297) ~ (all_52_7 = e3) % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | REDUCE: (96), (295) imply: % 155.12/23.71 | | | | | | | | | | | | (298) ~ (all_52_11 = e3) % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | SIMP: (298) implies: % 155.12/23.71 | | | | | | | | | | | | (299) ~ (all_52_11 = e3) % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (8), (12), (14), (26), (41), (55), % 155.12/23.71 | | | | | | | | | | | | (60), (66), (75), (84), (85), (90), (95), (99), % 155.12/23.71 | | | | | | | | | | | | (103), (104), (113), (264), (268), (272), (277), % 155.12/23.71 | | | | | | | | | | | | (297), (299) are inconsistent by sub-proof #758. % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | (300) ~ (all_56_12 = e3) % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | REDUCE: (46), (300) imply: % 155.12/23.71 | | | | | | | | | | | | (301) ~ (all_52_3 = e3) % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | BETA: splitting (51) gives: % 155.12/23.71 | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | (302) all_56_0 = e3 % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | COMBINE_EQS: (94), (302) imply: % 155.12/23.71 | | | | | | | | | | | | | (303) all_10_2 = e3 % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | REF_CLOSE: (3), (31), (34), (73), (74), (303) are % 155.12/23.71 | | | | | | | | | | | | | inconsistent by sub-proof #737. % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | (304) ~ (all_56_0 = e3) % 155.12/23.71 | | | | | | | | | | | | | (305) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | REDUCE: (94), (304) imply: % 155.12/23.71 | | | | | | | | | | | | | (306) ~ (all_10_2 = e3) % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | BETA: splitting (305) gives: % 155.12/23.71 | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | (307) all_56_2 = e3 % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | COMBINE_EQS: (77), (307) imply: % 155.12/23.71 | | | | | | | | | | | | | | (308) all_52_1 = e3 % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | REDUCE: (83), (308) imply: % 155.12/23.71 | | | | | | | | | | | | | | (309) ~ (all_52_3 = e3) % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | REDUCE: (122), (308) imply: % 155.12/23.71 | | | | | | | | | | | | | | (310) ~ (all_10_2 = e3) % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | REDUCE: (54), (308) imply: % 155.12/23.71 | | | | | | | | | | | | | | (311) ~ (all_8_2 = e3) % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | SIMP: (311) implies: % 155.12/23.71 | | | | | | | | | | | | | | (312) ~ (all_8_2 = e3) % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | REDUCE: (114), (308) imply: % 155.12/23.71 | | | | | | | | | | | | | | (313) op(e2, e3) = all_58_7 % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | REDUCE: (27), (308) imply: % 155.12/23.71 | | | | | | | | | | | | | | (314) op(e2, e3) = e3 % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | BETA: splitting (104) gives: % 155.12/23.71 | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | (315) all_58_28 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (315) imply: % 155.12/23.71 | | | | | | | | | | | | | | | (316) all_10_2 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | REDUCE: (306), (316) imply: % 155.12/23.71 | | | | | | | | | | | | | | | (317) $false % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | CLOSE: (317) is inconsistent. % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | (318) ~ (all_58_28 = e3) % 155.12/23.71 | | | | | | | | | | | | | | | (319) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 155.12/23.71 | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | (320) all_58_29 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | REF_CLOSE: (60), (312), (320) are inconsistent by sub-proof % 155.12/23.71 | | | | | | | | | | | | | | | | #756. % 155.12/23.71 | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | Case 2: % 155.12/23.71 | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | (321) all_58_30 = e3 | all_58_31 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 155.12/23.71 | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | (322) all_58_30 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (322) imply: % 155.12/23.71 | | | | | | | | | | | | | | | | | (323) all_6_2 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | SIMP: (323) implies: % 155.12/23.71 | | | | | | | | | | | | | | | | | (324) all_6_2 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (324) imply: % 155.12/23.71 | | | | | | | | | | | | | | | | | (325) all_46_2 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (324) imply: % 155.12/23.71 | | | | | | | | | | | | | | | | | (326) all_56_8 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | REDUCE: (26), (324) imply: % 155.12/23.71 | | | | | | | | | | | | | | | | | (327) ~ (all_52_8 = e3) % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | REDUCE: (71), (324) imply: % 155.12/23.71 | | | | | | | | | | | | | | | | | (328) op(e3, e1) = all_6_1 % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | BETA: splitting (109) gives: % 155.12/23.71 | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.71 | | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | | (329) all_56_0 = e3 % 155.12/23.71 | | | | | | | | | | | | | | | | | | % 155.12/23.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (329) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | (330) all_10_2 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | REDUCE: (306), (330) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | (331) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | CLOSE: (331) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | (332) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (333) all_56_1 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (95), (264), (321), (322), (333) are % 155.12/23.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #754. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (334) all_56_4 = e3 | all_56_9 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (335) all_56_4 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (327), (335) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | #753. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (336) all_56_9 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (336) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (337) all_52_12 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (338) ~ (all_46_1 = e2) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (338) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (339) ~ (all_6_1 = e2) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e3, all_58_7, e3, e2, % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (313), (314) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (340) all_58_7 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_8, all_6_1, e1, e3, % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (89), (328) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (341) all_52_8 = all_6_1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (341) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (342) all_54_2 = all_6_1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (341) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (343) all_56_4 = all_6_1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (341) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_10_2 = all_6_1) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | SIMP: (344) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (345) ~ (all_10_2 = all_6_1) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (327), (341) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_6_1 = e3) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (347) all_56_0 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (347) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (348) all_10_2 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (14), (21), (31), (42), (46), (73), (75), % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (98), (120), (257), (277), (287), (301), (305), % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (306), (307), (313), (314), (326), (327), (334), % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (336), (343), (345), (348) are inconsistent by % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | sub-proof #746. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_56_0 = e2) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (349) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (350) ~ (all_10_2 = e2) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (351) all_54_2 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (351) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (352) all_6_1 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (352) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (353) all_6_1 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (345), (353) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_10_2 = e1) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (282), (306), (350), (354) are inconsistent % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #813. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (355) all_54_2 = e3 | all_54_2 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (339), (342), (346), (355) are inconsistent by % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #752. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (356) ~ (all_46_2 = e3) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (325), (356) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (357) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | (358) all_58_31 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (95), (358) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | | | | | | | | | #853. % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | (359) ~ (all_56_2 = e3) % 155.12/23.72 | | | | | | | | | | | | | | (360) all_56_6 = e3 | all_56_12 = e3 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | REF_CLOSE: (42), (46), (75), (77), (83), (98), (105), (120), % 155.12/23.72 | | | | | | | | | | | | | | (121), (122), (257), (282), (287), (293), (301), % 155.12/23.72 | | | | | | | | | | | | | | (306), (359), (360) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | | | | | | #744. % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | End of split % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | End of split % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | Case 2: % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | (361) all_56_8 = e0 | all_56_14 = e0 % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | REF_CLOSE: (19), (78), (84), (99), (361) are inconsistent by % 155.12/23.72 | | | | | | | sub-proof #805. % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | End of split % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | End of split % 155.12/23.72 | | | | | % 155.12/23.72 | | | | Case 2: % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | (362) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | REF_CLOSE: (7), (17), (42), (55), (60), (62), (66), (75), (92), (95), % 155.12/23.72 | | | | | (104), (107), (108), (113), (115), (116), (262), (362) are % 155.12/23.72 | | | | | inconsistent by sub-proof #801. % 155.12/23.72 | | | | | % 155.12/23.72 | | | | End of split % 155.12/23.72 | | | | % 155.12/23.72 | | | Case 2: % 155.12/23.72 | | | | % 155.12/23.72 | | | | (363) ~ (all_56_6 = e0) % 155.12/23.72 | | | | (364) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 155.12/23.72 | | | | % 155.12/23.72 | | | | REDUCE: (64), (363) imply: % 155.12/23.72 | | | | (365) ~ (all_52_2 = e0) % 155.12/23.72 | | | | % 155.12/23.72 | | | | REF_CLOSE: (3), (6), (7), (12), (13), (14), (15), (16), (18), (19), % 155.12/23.72 | | | | (20), (22), (23), (26), (28), (29), (30), (31), (33), (34), % 155.12/23.72 | | | | (35), (37), (38), (39), (40), (43), (44), (45), (46), (48), % 155.12/23.72 | | | | (49), (50), (52), (53), (56), (59), (60), (61), (62), (63), % 155.12/23.72 | | | | (64), (65), (69), (72), (73), (74), (77), (78), (81), (84), % 155.12/23.72 | | | | (85), (86), (87), (90), (91), (94), (95), (97), (99), (100), % 155.12/23.72 | | | | (101), (102), (103), (104), (105), (108), (109), (110), % 155.12/23.72 | | | | (112), (113), (114), (115), (116), (117), (118), (119), % 155.12/23.72 | | | | (364), (365) are inconsistent by sub-proof #735. % 155.12/23.72 | | | | % 155.12/23.72 | | | End of split % 155.12/23.72 | | | % 155.12/23.72 | | End of split % 155.12/23.72 | | % 155.12/23.72 | End of split % 155.12/23.72 | % 155.12/23.72 End of proof % 155.12/23.72 % 155.12/23.72 Sub-proof #735 shows that the following formulas are inconsistent: % 155.12/23.72 ---------------------------------------------------------------- % 155.12/23.72 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.12/23.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.12/23.72 (2) all_32_0 = all_10_0 % 155.12/23.72 (3) all_56_7 = all_52_6 % 155.12/23.72 (4) ~ (all_52_2 = e0) % 155.12/23.72 (5) ~ (all_52_8 = all_10_2) % 155.12/23.72 (6) all_54_7 = all_52_13 % 155.12/23.72 (7) all_56_4 = all_52_8 % 155.12/23.72 (8) ~ (all_52_4 = all_8_2) % 155.12/23.72 (9) all_32_2 = all_10_2 % 155.12/23.72 (10) all_54_1 = all_52_4 % 155.12/23.72 (11) ~ (all_6_2 = e0) % 155.12/23.72 (12) ~ (all_52_4 = all_52_6) % 155.12/23.72 (13) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 155.12/23.72 (14) all_54_11 = all_52_14 % 155.12/23.72 (15) ~ (all_52_8 = all_6_2) % 155.12/23.72 (16) ~ (all_52_12 = all_52_13) % 155.12/23.72 (17) ~ (all_52_6 = all_52_14) % 155.12/23.72 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 155.12/23.72 (19) ~ (all_10_2 = e0) % 155.12/23.72 (20) ~ (all_32_0 = e1) | ~ (all_32_2 = e2) % 155.12/23.72 (21) op(e3, e3) = all_10_2 % 155.12/23.72 (22) op(e3, all_52_8) = all_58_3 % 155.12/23.72 (23) op(e1, e2) = all_52_6 % 155.12/23.72 (24) op(all_10_2, e0) = all_10_0 % 155.12/23.72 (25) ~ (all_52_3 = e0) % 155.12/23.72 (26) op(e1, all_52_6) = all_58_16 % 155.12/23.72 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 155.12/23.72 (28) ~ (all_52_1 = all_52_13) % 155.12/23.72 (29) all_56_5 = all_52_9 % 155.12/23.72 (30) all_56_12 = all_52_3 % 155.12/23.72 (31) all_56_11 = all_52_14 % 155.12/23.72 (32) all_56_1 = all_52_4 % 155.12/23.72 (33) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.12/23.72 (34) op(e1, e3) = all_52_2 % 155.12/23.72 (35) op(e1, e0) = all_52_14 % 155.12/23.72 (36) ~ (all_52_13 = all_52_14) % 155.12/23.72 (37) all_56_9 = all_52_12 % 155.12/23.72 (38) all_58_29 = all_8_2 % 155.12/23.72 (39) ~ (all_52_12 = all_52_14) % 155.12/23.72 (40) ~ (e2 = e1) % 155.12/23.72 (41) op(e3, e0) = all_52_12 % 155.12/23.72 (42) all_56_6 = all_52_2 % 155.12/23.72 (43) ~ (all_52_2 = all_52_6) % 155.12/23.72 (44) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.12/23.72 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.12/23.72 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.12/23.72 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.12/23.72 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.12/23.72 (all_58_27 = e0)) % 155.12/23.72 (45) all_56_9 = e1 | all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 155.12/23.72 (46) op(all_10_2, e3) = e0 % 155.12/23.72 (47) op(e3, all_10_2) = all_58_0 % 155.12/23.72 (48) all_56_2 = all_52_1 % 155.12/23.72 (49) ~ (all_52_11 = e0) % 155.12/23.72 (50) all_56_10 = all_52_13 % 155.12/23.72 (51) all_56_14 = all_52_11 % 155.12/23.72 (52) all_58_28 = all_10_2 % 155.12/23.72 (53) all_56_7 = e0 | all_56_8 = e0 | all_56_11 = e0 % 155.12/23.72 (54) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 155.12/23.72 (55) ~ (all_52_1 = all_52_9) % 155.12/23.72 (56) op(all_8_2, e2) = all_8_1 % 155.12/23.72 (57) all_56_15 = e0 % 155.12/23.72 (58) all_56_0 = all_10_2 % 155.12/23.72 (59) all_58_31 = e0 % 155.12/23.72 (60) all_56_0 = e0 | all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 155.12/23.72 (61) all_56_8 = all_6_2 % 155.12/23.72 (62) all_58_27 = e0 % 155.12/23.72 (63) op(e2, e0) = all_52_13 % 155.12/23.72 (64) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 155.12/23.72 (65) ~ (all_8_1 = e0) % 155.12/23.72 (66) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.12/23.72 (67) all_54_0 = all_10_2 % 155.12/23.72 (68) ~ (e1 = e0) % 155.12/23.72 (69) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.12/23.72 (70) ~ (all_52_14 = e0) % 155.12/23.72 (71) ~ (all_52_4 = all_10_2) % 155.12/23.72 (72) all_58_30 = all_6_2 % 155.12/23.72 (73) op(e2, all_52_1) = all_58_7 % 155.12/23.72 (74) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.12/23.72 (75) ~ (e3 = e2) % 155.12/23.72 (76) ~ (all_52_14 = all_6_2) % 155.12/23.72 (77) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 155.12/23.72 (78) ~ (all_52_4 = all_52_12) % 155.12/23.72 % 155.12/23.72 Begin of proof % 155.12/23.72 | % 155.12/23.72 | BETA: splitting (60) gives: % 155.12/23.72 | % 155.12/23.72 | Case 1: % 155.12/23.72 | | % 155.12/23.72 | | (79) all_56_0 = e0 % 155.12/23.72 | | % 155.12/23.72 | | REF_CLOSE: (19), (58), (79) are inconsistent by sub-proof #799. % 155.12/23.72 | | % 155.12/23.72 | Case 2: % 155.12/23.72 | | % 155.12/23.72 | | (80) all_56_2 = e0 | all_56_6 = e0 | all_56_12 = e0 % 155.12/23.72 | | % 155.12/23.72 | | BETA: splitting (80) gives: % 155.12/23.72 | | % 155.12/23.72 | | Case 1: % 155.12/23.72 | | | % 155.12/23.72 | | | (81) all_56_2 = e0 % 155.12/23.72 | | | % 155.12/23.72 | | | COMBINE_EQS: (48), (81) imply: % 155.12/23.72 | | | (82) all_52_1 = e0 % 155.12/23.72 | | | % 155.12/23.72 | | | REDUCE: (55), (82) imply: % 155.12/23.72 | | | (83) ~ (all_52_9 = e0) % 155.12/23.72 | | | % 155.12/23.72 | | | SIMP: (83) implies: % 155.12/23.72 | | | (84) ~ (all_52_9 = e0) % 155.12/23.72 | | | % 155.12/23.72 | | | REDUCE: (28), (82) imply: % 155.12/23.72 | | | (85) ~ (all_52_13 = e0) % 155.12/23.72 | | | % 155.12/23.72 | | | SIMP: (85) implies: % 155.12/23.72 | | | (86) ~ (all_52_13 = e0) % 155.12/23.72 | | | % 155.12/23.72 | | | REDUCE: (73), (82) imply: % 155.12/23.72 | | | (87) op(e2, e0) = all_58_7 % 155.12/23.72 | | | % 155.12/23.72 | | | BETA: splitting (33) gives: % 155.12/23.72 | | | % 155.12/23.72 | | | Case 1: % 155.12/23.72 | | | | % 155.12/23.72 | | | | (88) all_56_4 = e0 % 155.12/23.72 | | | | % 155.12/23.72 | | | | COMBINE_EQS: (7), (88) imply: % 155.12/23.72 | | | | (89) all_52_8 = e0 % 155.12/23.72 | | | | % 155.12/23.72 | | | | REDUCE: (5), (89) imply: % 155.12/23.72 | | | | (90) ~ (all_10_2 = e0) % 155.12/23.72 | | | | % 155.12/23.72 | | | | REDUCE: (15), (89) imply: % 155.12/23.72 | | | | (91) ~ (all_6_2 = e0) % 155.12/23.72 | | | | % 155.12/23.72 | | | | REDUCE: (22), (89) imply: % 155.12/23.72 | | | | (92) op(e3, e0) = all_58_3 % 155.12/23.72 | | | | % 155.12/23.72 | | | | BETA: splitting (53) gives: % 155.12/23.72 | | | | % 155.12/23.72 | | | | Case 1: % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | (93) all_56_7 = e0 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | COMBINE_EQS: (3), (93) imply: % 155.12/23.72 | | | | | (94) all_52_6 = e0 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | SIMP: (94) implies: % 155.12/23.72 | | | | | (95) all_52_6 = e0 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | REDUCE: (12), (95) imply: % 155.12/23.72 | | | | | (96) ~ (all_52_4 = e0) % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | REDUCE: (17), (95) imply: % 155.12/23.72 | | | | | (97) ~ (all_52_14 = e0) % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | REDUCE: (26), (95) imply: % 155.12/23.72 | | | | | (98) op(e1, e0) = all_58_16 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | REDUCE: (23), (95) imply: % 155.12/23.72 | | | | | (99) op(e1, e2) = e0 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | GROUND_INST: instantiating (1) with all_52_14, all_58_16, e0, e1, % 155.12/23.72 | | | | | simplifying with (35), (98) gives: % 155.12/23.72 | | | | | (100) all_58_16 = all_52_14 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | GROUND_INST: instantiating (1) with all_52_13, all_58_7, e0, e2, % 155.12/23.72 | | | | | simplifying with (63), (87) gives: % 155.12/23.72 | | | | | (101) all_58_7 = all_52_13 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | GROUND_INST: instantiating (1) with all_52_12, all_58_3, e0, e3, % 155.12/23.72 | | | | | simplifying with (41), (92) gives: % 155.12/23.72 | | | | | (102) all_58_3 = all_52_12 % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | BETA: splitting (27) gives: % 155.12/23.72 | | | | | % 155.12/23.72 | | | | | Case 1: % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | | (103) all_54_0 = e0 % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | | REF_CLOSE: (19), (67), (103) are inconsistent by sub-proof #861. % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | Case 2: % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | | (104) ~ (all_54_0 = e0) % 155.12/23.72 | | | | | | (105) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | | BETA: splitting (64) gives: % 155.12/23.72 | | | | | | % 155.12/23.72 | | | | | | Case 1: % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | (106) all_54_1 = e0 % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | REF_CLOSE: (10), (96), (106) are inconsistent by sub-proof #798. % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | Case 2: % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | (107) ~ (all_54_1 = e0) % 155.12/23.72 | | | | | | | (108) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | BETA: splitting (18) gives: % 155.12/23.72 | | | | | | | % 155.12/23.72 | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | | (109) all_54_11 = e0 % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | | REF_CLOSE: (14), (70), (109) are inconsistent by sub-proof #743. % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | | (110) ~ (all_54_11 = e0) % 155.12/23.72 | | | | | | | | (111) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | | BETA: splitting (77) gives: % 155.12/23.72 | | | | | | | | % 155.12/23.72 | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | | (112) all_54_7 = e0 % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | | REF_CLOSE: (6), (86), (112) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | #742. % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | | (113) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | | BETA: splitting (54) gives: % 155.12/23.72 | | | | | | | | | % 155.12/23.72 | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | (114) all_56_0 = e2 % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | COMBINE_EQS: (58), (114) imply: % 155.12/23.72 | | | | | | | | | | (115) all_10_2 = e2 % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | COMBINE_EQS: (9), (115) imply: % 155.12/23.72 | | | | | | | | | | (116) all_32_2 = e2 % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | COMBINE_EQS: (52), (115) imply: % 155.12/23.72 | | | | | | | | | | (117) all_58_28 = e2 % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | REDUCE: (71), (115) imply: % 155.12/23.72 | | | | | | | | | | (118) ~ (all_52_4 = e2) % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | REDUCE: (24), (115) imply: % 155.12/23.72 | | | | | | | | | | (119) op(e2, e0) = all_10_0 % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | BETA: splitting (20) gives: % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | (120) ~ (all_32_0 = e1) % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | REDUCE: (2), (120) imply: % 155.12/23.72 | | | | | | | | | | | (121) ~ (all_10_0 = e1) % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_52_13, all_10_0, e0, % 155.12/23.72 | | | | | | | | | | | e2, simplifying with (63), (119) gives: % 155.12/23.72 | | | | | | | | | | | (122) all_52_13 = all_10_0 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | COMBINE_EQS: (6), (122) imply: % 155.12/23.72 | | | | | | | | | | | (123) all_54_7 = all_10_0 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | COMBINE_EQS: (50), (122) imply: % 155.12/23.72 | | | | | | | | | | | (124) all_56_10 = all_10_0 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | COMBINE_EQS: (101), (122) imply: % 155.12/23.72 | | | | | | | | | | | (125) all_58_7 = all_10_0 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | REDUCE: (16), (122) imply: % 155.12/23.72 | | | | | | | | | | | (126) ~ (all_52_12 = all_10_0) % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | REDUCE: (36), (122) imply: % 155.12/23.72 | | | | | | | | | | | (127) ~ (all_52_14 = all_10_0) % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | SIMP: (127) implies: % 155.12/23.72 | | | | | | | | | | | (128) ~ (all_52_14 = all_10_0) % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | BETA: splitting (69) gives: % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | (129) all_56_0 = e3 % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | COMBINE_EQS: (114), (129) imply: % 155.12/23.72 | | | | | | | | | | | | (130) e3 = e2 % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | REDUCE: (75), (130) imply: % 155.12/23.72 | | | | | | | | | | | | (131) $false % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | CLOSE: (131) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | (132) all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | BETA: splitting (45) gives: % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | (133) all_56_9 = e1 % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | COMBINE_EQS: (37), (133) imply: % 155.12/23.72 | | | | | | | | | | | | | (134) all_52_12 = e1 % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | SIMP: (134) implies: % 155.12/23.72 | | | | | | | | | | | | | (135) all_52_12 = e1 % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | COMBINE_EQS: (102), (135) imply: % 155.12/23.72 | | | | | | | | | | | | | (136) all_58_3 = e1 % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | REDUCE: (78), (135) imply: % 155.12/23.72 | | | | | | | | | | | | | (137) ~ (all_52_4 = e1) % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | REDUCE: (39), (135) imply: % 155.12/23.72 | | | | | | | | | | | | | (138) ~ (all_52_14 = e1) % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | SIMP: (138) implies: % 155.12/23.72 | | | | | | | | | | | | | (139) ~ (all_52_14 = e1) % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | REDUCE: (126), (135) imply: % 155.12/23.72 | | | | | | | | | | | | | (140) ~ (all_10_0 = e1) % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | BETA: splitting (132) gives: % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | (141) all_56_1 = e3 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | COMBINE_EQS: (32), (141) imply: % 155.12/23.72 | | | | | | | | | | | | | | (142) all_52_4 = e3 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | SIMP: (142) implies: % 155.12/23.72 | | | | | | | | | | | | | | (143) all_52_4 = e3 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | REDUCE: (8), (143) imply: % 155.12/23.72 | | | | | | | | | | | | | | (144) ~ (all_8_2 = e3) % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | SIMP: (144) implies: % 155.12/23.72 | | | | | | | | | | | | | | (145) ~ (all_8_2 = e3) % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | REDUCE: (96), (143) imply: % 155.12/23.72 | | | | | | | | | | | | | | (146) ~ (e3 = e0) % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | BETA: splitting (66) gives: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | (147) all_58_28 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | COMBINE_EQS: (117), (147) imply: % 155.12/23.72 | | | | | | | | | | | | | | | (148) e3 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | REDUCE: (75), (148) imply: % 155.12/23.72 | | | | | | | | | | | | | | | (149) $false % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | (150) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | (151) all_58_29 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | REF_CLOSE: (38), (145), (151) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | | | | | | | | #756. % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | (152) all_58_30 = e3 | all_58_31 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | (153) all_58_30 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (153) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | (154) all_6_2 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | REDUCE: (76), (154) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | (155) ~ (all_52_14 = e3) % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | BETA: splitting (111) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | (156) all_54_11 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (156) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | (157) all_52_14 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | REDUCE: (139), (157) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | (158) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | (159) all_54_11 = e3 | all_54_11 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (160) all_54_11 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (160) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (161) all_52_14 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (161) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (162) all_58_16 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | REDUCE: (128), (161) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (163) ~ (all_10_0 = e2) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | SIMP: (163) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (164) ~ (all_10_0 = e2) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (165) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (166) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (167) ~ (all_58_3 = e1) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (167) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (168) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (169) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (170) ~ (all_58_7 = e3) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (170) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | (171) ~ (all_10_0 = e3) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (172) all_54_7 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (172) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (173) all_10_0 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (174) all_10_0 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (174) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (175) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | (176) all_54_7 = e3 | all_54_7 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (177) all_54_7 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (177) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (178) all_10_0 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (178) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (179) all_10_0 = e2 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (179) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (180) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (181) all_54_7 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (181) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (182) all_10_0 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (182) implies: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (183) all_10_0 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (183) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | (184) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (185) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (162), (185) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | #834. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (186) all_54_11 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (186) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (187) all_52_14 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | REDUCE: (155), (187) imply: % 155.12/23.72 | | | | | | | | | | | | | | | | | | | (188) $false % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | (189) all_58_31 = e3 % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (146), (189) are inconsistent by sub-proof % 155.12/23.72 | | | | | | | | | | | | | | | | | #853. % 155.12/23.72 | | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | (190) ~ (all_56_1 = e3) % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | REDUCE: (32), (190) imply: % 155.12/23.72 | | | | | | | | | | | | | | (191) ~ (all_52_4 = e3) % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | REF_CLOSE: (10), (108), (118), (137), (191) are inconsistent % 155.12/23.72 | | | | | | | | | | | | | | by sub-proof #738. % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | (192) all_56_10 = e1 | all_56_11 = e1 | all_56_15 = e1 % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | BETA: splitting (192) gives: % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | (193) all_56_10 = e1 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | COMBINE_EQS: (124), (193) imply: % 155.12/23.72 | | | | | | | | | | | | | | (194) all_10_0 = e1 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | SIMP: (194) implies: % 155.12/23.72 | | | | | | | | | | | | | | (195) all_10_0 = e1 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | REDUCE: (121), (195) imply: % 155.12/23.72 | | | | | | | | | | | | | | (196) $false % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | (197) all_56_11 = e1 | all_56_15 = e1 % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | BETA: splitting (197) gives: % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | (198) all_56_11 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | COMBINE_EQS: (31), (198) imply: % 155.12/23.72 | | | | | | | | | | | | | | | (199) all_52_14 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | SIMP: (199) implies: % 155.12/23.72 | | | | | | | | | | | | | | | (200) all_52_14 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | REDUCE: (76), (200) imply: % 155.12/23.72 | | | | | | | | | | | | | | | (201) ~ (all_6_2 = e1) % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | SIMP: (201) implies: % 155.12/23.72 | | | | | | | | | | | | | | | (202) ~ (all_6_2 = e1) % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | REF_CLOSE: (1), (38), (40), (56), (59), (65), (68), (72), % 155.12/23.72 | | | | | | | | | | | | | | | (74), (99), (117), (202) are inconsistent by % 155.12/23.72 | | | | | | | | | | | | | | | sub-proof #793. % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | (203) all_56_15 = e1 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | COMBINE_EQS: (57), (203) imply: % 155.12/23.72 | | | | | | | | | | | | | | | (204) e1 = e0 % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | REDUCE: (68), (204) imply: % 155.12/23.72 | | | | | | | | | | | | | | | (205) $false % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 155.12/23.72 | | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | (206) ~ (all_32_2 = e2) % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | REDUCE: (116), (206) imply: % 155.12/23.72 | | | | | | | | | | | (207) $false % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | CLOSE: (207) is inconsistent. % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | End of split % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | Case 2: % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | (208) ~ (all_56_0 = e2) % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | REDUCE: (58), (208) imply: % 155.12/23.72 | | | | | | | | | | (209) ~ (all_10_2 = e2) % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | BETA: splitting (13) gives: % 155.12/23.72 | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | Case 1: % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | (210) all_56_0 = e1 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | COMBINE_EQS: (58), (210) imply: % 155.12/23.72 | | | | | | | | | | | (211) all_10_2 = e1 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | SIMP: (211) implies: % 155.12/23.72 | | | | | | | | | | | (212) all_10_2 = e1 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.72 | | | | | | | | | | | REDUCE: (46), (212) imply: % 155.12/23.72 | | | | | | | | | | | (213) op(e1, e3) = e0 % 155.12/23.72 | | | | | | | | | | | % 155.12/23.73 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_52_2, e0, e3, e1, % 155.12/23.73 | | | | | | | | | | | simplifying with (34), (213) gives: % 155.12/23.73 | | | | | | | | | | | (214) all_52_2 = e0 % 155.12/23.73 | | | | | | | | | | | % 155.12/23.73 | | | | | | | | | | | REDUCE: (4), (214) imply: % 155.12/23.73 | | | | | | | | | | | (215) $false % 155.12/23.73 | | | | | | | | | | | % 155.12/23.73 | | | | | | | | | | | CLOSE: (215) is inconsistent. % 155.12/23.73 | | | | | | | | | | | % 155.12/23.73 | | | | | | | | | | Case 2: % 155.12/23.73 | | | | | | | | | | | % 155.14/23.73 | | | | | | | | | | | (216) ~ (all_56_0 = e1) % 155.14/23.73 | | | | | | | | | | | % 155.14/23.73 | | | | | | | | | | | REDUCE: (58), (216) imply: % 155.14/23.73 | | | | | | | | | | | (217) ~ (all_10_2 = e1) % 155.14/23.73 | | | | | | | | | | | % 155.14/23.73 | | | | | | | | | | | REF_CLOSE: (1), (19), (21), (46), (47), (67), (105), (209), % 155.14/23.73 | | | | | | | | | | | (217) are inconsistent by sub-proof #736. % 155.14/23.73 | | | | | | | | | | | % 155.14/23.73 | | | | | | | | | | End of split % 155.14/23.73 | | | | | | | | | | % 155.14/23.73 | | | | | | | | | End of split % 155.14/23.73 | | | | | | | | | % 155.14/23.73 | | | | | | | | End of split % 155.14/23.73 | | | | | | | | % 155.14/23.73 | | | | | | | End of split % 155.14/23.73 | | | | | | | % 155.14/23.73 | | | | | | End of split % 155.14/23.73 | | | | | | % 155.14/23.73 | | | | | End of split % 155.14/23.73 | | | | | % 155.14/23.73 | | | | Case 2: % 155.14/23.73 | | | | | % 155.14/23.73 | | | | | (218) all_56_8 = e0 | all_56_11 = e0 % 155.14/23.73 | | | | | % 155.14/23.73 | | | | | REF_CLOSE: (11), (31), (61), (70), (218) are inconsistent by sub-proof % 155.14/23.73 | | | | | #763. % 155.14/23.73 | | | | | % 155.14/23.73 | | | | End of split % 155.14/23.73 | | | | % 155.14/23.73 | | | Case 2: % 155.14/23.73 | | | | % 155.14/23.73 | | | | (219) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.14/23.73 | | | | % 155.14/23.73 | | | | REF_CLOSE: (11), (29), (49), (51), (61), (84), (219) are inconsistent by % 155.14/23.73 | | | | sub-proof #766. % 155.14/23.73 | | | | % 155.14/23.73 | | | End of split % 155.14/23.73 | | | % 155.14/23.73 | | Case 2: % 155.14/23.73 | | | % 155.14/23.73 | | | (220) all_56_6 = e0 | all_56_12 = e0 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (4), (25), (30), (42), (220) are inconsistent by sub-proof % 155.14/23.73 | | | #765. % 155.14/23.73 | | | % 155.14/23.73 | | End of split % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #736 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.73 (2) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.73 (3) ~ (all_10_2 = e0) % 155.14/23.73 (4) op(e3, e3) = all_10_2 % 155.14/23.73 (5) ~ (all_10_2 = e1) % 155.14/23.73 (6) ~ (all_10_2 = e2) % 155.14/23.73 (7) op(all_10_2, e3) = e0 % 155.14/23.73 (8) op(e3, all_10_2) = all_58_0 % 155.14/23.73 (9) all_54_0 = all_10_2 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (2) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (10) all_54_0 = e1 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (5), (9), (10) are inconsistent by sub-proof #841. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (11) all_54_0 = e3 | all_54_0 = e2 % 155.14/23.73 | | % 155.14/23.73 | | BETA: splitting (11) gives: % 155.14/23.73 | | % 155.14/23.73 | | Case 1: % 155.14/23.73 | | | % 155.14/23.73 | | | (12) all_54_0 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #822. % 155.14/23.73 | | | % 155.14/23.73 | | Case 2: % 155.14/23.73 | | | % 155.14/23.73 | | | (13) all_54_0 = e3 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (9), (13) imply: % 155.14/23.73 | | | (14) all_10_2 = e3 % 155.14/23.73 | | | % 155.14/23.73 | | | SIMP: (14) implies: % 155.14/23.73 | | | (15) all_10_2 = e3 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (1), (3), (4), (7), (8), (15) are inconsistent by sub-proof % 155.14/23.73 | | | #737. % 155.14/23.73 | | | % 155.14/23.73 | | End of split % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #737 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.73 (2) ~ (all_10_2 = e0) % 155.14/23.73 (3) op(e3, e3) = all_10_2 % 155.14/23.73 (4) all_10_2 = e3 % 155.14/23.73 (5) op(all_10_2, e3) = e0 % 155.14/23.73 (6) op(e3, all_10_2) = all_58_0 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | REDUCE: (2), (4) imply: % 155.14/23.73 | (7) ~ (e3 = e0) % 155.14/23.73 | % 155.14/23.73 | REDUCE: (4), (5) imply: % 155.14/23.73 | (8) op(e3, e3) = e0 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (4), (6) imply: % 155.14/23.73 | (9) op(e3, e3) = all_58_0 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (4) imply: % 155.14/23.73 | (10) op(e3, e3) = e3 % 155.14/23.73 | % 155.14/23.73 | REF_CLOSE: (1), (7), (8), (9), (10) are inconsistent by sub-proof #757. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #738 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_1 = all_52_4 % 155.14/23.73 (2) ~ (all_52_4 = e3) % 155.14/23.73 (3) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 % 155.14/23.73 (4) ~ (all_52_4 = e2) % 155.14/23.73 (5) ~ (all_52_4 = e1) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (3) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (6) all_54_1 = e1 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #741. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (7) all_54_1 = e3 | all_54_1 = e2 % 155.14/23.73 | | % 155.14/23.73 | | BETA: splitting (7) gives: % 155.14/23.73 | | % 155.14/23.73 | | Case 1: % 155.14/23.73 | | | % 155.14/23.73 | | | (8) all_54_1 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #740. % 155.14/23.73 | | | % 155.14/23.73 | | Case 2: % 155.14/23.73 | | | % 155.14/23.73 | | | (9) all_54_1 = e3 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #739. % 155.14/23.73 | | | % 155.14/23.73 | | End of split % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #739 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_1 = all_52_4 % 155.14/23.73 (2) all_54_1 = e3 % 155.14/23.73 (3) ~ (all_52_4 = e3) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_4 = e3 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_4 = e3 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #740 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_1 = all_52_4 % 155.14/23.73 (2) all_54_1 = e2 % 155.14/23.73 (3) ~ (all_52_4 = e2) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_4 = e2 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_4 = e2 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #741 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_1 = all_52_4 % 155.14/23.73 (2) all_54_1 = e1 % 155.14/23.73 (3) ~ (all_52_4 = e1) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_4 = e1 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_4 = e1 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #742 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_7 = all_52_13 % 155.14/23.73 (2) all_54_7 = e0 % 155.14/23.73 (3) ~ (all_52_13 = e0) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_13 = e0 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_13 = e0 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #743 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_11 = all_52_14 % 155.14/23.73 (2) all_54_11 = e0 % 155.14/23.73 (3) ~ (all_52_14 = e0) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_14 = e0 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_14 = e0 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #744 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ~ (all_52_3 = e3) % 155.14/23.73 (2) all_56_6 = e0 % 155.14/23.73 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.73 (4) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.14/23.73 (5) all_56_6 = e3 | all_56_12 = e3 % 155.14/23.73 (6) ~ (all_10_2 = e3) % 155.14/23.73 (7) ~ (e3 = e1) % 155.14/23.73 (8) all_56_12 = all_52_3 % 155.14/23.73 (9) ~ (e3 = e0) % 155.14/23.73 (10) all_56_2 = all_52_1 % 155.14/23.73 (11) ~ (all_52_1 = all_52_3) % 155.14/23.73 (12) ~ (all_52_3 = all_10_2) % 155.14/23.73 (13) all_54_0 = all_10_2 % 155.14/23.73 (14) ~ (all_56_2 = e3) % 155.14/23.73 (15) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 155.14/23.73 (16) all_54_12 = all_52_3 % 155.14/23.73 (17) all_54_4 = all_52_1 % 155.14/23.73 (18) ~ (all_52_1 = all_10_2) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | REDUCE: (10), (14) imply: % 155.14/23.73 | (19) ~ (all_52_1 = e3) % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (15) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (20) all_54_12 = e1 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (16), (20) imply: % 155.14/23.73 | | (21) all_52_3 = e1 % 155.14/23.73 | | % 155.14/23.73 | | SIMP: (21) implies: % 155.14/23.73 | | (22) all_52_3 = e1 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (8), (22) imply: % 155.14/23.73 | | (23) all_56_12 = e1 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (2), (5), (7), (9), (23) are inconsistent by sub-proof #838. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (24) all_54_12 = e3 | all_54_12 = e2 % 155.14/23.73 | | % 155.14/23.73 | | BETA: splitting (24) gives: % 155.14/23.73 | | % 155.14/23.73 | | Case 1: % 155.14/23.73 | | | % 155.14/23.73 | | | (25) all_54_12 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (16), (25) imply: % 155.14/23.73 | | | (26) all_52_3 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | SIMP: (26) implies: % 155.14/23.73 | | | (27) all_52_3 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | REDUCE: (11), (27) imply: % 155.14/23.73 | | | (28) ~ (all_52_1 = e2) % 155.14/23.73 | | | % 155.14/23.73 | | | REDUCE: (12), (27) imply: % 155.14/23.73 | | | (29) ~ (all_10_2 = e2) % 155.14/23.73 | | | % 155.14/23.73 | | | SIMP: (29) implies: % 155.14/23.73 | | | (30) ~ (all_10_2 = e2) % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (3), (4), (6), (13), (17), (18), (19), (28), (30) are % 155.14/23.73 | | | inconsistent by sub-proof #745. % 155.14/23.73 | | | % 155.14/23.73 | | Case 2: % 155.14/23.73 | | | % 155.14/23.73 | | | (31) all_54_12 = e3 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (1), (16), (31) are inconsistent by sub-proof #748. % 155.14/23.73 | | | % 155.14/23.73 | | End of split % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #745 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ~ (all_52_1 = e3) % 155.14/23.73 (2) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.73 (3) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.14/23.73 (4) ~ (all_10_2 = e3) % 155.14/23.73 (5) ~ (all_10_2 = e2) % 155.14/23.73 (6) all_54_0 = all_10_2 % 155.14/23.73 (7) ~ (all_52_1 = e2) % 155.14/23.73 (8) all_54_4 = all_52_1 % 155.14/23.73 (9) ~ (all_52_1 = all_10_2) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (3) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (10) all_54_4 = e1 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (8), (10) imply: % 155.14/23.73 | | (11) all_52_1 = e1 % 155.14/23.73 | | % 155.14/23.73 | | SIMP: (11) implies: % 155.14/23.73 | | (12) all_52_1 = e1 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (9), (12) imply: % 155.14/23.73 | | (13) ~ (all_10_2 = e1) % 155.14/23.73 | | % 155.14/23.73 | | SIMP: (13) implies: % 155.14/23.73 | | (14) ~ (all_10_2 = e1) % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (2), (4), (5), (6), (14) are inconsistent by sub-proof #813. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (15) all_54_4 = e3 | all_54_4 = e2 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (1), (7), (8), (15) are inconsistent by sub-proof #829. % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #746 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.73 (2) ~ (all_52_3 = e3) % 155.14/23.73 (3) ~ (all_10_2 = all_6_1) % 155.14/23.73 (4) op(e2, e3) = all_58_7 % 155.14/23.73 (5) all_56_4 = all_52_8 % 155.14/23.73 (6) all_56_9 = e3 % 155.14/23.73 (7) all_56_6 = e0 % 155.14/23.73 (8) all_56_4 = e2 | all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 155.14/23.73 (9) all_56_8 = e3 % 155.14/23.73 (10) ~ (all_10_2 = e0) % 155.14/23.73 (11) ~ (all_10_2 = e3) % 155.14/23.73 (12) ~ (e3 = e1) % 155.14/23.73 (13) ~ (all_52_8 = e3) % 155.14/23.73 (14) all_56_12 = all_52_3 % 155.14/23.73 (15) all_10_2 = e2 % 155.14/23.73 (16) op(all_10_2, e3) = e0 % 155.14/23.73 (17) ~ (e3 = e0) % 155.14/23.73 (18) all_56_4 = all_6_1 % 155.14/23.73 (19) all_56_5 = e0 % 155.14/23.73 (20) all_56_4 = e3 | all_56_9 = e3 % 155.14/23.73 (21) op(e2, e3) = e3 % 155.14/23.73 (22) ~ (all_52_3 = all_10_2) % 155.14/23.73 (23) all_56_2 = e3 % 155.14/23.73 (24) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.73 (25) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 % 155.14/23.73 (26) all_54_12 = all_52_3 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | REDUCE: (15), (22) imply: % 155.14/23.73 | (27) ~ (all_52_3 = e2) % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (15) imply: % 155.14/23.73 | (28) ~ (all_6_1 = e2) % 155.14/23.73 | % 155.14/23.73 | SIMP: (28) implies: % 155.14/23.73 | (29) ~ (all_6_1 = e2) % 155.14/23.73 | % 155.14/23.73 | REDUCE: (11), (15) imply: % 155.14/23.73 | (30) ~ (e3 = e2) % 155.14/23.73 | % 155.14/23.73 | SIMP: (30) implies: % 155.14/23.73 | (31) ~ (e3 = e2) % 155.14/23.73 | % 155.14/23.73 | REDUCE: (10), (15) imply: % 155.14/23.73 | (32) ~ (e2 = e0) % 155.14/23.73 | % 155.14/23.73 | REDUCE: (15), (16) imply: % 155.14/23.73 | (33) op(e2, e3) = e0 % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (8) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (34) all_56_4 = e2 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (18), (34) imply: % 155.14/23.73 | | (35) all_6_1 = e2 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (29), (35) imply: % 155.14/23.73 | | (36) $false % 155.14/23.73 | | % 155.14/23.73 | | CLOSE: (36) is inconsistent. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (37) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 155.14/23.73 | | % 155.14/23.73 | | BETA: splitting (25) gives: % 155.14/23.73 | | % 155.14/23.73 | | Case 1: % 155.14/23.73 | | | % 155.14/23.73 | | | (38) all_54_12 = e1 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (26), (38) imply: % 155.14/23.73 | | | (39) all_52_3 = e1 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (14), (39) imply: % 155.14/23.73 | | | (40) all_56_12 = e1 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (12), (13), (17), (19), (20), % 155.14/23.73 | | | (21), (23), (24), (31), (32), (33), (37), (40) are inconsistent % 155.14/23.73 | | | by sub-proof #750. % 155.14/23.73 | | | % 155.14/23.73 | | Case 2: % 155.14/23.73 | | | % 155.14/23.73 | | | (41) all_54_12 = e3 | all_54_12 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (2), (26), (27), (41) are inconsistent by sub-proof #747. % 155.14/23.73 | | | % 155.14/23.73 | | End of split % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #747 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_12 = e3 | all_54_12 = e2 % 155.14/23.73 (2) all_54_12 = all_52_3 % 155.14/23.73 (3) ~ (all_52_3 = e2) % 155.14/23.73 (4) ~ (all_52_3 = e3) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (1) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (5) all_54_12 = e2 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #749. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (6) all_54_12 = e3 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #748. % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #748 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_12 = all_52_3 % 155.14/23.73 (2) all_54_12 = e3 % 155.14/23.73 (3) ~ (all_52_3 = e3) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_3 = e3 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_3 = e3 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #749 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_12 = all_52_3 % 155.14/23.73 (2) all_54_12 = e2 % 155.14/23.73 (3) ~ (all_52_3 = e2) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_3 = e2 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_3 = e2 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #750 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.73 (2) all_56_5 = e2 | all_56_8 = e2 | all_56_14 = e2 % 155.14/23.73 (3) op(e2, e3) = all_58_7 % 155.14/23.73 (4) all_56_4 = all_52_8 % 155.14/23.73 (5) all_56_9 = e3 % 155.14/23.73 (6) all_56_6 = e0 % 155.14/23.73 (7) all_56_8 = e3 % 155.14/23.73 (8) op(e2, e3) = e0 % 155.14/23.73 (9) ~ (e3 = e1) % 155.14/23.73 (10) ~ (all_52_8 = e3) % 155.14/23.73 (11) all_56_12 = e1 % 155.14/23.73 (12) ~ (e3 = e0) % 155.14/23.73 (13) all_56_5 = e0 % 155.14/23.73 (14) all_56_4 = e3 | all_56_9 = e3 % 155.14/23.73 (15) ~ (e2 = e0) % 155.14/23.73 (16) op(e2, e3) = e3 % 155.14/23.73 (17) all_56_2 = e3 % 155.14/23.73 (18) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.73 (19) ~ (e3 = e2) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (2) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (20) all_56_5 = e2 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (13), (20) imply: % 155.14/23.73 | | (21) e2 = e0 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (15), (21) imply: % 155.14/23.73 | | (22) $false % 155.14/23.73 | | % 155.14/23.73 | | CLOSE: (22) is inconsistent. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (23) all_56_8 = e2 | all_56_14 = e2 % 155.14/23.73 | | % 155.14/23.73 | | BETA: splitting (23) gives: % 155.14/23.73 | | % 155.14/23.73 | | Case 1: % 155.14/23.73 | | | % 155.14/23.73 | | | (24) all_56_8 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (7), (24) imply: % 155.14/23.73 | | | (25) e3 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (17), (25) imply: % 155.14/23.73 | | | (26) all_56_2 = e2 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (6), (9), (11), (12), (18), (19), (26) are inconsistent by % 155.14/23.73 | | | sub-proof #837. % 155.14/23.73 | | | % 155.14/23.73 | | Case 2: % 155.14/23.73 | | | % 155.14/23.73 | | | % 155.14/23.73 | | | GROUND_INST: instantiating (1) with e3, all_58_7, e3, e2, simplifying with % 155.14/23.73 | | | (3), (16) gives: % 155.14/23.73 | | | (27) all_58_7 = e3 % 155.14/23.73 | | | % 155.14/23.73 | | | GROUND_INST: instantiating (1) with e0, all_58_7, e3, e2, simplifying with % 155.14/23.73 | | | (3), (8) gives: % 155.14/23.73 | | | (28) all_58_7 = e0 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (27), (28) imply: % 155.14/23.73 | | | (29) e3 = e0 % 155.14/23.73 | | | % 155.14/23.73 | | | SIMP: (29) implies: % 155.14/23.73 | | | (30) e3 = e0 % 155.14/23.73 | | | % 155.14/23.73 | | | COMBINE_EQS: (5), (30) imply: % 155.14/23.73 | | | (31) all_56_9 = e0 % 155.14/23.73 | | | % 155.14/23.73 | | | REF_CLOSE: (4), (10), (12), (14), (31) are inconsistent by sub-proof #751. % 155.14/23.73 | | | % 155.14/23.73 | | End of split % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #751 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_56_4 = all_52_8 % 155.14/23.73 (2) ~ (all_52_8 = e3) % 155.14/23.73 (3) ~ (e3 = e0) % 155.14/23.73 (4) all_56_4 = e3 | all_56_9 = e3 % 155.14/23.73 (5) all_56_9 = e0 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (4) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (6) all_56_4 = e3 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (1), (6) imply: % 155.14/23.73 | | (7) all_52_8 = e3 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (2), (7) imply: % 155.14/23.73 | | (8) $false % 155.14/23.73 | | % 155.14/23.73 | | CLOSE: (8) is inconsistent. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (9) all_56_9 = e3 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (5), (9) imply: % 155.14/23.73 | | (10) e3 = e0 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (3), (10) imply: % 155.14/23.73 | | (11) $false % 155.14/23.73 | | % 155.14/23.73 | | CLOSE: (11) is inconsistent. % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #752 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_54_2 = e3 | all_54_2 = e2 % 155.14/23.73 (2) all_54_2 = all_6_1 % 155.14/23.73 (3) ~ (all_6_1 = e2) % 155.14/23.73 (4) ~ (all_6_1 = e3) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (1) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (5) all_54_2 = e2 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (2), (5) imply: % 155.14/23.73 | | (6) all_6_1 = e2 % 155.14/23.73 | | % 155.14/23.73 | | SIMP: (6) implies: % 155.14/23.73 | | (7) all_6_1 = e2 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (3), (7) imply: % 155.14/23.73 | | (8) $false % 155.14/23.73 | | % 155.14/23.73 | | CLOSE: (8) is inconsistent. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (9) all_54_2 = e3 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (2), (9) imply: % 155.14/23.73 | | (10) all_6_1 = e3 % 155.14/23.73 | | % 155.14/23.73 | | SIMP: (10) implies: % 155.14/23.73 | | (11) all_6_1 = e3 % 155.14/23.73 | | % 155.14/23.73 | | REDUCE: (4), (11) imply: % 155.14/23.73 | | (12) $false % 155.14/23.73 | | % 155.14/23.73 | | CLOSE: (12) is inconsistent. % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #753 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_56_4 = all_52_8 % 155.14/23.73 (2) all_56_4 = e3 % 155.14/23.73 (3) ~ (all_52_8 = e3) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_52_8 = e3 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_52_8 = e3 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #754 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_58_30 = e3 % 155.14/23.73 (2) all_56_1 = e3 % 155.14/23.73 (3) all_56_1 = e0 % 155.14/23.73 (4) ~ (e3 = e0) % 155.14/23.73 (5) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.73 (6) all_58_31 = e0 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (2), (3) imply: % 155.14/23.73 | (7) e3 = e0 % 155.14/23.73 | % 155.14/23.73 | SIMP: (7) implies: % 155.14/23.73 | (8) e3 = e0 % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (8) imply: % 155.14/23.73 | (9) all_58_30 = e0 % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (5) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #755. % 155.14/23.73 | | % 155.14/23.73 | Case 2: % 155.14/23.73 | | % 155.14/23.73 | | (10) all_58_31 = e3 % 155.14/23.73 | | % 155.14/23.73 | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #853. % 155.14/23.73 | | % 155.14/23.73 | End of split % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #755 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_58_30 = e3 % 155.14/23.73 (2) all_58_30 = e0 % 155.14/23.73 (3) ~ (e3 = e0) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) e3 = e0 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) e3 = e0 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #756 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_58_29 = all_8_2 % 155.14/23.73 (2) all_58_29 = e3 % 155.14/23.73 (3) ~ (all_8_2 = e3) % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (1), (2) imply: % 155.14/23.73 | (4) all_8_2 = e3 % 155.14/23.73 | % 155.14/23.73 | SIMP: (4) implies: % 155.14/23.73 | (5) all_8_2 = e3 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (3), (5) imply: % 155.14/23.73 | (6) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (6) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #757 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.73 (2) op(e3, e3) = e0 % 155.14/23.73 (3) op(e3, e3) = all_58_0 % 155.14/23.73 (4) ~ (e3 = e0) % 155.14/23.73 (5) op(e3, e3) = e3 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | GROUND_INST: instantiating (1) with e3, all_58_0, e3, e3, simplifying with % 155.14/23.73 | (3), (5) gives: % 155.14/23.73 | (6) all_58_0 = e3 % 155.14/23.73 | % 155.14/23.73 | GROUND_INST: instantiating (1) with e0, all_58_0, e3, e3, simplifying with % 155.14/23.73 | (2), (3) gives: % 155.14/23.73 | (7) all_58_0 = e0 % 155.14/23.73 | % 155.14/23.73 | COMBINE_EQS: (6), (7) imply: % 155.14/23.73 | (8) e3 = e0 % 155.14/23.73 | % 155.14/23.73 | SIMP: (8) implies: % 155.14/23.73 | (9) e3 = e0 % 155.14/23.73 | % 155.14/23.73 | REDUCE: (4), (9) imply: % 155.14/23.73 | (10) $false % 155.14/23.73 | % 155.14/23.73 | CLOSE: (10) is inconsistent. % 155.14/23.73 | % 155.14/23.73 End of proof % 155.14/23.73 % 155.14/23.73 Sub-proof #758 shows that the following formulas are inconsistent: % 155.14/23.73 ---------------------------------------------------------------- % 155.14/23.73 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 155.14/23.73 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.73 (3) all_56_7 = all_52_6 % 155.14/23.73 (4) ~ (all_52_6 = all_6_2) % 155.14/23.73 (5) op(e3, e2) = e0 % 155.14/23.73 (6) ~ (all_52_8 = all_10_2) % 155.14/23.73 (7) all_56_4 = all_52_8 % 155.14/23.73 (8) ~ (all_52_8 = all_6_2) % 155.14/23.73 (9) all_56_1 = e3 | all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 155.14/23.73 (10) all_56_1 = e0 % 155.14/23.73 (11) all_56_3 = all_8_2 % 155.14/23.73 (12) all_58_29 = all_8_2 % 155.14/23.73 (13) all_56_13 = all_52_7 % 155.14/23.73 (14) ~ (e3 = e0) % 155.14/23.73 (15) all_56_5 = e0 % 155.14/23.73 (16) ~ (all_52_7 = e3) % 155.14/23.73 (17) all_56_14 = all_52_11 % 155.14/23.73 (18) all_58_28 = all_10_2 % 155.14/23.73 (19) op(all_8_2, e2) = all_8_1 % 155.14/23.73 (20) all_58_31 = e0 % 155.14/23.73 (21) all_56_8 = all_6_2 % 155.14/23.73 (22) ~ (all_8_1 = e0) % 155.14/23.73 (23) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.73 (24) ~ (all_52_11 = e3) % 155.14/23.73 (25) ~ (all_52_8 = e0) % 155.14/23.73 (26) all_58_30 = all_6_2 % 155.14/23.73 % 155.14/23.73 Begin of proof % 155.14/23.73 | % 155.14/23.73 | BETA: splitting (9) gives: % 155.14/23.73 | % 155.14/23.73 | Case 1: % 155.14/23.73 | | % 155.14/23.73 | | (27) all_56_1 = e3 % 155.14/23.73 | | % 155.14/23.73 | | COMBINE_EQS: (10), (27) imply: % 155.14/23.73 | | (28) e3 = e0 % 155.14/23.73 | | % 155.14/23.74 | | REDUCE: (14), (28) imply: % 155.14/23.74 | | (29) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (29) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (30) ~ (all_56_1 = e3) % 155.14/23.74 | | (31) all_56_3 = e3 | all_56_7 = e3 | all_56_13 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (10), (30) imply: % 155.14/23.74 | | (32) ~ (e3 = e0) % 155.14/23.74 | | % 155.14/23.74 | | BETA: splitting (1) gives: % 155.14/23.74 | | % 155.14/23.74 | | Case 1: % 155.14/23.74 | | | % 155.14/23.74 | | | (33) all_56_4 = e3 % 155.14/23.74 | | | % 155.14/23.74 | | | COMBINE_EQS: (7), (33) imply: % 155.14/23.74 | | | (34) all_52_8 = e3 % 155.14/23.74 | | | % 155.14/23.74 | | | SIMP: (34) implies: % 155.14/23.74 | | | (35) all_52_8 = e3 % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (6), (35) imply: % 155.14/23.74 | | | (36) ~ (all_10_2 = e3) % 155.14/23.74 | | | % 155.14/23.74 | | | SIMP: (36) implies: % 155.14/23.74 | | | (37) ~ (all_10_2 = e3) % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (8), (35) imply: % 155.14/23.74 | | | (38) ~ (all_6_2 = e3) % 155.14/23.74 | | | % 155.14/23.74 | | | SIMP: (38) implies: % 155.14/23.74 | | | (39) ~ (all_6_2 = e3) % 155.14/23.74 | | | % 155.14/23.74 | | | BETA: splitting (23) gives: % 155.14/23.74 | | | % 155.14/23.74 | | | Case 1: % 155.14/23.74 | | | | % 155.14/23.74 | | | | (40) all_58_28 = e3 % 155.14/23.74 | | | | % 155.14/23.74 | | | | REF_CLOSE: (18), (37), (40) are inconsistent by sub-proof #783. % 155.14/23.74 | | | | % 155.14/23.74 | | | Case 2: % 155.14/23.74 | | | | % 155.14/23.74 | | | | (41) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.74 | | | | % 155.14/23.74 | | | | BETA: splitting (41) gives: % 155.14/23.74 | | | | % 155.14/23.74 | | | | Case 1: % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | (42) all_58_29 = e3 % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | COMBINE_EQS: (12), (42) imply: % 155.14/23.74 | | | | | (43) all_8_2 = e3 % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | REF_CLOSE: (2), (5), (19), (22), (43) are inconsistent by sub-proof % 155.14/23.74 | | | | | #761. % 155.14/23.74 | | | | | % 155.14/23.74 | | | | Case 2: % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | (44) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | REF_CLOSE: (14), (20), (26), (39), (44) are inconsistent by sub-proof % 155.14/23.74 | | | | | #768. % 155.14/23.74 | | | | | % 155.14/23.74 | | | | End of split % 155.14/23.74 | | | | % 155.14/23.74 | | | End of split % 155.14/23.74 | | | % 155.14/23.74 | | Case 2: % 155.14/23.74 | | | % 155.14/23.74 | | | (45) all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 155.14/23.74 | | | % 155.14/23.74 | | | BETA: splitting (45) gives: % 155.14/23.74 | | | % 155.14/23.74 | | | Case 1: % 155.14/23.74 | | | | % 155.14/23.74 | | | | (46) all_56_5 = e3 % 155.14/23.74 | | | | % 155.14/23.74 | | | | COMBINE_EQS: (15), (46) imply: % 155.14/23.74 | | | | (47) e3 = e0 % 155.14/23.74 | | | | % 155.14/23.74 | | | | REDUCE: (14), (47) imply: % 155.14/23.74 | | | | (48) $false % 155.14/23.74 | | | | % 155.14/23.74 | | | | CLOSE: (48) is inconsistent. % 155.14/23.74 | | | | % 155.14/23.74 | | | Case 2: % 155.14/23.74 | | | | % 155.14/23.74 | | | | (49) all_56_8 = e3 | all_56_14 = e3 % 155.14/23.74 | | | | % 155.14/23.74 | | | | BETA: splitting (49) gives: % 155.14/23.74 | | | | % 155.14/23.74 | | | | Case 1: % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | (50) all_56_8 = e3 % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | COMBINE_EQS: (21), (50) imply: % 155.14/23.74 | | | | | (51) all_6_2 = e3 % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | REDUCE: (4), (51) imply: % 155.14/23.74 | | | | | (52) ~ (all_52_6 = e3) % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | BETA: splitting (31) gives: % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | Case 1: % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | | (53) all_56_3 = e3 % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | | COMBINE_EQS: (11), (53) imply: % 155.14/23.74 | | | | | | (54) all_8_2 = e3 % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | | REF_CLOSE: (2), (5), (19), (22), (54) are inconsistent by sub-proof % 155.14/23.74 | | | | | | #761. % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | Case 2: % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | | (55) all_56_7 = e3 | all_56_13 = e3 % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | | BETA: splitting (55) gives: % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | | Case 1: % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | | (56) all_56_7 = e3 % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | | COMBINE_EQS: (3), (56) imply: % 155.14/23.74 | | | | | | | (57) all_52_6 = e3 % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | | REDUCE: (52), (57) imply: % 155.14/23.74 | | | | | | | (58) $false % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | | CLOSE: (58) is inconsistent. % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | Case 2: % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | | (59) all_56_13 = e3 % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | | REF_CLOSE: (13), (16), (59) are inconsistent by sub-proof #760. % 155.14/23.74 | | | | | | | % 155.14/23.74 | | | | | | End of split % 155.14/23.74 | | | | | | % 155.14/23.74 | | | | | End of split % 155.14/23.74 | | | | | % 155.14/23.74 | | | | Case 2: % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | (60) all_56_14 = e3 % 155.14/23.74 | | | | | % 155.14/23.74 | | | | | REF_CLOSE: (17), (24), (60) are inconsistent by sub-proof #759. % 155.14/23.74 | | | | | % 155.14/23.74 | | | | End of split % 155.14/23.74 | | | | % 155.14/23.74 | | | End of split % 155.14/23.74 | | | % 155.14/23.74 | | End of split % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #759 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_56_14 = all_52_11 % 155.14/23.74 (2) all_56_14 = e3 % 155.14/23.74 (3) ~ (all_52_11 = e3) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_11 = e3 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_11 = e3 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #760 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_56_13 = all_52_7 % 155.14/23.74 (2) all_56_13 = e3 % 155.14/23.74 (3) ~ (all_52_7 = e3) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_7 = e3 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_7 = e3 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #761 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.74 (2) op(e3, e2) = e0 % 155.14/23.74 (3) op(all_8_2, e2) = all_8_1 % 155.14/23.74 (4) all_8_2 = e3 % 155.14/23.74 (5) ~ (all_8_1 = e0) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (6) all_8_2 = e3 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (6) imply: % 155.14/23.74 | (7) op(e3, e2) = all_8_1 % 155.14/23.74 | % 155.14/23.74 | GROUND_INST: instantiating (1) with e0, all_8_1, e2, e3, simplifying with (2), % 155.14/23.74 | (7) gives: % 155.14/23.74 | (8) all_8_1 = e0 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (5), (8) imply: % 155.14/23.74 | (9) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (9) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #762 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_12 = all_52_3 % 155.14/23.74 (2) all_54_12 = e0 % 155.14/23.74 (3) ~ (all_52_3 = e0) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_3 = e0 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_3 = e0 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #763 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ~ (all_6_2 = e0) % 155.14/23.74 (2) all_56_11 = all_52_14 % 155.14/23.74 (3) all_56_8 = all_6_2 % 155.14/23.74 (4) all_56_8 = e0 | all_56_11 = e0 % 155.14/23.74 (5) ~ (all_52_14 = e0) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (4) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (6) all_56_8 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #764. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (7) all_56_11 = e0 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (2), (7) imply: % 155.14/23.74 | | (8) all_52_14 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (5), (8) imply: % 155.14/23.74 | | (9) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (9) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #764 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_56_8 = all_6_2 % 155.14/23.74 (2) all_56_8 = e0 % 155.14/23.74 (3) ~ (all_6_2 = e0) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_6_2 = e0 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_6_2 = e0 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #765 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ~ (all_52_2 = e0) % 155.14/23.74 (2) all_56_6 = e0 | all_56_12 = e0 % 155.14/23.74 (3) ~ (all_52_3 = e0) % 155.14/23.74 (4) all_56_12 = all_52_3 % 155.14/23.74 (5) all_56_6 = all_52_2 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (2) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (6) all_56_6 = e0 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (5), (6) imply: % 155.14/23.74 | | (7) all_52_2 = e0 % 155.14/23.74 | | % 155.14/23.74 | | SIMP: (7) implies: % 155.14/23.74 | | (8) all_52_2 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (1), (8) imply: % 155.14/23.74 | | (9) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (9) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (10) all_56_12 = e0 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (4), (10) imply: % 155.14/23.74 | | (11) all_52_3 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (3), (11) imply: % 155.14/23.74 | | (12) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (12) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #766 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ~ (all_6_2 = e0) % 155.14/23.74 (2) all_56_5 = all_52_9 % 155.14/23.74 (3) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.14/23.74 (4) ~ (all_52_9 = e0) % 155.14/23.74 (5) ~ (all_52_11 = e0) % 155.14/23.74 (6) all_56_14 = all_52_11 % 155.14/23.74 (7) all_56_8 = all_6_2 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (3) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (8) all_56_5 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #767. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (9) all_56_8 = e0 | all_56_14 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (1), (5), (6), (7), (9) are inconsistent by sub-proof #805. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #767 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_56_5 = all_52_9 % 155.14/23.74 (2) all_56_5 = e0 % 155.14/23.74 (3) ~ (all_52_9 = e0) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_9 = e0 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_9 = e0 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #768 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ~ (e3 = e0) % 155.14/23.74 (2) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.74 (3) ~ (all_6_2 = e3) % 155.14/23.74 (4) all_58_31 = e0 % 155.14/23.74 (5) all_58_30 = all_6_2 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (2) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (6) all_58_30 = e3 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (5), (6) imply: % 155.14/23.74 | | (7) all_6_2 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (3), (7) imply: % 155.14/23.74 | | (8) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (8) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (9) all_58_31 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #853. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #769 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ~ (all_52_13 = e3) % 155.14/23.74 (2) all_56_11 = all_52_14 % 155.14/23.74 (3) ~ (e3 = e0) % 155.14/23.74 (4) all_56_10 = all_52_13 % 155.14/23.74 (5) all_56_15 = e0 % 155.14/23.74 (6) ~ (all_52_14 = e3) % 155.14/23.74 (7) all_56_10 = e3 | all_56_11 = e3 | all_56_15 = e3 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (7) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (8) all_56_10 = e3 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (4), (8) imply: % 155.14/23.74 | | (9) all_52_13 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (1), (9) imply: % 155.14/23.74 | | (10) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (10) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (11) all_56_11 = e3 | all_56_15 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (2), (3), (5), (6), (11) are inconsistent by sub-proof #770. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #770 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_56_11 = all_52_14 % 155.14/23.74 (2) ~ (e3 = e0) % 155.14/23.74 (3) all_56_15 = e0 % 155.14/23.74 (4) ~ (all_52_14 = e3) % 155.14/23.74 (5) all_56_11 = e3 | all_56_15 = e3 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (5) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (6) all_56_11 = e3 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (1), (6) imply: % 155.14/23.74 | | (7) all_52_14 = e3 % 155.14/23.74 | | % 155.14/23.74 | | SIMP: (7) implies: % 155.14/23.74 | | (8) all_52_14 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (4), (8) imply: % 155.14/23.74 | | (9) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (9) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (10) all_56_15 = e3 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (3), (10) imply: % 155.14/23.74 | | (11) e3 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (2), (11) imply: % 155.14/23.74 | | (12) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (12) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #771 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_6 = all_52_9 % 155.14/23.74 (2) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 % 155.14/23.74 (3) ~ (all_52_9 = e3) % 155.14/23.74 (4) ~ (all_52_9 = e1) % 155.14/23.74 (5) ~ (all_52_9 = e2) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (2) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (6) all_54_6 = e1 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #774. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (7) all_54_6 = e3 | all_54_6 = e2 % 155.14/23.74 | | % 155.14/23.74 | | BETA: splitting (7) gives: % 155.14/23.74 | | % 155.14/23.74 | | Case 1: % 155.14/23.74 | | | % 155.14/23.74 | | | (8) all_54_6 = e2 % 155.14/23.74 | | | % 155.14/23.74 | | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #773. % 155.14/23.74 | | | % 155.14/23.74 | | Case 2: % 155.14/23.74 | | | % 155.14/23.74 | | | (9) all_54_6 = e3 % 155.14/23.74 | | | % 155.14/23.74 | | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #772. % 155.14/23.74 | | | % 155.14/23.74 | | End of split % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #772 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_6 = all_52_9 % 155.14/23.74 (2) all_54_6 = e3 % 155.14/23.74 (3) ~ (all_52_9 = e3) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_9 = e3 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_9 = e3 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #773 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_6 = all_52_9 % 155.14/23.74 (2) all_54_6 = e2 % 155.14/23.74 (3) ~ (all_52_9 = e2) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_9 = e2 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_9 = e2 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #774 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_6 = all_52_9 % 155.14/23.74 (2) all_54_6 = e1 % 155.14/23.74 (3) ~ (all_52_9 = e1) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_9 = e1 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_9 = e1 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #775 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_11 = e3 | all_54_11 = e2 % 155.14/23.74 (2) all_54_11 = all_52_14 % 155.14/23.74 (3) ~ (all_52_14 = e2) % 155.14/23.74 (4) ~ (all_52_14 = e3) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (1) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (5) all_54_11 = e2 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #777. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (6) all_54_11 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #776. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #776 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_11 = all_52_14 % 155.14/23.74 (2) all_54_11 = e3 % 155.14/23.74 (3) ~ (all_52_14 = e3) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_14 = e3 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_14 = e3 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #777 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_54_11 = all_52_14 % 155.14/23.74 (2) all_54_11 = e2 % 155.14/23.74 (3) ~ (all_52_14 = e2) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_52_14 = e2 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_52_14 = e2 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #778 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_58_14 = e3 % 155.14/23.74 (2) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.74 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.74 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.14/23.74 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.74 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.74 (all_58_27 = e0)) % 155.14/23.74 (3) all_58_10 = e1 % 155.14/23.74 (4) all_58_27 = e0 % 155.14/23.74 (5) all_58_1 = e2 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (2) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (6) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.74 | | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.74 | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 155.14/23.74 | | % 155.14/23.74 | | BETA: splitting (6) gives: % 155.14/23.74 | | % 155.14/23.74 | | Case 1: % 155.14/23.74 | | | % 155.14/23.74 | | | (7) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.74 | | | (all_58_5 = e0) % 155.14/23.74 | | | % 155.14/23.74 | | | ALPHA: (7) implies: % 155.14/23.74 | | | (8) ~ (all_58_1 = e2) % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (5), (8) imply: % 155.14/23.74 | | | (9) $false % 155.14/23.74 | | | % 155.14/23.74 | | | CLOSE: (9) is inconsistent. % 155.14/23.74 | | | % 155.14/23.74 | | Case 2: % 155.14/23.74 | | | % 155.14/23.74 | | | (10) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 155.14/23.74 | | | (all_58_12 = e0) % 155.14/23.74 | | | % 155.14/23.74 | | | ALPHA: (10) implies: % 155.14/23.74 | | | (11) ~ (all_58_10 = e1) % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (3), (11) imply: % 155.14/23.74 | | | (12) $false % 155.14/23.74 | | | % 155.14/23.74 | | | CLOSE: (12) is inconsistent. % 155.14/23.74 | | | % 155.14/23.74 | | End of split % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (13) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 155.14/23.74 | | ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & % 155.14/23.74 | | ~ (all_58_25 = e1) & ~ (all_58_27 = e0)) % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #779. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #779 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 155.14/23.74 (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 155.14/23.74 (all_58_25 = e1) & ~ (all_58_27 = e0)) % 155.14/23.74 (2) all_58_14 = e3 % 155.14/23.74 (3) all_58_27 = e0 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (1) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (4) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 155.14/23.74 | | (all_58_19 = e0) % 155.14/23.74 | | % 155.14/23.74 | | ALPHA: (4) implies: % 155.14/23.74 | | (5) ~ (all_58_14 = e3) % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (2), (5) imply: % 155.14/23.74 | | (6) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (6) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (7) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.74 | | (all_58_27 = e0) % 155.14/23.74 | | % 155.14/23.74 | | ALPHA: (7) implies: % 155.14/23.74 | | (8) ~ (all_58_27 = e0) % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (3), (8) imply: % 155.14/23.74 | | (9) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (9) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #780 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_58_29 = e3 % 155.14/23.74 (2) all_58_29 = e2 % 155.14/23.74 (3) ~ (e3 = e2) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) e3 = e2 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) e3 = e2 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #781 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.74 (2) all_56_1 = e1 | all_56_4 = e1 | all_56_9 = e1 % 155.14/23.74 (3) all_56_9 = e3 % 155.14/23.74 (4) ~ (e3 = e1) % 155.14/23.74 (5) ~ (all_8_0 = e0) % 155.14/23.74 (6) all_56_4 = e0 % 155.14/23.74 (7) op(e3, all_8_1) = all_8_0 % 155.14/23.74 (8) all_56_1 = all_8_1 % 155.14/23.74 (9) ~ (e1 = e0) % 155.14/23.74 (10) op(e3, e1) = e0 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (2) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (11) all_56_1 = e1 % 155.14/23.74 | | % 155.14/23.74 | | COMBINE_EQS: (8), (11) imply: % 155.14/23.74 | | (12) all_8_1 = e1 % 155.14/23.74 | | % 155.14/23.74 | | SIMP: (12) implies: % 155.14/23.74 | | (13) all_8_1 = e1 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (7), (13) imply: % 155.14/23.74 | | (14) op(e3, e1) = all_8_0 % 155.14/23.74 | | % 155.14/23.74 | | GROUND_INST: instantiating (1) with e0, all_8_0, e1, e3, simplifying with % 155.14/23.74 | | (10), (14) gives: % 155.14/23.74 | | (15) all_8_0 = e0 % 155.14/23.74 | | % 155.14/23.74 | | REDUCE: (5), (15) imply: % 155.14/23.74 | | (16) $false % 155.14/23.74 | | % 155.14/23.74 | | CLOSE: (16) is inconsistent. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (17) all_56_4 = e1 | all_56_9 = e1 % 155.14/23.74 | | % 155.14/23.74 | | BETA: splitting (17) gives: % 155.14/23.74 | | % 155.14/23.74 | | Case 1: % 155.14/23.74 | | | % 155.14/23.74 | | | (18) all_56_4 = e1 % 155.14/23.74 | | | % 155.14/23.74 | | | REF_CLOSE: (6), (9), (18) are inconsistent by sub-proof #782. % 155.14/23.74 | | | % 155.14/23.74 | | Case 2: % 155.14/23.74 | | | % 155.14/23.74 | | | (19) all_56_9 = e1 % 155.14/23.74 | | | % 155.14/23.74 | | | COMBINE_EQS: (3), (19) imply: % 155.14/23.74 | | | (20) e3 = e1 % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (4), (20) imply: % 155.14/23.74 | | | (21) $false % 155.14/23.74 | | | % 155.14/23.74 | | | CLOSE: (21) is inconsistent. % 155.14/23.74 | | | % 155.14/23.74 | | End of split % 155.14/23.74 | | % 155.14/23.74 | End of split % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #782 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_56_4 = e1 % 155.14/23.74 (2) all_56_4 = e0 % 155.14/23.74 (3) ~ (e1 = e0) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) e1 = e0 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) e1 = e0 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #783 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) all_58_28 = all_10_2 % 155.14/23.74 (2) all_58_28 = e3 % 155.14/23.74 (3) ~ (all_10_2 = e3) % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | COMBINE_EQS: (1), (2) imply: % 155.14/23.74 | (4) all_10_2 = e3 % 155.14/23.74 | % 155.14/23.74 | SIMP: (4) implies: % 155.14/23.74 | (5) all_10_2 = e3 % 155.14/23.74 | % 155.14/23.74 | REDUCE: (3), (5) imply: % 155.14/23.74 | (6) $false % 155.14/23.74 | % 155.14/23.74 | CLOSE: (6) is inconsistent. % 155.14/23.74 | % 155.14/23.74 End of proof % 155.14/23.74 % 155.14/23.74 Sub-proof #784 shows that the following formulas are inconsistent: % 155.14/23.74 ---------------------------------------------------------------- % 155.14/23.74 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.74 (2) ~ (all_52_2 = e0) % 155.14/23.74 (3) all_54_8 = all_52_2 % 155.14/23.74 (4) op(e1, all_6_2) = all_58_18 % 155.14/23.74 (5) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.74 (6) ~ (all_6_2 = e0) % 155.14/23.74 (7) op(e2, e2) = all_8_2 % 155.14/23.74 (8) all_56_7 = e0 % 155.14/23.74 (9) ~ (all_52_2 = all_6_2) % 155.14/23.74 (10) ~ (e3 = e1) % 155.14/23.74 (11) op(e3, e3) = all_58_0 % 155.14/23.74 (12) all_58_29 = all_8_2 % 155.14/23.74 (13) ~ (e2 = e1) % 155.14/23.74 (14) all_56_6 = all_52_2 % 155.14/23.74 (15) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.74 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.74 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.14/23.74 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.74 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.74 (all_58_27 = e0)) % 155.14/23.74 (16) ~ (e3 = e0) % 155.14/23.74 (17) op(all_8_2, e2) = all_8_1 % 155.14/23.74 (18) all_58_31 = e0 % 155.14/23.74 (19) ~ (all_52_2 = e3) % 155.14/23.74 (20) all_56_8 = all_6_2 % 155.14/23.74 (21) op(e1, e1) = all_6_2 % 155.14/23.74 (22) all_58_27 = e0 % 155.14/23.74 (23) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 % 155.14/23.74 (24) ~ (all_8_1 = e0) % 155.14/23.74 (25) op(e1, e2) = e0 % 155.14/23.74 (26) all_58_28 = e3 % 155.14/23.74 (27) ~ (e1 = e0) % 155.14/23.74 (28) all_58_30 = e0 | all_58_31 = e0 % 155.14/23.74 (29) op(e3, e3) = e3 % 155.14/23.74 (30) all_56_6 = e3 | all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 155.14/23.74 (31) all_58_30 = all_6_2 % 155.14/23.74 (32) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.74 (33) all_56_6 = e2 | all_56_7 = e2 | all_56_8 = e2 | all_56_11 = e2 % 155.14/23.74 (34) op(e2, all_8_2) = all_58_9 % 155.14/23.74 % 155.14/23.74 Begin of proof % 155.14/23.74 | % 155.14/23.74 | BETA: splitting (30) gives: % 155.14/23.74 | % 155.14/23.74 | Case 1: % 155.14/23.74 | | % 155.14/23.74 | | (35) all_56_6 = e3 % 155.14/23.74 | | % 155.14/23.74 | | REF_CLOSE: (14), (19), (35) are inconsistent by sub-proof #788. % 155.14/23.74 | | % 155.14/23.74 | Case 2: % 155.14/23.74 | | % 155.14/23.74 | | (36) ~ (all_56_6 = e3) % 155.14/23.74 | | (37) all_56_7 = e3 | all_56_8 = e3 | all_56_11 = e3 % 155.14/23.74 | | % 155.14/23.74 | | BETA: splitting (33) gives: % 155.14/23.74 | | % 155.14/23.74 | | Case 1: % 155.14/23.74 | | | % 155.14/23.74 | | | (38) all_56_6 = e2 % 155.14/23.74 | | | % 155.14/23.74 | | | COMBINE_EQS: (14), (38) imply: % 155.14/23.74 | | | (39) all_52_2 = e2 % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (9), (39) imply: % 155.14/23.74 | | | (40) ~ (all_6_2 = e2) % 155.14/23.74 | | | % 155.14/23.74 | | | SIMP: (40) implies: % 155.14/23.74 | | | (41) ~ (all_6_2 = e2) % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (19), (39) imply: % 155.14/23.74 | | | (42) ~ (e3 = e2) % 155.14/23.74 | | | % 155.14/23.74 | | | SIMP: (42) implies: % 155.14/23.74 | | | (43) ~ (e3 = e2) % 155.14/23.74 | | | % 155.14/23.74 | | | REDUCE: (2), (39) imply: % 155.14/23.74 | | | (44) ~ (e2 = e0) % 155.14/23.74 | | | % 155.14/23.74 | | | BETA: splitting (5) gives: % 155.14/23.74 | | | % 155.14/23.74 | | | Case 1: % 155.14/23.74 | | | | % 155.14/23.74 | | | | (45) all_58_28 = e2 % 155.14/23.75 | | | | % 155.14/23.75 | | | | COMBINE_EQS: (26), (45) imply: % 155.14/23.75 | | | | (46) e3 = e2 % 155.14/23.75 | | | | % 155.14/23.75 | | | | REDUCE: (43), (46) imply: % 155.14/23.75 | | | | (47) $false % 155.14/23.75 | | | | % 155.14/23.75 | | | | CLOSE: (47) is inconsistent. % 155.14/23.75 | | | | % 155.14/23.75 | | | Case 2: % 155.14/23.75 | | | | % 155.14/23.75 | | | | (48) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.75 | | | | % 155.14/23.75 | | | | BETA: splitting (48) gives: % 155.14/23.75 | | | | % 155.14/23.75 | | | | Case 1: % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | (49) all_58_29 = e2 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | COMBINE_EQS: (12), (49) imply: % 155.14/23.75 | | | | | (50) all_8_2 = e2 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | REDUCE: (17), (50) imply: % 155.14/23.75 | | | | | (51) op(e2, e2) = all_8_1 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | REDUCE: (34), (50) imply: % 155.14/23.75 | | | | | (52) op(e2, e2) = all_58_9 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | REDUCE: (7), (50) imply: % 155.14/23.75 | | | | | (53) op(e2, e2) = e2 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | BETA: splitting (32) gives: % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | Case 1: % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | (54) all_58_28 = e1 % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | COMBINE_EQS: (26), (54) imply: % 155.14/23.75 | | | | | | (55) e3 = e1 % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | REDUCE: (10), (55) imply: % 155.14/23.75 | | | | | | (56) $false % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | CLOSE: (56) is inconsistent. % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | Case 2: % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | (57) ~ (all_58_28 = e1) % 155.14/23.75 | | | | | | (58) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | BETA: splitting (58) gives: % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | Case 1: % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | (59) all_58_29 = e1 % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | COMBINE_EQS: (49), (59) imply: % 155.14/23.75 | | | | | | | (60) e2 = e1 % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | REDUCE: (13), (60) imply: % 155.14/23.75 | | | | | | | (61) $false % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | CLOSE: (61) is inconsistent. % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | Case 2: % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | (62) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | BETA: splitting (62) gives: % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | | Case 1: % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | (63) all_58_30 = e1 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | COMBINE_EQS: (31), (63) imply: % 155.14/23.75 | | | | | | | | (64) all_6_2 = e1 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | SIMP: (64) implies: % 155.14/23.75 | | | | | | | | (65) all_6_2 = e1 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | COMBINE_EQS: (20), (65) imply: % 155.14/23.75 | | | | | | | | (66) all_56_8 = e1 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | REDUCE: (4), (65) imply: % 155.14/23.75 | | | | | | | | (67) op(e1, e1) = all_58_18 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | REDUCE: (21), (65) imply: % 155.14/23.75 | | | | | | | | (68) op(e1, e1) = e1 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | BETA: splitting (37) gives: % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | Case 1: % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | (69) all_56_7 = e3 % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | COMBINE_EQS: (8), (69) imply: % 155.14/23.75 | | | | | | | | | (70) e3 = e0 % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | REDUCE: (16), (70) imply: % 155.14/23.75 | | | | | | | | | (71) $false % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | CLOSE: (71) is inconsistent. % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | Case 2: % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | (72) all_56_8 = e3 | all_56_11 = e3 % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | BETA: splitting (72) gives: % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | | Case 1: % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | (73) all_56_8 = e3 % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | COMBINE_EQS: (66), (73) imply: % 155.14/23.75 | | | | | | | | | | (74) e3 = e1 % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | REDUCE: (10), (74) imply: % 155.14/23.75 | | | | | | | | | | (75) $false % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | CLOSE: (75) is inconsistent. % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | Case 2: % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | GROUND_INST: instantiating (1) with e1, all_58_18, e1, e1, % 155.14/23.75 | | | | | | | | | | simplifying with (67), (68) gives: % 155.14/23.75 | | | | | | | | | | (76) all_58_18 = e1 % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | | REF_CLOSE: (1), (11), (15), (22), (29), (51), (52), (53), % 155.14/23.75 | | | | | | | | | | (76) are inconsistent by sub-proof #818. % 155.14/23.75 | | | | | | | | | | % 155.14/23.75 | | | | | | | | | End of split % 155.14/23.75 | | | | | | | | | % 155.14/23.75 | | | | | | | | End of split % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | Case 2: % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | (77) all_58_31 = e1 % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | | REF_CLOSE: (6), (27), (28), (31), (77) are inconsistent by % 155.14/23.75 | | | | | | | | sub-proof #808. % 155.14/23.75 | | | | | | | | % 155.14/23.75 | | | | | | | End of split % 155.14/23.75 | | | | | | | % 155.14/23.75 | | | | | | End of split % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | End of split % 155.14/23.75 | | | | | % 155.14/23.75 | | | | Case 2: % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | (78) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | REF_CLOSE: (18), (31), (41), (44), (78) are inconsistent by sub-proof % 155.14/23.75 | | | | | #817. % 155.14/23.75 | | | | | % 155.14/23.75 | | | | End of split % 155.14/23.75 | | | | % 155.14/23.75 | | | End of split % 155.14/23.75 | | | % 155.14/23.75 | | Case 2: % 155.14/23.75 | | | % 155.14/23.75 | | | (79) ~ (all_56_6 = e2) % 155.14/23.75 | | | % 155.14/23.75 | | | REDUCE: (14), (79) imply: % 155.14/23.75 | | | (80) ~ (all_52_2 = e2) % 155.14/23.75 | | | % 155.14/23.75 | | | BETA: splitting (23) gives: % 155.14/23.75 | | | % 155.14/23.75 | | | Case 1: % 155.14/23.75 | | | | % 155.14/23.75 | | | | (81) all_54_8 = e1 % 155.14/23.75 | | | | % 155.14/23.75 | | | | COMBINE_EQS: (3), (81) imply: % 155.14/23.75 | | | | (82) all_52_2 = e1 % 155.14/23.75 | | | | % 155.14/23.75 | | | | SIMP: (82) implies: % 155.14/23.75 | | | | (83) all_52_2 = e1 % 155.14/23.75 | | | | % 155.14/23.75 | | | | REDUCE: (9), (83) imply: % 155.14/23.75 | | | | (84) ~ (all_6_2 = e1) % 155.14/23.75 | | | | % 155.14/23.75 | | | | SIMP: (84) implies: % 155.14/23.75 | | | | (85) ~ (all_6_2 = e1) % 155.14/23.75 | | | | % 155.14/23.75 | | | | REDUCE: (19), (83) imply: % 155.14/23.75 | | | | (86) ~ (e3 = e1) % 155.14/23.75 | | | | % 155.14/23.75 | | | | BETA: splitting (32) gives: % 155.14/23.75 | | | | % 155.14/23.75 | | | | Case 1: % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | (87) all_58_28 = e1 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | COMBINE_EQS: (26), (87) imply: % 155.14/23.75 | | | | | (88) e3 = e1 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | REDUCE: (10), (88) imply: % 155.14/23.75 | | | | | (89) $false % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | CLOSE: (89) is inconsistent. % 155.14/23.75 | | | | | % 155.14/23.75 | | | | Case 2: % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | (90) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | BETA: splitting (90) gives: % 155.14/23.75 | | | | | % 155.14/23.75 | | | | | Case 1: % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | (91) all_58_29 = e1 % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | REF_CLOSE: (1), (12), (17), (24), (25), (91) are inconsistent by % 155.14/23.75 | | | | | | sub-proof #794. % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | Case 2: % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | (92) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | | REF_CLOSE: (18), (27), (31), (85), (92) are inconsistent by % 155.14/23.75 | | | | | | sub-proof #824. % 155.14/23.75 | | | | | | % 155.14/23.75 | | | | | End of split % 155.14/23.75 | | | | | % 155.14/23.75 | | | | End of split % 155.14/23.75 | | | | % 155.14/23.75 | | | Case 2: % 155.14/23.75 | | | | % 155.14/23.75 | | | | (93) all_54_8 = e3 | all_54_8 = e2 % 155.14/23.75 | | | | % 155.14/23.75 | | | | REF_CLOSE: (3), (19), (80), (93) are inconsistent by sub-proof #785. % 155.14/23.75 | | | | % 155.14/23.75 | | | End of split % 155.14/23.75 | | | % 155.14/23.75 | | End of split % 155.14/23.75 | | % 155.14/23.75 | End of split % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #785 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_54_8 = e3 | all_54_8 = e2 % 155.14/23.75 (2) all_54_8 = all_52_2 % 155.14/23.75 (3) ~ (all_52_2 = e2) % 155.14/23.75 (4) ~ (all_52_2 = e3) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | BETA: splitting (1) gives: % 155.14/23.75 | % 155.14/23.75 | Case 1: % 155.14/23.75 | | % 155.14/23.75 | | (5) all_54_8 = e2 % 155.14/23.75 | | % 155.14/23.75 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #787. % 155.14/23.75 | | % 155.14/23.75 | Case 2: % 155.14/23.75 | | % 155.14/23.75 | | (6) all_54_8 = e3 % 155.14/23.75 | | % 155.14/23.75 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #786. % 155.14/23.75 | | % 155.14/23.75 | End of split % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #786 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_54_8 = all_52_2 % 155.14/23.75 (2) all_54_8 = e3 % 155.14/23.75 (3) ~ (all_52_2 = e3) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) all_52_2 = e3 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) all_52_2 = e3 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #787 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_54_8 = all_52_2 % 155.14/23.75 (2) all_54_8 = e2 % 155.14/23.75 (3) ~ (all_52_2 = e2) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) all_52_2 = e2 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) all_52_2 = e2 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #788 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_56_6 = all_52_2 % 155.14/23.75 (2) all_56_6 = e3 % 155.14/23.75 (3) ~ (all_52_2 = e3) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) all_52_2 = e3 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) all_52_2 = e3 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #789 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (2) op(all_6_2, e1) = all_6_1 % 155.14/23.75 (3) op(e3, e1) = all_58_0 % 155.14/23.75 (4) ~ (e3 = e0) % 155.14/23.75 (5) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.75 (6) ~ (all_6_1 = e0) % 155.14/23.75 (7) all_58_29 = e2 % 155.14/23.75 (8) all_58_31 = e0 % 155.14/23.75 (9) all_58_30 = all_6_2 % 155.14/23.75 (10) ~ (e3 = e2) % 155.14/23.75 (11) op(e3, e1) = e0 % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | BETA: splitting (5) gives: % 155.14/23.75 | % 155.14/23.75 | Case 1: % 155.14/23.75 | | % 155.14/23.75 | | (12) all_58_29 = e3 % 155.14/23.75 | | % 155.14/23.75 | | COMBINE_EQS: (7), (12) imply: % 155.14/23.75 | | (13) e3 = e2 % 155.14/23.75 | | % 155.14/23.75 | | REDUCE: (10), (13) imply: % 155.14/23.75 | | (14) $false % 155.14/23.75 | | % 155.14/23.75 | | CLOSE: (14) is inconsistent. % 155.14/23.75 | | % 155.14/23.75 | Case 2: % 155.14/23.75 | | % 155.14/23.75 | | (15) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.75 | | % 155.14/23.75 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (15) are inconsistent by % 155.14/23.75 | | sub-proof #790. % 155.14/23.75 | | % 155.14/23.75 | End of split % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #790 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (2) op(all_6_2, e1) = all_6_1 % 155.14/23.75 (3) op(e3, e1) = all_58_0 % 155.14/23.75 (4) ~ (e3 = e0) % 155.14/23.75 (5) ~ (all_6_1 = e0) % 155.14/23.75 (6) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.75 (7) all_58_31 = e0 % 155.14/23.75 (8) all_58_30 = all_6_2 % 155.14/23.75 (9) op(e3, e1) = e0 % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | BETA: splitting (6) gives: % 155.14/23.75 | % 155.14/23.75 | Case 1: % 155.14/23.75 | | % 155.14/23.75 | | (10) all_58_30 = e3 % 155.14/23.75 | | % 155.14/23.75 | | COMBINE_EQS: (8), (10) imply: % 155.14/23.75 | | (11) all_6_2 = e3 % 155.14/23.75 | | % 155.14/23.75 | | REDUCE: (2), (11) imply: % 155.14/23.75 | | (12) op(e3, e1) = all_6_1 % 155.14/23.75 | | % 155.14/23.75 | | GROUND_INST: instantiating (1) with e0, all_58_0, e1, e3, simplifying with % 155.14/23.75 | | (3), (9) gives: % 155.14/23.75 | | (13) all_58_0 = e0 % 155.14/23.75 | | % 155.14/23.75 | | GROUND_INST: instantiating (1) with all_6_1, all_58_0, e1, e3, simplifying % 155.14/23.75 | | with (3), (12) gives: % 155.14/23.75 | | (14) all_58_0 = all_6_1 % 155.14/23.75 | | % 155.14/23.75 | | COMBINE_EQS: (13), (14) imply: % 155.14/23.75 | | (15) all_6_1 = e0 % 155.14/23.75 | | % 155.14/23.75 | | SIMP: (15) implies: % 155.14/23.75 | | (16) all_6_1 = e0 % 155.14/23.75 | | % 155.14/23.75 | | REDUCE: (5), (16) imply: % 155.14/23.75 | | (17) $false % 155.14/23.75 | | % 155.14/23.75 | | CLOSE: (17) is inconsistent. % 155.14/23.75 | | % 155.14/23.75 | Case 2: % 155.14/23.75 | | % 155.14/23.75 | | (18) all_58_31 = e3 % 155.14/23.75 | | % 155.14/23.75 | | REF_CLOSE: (4), (7), (18) are inconsistent by sub-proof #853. % 155.14/23.75 | | % 155.14/23.75 | End of split % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #791 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (2) ~ (all_52_2 = e0) % 155.14/23.75 (3) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 155.14/23.75 (4) ~ (all_52_2 = all_6_2) % 155.14/23.75 (5) ~ (e3 = e1) % 155.14/23.75 (6) all_58_29 = all_8_2 % 155.14/23.75 (7) ~ (e2 = e1) % 155.14/23.75 (8) all_56_6 = all_52_2 % 155.14/23.75 (9) all_56_2 = e0 % 155.14/23.75 (10) all_56_0 = e2 % 155.14/23.75 (11) op(all_8_2, e2) = all_8_1 % 155.14/23.75 (12) all_56_12 = e3 % 155.14/23.75 (13) all_58_31 = e0 % 155.14/23.75 (14) all_58_28 = e2 % 155.14/23.75 (15) ~ (all_8_1 = e0) % 155.14/23.75 (16) op(e1, e2) = e0 % 155.14/23.75 (17) ~ (e1 = e0) % 155.14/23.75 (18) all_58_30 = all_6_2 % 155.14/23.75 (19) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 (20) ~ (all_52_2 = e2) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | BETA: splitting (3) gives: % 155.14/23.75 | % 155.14/23.75 | Case 1: % 155.14/23.75 | | % 155.14/23.75 | | (21) all_56_0 = e1 % 155.14/23.75 | | % 155.14/23.75 | | REF_CLOSE: (7), (10), (21) are inconsistent by sub-proof #796. % 155.14/23.75 | | % 155.14/23.75 | Case 2: % 155.14/23.75 | | % 155.14/23.75 | | (22) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 155.14/23.75 | | % 155.14/23.75 | | BETA: splitting (22) gives: % 155.14/23.75 | | % 155.14/23.75 | | Case 1: % 155.14/23.75 | | | % 155.14/23.75 | | | (23) all_56_2 = e1 % 155.14/23.75 | | | % 155.14/23.75 | | | COMBINE_EQS: (9), (23) imply: % 155.14/23.75 | | | (24) e1 = e0 % 155.14/23.75 | | | % 155.14/23.75 | | | REDUCE: (17), (24) imply: % 155.14/23.75 | | | (25) $false % 155.14/23.75 | | | % 155.14/23.75 | | | CLOSE: (25) is inconsistent. % 155.14/23.75 | | | % 155.14/23.75 | | Case 2: % 155.14/23.75 | | | % 155.14/23.75 | | | (26) all_56_6 = e1 | all_56_12 = e1 % 155.14/23.75 | | | % 155.14/23.75 | | | BETA: splitting (26) gives: % 155.14/23.75 | | | % 155.14/23.75 | | | Case 1: % 155.14/23.75 | | | | % 155.14/23.75 | | | | (27) all_56_6 = e1 % 155.14/23.75 | | | | % 155.14/23.75 | | | | COMBINE_EQS: (8), (27) imply: % 155.14/23.75 | | | | (28) all_52_2 = e1 % 155.14/23.75 | | | | % 155.14/23.75 | | | | REDUCE: (4), (28) imply: % 155.14/23.75 | | | | (29) ~ (all_6_2 = e1) % 155.14/23.75 | | | | % 155.14/23.75 | | | | SIMP: (29) implies: % 155.14/23.75 | | | | (30) ~ (all_6_2 = e1) % 155.14/23.75 | | | | % 155.14/23.75 | | | | REDUCE: (20), (28) imply: % 155.14/23.75 | | | | (31) ~ (e2 = e1) % 155.14/23.75 | | | | % 155.14/23.75 | | | | REF_CLOSE: (1), (6), (7), (11), (13), (14), (15), (16), (17), (18), % 155.14/23.75 | | | | (19), (30) are inconsistent by sub-proof #793. % 155.14/23.75 | | | | % 155.14/23.75 | | | Case 2: % 155.14/23.75 | | | | % 155.14/23.75 | | | | (32) all_56_12 = e1 % 155.14/23.75 | | | | % 155.14/23.75 | | | | REF_CLOSE: (5), (12), (32) are inconsistent by sub-proof #792. % 155.14/23.75 | | | | % 155.14/23.75 | | | End of split % 155.14/23.75 | | | % 155.14/23.75 | | End of split % 155.14/23.75 | | % 155.14/23.75 | End of split % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #792 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_56_12 = e3 % 155.14/23.75 (2) all_56_12 = e1 % 155.14/23.75 (3) ~ (e3 = e1) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) e3 = e1 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) e3 = e1 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #793 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (2) all_58_29 = all_8_2 % 155.14/23.75 (3) ~ (e2 = e1) % 155.14/23.75 (4) op(all_8_2, e2) = all_8_1 % 155.14/23.75 (5) all_58_31 = e0 % 155.14/23.75 (6) all_58_28 = e2 % 155.14/23.75 (7) ~ (all_8_1 = e0) % 155.14/23.75 (8) op(e1, e2) = e0 % 155.14/23.75 (9) ~ (e1 = e0) % 155.14/23.75 (10) ~ (all_6_2 = e1) % 155.14/23.75 (11) all_58_30 = all_6_2 % 155.14/23.75 (12) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | BETA: splitting (12) gives: % 155.14/23.75 | % 155.14/23.75 | Case 1: % 155.14/23.75 | | % 155.14/23.75 | | (13) all_58_28 = e1 % 155.14/23.75 | | % 155.14/23.75 | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #856. % 155.14/23.75 | | % 155.14/23.75 | Case 2: % 155.14/23.75 | | % 155.14/23.75 | | (14) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 | | % 155.14/23.75 | | BETA: splitting (14) gives: % 155.14/23.75 | | % 155.14/23.75 | | Case 1: % 155.14/23.75 | | | % 155.14/23.75 | | | (15) all_58_29 = e1 % 155.14/23.75 | | | % 155.14/23.75 | | | REF_CLOSE: (1), (2), (4), (7), (8), (15) are inconsistent by sub-proof % 155.14/23.75 | | | #794. % 155.14/23.75 | | | % 155.14/23.75 | | Case 2: % 155.14/23.75 | | | % 155.14/23.75 | | | (16) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 | | | % 155.14/23.75 | | | REF_CLOSE: (5), (9), (10), (11), (16) are inconsistent by sub-proof #824. % 155.14/23.75 | | | % 155.14/23.75 | | End of split % 155.14/23.75 | | % 155.14/23.75 | End of split % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #794 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (2) all_58_29 = all_8_2 % 155.14/23.75 (3) all_58_29 = e1 % 155.14/23.75 (4) op(all_8_2, e2) = all_8_1 % 155.14/23.75 (5) ~ (all_8_1 = e0) % 155.14/23.75 (6) op(e1, e2) = e0 % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (2), (3) imply: % 155.14/23.75 | (7) all_8_2 = e1 % 155.14/23.75 | % 155.14/23.75 | SIMP: (7) implies: % 155.14/23.75 | (8) all_8_2 = e1 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (4), (8) imply: % 155.14/23.75 | (9) op(e1, e2) = all_8_1 % 155.14/23.75 | % 155.14/23.75 | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #795. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #795 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (2) op(e1, e2) = all_8_1 % 155.14/23.75 (3) op(e1, e2) = e0 % 155.14/23.75 (4) ~ (all_8_1 = e0) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | GROUND_INST: instantiating (1) with e0, all_8_1, e2, e1, simplifying with (2), % 155.14/23.75 | (3) gives: % 155.14/23.75 | (5) all_8_1 = e0 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (4), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #796 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_56_0 = e2 % 155.14/23.75 (2) all_56_0 = e1 % 155.14/23.75 (3) ~ (e2 = e1) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) e2 = e1 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) e2 = e1 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #797 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_54_6 = all_52_9 % 155.14/23.75 (2) all_54_6 = e0 % 155.14/23.75 (3) ~ (all_52_9 = e0) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) all_52_9 = e0 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) all_52_9 = e0 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #798 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_54_1 = all_52_4 % 155.14/23.75 (2) all_54_1 = e0 % 155.14/23.75 (3) ~ (all_52_4 = e0) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) all_52_4 = e0 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) all_52_4 = e0 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #799 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_56_0 = all_10_2 % 155.14/23.75 (2) all_56_0 = e0 % 155.14/23.75 (3) ~ (all_10_2 = e0) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | COMBINE_EQS: (1), (2) imply: % 155.14/23.75 | (4) all_10_2 = e0 % 155.14/23.75 | % 155.14/23.75 | SIMP: (4) implies: % 155.14/23.75 | (5) all_10_2 = e0 % 155.14/23.75 | % 155.14/23.75 | REDUCE: (3), (5) imply: % 155.14/23.75 | (6) $false % 155.14/23.75 | % 155.14/23.75 | CLOSE: (6) is inconsistent. % 155.14/23.75 | % 155.14/23.75 End of proof % 155.14/23.75 % 155.14/23.75 Sub-proof #800 shows that the following formulas are inconsistent: % 155.14/23.75 ---------------------------------------------------------------- % 155.14/23.75 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 155.14/23.75 (2) ~ (all_52_8 = all_52_9) % 155.14/23.75 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.75 (4) all_56_7 = all_52_6 % 155.14/23.75 (5) ~ (all_52_6 = all_6_2) % 155.14/23.75 (6) all_54_2 = all_52_8 % 155.14/23.75 (7) ~ (all_10_1 = e0) % 155.14/23.75 (8) op(e1, all_6_2) = all_58_18 % 155.14/23.75 (9) op(all_8_2, all_8_1) = all_8_0 % 155.14/23.75 (10) ~ (all_52_8 = all_10_2) % 155.14/23.75 (11) ~ (all_52_6 = all_8_2) % 155.14/23.75 (12) all_56_4 = all_52_8 % 155.14/23.75 (13) all_56_6 = e0 % 155.14/23.75 (14) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.75 (15) ~ (all_6_2 = e0) % 155.14/23.75 (16) ~ (all_52_4 = all_52_6) % 155.14/23.75 (17) op(e2, e2) = all_8_2 % 155.14/23.75 (18) all_56_0 = e1 | all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 155.14/23.75 (19) op(e3, e2) = all_52_4 % 155.14/23.75 (20) ~ (all_52_8 = all_6_2) % 155.14/23.75 (21) op(e2, e3) = all_52_1 % 155.14/23.75 (22) all_56_4 = e1 | all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 155.14/23.75 (23) ~ (all_52_6 = all_52_14) % 155.14/23.75 (24) op(e3, e3) = all_10_2 % 155.14/23.75 (25) op(e3, all_52_8) = all_58_3 % 155.14/23.75 (26) all_54_9 = all_52_6 % 155.14/23.75 (27) op(e1, e2) = all_52_6 % 155.14/23.75 (28) ~ (all_52_3 = e0) % 155.14/23.75 (29) op(e1, all_52_6) = all_58_16 % 155.14/23.75 (30) ~ (e3 = e1) % 155.14/23.75 (31) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 155.14/23.75 (32) ~ (all_52_6 = e0) % 155.14/23.75 (33) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 155.14/23.75 (34) all_56_5 = all_52_9 % 155.14/23.75 (35) all_56_12 = all_52_3 % 155.14/23.75 (36) all_56_11 = all_52_14 % 155.14/23.75 (37) all_56_1 = all_52_4 % 155.14/23.75 (38) all_56_4 = e0 | all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.14/23.75 (39) all_56_0 = e3 | all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.75 (40) ~ (all_52_1 = all_8_2) % 155.14/23.75 (41) all_56_3 = all_8_2 % 155.14/23.75 (42) ~ (all_52_4 = all_52_8) % 155.14/23.75 (43) op(e2, e1) = all_52_9 % 155.14/23.75 (44) all_58_29 = all_8_2 % 155.14/23.75 (45) op(e1, e3) = e0 % 155.14/23.75 (46) ~ (e2 = e1) % 155.14/23.75 (47) all_56_13 = all_52_7 % 155.14/23.75 (48) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 155.14/23.75 (49) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.75 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.75 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.14/23.75 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.75 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.75 (all_58_27 = e0)) % 155.14/23.75 (50) all_56_1 = e0 | all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 155.14/23.75 (51) op(all_6_2, e1) = all_6_1 % 155.14/23.75 (52) op(e3, all_10_2) = all_58_0 % 155.14/23.75 (53) ~ (e3 = e0) % 155.14/23.75 (54) all_56_2 = all_52_1 % 155.14/23.75 (55) ~ (all_52_11 = e0) % 155.14/23.75 (56) ~ (all_52_9 = all_8_2) % 155.14/23.75 (57) all_56_14 = all_52_11 % 155.14/23.75 (58) all_58_28 = all_10_2 % 155.14/23.75 (59) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 155.14/23.75 (60) ~ (all_6_1 = e0) % 155.14/23.75 (61) ~ (all_52_1 = all_52_9) % 155.14/23.75 (62) op(e3, e1) = all_52_8 % 155.14/23.75 (63) all_56_6 = e1 | all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 155.14/23.75 (64) op(all_8_2, e2) = all_8_1 % 155.14/23.75 (65) all_56_12 = e1 | all_56_13 = e1 | all_56_14 = e1 | all_56_15 = e1 % 155.14/23.75 (66) ~ (e2 = e0) % 155.14/23.75 (67) ~ (all_52_9 = all_6_2) % 155.14/23.75 (68) all_56_0 = all_10_2 % 155.14/23.75 (69) all_58_31 = e0 % 155.14/23.75 (70) ~ (all_52_3 = all_52_11) % 155.14/23.75 (71) ~ (all_52_3 = all_10_2) % 155.14/23.75 (72) all_56_8 = all_6_2 % 155.14/23.75 (73) op(e1, e1) = all_6_2 % 155.14/23.75 (74) all_58_27 = e0 % 155.14/23.75 (75) ~ (all_8_1 = e0) % 155.14/23.75 (76) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.75 (77) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 155.14/23.75 (78) all_54_0 = all_10_2 % 155.14/23.75 (79) ~ (all_52_7 = e0) % 155.14/23.75 (80) ~ (e1 = e0) % 155.14/23.75 (81) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.14/23.75 (82) all_58_30 = e0 | all_58_31 = e0 % 155.14/23.75 (83) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 155.14/23.75 (84) ~ (all_52_4 = all_10_2) % 155.14/23.75 (85) all_58_30 = all_6_2 % 155.14/23.75 (86) op(e2, all_52_1) = all_58_7 % 155.14/23.75 (87) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.75 (88) ~ (e3 = e2) % 155.14/23.75 (89) op(all_10_2, e3) = all_10_1 % 155.14/23.75 (90) op(e2, all_8_2) = all_58_9 % 155.14/23.75 (91) all_54_4 = all_52_1 % 155.14/23.75 (92) ~ (all_52_1 = all_10_2) % 155.14/23.75 % 155.14/23.75 Begin of proof % 155.14/23.75 | % 155.14/23.75 | BETA: splitting (50) gives: % 155.14/23.75 | % 155.14/23.75 | Case 1: % 155.14/23.75 | | % 155.14/23.75 | | (93) all_56_1 = e0 % 155.14/23.75 | | % 155.14/23.75 | | COMBINE_EQS: (37), (93) imply: % 155.14/23.75 | | (94) all_52_4 = e0 % 155.14/23.75 | | % 155.14/23.75 | | SIMP: (94) implies: % 155.14/23.75 | | (95) all_52_4 = e0 % 155.14/23.75 | | % 155.14/23.75 | | REDUCE: (16), (95) imply: % 155.14/23.75 | | (96) ~ (all_52_6 = e0) % 155.14/23.75 | | % 155.14/23.75 | | REDUCE: (42), (95) imply: % 155.14/23.75 | | (97) ~ (all_52_8 = e0) % 155.14/23.75 | | % 155.14/23.75 | | SIMP: (97) implies: % 155.14/23.75 | | (98) ~ (all_52_8 = e0) % 155.14/23.75 | | % 155.14/23.75 | | REDUCE: (84), (95) imply: % 155.14/23.75 | | (99) ~ (all_10_2 = e0) % 155.14/23.75 | | % 155.14/23.75 | | SIMP: (99) implies: % 155.14/23.76 | | (100) ~ (all_10_2 = e0) % 155.14/23.76 | | % 155.14/23.76 | | REDUCE: (19), (95) imply: % 155.14/23.76 | | (101) op(e3, e2) = e0 % 155.14/23.76 | | % 155.14/23.76 | | BETA: splitting (38) gives: % 155.14/23.76 | | % 155.14/23.76 | | Case 1: % 155.14/23.76 | | | % 155.14/23.76 | | | (102) all_56_4 = e0 % 155.14/23.76 | | | % 155.14/23.76 | | | REF_CLOSE: (12), (98), (102) are inconsistent by sub-proof #862. % 155.14/23.76 | | | % 155.14/23.76 | | Case 2: % 155.14/23.76 | | | % 155.14/23.76 | | | (103) all_56_5 = e0 | all_56_8 = e0 | all_56_14 = e0 % 155.14/23.76 | | | % 155.14/23.76 | | | BETA: splitting (103) gives: % 155.14/23.76 | | | % 155.14/23.76 | | | Case 1: % 155.14/23.76 | | | | % 155.14/23.76 | | | | (104) all_56_5 = e0 % 155.14/23.76 | | | | % 155.14/23.76 | | | | COMBINE_EQS: (34), (104) imply: % 155.14/23.76 | | | | (105) all_52_9 = e0 % 155.14/23.76 | | | | % 155.14/23.76 | | | | SIMP: (105) implies: % 155.14/23.76 | | | | (106) all_52_9 = e0 % 155.14/23.76 | | | | % 155.14/23.76 | | | | REDUCE: (61), (106) imply: % 155.14/23.76 | | | | (107) ~ (all_52_1 = e0) % 155.14/23.76 | | | | % 155.14/23.76 | | | | REDUCE: (56), (106) imply: % 155.14/23.76 | | | | (108) ~ (all_8_2 = e0) % 155.14/23.76 | | | | % 155.14/23.76 | | | | SIMP: (108) implies: % 155.14/23.76 | | | | (109) ~ (all_8_2 = e0) % 155.14/23.76 | | | | % 155.14/23.76 | | | | REDUCE: (67), (106) imply: % 155.14/23.76 | | | | (110) ~ (all_6_2 = e0) % 155.14/23.76 | | | | % 155.14/23.76 | | | | REDUCE: (43), (106) imply: % 155.14/23.76 | | | | (111) op(e2, e1) = e0 % 155.14/23.76 | | | | % 155.14/23.76 | | | | BETA: splitting (33) gives: % 155.14/23.76 | | | | % 155.14/23.76 | | | | Case 1: % 155.14/23.76 | | | | | % 155.14/23.76 | | | | | (112) all_54_0 = e0 % 155.14/23.76 | | | | | % 155.14/23.76 | | | | | REF_CLOSE: (78), (100), (112) are inconsistent by sub-proof #861. % 155.14/23.76 | | | | | % 155.14/23.76 | | | | Case 2: % 155.14/23.76 | | | | | % 155.14/23.76 | | | | | (113) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.76 | | | | | % 155.14/23.76 | | | | | BETA: splitting (83) gives: % 155.14/23.76 | | | | | % 155.14/23.76 | | | | | Case 1: % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | | (114) all_54_2 = e0 % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | | REF_CLOSE: (6), (98), (114) are inconsistent by sub-proof #860. % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | Case 2: % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | | (115) ~ (all_54_2 = e0) % 155.14/23.76 | | | | | | (116) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | | BETA: splitting (31) gives: % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | | Case 1: % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | (117) all_54_9 = e0 % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | COMBINE_EQS: (26), (117) imply: % 155.14/23.76 | | | | | | | (118) all_52_6 = e0 % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | REDUCE: (32), (118) imply: % 155.14/23.76 | | | | | | | (119) $false % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | CLOSE: (119) is inconsistent. % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | Case 2: % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | (120) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | BETA: splitting (48) gives: % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | | (121) all_54_4 = e0 % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | | REF_CLOSE: (91), (107), (121) are inconsistent by sub-proof % 155.14/23.76 | | | | | | | | #859. % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | | (122) ~ (all_54_4 = e0) % 155.14/23.76 | | | | | | | | (123) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | | BETA: splitting (65) gives: % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | (124) all_56_12 = e1 % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | COMBINE_EQS: (35), (124) imply: % 155.14/23.76 | | | | | | | | | (125) all_52_3 = e1 % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | SIMP: (125) implies: % 155.14/23.76 | | | | | | | | | (126) all_52_3 = e1 % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | REDUCE: (70), (126) imply: % 155.14/23.76 | | | | | | | | | (127) ~ (all_52_11 = e1) % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | SIMP: (127) implies: % 155.14/23.76 | | | | | | | | | (128) ~ (all_52_11 = e1) % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | REDUCE: (71), (126) imply: % 155.14/23.76 | | | | | | | | | (129) ~ (all_10_2 = e1) % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | SIMP: (129) implies: % 155.14/23.76 | | | | | | | | | (130) ~ (all_10_2 = e1) % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | BETA: splitting (22) gives: % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | (131) all_56_4 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | COMBINE_EQS: (12), (131) imply: % 155.14/23.76 | | | | | | | | | | (132) all_52_8 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | SIMP: (132) implies: % 155.14/23.76 | | | | | | | | | | (133) all_52_8 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | REDUCE: (20), (133) imply: % 155.14/23.76 | | | | | | | | | | (134) ~ (all_6_2 = e1) % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | SIMP: (134) implies: % 155.14/23.76 | | | | | | | | | | (135) ~ (all_6_2 = e1) % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | REDUCE: (25), (133) imply: % 155.14/23.76 | | | | | | | | | | (136) op(e3, e1) = all_58_3 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | REDUCE: (62), (133) imply: % 155.14/23.76 | | | | | | | | | | (137) op(e3, e1) = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | BETA: splitting (87) gives: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | (138) all_58_28 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | REF_CLOSE: (58), (130), (138) are inconsistent by sub-proof % 155.14/23.76 | | | | | | | | | | | #858. % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | (139) ~ (all_58_28 = e1) % 155.14/23.76 | | | | | | | | | | | (140) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | BETA: splitting (140) gives: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | (141) all_58_29 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | COMBINE_EQS: (44), (141) imply: % 155.14/23.76 | | | | | | | | | | | | (142) all_8_2 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | SIMP: (142) implies: % 155.14/23.76 | | | | | | | | | | | | (143) all_8_2 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REDUCE: (40), (143) imply: % 155.14/23.76 | | | | | | | | | | | | (144) ~ (all_52_1 = e1) % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REDUCE: (11), (143) imply: % 155.14/23.76 | | | | | | | | | | | | (145) ~ (all_52_6 = e1) % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REDUCE: (9), (143) imply: % 155.14/23.76 | | | | | | | | | | | | (146) op(e1, all_8_1) = all_8_0 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REDUCE: (64), (143) imply: % 155.14/23.76 | | | | | | | | | | | | (147) op(e1, e2) = all_8_1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REDUCE: (90), (143) imply: % 155.14/23.76 | | | | | | | | | | | | (148) op(e2, e1) = all_58_9 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | BETA: splitting (63) gives: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | (149) all_56_6 = e1 % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | REF_CLOSE: (13), (14), (30), (46), (53), (66), (69), (76), % 155.14/23.76 | | | | | | | | | | | | | (80), (85), (87), (88), (141), (149) are % 155.14/23.76 | | | | | | | | | | | | | inconsistent by sub-proof #843. % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | (150) all_56_7 = e1 | all_56_8 = e1 | all_56_11 = e1 % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | BETA: splitting (150) gives: % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | (151) all_56_7 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | COMBINE_EQS: (4), (151) imply: % 155.14/23.76 | | | | | | | | | | | | | | (152) all_52_6 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | REDUCE: (145), (152) imply: % 155.14/23.76 | | | | | | | | | | | | | | (153) $false % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | (154) all_56_8 = e1 | all_56_11 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | BETA: splitting (154) gives: % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | (155) all_56_8 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | COMBINE_EQS: (72), (155) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (156) all_6_2 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | REDUCE: (135), (156) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (157) $false % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | (158) all_56_11 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | COMBINE_EQS: (36), (158) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (159) all_52_14 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | SIMP: (159) implies: % 155.14/23.76 | | | | | | | | | | | | | | | (160) all_52_14 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_52_6, all_8_1, e2, e1, % 155.14/23.76 | | | | | | | | | | | | | | | simplifying with (27), (147) gives: % 155.14/23.76 | | | | | | | | | | | | | | | (161) all_52_6 = all_8_1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_58_9, e1, e2, % 155.14/23.76 | | | | | | | | | | | | | | | simplifying with (111), (148) gives: % 155.14/23.76 | | | | | | | | | | | | | | | (162) all_58_9 = e0 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with e1, all_58_3, e1, e3, % 155.14/23.76 | | | | | | | | | | | | | | | simplifying with (136), (137) gives: % 155.14/23.76 | | | | | | | | | | | | | | | (163) all_58_3 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | COMBINE_EQS: (26), (161) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (164) all_54_9 = all_8_1 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | REDUCE: (5), (161) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (165) ~ (all_8_1 = all_6_2) % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | REDUCE: (145), (161) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (166) ~ (all_8_1 = e1) % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | REDUCE: (29), (161) imply: % 155.14/23.76 | | | | | | | | | | | | | | | (167) op(e1, all_8_1) = all_58_16 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_8_0, all_58_16, % 155.14/23.76 | | | | | | | | | | | | | | | all_8_1, e1, simplifying with (146), (167) gives: % 155.14/23.76 | | | | | | | | | | | | | | | (168) all_58_16 = all_8_0 % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | (169) all_56_0 = e3 % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (169) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | (170) all_10_2 = e3 % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | SIMP: (170) implies: % 155.14/23.76 | | | | | | | | | | | | | | | | (171) all_10_2 = e3 % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (171) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | (172) all_58_28 = e3 % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | BETA: splitting (14) gives: % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | (173) all_58_28 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (173) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | (174) e3 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | REDUCE: (88), (174) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | (175) $false % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent. % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | (176) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | (177) all_58_29 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (177) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | | (178) e2 = e1 % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | REDUCE: (46), (178) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | | (179) $false % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent. % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | (180) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | (181) all_58_30 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (181) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | | | (182) all_6_2 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | SIMP: (182) implies: % 155.14/23.76 | | | | | | | | | | | | | | | | | | | (183) all_6_2 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (51), (60), (111), (183) are inconsistent by % 155.14/23.76 | | | | | | | | | | | | | | | | | | | sub-proof #842. % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | (184) all_58_31 = e2 % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (184) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | | | (185) e2 = e0 % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | REDUCE: (66), (185) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | | | | (186) $false % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | | CLOSE: (186) is inconsistent. % 155.14/23.76 | | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | (187) ~ (all_56_0 = e3) % 155.14/23.76 | | | | | | | | | | | | | | | | (188) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | REDUCE: (68), (187) imply: % 155.14/23.76 | | | | | | | | | | | | | | | | (189) ~ (all_10_2 = e3) % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (21), (49), (54), (58), (69), (74), % 155.14/23.76 | | | | | | | | | | | | | | | | (76), (77), (78), (85), (86), (91), (92), (107), % 155.14/23.76 | | | | | | | | | | | | | | | | (113), (120), (123), (124), (130), (141), (144), % 155.14/23.76 | | | | | | | | | | | | | | | | (146), (147), (163), (164), (165), (166), (168), % 155.14/23.76 | | | | | | | | | | | | | | | | (188), (189) are inconsistent by sub-proof #826. % 155.14/23.76 | | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | (190) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REF_CLOSE: (69), (80), (85), (135), (190) are inconsistent by % 155.14/23.76 | | | | | | | | | | | | sub-proof #824. % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | (191) all_56_5 = e1 | all_56_8 = e1 | all_56_14 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | BETA: splitting (191) gives: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | (192) all_56_5 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | COMBINE_EQS: (104), (192) imply: % 155.14/23.76 | | | | | | | | | | | (193) e1 = e0 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | REDUCE: (80), (193) imply: % 155.14/23.76 | | | | | | | | | | | (194) $false % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | CLOSE: (194) is inconsistent. % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | (195) all_56_8 = e1 | all_56_14 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | BETA: splitting (195) gives: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | (196) all_56_8 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | COMBINE_EQS: (72), (196) imply: % 155.14/23.76 | | | | | | | | | | | | (197) all_6_2 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | SIMP: (197) implies: % 155.14/23.76 | | | | | | | | | | | | (198) all_6_2 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | COMBINE_EQS: (85), (198) imply: % 155.14/23.76 | | | | | | | | | | | | (199) all_58_30 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (12), (14), (17), (20), % 155.14/23.76 | | | | | | | | | | | | (24), (44), (49), (52), (58), (59), (64), (68), % 155.14/23.76 | | | | | | | | | | | | (69), (73), (74), (75), (76), (78), (81), (85), % 155.14/23.76 | | | | | | | | | | | | (90), (98), (101), (113), (116), (130), (198), % 155.14/23.76 | | | | | | | | | | | | (199) are inconsistent by sub-proof #812. % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | (200) all_56_14 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REF_CLOSE: (57), (128), (200) are inconsistent by sub-proof % 155.14/23.76 | | | | | | | | | | | | #811. % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | (201) ~ (all_56_12 = e1) % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | REDUCE: (35), (201) imply: % 155.14/23.76 | | | | | | | | | (202) ~ (all_52_3 = e1) % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | BETA: splitting (18) gives: % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | (203) all_56_0 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | COMBINE_EQS: (68), (203) imply: % 155.14/23.76 | | | | | | | | | | (204) all_10_2 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | REDUCE: (89), (204) imply: % 155.14/23.76 | | | | | | | | | | (205) op(e1, e3) = all_10_1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | REF_CLOSE: (3), (7), (45), (205) are inconsistent by % 155.14/23.76 | | | | | | | | | | sub-proof #810. % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | (206) all_56_2 = e1 | all_56_6 = e1 | all_56_12 = e1 % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | BETA: splitting (206) gives: % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | (207) all_56_2 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | COMBINE_EQS: (54), (207) imply: % 155.14/23.76 | | | | | | | | | | | (208) all_52_1 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | SIMP: (208) implies: % 155.14/23.76 | | | | | | | | | | | (209) all_52_1 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | REDUCE: (92), (209) imply: % 155.14/23.76 | | | | | | | | | | | (210) ~ (all_10_2 = e1) % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | SIMP: (210) implies: % 155.14/23.76 | | | | | | | | | | | (211) ~ (all_10_2 = e1) % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | REDUCE: (40), (209) imply: % 155.14/23.76 | | | | | | | | | | | (212) ~ (all_8_2 = e1) % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | SIMP: (212) implies: % 155.14/23.76 | | | | | | | | | | | (213) ~ (all_8_2 = e1) % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | BETA: splitting (87) gives: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | (214) all_58_28 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | REF_CLOSE: (58), (211), (214) are inconsistent by sub-proof % 155.14/23.76 | | | | | | | | | | | | #858. % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | (215) ~ (all_58_28 = e1) % 155.14/23.76 | | | | | | | | | | | | (216) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | BETA: splitting (216) gives: % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | (217) all_58_29 = e1 % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | REF_CLOSE: (44), (213), (217) are inconsistent by sub-proof % 155.14/23.76 | | | | | | | | | | | | | #809. % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | (218) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | BETA: splitting (218) gives: % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | Case 1: % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | (219) all_58_30 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | COMBINE_EQS: (85), (219) imply: % 155.14/23.76 | | | | | | | | | | | | | | (220) all_6_2 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | SIMP: (220) implies: % 155.14/23.76 | | | | | | | | | | | | | | (221) all_6_2 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (12), (14), (17), (20), % 155.14/23.76 | | | | | | | | | | | | | | (24), (44), (49), (52), (58), (59), (64), (68), % 155.14/23.76 | | | | | | | | | | | | | | (69), (73), (74), (75), (76), (78), (81), (85), % 155.14/23.76 | | | | | | | | | | | | | | (90), (98), (101), (113), (116), (211), (219), % 155.14/23.76 | | | | | | | | | | | | | | (221) are inconsistent by sub-proof #812. % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | (222) all_58_31 = e1 % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | | REF_CLOSE: (15), (80), (82), (85), (222) are inconsistent by % 155.14/23.76 | | | | | | | | | | | | | | sub-proof #808. % 155.14/23.76 | | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | Case 2: % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | (223) all_56_6 = e1 | all_56_12 = e1 % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | | REF_CLOSE: (13), (35), (80), (202), (223) are inconsistent by % 155.14/23.76 | | | | | | | | | | | sub-proof #807. % 155.14/23.76 | | | | | | | | | | | % 155.14/23.76 | | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | | % 155.14/23.76 | | | | | | | | | End of split % 155.14/23.76 | | | | | | | | | % 155.14/23.76 | | | | | | | | End of split % 155.14/23.76 | | | | | | | | % 155.14/23.76 | | | | | | | End of split % 155.14/23.76 | | | | | | | % 155.14/23.76 | | | | | | End of split % 155.14/23.76 | | | | | | % 155.14/23.76 | | | | | End of split % 155.14/23.76 | | | | | % 155.14/23.76 | | | | End of split % 155.14/23.76 | | | | % 155.14/23.76 | | | Case 2: % 155.14/23.76 | | | | % 155.14/23.76 | | | | (224) all_56_8 = e0 | all_56_14 = e0 % 155.14/23.76 | | | | % 155.14/23.76 | | | | REF_CLOSE: (15), (55), (57), (72), (224) are inconsistent by sub-proof % 155.14/23.76 | | | | #805. % 155.14/23.76 | | | | % 155.14/23.76 | | | End of split % 155.14/23.76 | | | % 155.14/23.76 | | End of split % 155.14/23.76 | | % 155.14/23.76 | Case 2: % 155.14/23.76 | | % 155.14/23.76 | | (225) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REF_CLOSE: (4), (14), (30), (32), (41), (44), (46), (47), (53), (66), (69), % 155.14/23.76 | | (76), (79), (80), (85), (87), (88), (225) are inconsistent by % 155.14/23.76 | | sub-proof #801. % 155.14/23.76 | | % 155.14/23.76 | End of split % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #801 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_7 = all_52_6 % 155.14/23.76 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.76 (3) ~ (e3 = e1) % 155.14/23.76 (4) ~ (all_52_6 = e0) % 155.14/23.76 (5) all_56_3 = all_8_2 % 155.14/23.76 (6) all_58_29 = all_8_2 % 155.14/23.76 (7) ~ (e2 = e1) % 155.14/23.76 (8) all_56_13 = all_52_7 % 155.14/23.76 (9) ~ (e3 = e0) % 155.14/23.76 (10) ~ (e2 = e0) % 155.14/23.76 (11) all_58_31 = e0 % 155.14/23.76 (12) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.76 (13) ~ (all_52_7 = e0) % 155.14/23.76 (14) ~ (e1 = e0) % 155.14/23.76 (15) all_56_3 = e0 | all_56_7 = e0 | all_56_13 = e0 % 155.14/23.76 (16) all_58_30 = all_6_2 % 155.14/23.76 (17) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.76 (18) ~ (e3 = e2) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | BETA: splitting (15) gives: % 155.14/23.76 | % 155.14/23.76 | Case 1: % 155.14/23.76 | | % 155.14/23.76 | | (19) all_56_3 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (11), (12), (14), (16), (17), % 155.14/23.76 | | (18), (19) are inconsistent by sub-proof #804. % 155.14/23.76 | | % 155.14/23.76 | Case 2: % 155.14/23.76 | | % 155.14/23.76 | | (20) all_56_7 = e0 | all_56_13 = e0 % 155.14/23.76 | | % 155.14/23.76 | | BETA: splitting (20) gives: % 155.14/23.76 | | % 155.14/23.76 | | Case 1: % 155.14/23.76 | | | % 155.14/23.76 | | | (21) all_56_7 = e0 % 155.14/23.76 | | | % 155.14/23.76 | | | REF_CLOSE: (1), (4), (21) are inconsistent by sub-proof #803. % 155.14/23.76 | | | % 155.14/23.76 | | Case 2: % 155.14/23.76 | | | % 155.14/23.76 | | | (22) all_56_13 = e0 % 155.14/23.76 | | | % 155.14/23.76 | | | REF_CLOSE: (8), (13), (22) are inconsistent by sub-proof #802. % 155.14/23.76 | | | % 155.14/23.76 | | End of split % 155.14/23.76 | | % 155.14/23.76 | End of split % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #802 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_13 = all_52_7 % 155.14/23.76 (2) all_56_13 = e0 % 155.14/23.76 (3) ~ (all_52_7 = e0) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (1), (2) imply: % 155.14/23.76 | (4) all_52_7 = e0 % 155.14/23.76 | % 155.14/23.76 | SIMP: (4) implies: % 155.14/23.76 | (5) all_52_7 = e0 % 155.14/23.76 | % 155.14/23.76 | REDUCE: (3), (5) imply: % 155.14/23.76 | (6) $false % 155.14/23.76 | % 155.14/23.76 | CLOSE: (6) is inconsistent. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #803 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_7 = all_52_6 % 155.14/23.76 (2) all_56_7 = e0 % 155.14/23.76 (3) ~ (all_52_6 = e0) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (1), (2) imply: % 155.14/23.76 | (4) all_52_6 = e0 % 155.14/23.76 | % 155.14/23.76 | SIMP: (4) implies: % 155.14/23.76 | (5) all_52_6 = e0 % 155.14/23.76 | % 155.14/23.76 | REDUCE: (3), (5) imply: % 155.14/23.76 | (6) $false % 155.14/23.76 | % 155.14/23.76 | CLOSE: (6) is inconsistent. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #804 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_3 = e0 % 155.14/23.76 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.76 (3) ~ (e3 = e1) % 155.14/23.76 (4) all_56_3 = all_8_2 % 155.14/23.76 (5) all_58_29 = all_8_2 % 155.14/23.76 (6) ~ (e2 = e1) % 155.14/23.76 (7) ~ (e3 = e0) % 155.14/23.76 (8) ~ (e2 = e0) % 155.14/23.76 (9) all_58_31 = e0 % 155.14/23.76 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.76 (11) ~ (e1 = e0) % 155.14/23.76 (12) all_58_30 = all_6_2 % 155.14/23.76 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.76 (14) ~ (e3 = e2) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (1), (4) imply: % 155.14/23.76 | (15) all_8_2 = e0 % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (5), (15) imply: % 155.14/23.76 | (16) all_58_29 = e0 % 155.14/23.76 | % 155.14/23.76 | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14), (16) % 155.14/23.76 | are inconsistent by sub-proof #844. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #805 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_8 = e0 | all_56_14 = e0 % 155.14/23.76 (2) ~ (all_6_2 = e0) % 155.14/23.76 (3) ~ (all_52_11 = e0) % 155.14/23.76 (4) all_56_14 = all_52_11 % 155.14/23.76 (5) all_56_8 = all_6_2 % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | BETA: splitting (1) gives: % 155.14/23.76 | % 155.14/23.76 | Case 1: % 155.14/23.76 | | % 155.14/23.76 | | (6) all_56_8 = e0 % 155.14/23.76 | | % 155.14/23.76 | | COMBINE_EQS: (5), (6) imply: % 155.14/23.76 | | (7) all_6_2 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REDUCE: (2), (7) imply: % 155.14/23.76 | | (8) $false % 155.14/23.76 | | % 155.14/23.76 | | CLOSE: (8) is inconsistent. % 155.14/23.76 | | % 155.14/23.76 | Case 2: % 155.14/23.76 | | % 155.14/23.76 | | (9) all_56_14 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #806. % 155.14/23.76 | | % 155.14/23.76 | End of split % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #806 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_14 = all_52_11 % 155.14/23.76 (2) all_56_14 = e0 % 155.14/23.76 (3) ~ (all_52_11 = e0) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (1), (2) imply: % 155.14/23.76 | (4) all_52_11 = e0 % 155.14/23.76 | % 155.14/23.76 | SIMP: (4) implies: % 155.14/23.76 | (5) all_52_11 = e0 % 155.14/23.76 | % 155.14/23.76 | REDUCE: (3), (5) imply: % 155.14/23.76 | (6) $false % 155.14/23.76 | % 155.14/23.76 | CLOSE: (6) is inconsistent. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #807 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_6 = e0 % 155.14/23.76 (2) ~ (all_52_3 = e1) % 155.14/23.76 (3) all_56_12 = all_52_3 % 155.14/23.76 (4) all_56_6 = e1 | all_56_12 = e1 % 155.14/23.76 (5) ~ (e1 = e0) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | BETA: splitting (4) gives: % 155.14/23.76 | % 155.14/23.76 | Case 1: % 155.14/23.76 | | % 155.14/23.76 | | (6) all_56_6 = e1 % 155.14/23.76 | | % 155.14/23.76 | | COMBINE_EQS: (1), (6) imply: % 155.14/23.76 | | (7) e1 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REDUCE: (5), (7) imply: % 155.14/23.76 | | (8) $false % 155.14/23.76 | | % 155.14/23.76 | | CLOSE: (8) is inconsistent. % 155.14/23.76 | | % 155.14/23.76 | Case 2: % 155.14/23.76 | | % 155.14/23.76 | | (9) all_56_12 = e1 % 155.14/23.76 | | % 155.14/23.76 | | COMBINE_EQS: (3), (9) imply: % 155.14/23.76 | | (10) all_52_3 = e1 % 155.14/23.76 | | % 155.14/23.76 | | REDUCE: (2), (10) imply: % 155.14/23.76 | | (11) $false % 155.14/23.76 | | % 155.14/23.76 | | CLOSE: (11) is inconsistent. % 155.14/23.76 | | % 155.14/23.76 | End of split % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #808 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_58_31 = e1 % 155.14/23.76 (2) ~ (all_6_2 = e0) % 155.14/23.76 (3) ~ (e1 = e0) % 155.14/23.76 (4) all_58_30 = e0 | all_58_31 = e0 % 155.14/23.76 (5) all_58_30 = all_6_2 % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | BETA: splitting (4) gives: % 155.14/23.76 | % 155.14/23.76 | Case 1: % 155.14/23.76 | | % 155.14/23.76 | | (6) all_58_30 = e0 % 155.14/23.76 | | % 155.14/23.76 | | COMBINE_EQS: (5), (6) imply: % 155.14/23.76 | | (7) all_6_2 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REDUCE: (2), (7) imply: % 155.14/23.76 | | (8) $false % 155.14/23.76 | | % 155.14/23.76 | | CLOSE: (8) is inconsistent. % 155.14/23.76 | | % 155.14/23.76 | Case 2: % 155.14/23.76 | | % 155.14/23.76 | | (9) all_58_31 = e0 % 155.14/23.76 | | % 155.14/23.76 | | COMBINE_EQS: (1), (9) imply: % 155.14/23.76 | | (10) e1 = e0 % 155.14/23.76 | | % 155.14/23.76 | | REDUCE: (3), (10) imply: % 155.14/23.76 | | (11) $false % 155.14/23.76 | | % 155.14/23.76 | | CLOSE: (11) is inconsistent. % 155.14/23.76 | | % 155.14/23.76 | End of split % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #809 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_58_29 = all_8_2 % 155.14/23.76 (2) all_58_29 = e1 % 155.14/23.76 (3) ~ (all_8_2 = e1) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (1), (2) imply: % 155.14/23.76 | (4) all_8_2 = e1 % 155.14/23.76 | % 155.14/23.76 | SIMP: (4) implies: % 155.14/23.76 | (5) all_8_2 = e1 % 155.14/23.76 | % 155.14/23.76 | REDUCE: (3), (5) imply: % 155.14/23.76 | (6) $false % 155.14/23.76 | % 155.14/23.76 | CLOSE: (6) is inconsistent. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #810 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.76 (2) op(e1, e3) = all_10_1 % 155.14/23.76 (3) op(e1, e3) = e0 % 155.14/23.76 (4) ~ (all_10_1 = e0) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | GROUND_INST: instantiating (1) with e0, all_10_1, e3, e1, simplifying with % 155.14/23.76 | (2), (3) gives: % 155.14/23.76 | (5) all_10_1 = e0 % 155.14/23.76 | % 155.14/23.76 | REDUCE: (4), (5) imply: % 155.14/23.76 | (6) $false % 155.14/23.76 | % 155.14/23.76 | CLOSE: (6) is inconsistent. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #811 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_14 = all_52_11 % 155.14/23.76 (2) all_56_14 = e1 % 155.14/23.76 (3) ~ (all_52_11 = e1) % 155.14/23.76 % 155.14/23.76 Begin of proof % 155.14/23.76 | % 155.14/23.76 | COMBINE_EQS: (1), (2) imply: % 155.14/23.76 | (4) all_52_11 = e1 % 155.14/23.76 | % 155.14/23.76 | SIMP: (4) implies: % 155.14/23.76 | (5) all_52_11 = e1 % 155.14/23.76 | % 155.14/23.76 | REDUCE: (3), (5) imply: % 155.14/23.76 | (6) $false % 155.14/23.76 | % 155.14/23.76 | CLOSE: (6) is inconsistent. % 155.14/23.76 | % 155.14/23.76 End of proof % 155.14/23.76 % 155.14/23.76 Sub-proof #812 shows that the following formulas are inconsistent: % 155.14/23.76 ---------------------------------------------------------------- % 155.14/23.76 (1) all_56_4 = e3 | all_56_5 = e3 | all_56_8 = e3 | all_56_14 = e3 % 155.14/23.76 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.76 (3) all_54_2 = all_52_8 % 155.14/23.76 (4) op(e3, e2) = e0 % 155.14/23.76 (5) op(e1, all_6_2) = all_58_18 % 155.14/23.76 (6) ~ (all_52_8 = all_10_2) % 155.14/23.76 (7) all_56_4 = all_52_8 % 155.14/23.76 (8) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.76 (9) op(e2, e2) = all_8_2 % 155.14/23.76 (10) ~ (all_52_8 = all_6_2) % 155.14/23.76 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.76 (12) op(e3, e3) = all_10_2 % 155.14/23.76 (13) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 155.14/23.76 (14) ~ (all_10_2 = e1) % 155.14/23.76 (15) all_58_29 = all_8_2 % 155.14/23.76 (16) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.76 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.76 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.14/23.76 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.76 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.76 (all_58_27 = e0)) % 155.14/23.76 (17) op(e3, all_10_2) = all_58_0 % 155.14/23.76 (18) all_58_28 = all_10_2 % 155.14/23.76 (19) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 155.14/23.77 (20) all_58_30 = e1 % 155.14/23.77 (21) op(all_8_2, e2) = all_8_1 % 155.14/23.77 (22) all_56_0 = all_10_2 % 155.14/23.77 (23) all_58_31 = e0 % 155.14/23.77 (24) op(e1, e1) = all_6_2 % 155.14/23.77 (25) all_58_27 = e0 % 155.14/23.77 (26) ~ (all_8_1 = e0) % 155.14/23.77 (27) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 (28) all_54_0 = all_10_2 % 155.14/23.77 (29) all_56_0 = e3 | all_56_1 = e3 | all_56_4 = e3 | all_56_9 = e3 % 155.14/23.77 (30) all_6_2 = e1 % 155.14/23.77 (31) ~ (all_52_8 = e0) % 155.14/23.77 (32) all_58_30 = all_6_2 % 155.14/23.77 (33) op(e2, all_8_2) = all_58_9 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | REDUCE: (10), (30) imply: % 155.14/23.77 | (34) ~ (all_52_8 = e1) % 155.14/23.77 | % 155.14/23.77 | REDUCE: (5), (30) imply: % 155.14/23.77 | (35) op(e1, e1) = all_58_18 % 155.14/23.77 | % 155.14/23.77 | REDUCE: (24), (30) imply: % 155.14/23.77 | (36) op(e1, e1) = e1 % 155.14/23.77 | % 155.14/23.77 | GROUND_INST: instantiating (2) with e1, all_58_18, e1, e1, simplifying with % 155.14/23.77 | (35), (36) gives: % 155.14/23.77 | (37) all_58_18 = e1 % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (1) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (38) all_56_4 = e3 % 155.14/23.77 | | % 155.14/23.77 | | COMBINE_EQS: (7), (38) imply: % 155.14/23.77 | | (39) all_52_8 = e3 % 155.14/23.77 | | % 155.14/23.77 | | REDUCE: (6), (39) imply: % 155.14/23.77 | | (40) ~ (all_10_2 = e3) % 155.14/23.77 | | % 155.14/23.77 | | SIMP: (40) implies: % 155.14/23.77 | | (41) ~ (all_10_2 = e3) % 155.14/23.77 | | % 155.14/23.77 | | REDUCE: (34), (39) imply: % 155.14/23.77 | | (42) ~ (e3 = e1) % 155.14/23.77 | | % 155.14/23.77 | | REDUCE: (31), (39) imply: % 155.14/23.77 | | (43) ~ (e3 = e0) % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (2), (4), (11), (14), (15), (17), (18), (19), (20), (21), (22), % 155.14/23.77 | | (23), (26), (27), (28), (41), (42), (43) are inconsistent by % 155.14/23.77 | | sub-proof #820. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (44) ~ (all_56_4 = e3) % 155.14/23.77 | | % 155.14/23.77 | | REDUCE: (7), (44) imply: % 155.14/23.77 | | (45) ~ (all_52_8 = e3) % 155.14/23.77 | | % 155.14/23.77 | | BETA: splitting (13) gives: % 155.14/23.77 | | % 155.14/23.77 | | Case 1: % 155.14/23.77 | | | % 155.14/23.77 | | | (46) all_54_2 = e1 % 155.14/23.77 | | | % 155.14/23.77 | | | REF_CLOSE: (3), (34), (46) are inconsistent by sub-proof #819. % 155.14/23.77 | | | % 155.14/23.77 | | Case 2: % 155.14/23.77 | | | % 155.14/23.77 | | | (47) ~ (all_54_2 = e1) % 155.14/23.77 | | | (48) all_54_2 = e3 | all_54_2 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | BETA: splitting (48) gives: % 155.14/23.77 | | | % 155.14/23.77 | | | Case 1: % 155.14/23.77 | | | | % 155.14/23.77 | | | | (49) all_54_2 = e2 % 155.14/23.77 | | | | % 155.14/23.77 | | | | COMBINE_EQS: (3), (49) imply: % 155.14/23.77 | | | | (50) all_52_8 = e2 % 155.14/23.77 | | | | % 155.14/23.77 | | | | SIMP: (50) implies: % 155.14/23.77 | | | | (51) all_52_8 = e2 % 155.14/23.77 | | | | % 155.14/23.77 | | | | REDUCE: (6), (51) imply: % 155.14/23.77 | | | | (52) ~ (all_10_2 = e2) % 155.14/23.77 | | | | % 155.14/23.77 | | | | SIMP: (52) implies: % 155.14/23.77 | | | | (53) ~ (all_10_2 = e2) % 155.14/23.77 | | | | % 155.14/23.77 | | | | BETA: splitting (29) gives: % 155.14/23.77 | | | | % 155.14/23.77 | | | | Case 1: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | (54) all_56_0 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | COMBINE_EQS: (22), (54) imply: % 155.14/23.77 | | | | | (55) all_10_2 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | SIMP: (55) implies: % 155.14/23.77 | | | | | (56) all_10_2 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | COMBINE_EQS: (18), (56) imply: % 155.14/23.77 | | | | | (57) all_58_28 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REDUCE: (53), (56) imply: % 155.14/23.77 | | | | | (58) ~ (e3 = e2) % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REDUCE: (17), (56) imply: % 155.14/23.77 | | | | | (59) op(e3, e3) = all_58_0 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REDUCE: (12), (56) imply: % 155.14/23.77 | | | | | (60) op(e3, e3) = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | BETA: splitting (8) gives: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | Case 1: % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | (61) all_58_28 = e2 % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | COMBINE_EQS: (57), (61) imply: % 155.14/23.77 | | | | | | (62) e3 = e2 % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | REDUCE: (58), (62) imply: % 155.14/23.77 | | | | | | (63) $false % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | CLOSE: (63) is inconsistent. % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | Case 2: % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | (64) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | BETA: splitting (64) gives: % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | Case 1: % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | (65) all_58_29 = e2 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | COMBINE_EQS: (15), (65) imply: % 155.14/23.77 | | | | | | | (66) all_8_2 = e2 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | REDUCE: (21), (66) imply: % 155.14/23.77 | | | | | | | (67) op(e2, e2) = all_8_1 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | REDUCE: (33), (66) imply: % 155.14/23.77 | | | | | | | (68) op(e2, e2) = all_58_9 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | REDUCE: (9), (66) imply: % 155.14/23.77 | | | | | | | (69) op(e2, e2) = e2 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | REF_CLOSE: (2), (16), (25), (37), (59), (60), (67), (68), (69) are % 155.14/23.77 | | | | | | | inconsistent by sub-proof #818. % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | Case 2: % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | (70) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | REF_CLOSE: (3), (10), (13), (23), (31), (32), (34), (45), (70) are % 155.14/23.77 | | | | | | | inconsistent by sub-proof #815. % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | End of split % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | End of split % 155.14/23.77 | | | | | % 155.14/23.77 | | | | Case 2: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | (71) ~ (all_56_0 = e3) % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REDUCE: (22), (71) imply: % 155.14/23.77 | | | | | (72) ~ (all_10_2 = e3) % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REF_CLOSE: (11), (14), (28), (53), (72) are inconsistent by sub-proof % 155.14/23.77 | | | | | #813. % 155.14/23.77 | | | | | % 155.14/23.77 | | | | End of split % 155.14/23.77 | | | | % 155.14/23.77 | | | Case 2: % 155.14/23.77 | | | | % 155.14/23.77 | | | | (73) all_54_2 = e3 % 155.14/23.77 | | | | % 155.14/23.77 | | | | REF_CLOSE: (3), (45), (73) are inconsistent by sub-proof #816. % 155.14/23.77 | | | | % 155.14/23.77 | | | End of split % 155.14/23.77 | | | % 155.14/23.77 | | End of split % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #813 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.77 (2) ~ (all_10_2 = e3) % 155.14/23.77 (3) ~ (all_10_2 = e1) % 155.14/23.77 (4) ~ (all_10_2 = e2) % 155.14/23.77 (5) all_54_0 = all_10_2 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (1) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (6) all_54_0 = e1 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #841. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (7) all_54_0 = e3 | all_54_0 = e2 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #814. % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #814 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_0 = e3 | all_54_0 = e2 % 155.14/23.77 (2) all_54_0 = all_10_2 % 155.14/23.77 (3) ~ (all_10_2 = e2) % 155.14/23.77 (4) ~ (all_10_2 = e3) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (1) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (5) all_54_0 = e2 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #822. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (6) all_54_0 = e3 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #827. % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #815 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_2 = all_52_8 % 155.14/23.77 (2) ~ (all_52_8 = all_6_2) % 155.14/23.77 (3) ~ (all_52_8 = e3) % 155.14/23.77 (4) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 % 155.14/23.77 (5) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.77 (6) ~ (all_52_8 = e1) % 155.14/23.77 (7) all_58_31 = e0 % 155.14/23.77 (8) ~ (all_52_8 = e0) % 155.14/23.77 (9) all_58_30 = all_6_2 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (4) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (10) all_54_2 = e1 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #819. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (11) all_54_2 = e3 | all_54_2 = e2 % 155.14/23.77 | | % 155.14/23.77 | | BETA: splitting (11) gives: % 155.14/23.77 | | % 155.14/23.77 | | Case 1: % 155.14/23.77 | | | % 155.14/23.77 | | | (12) all_54_2 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | COMBINE_EQS: (1), (12) imply: % 155.14/23.77 | | | (13) all_52_8 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | SIMP: (13) implies: % 155.14/23.77 | | | (14) all_52_8 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (2), (14) imply: % 155.14/23.77 | | | (15) ~ (all_6_2 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | SIMP: (15) implies: % 155.14/23.77 | | | (16) ~ (all_6_2 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (8), (14) imply: % 155.14/23.77 | | | (17) ~ (e2 = e0) % 155.14/23.77 | | | % 155.14/23.77 | | | REF_CLOSE: (5), (7), (9), (16), (17) are inconsistent by sub-proof #817. % 155.14/23.77 | | | % 155.14/23.77 | | Case 2: % 155.14/23.77 | | | % 155.14/23.77 | | | (18) all_54_2 = e3 % 155.14/23.77 | | | % 155.14/23.77 | | | REF_CLOSE: (1), (3), (18) are inconsistent by sub-proof #816. % 155.14/23.77 | | | % 155.14/23.77 | | End of split % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #816 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_2 = all_52_8 % 155.14/23.77 (2) all_54_2 = e3 % 155.14/23.77 (3) ~ (all_52_8 = e3) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | COMBINE_EQS: (1), (2) imply: % 155.14/23.77 | (4) all_52_8 = e3 % 155.14/23.77 | % 155.14/23.77 | SIMP: (4) implies: % 155.14/23.77 | (5) all_52_8 = e3 % 155.14/23.77 | % 155.14/23.77 | REDUCE: (3), (5) imply: % 155.14/23.77 | (6) $false % 155.14/23.77 | % 155.14/23.77 | CLOSE: (6) is inconsistent. % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #817 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.77 (2) ~ (e2 = e0) % 155.14/23.77 (3) all_58_31 = e0 % 155.14/23.77 (4) ~ (all_6_2 = e2) % 155.14/23.77 (5) all_58_30 = all_6_2 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (1) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (6) all_58_30 = e2 % 155.14/23.77 | | % 155.14/23.77 | | COMBINE_EQS: (5), (6) imply: % 155.14/23.77 | | (7) all_6_2 = e2 % 155.14/23.77 | | % 155.14/23.77 | | SIMP: (7) implies: % 155.14/23.77 | | (8) all_6_2 = e2 % 155.14/23.77 | | % 155.14/23.77 | | REDUCE: (4), (8) imply: % 155.14/23.77 | | (9) $false % 155.14/23.77 | | % 155.14/23.77 | | CLOSE: (9) is inconsistent. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (10) all_58_31 = e2 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #855. % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #818 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.77 (2) op(e2, e2) = all_8_1 % 155.14/23.77 (3) op(e3, e3) = all_58_0 % 155.14/23.77 (4) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.77 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.77 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.14/23.77 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.77 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.77 (all_58_27 = e0)) % 155.14/23.77 (5) all_58_18 = e1 % 155.14/23.77 (6) op(e2, e2) = e2 % 155.14/23.77 (7) all_58_27 = e0 % 155.14/23.77 (8) op(e2, e2) = all_58_9 % 155.14/23.77 (9) op(e3, e3) = e3 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | GROUND_INST: instantiating (1) with all_8_1, all_58_9, e2, e2, simplifying % 155.14/23.77 | with (2), (8) gives: % 155.14/23.77 | (10) all_58_9 = all_8_1 % 155.14/23.77 | % 155.14/23.77 | GROUND_INST: instantiating (1) with e2, all_58_9, e2, e2, simplifying with % 155.14/23.77 | (6), (8) gives: % 155.14/23.77 | (11) all_58_9 = e2 % 155.14/23.77 | % 155.14/23.77 | GROUND_INST: instantiating (1) with e3, all_58_0, e3, e3, simplifying with % 155.14/23.77 | (3), (9) gives: % 155.14/23.77 | (12) all_58_0 = e3 % 155.14/23.77 | % 155.14/23.77 | COMBINE_EQS: (10), (11) imply: % 155.14/23.77 | (13) all_8_1 = e2 % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (4) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (14) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.77 | | (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.77 | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 155.14/23.77 | | % 155.14/23.77 | | BETA: splitting (14) gives: % 155.14/23.77 | | % 155.14/23.77 | | Case 1: % 155.14/23.77 | | | % 155.14/23.77 | | | (15) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.77 | | | (all_58_5 = e0) % 155.14/23.77 | | | % 155.14/23.77 | | | ALPHA: (15) implies: % 155.14/23.77 | | | (16) ~ (all_58_0 = e3) % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (12), (16) imply: % 155.14/23.77 | | | (17) $false % 155.14/23.77 | | | % 155.14/23.77 | | | CLOSE: (17) is inconsistent. % 155.14/23.77 | | | % 155.14/23.77 | | Case 2: % 155.14/23.77 | | | % 155.14/23.77 | | | (18) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ (all_58_10 = e1) & ~ % 155.14/23.77 | | | (all_58_12 = e0) % 155.14/23.77 | | | % 155.14/23.77 | | | ALPHA: (18) implies: % 155.14/23.77 | | | (19) ~ (all_58_9 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (11), (19) imply: % 155.14/23.77 | | | (20) $false % 155.14/23.77 | | | % 155.14/23.77 | | | CLOSE: (20) is inconsistent. % 155.14/23.77 | | | % 155.14/23.77 | | End of split % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (21) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 155.14/23.77 | | ~ (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & % 155.14/23.77 | | ~ (all_58_25 = e1) & ~ (all_58_27 = e0)) % 155.14/23.77 | | % 155.14/23.77 | | BETA: splitting (21) gives: % 155.14/23.77 | | % 155.14/23.77 | | Case 1: % 155.14/23.77 | | | % 155.14/23.77 | | | (22) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & % 155.14/23.77 | | | ~ (all_58_19 = e0) % 155.14/23.77 | | | % 155.14/23.77 | | | ALPHA: (22) implies: % 155.14/23.77 | | | (23) ~ (all_58_18 = e1) % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (5), (23) imply: % 155.14/23.77 | | | (24) $false % 155.14/23.77 | | | % 155.14/23.77 | | | CLOSE: (24) is inconsistent. % 155.14/23.77 | | | % 155.14/23.77 | | Case 2: % 155.14/23.77 | | | % 155.14/23.77 | | | (25) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & % 155.14/23.77 | | | ~ (all_58_27 = e0) % 155.14/23.77 | | | % 155.14/23.77 | | | ALPHA: (25) implies: % 155.14/23.77 | | | (26) ~ (all_58_27 = e0) % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (7), (26) imply: % 155.14/23.77 | | | (27) $false % 155.14/23.77 | | | % 155.14/23.77 | | | CLOSE: (27) is inconsistent. % 155.14/23.77 | | | % 155.14/23.77 | | End of split % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #819 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_2 = all_52_8 % 155.14/23.77 (2) all_54_2 = e1 % 155.14/23.77 (3) ~ (all_52_8 = e1) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | COMBINE_EQS: (1), (2) imply: % 155.14/23.77 | (4) all_52_8 = e1 % 155.14/23.77 | % 155.14/23.77 | SIMP: (4) implies: % 155.14/23.77 | (5) all_52_8 = e1 % 155.14/23.77 | % 155.14/23.77 | REDUCE: (3), (5) imply: % 155.14/23.77 | (6) $false % 155.14/23.77 | % 155.14/23.77 | CLOSE: (6) is inconsistent. % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #820 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.77 (2) op(e3, e2) = e0 % 155.14/23.77 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.77 (4) ~ (all_10_2 = e3) % 155.14/23.77 (5) ~ (e3 = e1) % 155.14/23.77 (6) ~ (all_10_2 = e1) % 155.14/23.77 (7) all_58_29 = all_8_2 % 155.14/23.77 (8) op(e3, all_10_2) = all_58_0 % 155.14/23.77 (9) ~ (e3 = e0) % 155.14/23.77 (10) all_58_28 = all_10_2 % 155.14/23.77 (11) all_56_0 = e2 | all_56_2 = e2 | all_56_6 = e2 | all_56_12 = e2 % 155.14/23.77 (12) all_58_30 = e1 % 155.14/23.77 (13) op(all_8_2, e2) = all_8_1 % 155.14/23.77 (14) all_56_0 = all_10_2 % 155.14/23.77 (15) all_58_31 = e0 % 155.14/23.77 (16) ~ (all_8_1 = e0) % 155.14/23.77 (17) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 (18) all_54_0 = all_10_2 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (3) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (19) all_54_0 = e1 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (6), (18), (19) are inconsistent by sub-proof #841. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (20) all_54_0 = e3 | all_54_0 = e2 % 155.14/23.77 | | % 155.14/23.77 | | BETA: splitting (11) gives: % 155.14/23.77 | | % 155.14/23.77 | | Case 1: % 155.14/23.77 | | | % 155.14/23.77 | | | (21) all_56_0 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | COMBINE_EQS: (14), (21) imply: % 155.14/23.77 | | | (22) all_10_2 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | SIMP: (22) implies: % 155.14/23.77 | | | (23) all_10_2 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | COMBINE_EQS: (10), (23) imply: % 155.14/23.77 | | | (24) all_58_28 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (4), (23) imply: % 155.14/23.77 | | | (25) ~ (e3 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | SIMP: (25) implies: % 155.14/23.77 | | | (26) ~ (e3 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (8), (23) imply: % 155.14/23.77 | | | (27) op(e3, e2) = all_58_0 % 155.14/23.77 | | | % 155.14/23.77 | | | BETA: splitting (17) gives: % 155.14/23.77 | | | % 155.14/23.77 | | | Case 1: % 155.14/23.77 | | | | % 155.14/23.77 | | | | (28) all_58_28 = e3 % 155.14/23.77 | | | | % 155.14/23.77 | | | | REF_CLOSE: (24), (26), (28) are inconsistent by sub-proof #849. % 155.14/23.77 | | | | % 155.14/23.77 | | | Case 2: % 155.14/23.77 | | | | % 155.14/23.77 | | | | (29) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 | | | | % 155.14/23.77 | | | | BETA: splitting (29) gives: % 155.14/23.77 | | | | % 155.14/23.77 | | | | Case 1: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | (30) all_58_29 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | COMBINE_EQS: (7), (30) imply: % 155.14/23.77 | | | | | (31) all_8_2 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REDUCE: (13), (31) imply: % 155.14/23.77 | | | | | (32) op(e3, e2) = all_8_1 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REF_CLOSE: (1), (2), (16), (27), (32) are inconsistent by sub-proof % 155.14/23.77 | | | | | #823. % 155.14/23.77 | | | | | % 155.14/23.77 | | | | Case 2: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | (33) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REF_CLOSE: (5), (9), (12), (15), (33) are inconsistent by sub-proof % 155.14/23.77 | | | | | #848. % 155.14/23.77 | | | | | % 155.14/23.77 | | | | End of split % 155.14/23.77 | | | | % 155.14/23.77 | | | End of split % 155.14/23.77 | | | % 155.14/23.77 | | Case 2: % 155.14/23.77 | | | % 155.14/23.77 | | | (34) ~ (all_56_0 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | REF_CLOSE: (4), (14), (18), (20), (34) are inconsistent by sub-proof #821. % 155.14/23.77 | | | % 155.14/23.77 | | End of split % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #821 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_0 = e3 | all_54_0 = e2 % 155.14/23.77 (2) ~ (all_10_2 = e3) % 155.14/23.77 (3) ~ (all_56_0 = e2) % 155.14/23.77 (4) all_56_0 = all_10_2 % 155.14/23.77 (5) all_54_0 = all_10_2 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | REDUCE: (3), (4) imply: % 155.14/23.77 | (6) ~ (all_10_2 = e2) % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (1) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (7) all_54_0 = e2 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #822. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (8) all_54_0 = e3 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #827. % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #822 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_54_0 = all_10_2 % 155.14/23.77 (2) all_54_0 = e2 % 155.14/23.77 (3) ~ (all_10_2 = e2) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | COMBINE_EQS: (1), (2) imply: % 155.14/23.77 | (4) all_10_2 = e2 % 155.14/23.77 | % 155.14/23.77 | SIMP: (4) implies: % 155.14/23.77 | (5) all_10_2 = e2 % 155.14/23.77 | % 155.14/23.77 | REDUCE: (3), (5) imply: % 155.14/23.77 | (6) $false % 155.14/23.77 | % 155.14/23.77 | CLOSE: (6) is inconsistent. % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #823 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.77 (2) op(e3, e2) = e0 % 155.14/23.77 (3) op(e3, e2) = all_8_1 % 155.14/23.77 (4) op(e3, e2) = all_58_0 % 155.14/23.77 (5) ~ (all_8_1 = e0) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | GROUND_INST: instantiating (1) with e0, all_58_0, e2, e3, simplifying with % 155.14/23.77 | (2), (4) gives: % 155.14/23.77 | (6) all_58_0 = e0 % 155.14/23.77 | % 155.14/23.77 | GROUND_INST: instantiating (1) with all_8_1, all_58_0, e2, e3, simplifying % 155.14/23.77 | with (3), (4) gives: % 155.14/23.77 | (7) all_58_0 = all_8_1 % 155.14/23.77 | % 155.14/23.77 | COMBINE_EQS: (6), (7) imply: % 155.14/23.77 | (8) all_8_1 = e0 % 155.14/23.77 | % 155.14/23.77 | SIMP: (8) implies: % 155.14/23.77 | (9) all_8_1 = e0 % 155.14/23.77 | % 155.14/23.77 | REDUCE: (5), (9) imply: % 155.14/23.77 | (10) $false % 155.14/23.77 | % 155.14/23.77 | CLOSE: (10) is inconsistent. % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #824 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_58_31 = e0 % 155.14/23.77 (2) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.77 (3) ~ (e1 = e0) % 155.14/23.77 (4) ~ (all_6_2 = e1) % 155.14/23.77 (5) all_58_30 = all_6_2 % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (2) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (6) all_58_30 = e1 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #825. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (7) all_58_31 = e1 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #845. % 155.14/23.77 | | % 155.14/23.77 | End of split % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #825 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) all_58_30 = all_6_2 % 155.14/23.77 (2) all_58_30 = e1 % 155.14/23.77 (3) ~ (all_6_2 = e1) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | COMBINE_EQS: (1), (2) imply: % 155.14/23.77 | (4) all_6_2 = e1 % 155.14/23.77 | % 155.14/23.77 | SIMP: (4) implies: % 155.14/23.77 | (5) all_6_2 = e1 % 155.14/23.77 | % 155.14/23.77 | REDUCE: (3), (5) imply: % 155.14/23.77 | (6) $false % 155.14/23.77 | % 155.14/23.77 | CLOSE: (6) is inconsistent. % 155.14/23.77 | % 155.14/23.77 End of proof % 155.14/23.77 % 155.14/23.77 Sub-proof #826 shows that the following formulas are inconsistent: % 155.14/23.77 ---------------------------------------------------------------- % 155.14/23.77 (1) ~ (all_52_1 = e1) % 155.14/23.77 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.77 (3) op(e1, all_8_1) = all_8_0 % 155.14/23.77 (4) all_56_6 = e0 % 155.14/23.77 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 % 155.14/23.77 (6) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.14/23.77 (7) op(e2, e3) = all_52_1 % 155.14/23.77 (8) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 % 155.14/23.77 (9) ~ (all_10_2 = e3) % 155.14/23.77 (10) ~ (all_8_1 = all_6_2) % 155.14/23.77 (11) all_56_12 = e1 % 155.14/23.77 (12) ~ (all_10_2 = e1) % 155.14/23.77 (13) all_58_29 = e1 % 155.14/23.77 (14) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ (all_58_3 = e1) & ~ % 155.14/23.77 (all_58_5 = e0)) | ( ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.77 (all_58_10 = e1) & ~ (all_58_12 = e0)) | ( ~ (all_58_14 = e3) & ~ % 155.14/23.77 (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.77 (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.77 (all_58_27 = e0)) % 155.14/23.77 (15) all_56_2 = all_52_1 % 155.14/23.77 (16) op(e1, e2) = all_8_1 % 155.14/23.77 (17) all_58_28 = all_10_2 % 155.14/23.77 (18) ~ (all_52_1 = e0) % 155.14/23.77 (19) all_58_31 = e0 % 155.14/23.77 (20) all_54_9 = all_8_1 % 155.14/23.77 (21) all_58_27 = e0 % 155.14/23.77 (22) all_58_3 = e1 % 155.14/23.77 (23) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 (24) all_56_2 = e3 | all_56_3 = e3 | all_56_5 = e3 | all_56_10 = e3 % 155.14/23.77 (25) all_58_16 = all_8_0 % 155.14/23.77 (26) all_54_0 = all_10_2 % 155.14/23.77 (27) ~ (all_8_1 = e1) % 155.14/23.77 (28) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.77 (29) all_58_30 = all_6_2 % 155.14/23.77 (30) op(e2, all_52_1) = all_58_7 % 155.14/23.77 (31) all_54_4 = all_52_1 % 155.14/23.77 (32) ~ (all_52_1 = all_10_2) % 155.14/23.77 % 155.14/23.77 Begin of proof % 155.14/23.77 | % 155.14/23.77 | BETA: splitting (5) gives: % 155.14/23.77 | % 155.14/23.77 | Case 1: % 155.14/23.77 | | % 155.14/23.77 | | (33) all_54_0 = e1 % 155.14/23.77 | | % 155.14/23.77 | | REF_CLOSE: (12), (26), (33) are inconsistent by sub-proof #841. % 155.14/23.77 | | % 155.14/23.77 | Case 2: % 155.14/23.77 | | % 155.14/23.77 | | (34) all_54_0 = e3 | all_54_0 = e2 % 155.14/23.77 | | % 155.14/23.77 | | BETA: splitting (34) gives: % 155.14/23.77 | | % 155.14/23.77 | | Case 1: % 155.14/23.77 | | | % 155.14/23.77 | | | (35) all_54_0 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | COMBINE_EQS: (26), (35) imply: % 155.14/23.77 | | | (36) all_10_2 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | SIMP: (36) implies: % 155.14/23.77 | | | (37) all_10_2 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | COMBINE_EQS: (17), (37) imply: % 155.14/23.77 | | | (38) all_58_28 = e2 % 155.14/23.77 | | | % 155.14/23.77 | | | REDUCE: (32), (37) imply: % 155.14/23.77 | | | (39) ~ (all_52_1 = e2) % 155.14/23.77 | | | % 155.14/23.77 | | | BETA: splitting (24) gives: % 155.14/23.77 | | | % 155.14/23.77 | | | Case 1: % 155.14/23.77 | | | | % 155.14/23.77 | | | | (40) all_56_2 = e3 % 155.14/23.77 | | | | % 155.14/23.77 | | | | COMBINE_EQS: (15), (40) imply: % 155.14/23.77 | | | | (41) all_52_1 = e3 % 155.14/23.77 | | | | % 155.14/23.77 | | | | REDUCE: (39), (41) imply: % 155.14/23.77 | | | | (42) ~ (e3 = e2) % 155.14/23.77 | | | | % 155.14/23.77 | | | | REDUCE: (1), (41) imply: % 155.14/23.77 | | | | (43) ~ (e3 = e1) % 155.14/23.77 | | | | % 155.14/23.77 | | | | REDUCE: (18), (41) imply: % 155.14/23.77 | | | | (44) ~ (e3 = e0) % 155.14/23.77 | | | | % 155.14/23.77 | | | | REDUCE: (30), (41) imply: % 155.14/23.77 | | | | (45) op(e2, e3) = all_58_7 % 155.14/23.77 | | | | % 155.14/23.77 | | | | REDUCE: (7), (41) imply: % 155.14/23.77 | | | | (46) op(e2, e3) = e3 % 155.14/23.77 | | | | % 155.14/23.77 | | | | BETA: splitting (23) gives: % 155.14/23.77 | | | | % 155.14/23.77 | | | | Case 1: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | (47) all_58_28 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | COMBINE_EQS: (38), (47) imply: % 155.14/23.77 | | | | | (48) e3 = e2 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | REF_CLOSE: (4), (11), (28), (40), (42), (43), (44), (48) are % 155.14/23.77 | | | | | inconsistent by sub-proof #836. % 155.14/23.77 | | | | | % 155.14/23.77 | | | | Case 2: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | (49) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | BETA: splitting (49) gives: % 155.14/23.77 | | | | | % 155.14/23.77 | | | | | Case 1: % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | (50) all_58_29 = e3 % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | COMBINE_EQS: (13), (50) imply: % 155.14/23.77 | | | | | | (51) e3 = e1 % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | REDUCE: (43), (51) imply: % 155.14/23.77 | | | | | | (52) $false % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | CLOSE: (52) is inconsistent. % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | Case 2: % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | (53) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | BETA: splitting (53) gives: % 155.14/23.77 | | | | | | % 155.14/23.77 | | | | | | Case 1: % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | (54) all_58_30 = e3 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | COMBINE_EQS: (29), (54) imply: % 155.14/23.77 | | | | | | | (55) all_6_2 = e3 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | SIMP: (55) implies: % 155.14/23.77 | | | | | | | (56) all_6_2 = e3 % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | REDUCE: (10), (56) imply: % 155.14/23.77 | | | | | | | (57) ~ (all_8_1 = e3) % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | BETA: splitting (8) gives: % 155.14/23.77 | | | | | | | % 155.14/23.77 | | | | | | | Case 1: % 155.14/23.77 | | | | | | | | % 155.14/23.77 | | | | | | | | (58) all_54_9 = e1 % 155.14/23.77 | | | | | | | | % 155.14/23.77 | | | | | | | | REF_CLOSE: (20), (27), (58) are inconsistent by sub-proof #835. % 155.14/23.77 | | | | | | | | % 155.14/23.77 | | | | | | | Case 2: % 155.14/23.77 | | | | | | | | % 155.14/23.77 | | | | | | | | (59) all_54_9 = e3 | all_54_9 = e2 % 155.14/23.77 | | | | | | | | % 155.14/23.77 | | | | | | | | BETA: splitting (59) gives: % 155.14/23.77 | | | | | | | | % 155.14/23.77 | | | | | | | | Case 1: % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | (60) all_54_9 = e2 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | COMBINE_EQS: (20), (60) imply: % 155.14/23.77 | | | | | | | | | (61) all_8_1 = e2 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | SIMP: (61) implies: % 155.14/23.77 | | | | | | | | | (62) all_8_1 = e2 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | REDUCE: (3), (62) imply: % 155.14/23.77 | | | | | | | | | (63) op(e1, e2) = all_8_0 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | REDUCE: (16), (62) imply: % 155.14/23.77 | | | | | | | | | (64) op(e1, e2) = e2 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | GROUND_INST: instantiating (2) with e2, all_8_0, e2, e1, % 155.14/23.77 | | | | | | | | | simplifying with (63), (64) gives: % 155.14/23.77 | | | | | | | | | (65) all_8_0 = e2 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | GROUND_INST: instantiating (2) with e3, all_58_7, e3, e2, % 155.14/23.77 | | | | | | | | | simplifying with (45), (46) gives: % 155.14/23.77 | | | | | | | | | (66) all_58_7 = e3 % 155.14/23.77 | | | | | | | | | % 155.14/23.77 | | | | | | | | | COMBINE_EQS: (25), (65) imply: % 155.14/23.78 | | | | | | | | | (67) all_58_16 = e2 % 155.14/23.78 | | | | | | | | | % 155.14/23.78 | | | | | | | | | BETA: splitting (14) gives: % 155.14/23.78 | | | | | | | | | % 155.14/23.78 | | | | | | | | | Case 1: % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | (68) ( ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 155.14/23.78 | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0)) | ( ~ % 155.14/23.78 | | | | | | | | | | (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.78 | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0)) % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | BETA: splitting (68) gives: % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | Case 1: % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | (69) ~ (all_58_0 = e3) & ~ (all_58_1 = e2) & ~ % 155.14/23.78 | | | | | | | | | | | (all_58_3 = e1) & ~ (all_58_5 = e0) % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | ALPHA: (69) implies: % 155.14/23.78 | | | | | | | | | | | (70) ~ (all_58_3 = e1) % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | REDUCE: (22), (70) imply: % 155.14/23.78 | | | | | | | | | | | (71) $false % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | CLOSE: (71) is inconsistent. % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | Case 2: % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | (72) ~ (all_58_7 = e3) & ~ (all_58_9 = e2) & ~ % 155.14/23.78 | | | | | | | | | | | (all_58_10 = e1) & ~ (all_58_12 = e0) % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | ALPHA: (72) implies: % 155.14/23.78 | | | | | | | | | | | (73) ~ (all_58_7 = e3) % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | REDUCE: (66), (73) imply: % 155.14/23.78 | | | | | | | | | | | (74) $false % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | | CLOSE: (74) is inconsistent. % 155.14/23.78 | | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | End of split % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | Case 2: % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | (75) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ % 155.14/23.78 | | | | | | | | | | (all_58_18 = e1) & ~ (all_58_19 = e0)) | ( ~ % 155.14/23.78 | | | | | | | | | | (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 155.14/23.78 | | | | | | | | | | (all_58_25 = e1) & ~ (all_58_27 = e0)) % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | | REF_CLOSE: (21), (67), (75) are inconsistent by sub-proof % 155.14/23.78 | | | | | | | | | | #834. % 155.14/23.78 | | | | | | | | | | % 155.14/23.78 | | | | | | | | | End of split % 155.14/23.78 | | | | | | | | | % 155.14/23.78 | | | | | | | | Case 2: % 155.14/23.78 | | | | | | | | | % 155.14/23.78 | | | | | | | | | (76) all_54_9 = e3 % 155.14/23.78 | | | | | | | | | % 155.14/23.78 | | | | | | | | | REF_CLOSE: (20), (57), (76) are inconsistent by sub-proof % 155.14/23.78 | | | | | | | | | #833. % 155.14/23.78 | | | | | | | | | % 155.14/23.78 | | | | | | | | End of split % 155.14/23.78 | | | | | | | | % 155.14/23.78 | | | | | | | End of split % 155.14/23.78 | | | | | | | % 155.14/23.78 | | | | | | Case 2: % 155.14/23.78 | | | | | | | % 155.14/23.78 | | | | | | | (77) all_58_31 = e3 % 155.14/23.78 | | | | | | | % 155.14/23.78 | | | | | | | COMBINE_EQS: (19), (77) imply: % 155.14/23.78 | | | | | | | (78) e3 = e0 % 155.14/23.78 | | | | | | | % 155.14/23.78 | | | | | | | REDUCE: (44), (78) imply: % 155.14/23.78 | | | | | | | (79) $false % 155.14/23.78 | | | | | | | % 155.14/23.78 | | | | | | | CLOSE: (79) is inconsistent. % 155.14/23.78 | | | | | | | % 155.14/23.78 | | | | | | End of split % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | End of split % 155.14/23.78 | | | | | % 155.14/23.78 | | | | End of split % 155.14/23.78 | | | | % 155.14/23.78 | | | Case 2: % 155.14/23.78 | | | | % 155.14/23.78 | | | | (80) ~ (all_56_2 = e3) % 155.14/23.78 | | | | % 155.14/23.78 | | | | REDUCE: (15), (80) imply: % 155.14/23.78 | | | | (81) ~ (all_52_1 = e3) % 155.14/23.78 | | | | % 155.14/23.78 | | | | REF_CLOSE: (1), (6), (31), (39), (81) are inconsistent by sub-proof % 155.14/23.78 | | | | #828. % 155.14/23.78 | | | | % 155.14/23.78 | | | End of split % 155.14/23.78 | | | % 155.14/23.78 | | Case 2: % 155.14/23.78 | | | % 155.14/23.78 | | | (82) all_54_0 = e3 % 155.14/23.78 | | | % 155.14/23.78 | | | REF_CLOSE: (9), (26), (82) are inconsistent by sub-proof #827. % 155.14/23.78 | | | % 155.14/23.78 | | End of split % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #827 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_0 = all_10_2 % 155.14/23.78 (2) all_54_0 = e3 % 155.14/23.78 (3) ~ (all_10_2 = e3) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_10_2 = e3 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_10_2 = e3 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #828 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ~ (all_52_1 = e1) % 155.14/23.78 (2) ~ (all_52_1 = e3) % 155.14/23.78 (3) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 % 155.14/23.78 (4) ~ (all_52_1 = e2) % 155.14/23.78 (5) all_54_4 = all_52_1 % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (3) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (6) all_54_4 = e1 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #832. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (7) all_54_4 = e3 | all_54_4 = e2 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #829. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #829 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_4 = e3 | all_54_4 = e2 % 155.14/23.78 (2) all_54_4 = all_52_1 % 155.14/23.78 (3) ~ (all_52_1 = e2) % 155.14/23.78 (4) ~ (all_52_1 = e3) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (1) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (5) all_54_4 = e2 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #831. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (6) all_54_4 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #830. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #830 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_4 = all_52_1 % 155.14/23.78 (2) all_54_4 = e3 % 155.14/23.78 (3) ~ (all_52_1 = e3) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_52_1 = e3 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_52_1 = e3 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #831 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_4 = all_52_1 % 155.14/23.78 (2) all_54_4 = e2 % 155.14/23.78 (3) ~ (all_52_1 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_52_1 = e2 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_52_1 = e2 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #832 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_4 = all_52_1 % 155.14/23.78 (2) all_54_4 = e1 % 155.14/23.78 (3) ~ (all_52_1 = e1) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_52_1 = e1 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_52_1 = e1 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #833 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_9 = all_8_1 % 155.14/23.78 (2) all_54_9 = e3 % 155.14/23.78 (3) ~ (all_8_1 = e3) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_8_1 = e3 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_8_1 = e3 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #834 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ( ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 155.14/23.78 (all_58_19 = e0)) | ( ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ % 155.14/23.78 (all_58_25 = e1) & ~ (all_58_27 = e0)) % 155.14/23.78 (2) all_58_16 = e2 % 155.14/23.78 (3) all_58_27 = e0 % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (1) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (4) ~ (all_58_14 = e3) & ~ (all_58_16 = e2) & ~ (all_58_18 = e1) & ~ % 155.14/23.78 | | (all_58_19 = e0) % 155.14/23.78 | | % 155.14/23.78 | | ALPHA: (4) implies: % 155.14/23.78 | | (5) ~ (all_58_16 = e2) % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (2), (5) imply: % 155.14/23.78 | | (6) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (6) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (7) ~ (all_58_21 = e3) & ~ (all_58_23 = e2) & ~ (all_58_25 = e1) & ~ % 155.14/23.78 | | (all_58_27 = e0) % 155.14/23.78 | | % 155.14/23.78 | | ALPHA: (7) implies: % 155.14/23.78 | | (8) ~ (all_58_27 = e0) % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (3), (8) imply: % 155.14/23.78 | | (9) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (9) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #835 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_9 = all_8_1 % 155.14/23.78 (2) all_54_9 = e1 % 155.14/23.78 (3) ~ (all_8_1 = e1) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_8_1 = e1 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_8_1 = e1 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #836 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_56_6 = e0 % 155.14/23.78 (2) ~ (e3 = e1) % 155.14/23.78 (3) e3 = e2 % 155.14/23.78 (4) all_56_12 = e1 % 155.14/23.78 (5) ~ (e3 = e0) % 155.14/23.78 (6) all_56_2 = e3 % 155.14/23.78 (7) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.78 (8) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | SIMP: (3) implies: % 155.14/23.78 | (9) e3 = e2 % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (6), (9) imply: % 155.14/23.78 | (10) all_56_2 = e2 % 155.14/23.78 | % 155.14/23.78 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10) are inconsistent by sub-proof % 155.14/23.78 | #837. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #837 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_56_6 = e0 % 155.14/23.78 (2) ~ (e3 = e1) % 155.14/23.78 (3) all_56_12 = e1 % 155.14/23.78 (4) all_56_2 = e2 % 155.14/23.78 (5) ~ (e3 = e0) % 155.14/23.78 (6) all_56_2 = e3 | all_56_6 = e3 | all_56_12 = e3 % 155.14/23.78 (7) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (6) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (8) all_56_2 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (4), (7), (8) are inconsistent by sub-proof #840. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (9) all_56_6 = e3 | all_56_12 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (1), (2), (3), (5), (9) are inconsistent by sub-proof #838. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #838 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_56_6 = e0 % 155.14/23.78 (2) all_56_6 = e3 | all_56_12 = e3 % 155.14/23.78 (3) ~ (e3 = e1) % 155.14/23.78 (4) all_56_12 = e1 % 155.14/23.78 (5) ~ (e3 = e0) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (2) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (6) all_56_6 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #839. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (7) all_56_12 = e3 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (4), (7) imply: % 155.14/23.78 | | (8) e3 = e1 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (3), (8) imply: % 155.14/23.78 | | (9) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (9) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #839 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_56_6 = e3 % 155.14/23.78 (2) all_56_6 = e0 % 155.14/23.78 (3) ~ (e3 = e0) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e3 = e0 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e3 = e0 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #840 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_56_2 = e3 % 155.14/23.78 (2) all_56_2 = e2 % 155.14/23.78 (3) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e3 = e2 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e3 = e2 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #841 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_0 = all_10_2 % 155.14/23.78 (2) all_54_0 = e1 % 155.14/23.78 (3) ~ (all_10_2 = e1) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_10_2 = e1 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_10_2 = e1 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #842 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 155.14/23.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 155.14/23.78 (2) op(all_6_2, e1) = all_6_1 % 155.14/23.78 (3) ~ (all_6_1 = e0) % 155.14/23.78 (4) all_6_2 = e2 % 155.14/23.78 (5) op(e2, e1) = e0 % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | REDUCE: (2), (4) imply: % 155.14/23.78 | (6) op(e2, e1) = all_6_1 % 155.14/23.78 | % 155.14/23.78 | GROUND_INST: instantiating (1) with e0, all_6_1, e1, e2, simplifying with (5), % 155.14/23.78 | (6) gives: % 155.14/23.78 | (7) all_6_1 = e0 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (7) imply: % 155.14/23.78 | (8) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (8) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #843 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_56_6 = e0 % 155.14/23.78 (2) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (3) ~ (e3 = e1) % 155.14/23.78 (4) ~ (e2 = e1) % 155.14/23.78 (5) all_58_29 = e1 % 155.14/23.78 (6) ~ (e3 = e0) % 155.14/23.78 (7) all_56_6 = e1 % 155.14/23.78 (8) ~ (e2 = e0) % 155.14/23.78 (9) all_58_31 = e0 % 155.14/23.78 (10) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (11) ~ (e1 = e0) % 155.14/23.78 (12) all_58_30 = all_6_2 % 155.14/23.78 (13) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.78 (14) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (7) imply: % 155.14/23.78 | (15) e1 = e0 % 155.14/23.78 | % 155.14/23.78 | SIMP: (15) implies: % 155.14/23.78 | (16) e1 = e0 % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (5), (16) imply: % 155.14/23.78 | (17) all_58_29 = e0 % 155.14/23.78 | % 155.14/23.78 | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14), (17) % 155.14/23.78 | are inconsistent by sub-proof #844. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #844 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (2) ~ (e3 = e1) % 155.14/23.78 (3) all_58_29 = e0 % 155.14/23.78 (4) ~ (e2 = e1) % 155.14/23.78 (5) ~ (e3 = e0) % 155.14/23.78 (6) ~ (e2 = e0) % 155.14/23.78 (7) all_58_31 = e0 % 155.14/23.78 (8) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (9) ~ (e1 = e0) % 155.14/23.78 (10) all_58_30 = all_6_2 % 155.14/23.78 (11) all_58_28 = e1 | all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.78 (12) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (11) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (13) all_58_28 = e1 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12), (13) are % 155.14/23.78 | | inconsistent by sub-proof #850. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (14) all_58_29 = e1 | all_58_30 = e1 | all_58_31 = e1 % 155.14/23.78 | | % 155.14/23.78 | | BETA: splitting (14) gives: % 155.14/23.78 | | % 155.14/23.78 | | Case 1: % 155.14/23.78 | | | % 155.14/23.78 | | | (15) all_58_29 = e1 % 155.14/23.78 | | | % 155.14/23.78 | | | COMBINE_EQS: (3), (15) imply: % 155.14/23.78 | | | (16) e1 = e0 % 155.14/23.78 | | | % 155.14/23.78 | | | REDUCE: (9), (16) imply: % 155.14/23.78 | | | (17) $false % 155.14/23.78 | | | % 155.14/23.78 | | | CLOSE: (17) is inconsistent. % 155.14/23.78 | | | % 155.14/23.78 | | Case 2: % 155.14/23.78 | | | % 155.14/23.78 | | | (18) ~ (all_58_29 = e1) % 155.14/23.78 | | | (19) all_58_30 = e1 | all_58_31 = e1 % 155.14/23.78 | | | % 155.14/23.78 | | | REDUCE: (3), (18) imply: % 155.14/23.78 | | | (20) ~ (e1 = e0) % 155.14/23.78 | | | % 155.14/23.78 | | | BETA: splitting (19) gives: % 155.14/23.78 | | | % 155.14/23.78 | | | Case 1: % 155.14/23.78 | | | | % 155.14/23.78 | | | | (21) all_58_30 = e1 % 155.14/23.78 | | | | % 155.14/23.78 | | | | COMBINE_EQS: (10), (21) imply: % 155.14/23.78 | | | | (22) all_6_2 = e1 % 155.14/23.78 | | | | % 155.14/23.78 | | | | BETA: splitting (1) gives: % 155.14/23.78 | | | | % 155.14/23.78 | | | | Case 1: % 155.14/23.78 | | | | | % 155.14/23.78 | | | | | (23) all_58_28 = e2 % 155.14/23.78 | | | | | % 155.14/23.78 | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (12), (21), (23) are inconsistent % 155.14/23.78 | | | | | by sub-proof #847. % 155.14/23.78 | | | | | % 155.14/23.78 | | | | Case 2: % 155.14/23.78 | | | | | % 155.14/23.78 | | | | | (24) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 | | | | | % 155.14/23.78 | | | | | BETA: splitting (24) gives: % 155.14/23.78 | | | | | % 155.14/23.78 | | | | | Case 1: % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | | (25) all_58_29 = e2 % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | | COMBINE_EQS: (3), (25) imply: % 155.14/23.78 | | | | | | (26) e2 = e0 % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | | REDUCE: (6), (26) imply: % 155.14/23.78 | | | | | | (27) $false % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | | CLOSE: (27) is inconsistent. % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | Case 2: % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | | (28) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | | REF_CLOSE: (4), (6), (7), (21), (28) are inconsistent by sub-proof % 155.14/23.78 | | | | | | #846. % 155.14/23.78 | | | | | | % 155.14/23.78 | | | | | End of split % 155.14/23.78 | | | | | % 155.14/23.78 | | | | End of split % 155.14/23.78 | | | | % 155.14/23.78 | | | Case 2: % 155.14/23.78 | | | | % 155.14/23.78 | | | | (29) all_58_31 = e1 % 155.14/23.78 | | | | % 155.14/23.78 | | | | REF_CLOSE: (7), (9), (29) are inconsistent by sub-proof #845. % 155.14/23.78 | | | | % 155.14/23.78 | | | End of split % 155.14/23.78 | | | % 155.14/23.78 | | End of split % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #845 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_31 = e1 % 155.14/23.78 (2) all_58_31 = e0 % 155.14/23.78 (3) ~ (e1 = e0) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e1 = e0 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e1 = e0 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #846 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ~ (e2 = e1) % 155.14/23.78 (2) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (3) all_58_30 = e1 % 155.14/23.78 (4) ~ (e2 = e0) % 155.14/23.78 (5) all_58_31 = e0 % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (2) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (6) all_58_30 = e2 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (3), (6) imply: % 155.14/23.78 | | (7) e2 = e1 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (1), (7) imply: % 155.14/23.78 | | (8) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (8) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (9) all_58_31 = e2 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (5), (9) imply: % 155.14/23.78 | | (10) e2 = e0 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (4), (10) imply: % 155.14/23.78 | | (11) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (11) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #847 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ~ (e3 = e1) % 155.14/23.78 (2) all_58_29 = e0 % 155.14/23.78 (3) ~ (e3 = e0) % 155.14/23.78 (4) all_58_30 = e1 % 155.14/23.78 (5) all_58_31 = e0 % 155.14/23.78 (6) all_58_28 = e2 % 155.14/23.78 (7) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (8) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (7) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (9) all_58_28 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (6), (8), (9) are inconsistent by sub-proof #849. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (10) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 | | % 155.14/23.78 | | BETA: splitting (10) gives: % 155.14/23.78 | | % 155.14/23.78 | | Case 1: % 155.14/23.78 | | | % 155.14/23.78 | | | (11) all_58_29 = e3 % 155.14/23.78 | | | % 155.14/23.78 | | | COMBINE_EQS: (2), (11) imply: % 155.14/23.78 | | | (12) e3 = e0 % 155.14/23.78 | | | % 155.14/23.78 | | | REDUCE: (3), (12) imply: % 155.14/23.78 | | | (13) $false % 155.14/23.78 | | | % 155.14/23.78 | | | CLOSE: (13) is inconsistent. % 155.14/23.78 | | | % 155.14/23.78 | | Case 2: % 155.14/23.78 | | | % 155.14/23.78 | | | (14) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 | | | % 155.14/23.78 | | | REF_CLOSE: (1), (3), (4), (5), (14) are inconsistent by sub-proof #848. % 155.14/23.78 | | | % 155.14/23.78 | | End of split % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #848 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ~ (e3 = e1) % 155.14/23.78 (2) ~ (e3 = e0) % 155.14/23.78 (3) all_58_30 = e1 % 155.14/23.78 (4) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (5) all_58_31 = e0 % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (4) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (6) all_58_30 = e3 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (3), (6) imply: % 155.14/23.78 | | (7) e3 = e1 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (1), (7) imply: % 155.14/23.78 | | (8) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (8) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (9) all_58_31 = e3 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (5), (9) imply: % 155.14/23.78 | | (10) e3 = e0 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (2), (10) imply: % 155.14/23.78 | | (11) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (11) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #849 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_28 = e3 % 155.14/23.78 (2) all_58_28 = e2 % 155.14/23.78 (3) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e3 = e2 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e3 = e2 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #850 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_28 = e2 | all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (2) ~ (e3 = e1) % 155.14/23.78 (3) all_58_28 = e1 % 155.14/23.78 (4) all_58_29 = e0 % 155.14/23.78 (5) ~ (e2 = e1) % 155.14/23.78 (6) ~ (e3 = e0) % 155.14/23.78 (7) ~ (e2 = e0) % 155.14/23.78 (8) all_58_31 = e0 % 155.14/23.78 (9) all_58_28 = e3 | all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (10) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (9) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (11) all_58_28 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #857. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (12) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 | | % 155.14/23.78 | | BETA: splitting (1) gives: % 155.14/23.78 | | % 155.14/23.78 | | Case 1: % 155.14/23.78 | | | % 155.14/23.78 | | | (13) all_58_28 = e2 % 155.14/23.78 | | | % 155.14/23.78 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #856. % 155.14/23.78 | | | % 155.14/23.78 | | Case 2: % 155.14/23.78 | | | % 155.14/23.78 | | | (14) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 | | | % 155.14/23.78 | | | REF_CLOSE: (4), (6), (7), (8), (10), (12), (14) are inconsistent by % 155.14/23.78 | | | sub-proof #851. % 155.14/23.78 | | | % 155.14/23.78 | | End of split % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #851 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_29 = e0 % 155.14/23.78 (2) ~ (e3 = e0) % 155.14/23.78 (3) all_58_29 = e3 | all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (4) ~ (e2 = e0) % 155.14/23.78 (5) all_58_29 = e2 | all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (6) all_58_31 = e0 % 155.14/23.78 (7) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (5) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (8) all_58_29 = e2 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (1), (8) imply: % 155.14/23.78 | | (9) e2 = e0 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (4), (9) imply: % 155.14/23.78 | | (10) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (10) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (11) ~ (all_58_29 = e2) % 155.14/23.78 | | (12) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (1), (11) imply: % 155.14/23.78 | | (13) ~ (e2 = e0) % 155.14/23.78 | | % 155.14/23.78 | | BETA: splitting (3) gives: % 155.14/23.78 | | % 155.14/23.78 | | Case 1: % 155.14/23.78 | | | % 155.14/23.78 | | | (14) all_58_29 = e3 % 155.14/23.78 | | | % 155.14/23.78 | | | COMBINE_EQS: (1), (14) imply: % 155.14/23.78 | | | (15) e3 = e0 % 155.14/23.78 | | | % 155.14/23.78 | | | REDUCE: (2), (15) imply: % 155.14/23.78 | | | (16) $false % 155.14/23.78 | | | % 155.14/23.78 | | | CLOSE: (16) is inconsistent. % 155.14/23.78 | | | % 155.14/23.78 | | Case 2: % 155.14/23.78 | | | % 155.14/23.78 | | | (17) ~ (all_58_29 = e3) % 155.14/23.78 | | | (18) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 | | | % 155.14/23.78 | | | REDUCE: (1), (17) imply: % 155.14/23.78 | | | (19) ~ (e3 = e0) % 155.14/23.78 | | | % 155.14/23.78 | | | REF_CLOSE: (2), (4), (6), (7), (12), (18) are inconsistent by sub-proof % 155.14/23.78 | | | #852. % 155.14/23.78 | | | % 155.14/23.78 | | End of split % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #852 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) ~ (e3 = e0) % 155.14/23.78 (2) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (3) all_58_30 = e3 | all_58_31 = e3 % 155.14/23.78 (4) ~ (e2 = e0) % 155.14/23.78 (5) all_58_31 = e0 % 155.14/23.78 (6) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (3) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (7) all_58_30 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (2), (4), (5), (6), (7) are inconsistent by sub-proof #854. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (8) all_58_31 = e3 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #853. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #853 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_31 = e3 % 155.14/23.78 (2) all_58_31 = e0 % 155.14/23.78 (3) ~ (e3 = e0) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e3 = e0 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e3 = e0 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #854 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_30 = e3 % 155.14/23.78 (2) all_58_30 = e2 | all_58_31 = e2 % 155.14/23.78 (3) ~ (e2 = e0) % 155.14/23.78 (4) all_58_31 = e0 % 155.14/23.78 (5) ~ (e3 = e2) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | BETA: splitting (2) gives: % 155.14/23.78 | % 155.14/23.78 | Case 1: % 155.14/23.78 | | % 155.14/23.78 | | (6) all_58_30 = e2 % 155.14/23.78 | | % 155.14/23.78 | | COMBINE_EQS: (1), (6) imply: % 155.14/23.78 | | (7) e3 = e2 % 155.14/23.78 | | % 155.14/23.78 | | REDUCE: (5), (7) imply: % 155.14/23.78 | | (8) $false % 155.14/23.78 | | % 155.14/23.78 | | CLOSE: (8) is inconsistent. % 155.14/23.78 | | % 155.14/23.78 | Case 2: % 155.14/23.78 | | % 155.14/23.78 | | (9) all_58_31 = e2 % 155.14/23.78 | | % 155.14/23.78 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #855. % 155.14/23.78 | | % 155.14/23.78 | End of split % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #855 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_31 = e2 % 155.14/23.78 (2) all_58_31 = e0 % 155.14/23.78 (3) ~ (e2 = e0) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e2 = e0 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e2 = e0 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #856 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_28 = e2 % 155.14/23.78 (2) all_58_28 = e1 % 155.14/23.78 (3) ~ (e2 = e1) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e2 = e1 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e2 = e1 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #857 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_28 = e3 % 155.14/23.78 (2) all_58_28 = e1 % 155.14/23.78 (3) ~ (e3 = e1) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) e3 = e1 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) e3 = e1 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #858 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_58_28 = all_10_2 % 155.14/23.78 (2) all_58_28 = e1 % 155.14/23.78 (3) ~ (all_10_2 = e1) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.78 | % 155.14/23.78 | COMBINE_EQS: (1), (2) imply: % 155.14/23.78 | (4) all_10_2 = e1 % 155.14/23.78 | % 155.14/23.78 | SIMP: (4) implies: % 155.14/23.78 | (5) all_10_2 = e1 % 155.14/23.78 | % 155.14/23.78 | REDUCE: (3), (5) imply: % 155.14/23.78 | (6) $false % 155.14/23.78 | % 155.14/23.78 | CLOSE: (6) is inconsistent. % 155.14/23.78 | % 155.14/23.78 End of proof % 155.14/23.78 % 155.14/23.78 Sub-proof #859 shows that the following formulas are inconsistent: % 155.14/23.78 ---------------------------------------------------------------- % 155.14/23.78 (1) all_54_4 = all_52_1 % 155.14/23.78 (2) all_54_4 = e0 % 155.14/23.78 (3) ~ (all_52_1 = e0) % 155.14/23.78 % 155.14/23.78 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_52_1 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_52_1 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % 155.14/23.79 Sub-proof #860 shows that the following formulas are inconsistent: % 155.14/23.79 ---------------------------------------------------------------- % 155.14/23.79 (1) all_54_2 = all_52_8 % 155.14/23.79 (2) all_54_2 = e0 % 155.14/23.79 (3) ~ (all_52_8 = e0) % 155.14/23.79 % 155.14/23.79 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_52_8 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_52_8 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % 155.14/23.79 Sub-proof #861 shows that the following formulas are inconsistent: % 155.14/23.79 ---------------------------------------------------------------- % 155.14/23.79 (1) all_54_0 = all_10_2 % 155.14/23.79 (2) all_54_0 = e0 % 155.14/23.79 (3) ~ (all_10_2 = e0) % 155.14/23.79 % 155.14/23.79 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_10_2 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_10_2 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % 155.14/23.79 Sub-proof #862 shows that the following formulas are inconsistent: % 155.14/23.79 ---------------------------------------------------------------- % 155.14/23.79 (1) all_56_4 = all_52_8 % 155.14/23.79 (2) all_56_4 = e0 % 155.14/23.79 (3) ~ (all_52_8 = e0) % 155.14/23.79 % 155.14/23.79 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_52_8 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_52_8 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % 155.14/23.79 Sub-proof #863 shows that the following formulas are inconsistent: % 155.14/23.79 ---------------------------------------------------------------- % 155.14/23.79 (1) all_58_30 = all_6_2 % 155.14/23.79 (2) all_58_30 = e0 % 155.14/23.79 (3) ~ (all_6_2 = e0) % 155.14/23.79 % 155.14/23.79 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_6_2 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_6_2 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % 155.14/23.79 Sub-proof #864 shows that the following formulas are inconsistent: % 155.14/23.79 ---------------------------------------------------------------- % 155.14/23.79 (1) all_58_29 = all_8_2 % 155.14/23.79 (2) all_58_29 = e0 % 155.14/23.79 (3) ~ (all_8_2 = e0) % 155.14/23.79 % 155.14/23.79 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_8_2 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_8_2 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % 155.14/23.79 Sub-proof #865 shows that the following formulas are inconsistent: % 155.14/23.79 ---------------------------------------------------------------- % 155.14/23.79 (1) all_58_28 = all_10_2 % 155.14/23.79 (2) all_58_28 = e0 % 155.14/23.79 (3) ~ (all_10_2 = e0) % 155.14/23.79 % 155.14/23.79 Begin of proof % 155.14/23.79 | % 155.14/23.79 | COMBINE_EQS: (1), (2) imply: % 155.14/23.79 | (4) all_10_2 = e0 % 155.14/23.79 | % 155.14/23.79 | SIMP: (4) implies: % 155.14/23.79 | (5) all_10_2 = e0 % 155.14/23.79 | % 155.14/23.79 | REDUCE: (3), (5) imply: % 155.14/23.79 | (6) $false % 155.14/23.79 | % 155.14/23.79 | CLOSE: (6) is inconsistent. % 155.14/23.79 | % 155.14/23.79 End of proof % 155.14/23.79 % SZS output end Proof for theBenchmark % 155.14/23.79 % 155.14/23.79 23174ms %------------------------------------------------------------------------------